# bibtab

bibtype: article
filename: fparith.bib
label: Baker:1975:MER
author: P. W. Baker
title: More Efficient Radix-2 Algorithms for Some Elementary Functions
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 11
pages: 1049--1054
month: nov
monthnumber: 11
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224132
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:39 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 10:15:39 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. W. Baker
rawtitle: More Efficient Radix-2 Algorithms for Some Elementary Functions
entry:
@Article{Baker:1975:MER,
  author =       "P. W. Baker",
  title =        "More Efficient Radix-2 Algorithms for Some Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "11",
  pages =        "1049--1054",
  month =        nov,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224132",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Banerji:1975:CLS
author: D. K. Banerji
title: On Combinational Logic for Sign Detection in Residue Number Systems
crossref: IEEE:1975:SCA
pages: 113--116
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Banerji.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: D. K. Banerji
rawtitle: On Combinational Logic for Sign Detection in Residue Number Systems
abstract:
This paper is concerned with the algebraic sign detection of a number in a residue number system. The proposed solution is applicable only to nonredundant systems. The method utilizes a systematic decomposition of the sign function $S$ that is based on some special properties of $S$. Starting with the canonical sum-of-products expression for $S$, we transform the expression to a form whose realization is simpler than the canonical form realization and, if possible, also simpler than the minimal sum-of-products realization. In some cases, the proposed method yields savings as high as 85% compared to the minimal sum-of-products realization for $S$.

rawabstract:
This paper is concerned with the algebraic sign detection of a number in a residue number system. The proposed solution is applicable only to nonredundant systems. The method utilizes a systematic decomposition of the sign function $S$ that is based on some special properties of $S$. Starting with the canonical sum-of-products expression for $S$, we transform the expression to a form whose realization is simpler than the canonical form realization and, if possible, also simpler than the minimal sum-of-products realization. In some cases, the proposed method yields savings as high as 85\% compared to the minimal sum-of-products realization for $S$.

entry:
@InProceedings{Banerji:1975:CLS,
  author =       "D. K. Banerji",
  title =        "On Combinational Logic for Sign Detection in Residue
                 Number Systems",
  crossref =     "IEEE:1975:SCA",
  pages =        "113--116",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Banerji.pdf",
  abstract =     "This paper is concerned with the algebraic sign
                 detection of a number in a residue number system. The
                 proposed solution is applicable only to nonredundant
                 systems. The method utilizes a systematic decomposition
                 of the sign function $S$ that is based on some special
                 properties of $S$. Starting with the canonical
                 sum-of-products expression for $S$, we transform the
                 expression to a form whose realization is simpler than
                 the canonical form realization and, if possible, also
                 simpler than the minimal sum-of-products realization.
                 In some cases, the proposed method yields savings as
                 high as 85\% compared to the minimal sum-of-products
                 realization for $S$.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Basu:1975:SPN
author: D. Basu and T. Jayashree
title: On a Simple Postcorrection for Nonrestoring Division
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 10
pages: 1019--1020
month: oct
monthnumber: 10
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224116
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:57 MDT 2011
bibtimestamp: 2011.07.12 07:57:57 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672709
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Basu and T. Jayashree
rawtitle: On a Simple Postcorrection for Nonrestoring Division
entry:
@Article{Basu:1975:SPN,
  author =       "D. Basu and T. Jayashree",
  title =        "On a Simple Postcorrection for Nonrestoring Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "10",
  pages =        "1019--1020",
  month =        oct,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224116",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672709",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Benedek:1975:DLB
author: M. Benedek
title: Developing Large Binary to BCD Conversion Structures
crossref: IEEE:1975:SCA
pages: 188--196
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Benedek.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: M. Benedek
rawtitle: Developing Large Binary to {BCD} Conversion Structures
abstract:
Static binary to BCD conversion has been described in many papers during the last decade, but none of the methods presented were practical for the conversion of large number of binary bits.par In this paper it is intended to further develop static conversions by the expansion of the original BIDEC method (Ref. 1). There are quite a few static conversion schemes published which use other methods of conversion. The static method, developed from the BIDEC, lends itself best for the expansion to larger structures as in its original ``correct and shift'' form there were no basic limitations on the size of the binary words to be converted. with the appearance of large bipolar ROMs and the even larger but somewhat slower MOS ROMs there is a renewed interest in large structures for fast binary to BCD conversions.

rawabstract:
Static binary to BCD conversion has been described in many papers during the last decade, but none of the methods presented were practical for the conversion of large number of binary bits.\par In this paper it is intended to further develop static conversions by the expansion of the original BIDEC method (Ref. 1). There are quite a few static conversion schemes published which use other methods of conversion. The static method, developed from the BIDEC, lends itself best for the expansion to larger structures as in its original ``correct and shift'' form there were no basic limitations on the size of the binary words to be converted. with the appearance of large bipolar ROMs and the even larger but somewhat slower MOS ROMs there is a renewed interest in large structures for fast binary to BCD conversions.

entry:
@InProceedings{Benedek:1975:DLB,
  author =       "M. Benedek",
  title =        "Developing Large Binary to {BCD} Conversion
                 Structures",
  crossref =     "IEEE:1975:SCA",
  pages =        "188--196",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Benedek.pdf",
  abstract =     "Static binary to BCD conversion has been described in
                 many papers during the last decade, but none of the
                 methods presented were practical for the conversion of
                 large number of binary bits.\par

                 In this paper it is intended to further develop static
                 conversions by the expansion of the original BIDEC
                 method (Ref. 1). There are quite a few static
                 conversion schemes published which use other methods of
                 conversion. The static method, developed from the
                 BIDEC, lends itself best for the expansion to larger
                 structures as in its original ``correct and shift''
                 form there were no basic limitations on the size of the
                 binary words to be converted. with the appearance of
                 large bipolar ROMs and the even larger but somewhat
                 slower MOS ROMs there is a renewed interest in large
                 structures for fast binary to BCD conversions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Bivins:1975:SAA
author: R. L. Bivins and N. Metropolis
title: Significance Arithmetic: Application to a Partial Differential Equation
crossref: IEEE:1975:SCA
pages: 64--66
year: 1975
DOI: https://doi.org/10.1109/ARITH.1975.6156973
bibdate: Mon Mar 19 18:17:32 2007
bibtimestamp: 2007.03.19 18:17:32 ???
note: Also available as Los Alamos Technical Report LA-UR-75-1763 CONF-751103-1.
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bivins.pdf
keywords: ARITH-3; significance arithmetic
acknowledgement: ack-nhfb
rawauthor: R. L. Bivins and N. Metropolis
rawnote: Also available as Los Alamos Technical Report LA-UR-75-1763 CONF-751103-1.
rawtitle: Significance Arithmetic: Application to a Partial Differential Equation
abstract:
The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial differential equation. The authors approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference equation approximation to Burger's equation.

rawabstract:
The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial differential equation. The authors approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference equation approximation to Burger's equation.

entry:
@InProceedings{Bivins:1975:SAA,
  author =       "R. L. Bivins and N. Metropolis",
  title =        "Significance Arithmetic: Application to a Partial
                 Differential Equation",
  crossref =     "IEEE:1975:SCA",
  pages =        "64--66",
  year =         "1975",
  DOI =          "https://doi.org/10.1109/ARITH.1975.6156973",
  bibdate =      "Mon Mar 19 18:17:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also available as Los Alamos Technical Report
                 LA-UR-75-1763 CONF-751103-1.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bivins.pdf",
  abstract =     "The methods of significance arithmetic are applied to
                 the numerical solution of a nonlinear partial
                 differential equation. The authors approach permits the
                 use of initial values having imprecision considerably
                 greater than that of rounding error; moreover, the
                 intermediate and final quantities are monitored so that
                 at any stage the precision of such quantities is
                 available. An algorithm is found that represents
                 faithfully the solution to a difference equation
                 approximation to Burger's equation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; significance arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Bohlender:1975:FPC
author: G. Bohlender
title: Floating-Point Computation of Functions with Maximum Accuracy
crossref: IEEE:1975:SCA
pages: 14--23
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bohlender.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: G. Bohlender
rawtitle: Floating-Point Computation of Functions with Maximum Accuracy
abstract:
Algorithms are given which compute multiple sums and products and arbitrary roots of floating-point numbers with maximum accuracy. The summation algorithm can be applied to compute scalar products, matrix products, etc. For all these functions, simple error formulas and the smallest floating-point intervals containing the exact result can be obtained.

rawabstract:
Algorithms are given which compute multiple sums and products and arbitrary roots of floating-point numbers with maximum accuracy. The summation algorithm can be applied to compute scalar products, matrix products, etc. For all these functions, simple error formulas and the smallest floating-point intervals containing the exact result can be obtained.

entry:
@InProceedings{Bohlender:1975:FPC,
  author =       "G. Bohlender",
  title =        "Floating-Point Computation of Functions with Maximum
                 Accuracy",
  crossref =     "IEEE:1975:SCA",
  pages =        "14--23",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bohlender.pdf",
  abstract =     "Algorithms are given which compute multiple sums and
                 products and arbitrary roots of floating-point numbers
                 with maximum accuracy. The summation algorithm can be
                 applied to compute scalar products, matrix products,
                 etc. For all these functions, simple error formulas and
                 the smallest floating-point intervals containing the
                 exact result can be obtained.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: techreport
filename: fparith.bib
label: Brent:1975:FMP
author: R. P. Brent
title: A Fortran Multiple-Precision Arithmetic Package
type: Technical report
institution: Department of Computer Science, Australian National University
address: Canberra, Australia
pages: 14--23
year: 1975
bibdate: Fri Jan 06 07:38:05 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.06 07:38:05 ???
keywords: floating-point arithmetic; multiple-precision arithmetic
acknowledgement: ack-nhfb
rawauthor: R. P. Brent
rawtitle: A {Fortran} Multiple-Precision Arithmetic Package
entry:
@TechReport{Brent:1975:FMP,
  author =       "R. P. Brent",
  title =        "A {Fortran} Multiple-Precision Arithmetic Package",
  type =         "Technical report",
  institution =  "Department of Computer Science, Australian National
                 University",
  address =      "Canberra, Australia",
  year =         "1975",
  bibdate =      "Fri Jan 06 07:38:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; multiple-precision
                 arithmetic",
}


bibtype: techreport
filename: fparith.bib
label: Brent:1975:MZM
author: R. P. (Richard P.) Brent
title: Multiple-precision zero-finding methods and the complexity of elementary function evaluation
institution: Department of Computer Science, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 26
year: 1975
bibdate: Sat Jan 11 10:14:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.01.11 10:14:06 MST
keywords: Iterative methods (Mathematics)
acknowledgement: ack-nhfb
rawauthor: R. P. (Richard P.) Brent
rawtitle: Multiple-precision zero-finding methods and the complexity of elementary function evaluation
entry:
@TechReport{Brent:1975:MZM,
  author =       "R. P. (Richard P.) Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "26",
  year =         "1975",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Iterative methods (Mathematics)",
  searchkey =    "ti:elementary n1 function",
}


bibtype: article
filename: fparith.bib
label: Brubaker:1975:MUL
author: T. A. Brubaker and J. C. Becker
title: Multiplication Using Logarithms Implemented with Read-Only Memory
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 8
pages: 761--765
month: aug
monthnumber: 8
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224307
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:56 MDT 2011
bibtimestamp: 2011.07.12 07:57:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672900
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. A. Brubaker and J. C. Becker
rawtitle: Multiplication Using Logarithms Implemented with Read-Only Memory
entry:
@Article{Brubaker:1975:MUL,
  author =       "T. A. Brubaker and J. C. Becker",
  title =        "Multiplication Using Logarithms Implemented with
                 Read-Only Memory",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "8",
  pages =        "761--765",
  month =        aug,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224307",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672900",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Caprani:1975:REF
author: Ole Caprani
title: Round-off Errors in Floating-Point Summation
journal: j-BIT
volume: 15
number: 1
pages: 5--9
month: mar
monthnumber: 3
year: 1975
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01932993
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65G05
MRnumber: 58 19088
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: BIT (Nordisk tidskrift for informationsbehandling)
keywords: accurate floating-point summation; floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Ole Caprani
rawtitle: Round-off Errors in Floating-Point Summation
entry:
@Article{Caprani:1975:REF,
  author =       "Ole Caprani",
  title =        "Round-off Errors in Floating-Point Summation",
  journal =      j-BIT,
  volume =       "15",
  number =       "1",
  pages =        "5--9",
  month =        mar,
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932993",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "58 19088",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
  xxtitle =      "Roundoff errors in floating-point summation",
}


bibtype: article
filename: fparith.bib
label: Chen:1975:SER
author: Tien Chi Chen and Irving T. Ho
title: Storage-Efficient Representation of Decimal Data
journal: j-CACM
volume: 18
number: 1
pages: 49--52
month: jan
monthnumber: 1
year: 1975
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 94A15 (68A20)
MRnumber: 50 16105
MRreviewer: R. N. Goss
bibdate: Mon Jan 22 06:30:44 MST 2001
bibtimestamp: 2001.01.22 06:30:44 MST
note: Collection of articles honoring Alston S. Householder. See comment cite Smith:1975:CPC.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C6130 (Data handling techniques)
corpsource: IBM San Jose Res. Lab., CA, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
treatment: T Theoretical or Mathematical
rawauthor: Tien Chi Chen and Irving T. Ho
rawnote: Collection of articles honoring {Alston S. Householder}. See comment \cite{Smith:1975:CPC}.
rawtitle: Storage-Efficient Representation of Decimal Data
bibsource:
Compendex database; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#ChenH75; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Usually $n$ decimal digits are represented by $ 4 n $ bits in computers. Actually, two BCD digits can be compressed optimally and reversibly into $7$ bits, and three digits into $ 10 $ bits, by a very simple algorithm based on the fixed-length combination of two variable field-length encodings. In over half of the cases the compressed code results from the conventional BCD code by simple removal of redundant $0$ bits. A long decimal message can be subdivided into three-digit blocks, and separately compressed; the result differs from the asymptotic minimum length by only $ 0.34 $ percent. The hardware requirement is small, and the mappings can be done manually.

keywords:
asymptotic minimum; binary coded decimal; codes; compressed code; data compression; data storage units; decimal data; decimal floating-point arithmetic; fixed length combination; hardware; length; length encodings; mathematical techniques --- Digital Arithmetic; representation; storage efficient; variable field

rawabstract:
Usually $n$ decimal digits are represented by $ 4 n $ bits in computers. Actually, two BCD digits can be compressed optimally and reversibly into $7$ bits, and three digits into $ 10 $ bits, by a very simple algorithm based on the fixed-length combination of two variable field-length encodings. In over half of the cases the compressed code results from the conventional BCD code by simple removal of redundant $0$ bits. A long decimal message can be subdivided into three-digit blocks, and separately compressed; the result differs from the asymptotic minimum length by only $ 0.34 $ percent. The hardware requirement is small, and the mappings can be done manually.

entry:
@Article{Chen:1975:SER,
  author =       "Tien Chi Chen and Irving T. Ho",
  title =        "Storage-Efficient Representation of Decimal Data",
  journal =      j-CACM,
  volume =       "18",
  number =       "1",
  pages =        "49--52",
  month =        jan,
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "94A15 (68A20)",
  MRnumber =     "50 16105",
  MRreviewer =   "R. N. Goss",
  bibdate =      "Mon Jan 22 06:30:44 MST 2001",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#ChenH75;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Collection of articles honoring {Alston S.
                 Householder}. See comment \cite{Smith:1975:CPC}.",
  abstract =     "Usually $n$ decimal digits are represented by $ 4 n $
                 bits in computers. Actually, two BCD digits can be
                 compressed optimally and reversibly into $7$ bits, and
                 three digits into $ 10 $ bits, by a very simple
                 algorithm based on the fixed-length combination of two
                 variable field-length encodings. In over half of the
                 cases the compressed code results from the conventional
                 BCD code by simple removal of redundant $0$ bits. A
                 long decimal message can be subdivided into three-digit
                 blocks, and separately compressed; the result differs
                 from the asymptotic minimum length by only $ 0.34 $
                 percent. The hardware requirement is small, and the
                 mappings can be done manually.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6130 (Data handling techniques)",
  classification = "722; 921",
  corpsource =   "IBM San Jose Res. Lab., CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "asymptotic minimum; binary coded decimal; codes;
                 compressed code; data compression; data storage units;
                 decimal data; decimal floating-point arithmetic; fixed
                 length combination; hardware; length; length encodings;
                 mathematical techniques --- Digital Arithmetic;
                 representation; storage efficient; variable field",
  oldlabel =     "ChenH75",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ChenH75",
}


bibtype: inproceedings
filename: fparith.bib
label: Chinal:1975:LMA
author: Jean P. Chinal
title: The Logic of Modulo $ 2^k + 1 $ Adders
crossref: IEEE:1975:SCA
pages: 126--136
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_2.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Jean P. Chinal
rawtitle: The Logic of Modulo $ 2^k + 1 $ Adders
abstract:
The design of modulo $ 2^k + 1 $ adders for arbitrary $k$ is considered, with the objective of achieving a logic structure as regular as possible so as to allow a convenient implementation in large-scale integration technology (LSI). It is shown how the design problem can be reduced. to the recursive generation of a subtract signal and to the merging, in various degrees, of the corresponding logic with the logic of an ordinary adder or, alternately, of a so-called em signed-carry adder which is defined and designed itself in general, with both recursive and explicit carry schemes. Modulo $ 2^k + 1 $ adder designs are given, one with conventional adder, another based on signed-carry adder and a third, derived from the signed-carry scheme, where subtract signal generation and carry logic are merged. This last scheme can be set up with two backward recursion chains and five or six forward ones. Two more basic variants are finally indicated for this integrated scheme, aiming at reducing as much as possible the residual logic structure irregularity presented by the most significant position in the word.

rawabstract:
The design of modulo $ 2^k + 1 $ adders for arbitrary $k$ is considered, with the objective of achieving a logic structure as regular as possible so as to allow a convenient implementation in large-scale integration technology (LSI). It is shown how the design problem can be reduced. to the recursive generation of a subtract signal and to the merging, in various degrees, of the corresponding logic with the logic of an ordinary adder or, alternately, of a so-called {\em signed-carry adder\/} which is defined and designed itself in general, with both recursive and explicit carry schemes. Modulo $ 2^k + 1 $ adder designs are given, one with conventional adder, another based on signed-carry adder and a third, derived from the signed-carry scheme, where subtract signal generation and carry logic are merged. This last scheme can be set up with two backward recursion chains and five or six forward ones. Two more basic variants are finally indicated for this integrated scheme, aiming at reducing as much as possible the residual logic structure irregularity presented by the most significant position in the word.

entry:
@InProceedings{Chinal:1975:LMA,
  author =       "Jean P. Chinal",
  title =        "The Logic of Modulo $ 2^k + 1 $ Adders",
  crossref =     "IEEE:1975:SCA",
  pages =        "126--136",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_2.pdf",
  abstract =     "The design of modulo $ 2^k + 1 $ adders for arbitrary
                 $k$ is considered, with the objective of achieving a
                 logic structure as regular as possible so as to allow a
                 convenient implementation in large-scale integration
                 technology (LSI). It is shown how the design problem
                 can be reduced. to the recursive generation of a
                 subtract signal and to the merging, in various degrees,
                 of the corresponding logic with the logic of an
                 ordinary adder or, alternately, of a so-called {\em
                 signed-carry adder\/} which is defined and designed
                 itself in general, with both recursive and explicit
                 carry schemes. Modulo $ 2^k + 1 $ adder designs are
                 given, one with conventional adder, another based on
                 signed-carry adder and a third, derived from the
                 signed-carry scheme, where subtract signal generation
                 and carry logic are merged. This last scheme can be set
                 up with two backward recursion chains and five or six
                 forward ones. Two more basic variants are finally
                 indicated for this integrated scheme, aiming at
                 reducing as much as possible the residual logic
                 structure irregularity presented by the most
                 significant position in the word.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Chinal:1975:MA
author: Jean P. Chinal
title: Mirror Arithmetic
crossref: IEEE:1975:SCA
pages: 98--107
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_1.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Jean P. Chinal
rawtitle: Mirror Arithmetic
abstract:
Mirror coding for signed numbers is defined by means of a set of primitive powers of two $ + 2^n, - 2^n - 1, ldots , - 2^0 $ where signs of the usual set used in 2's complement representation are reversed. Use of the mirror representation is shown as an alternate design approach and is illustrated by a special purpose adder design in mirror code, by an alternate proof of a basic property of signed-digit arithmetic and as another interpretation of cells used in some array multipliers for signed numbers. Lastly, the concept is used to define a variable mode redundant coding, allowing simple sign-flipping without overflow.

rawabstract:
Mirror coding for signed numbers is defined by means of a set of primitive powers of two $ \{ + 2^n, - 2^{n - 1}, \ldots {}, - 2^0 \} $ where signs of the usual set used in 2's complement representation are reversed. Use of the mirror representation is shown as an alternate design approach and is illustrated by a special purpose adder design in mirror code, by an alternate proof of a basic property of signed-digit arithmetic and as another interpretation of cells used in some array multipliers for signed numbers. Lastly, the concept is used to define a variable mode redundant coding, allowing simple sign-flipping without overflow.

entry:
@InProceedings{Chinal:1975:MA,
  author =       "Jean P. Chinal",
  title =        "Mirror Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "98--107",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_1.pdf",
  abstract =     "Mirror coding for signed numbers is defined by means
                 of a set of primitive powers of two $ \{ + 2^n, - 2^{n
                 - 1}, \ldots {}, - 2^0 \} $ where signs of the usual
                 set used in 2's complement representation are reversed.
                 Use of the mirror representation is shown as an
                 alternate design approach and is illustrated by a
                 special purpose adder design in mirror code, by an
                 alternate proof of a basic property of signed-digit
                 arithmetic and as another interpretation of cells used
                 in some array multipliers for signed numbers. Lastly,
                 the concept is used to define a variable mode redundant
                 coding, allowing simple sign-flipping without
                 overflow.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Cobb:1975:IPS
author: Gary W. Cobb
title: The Impact of Parallelism on Software
crossref: IEEE:1975:SCA
pages: 220--222
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Cobb.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Gary W. Cobb
rawtitle: The Impact of Parallelism on Software
abstract:
There seems to be a tug-of-war raging between computer procurement technical evaluation committees, computer designers and scholars of computer science and numerical analysis over the issue of parallelism in computations. Caught in the middle seems to be the user community and the compiler writers. For the scope of this paper, the term ``user community'' will be assumed to be Fortran programmers who are involved in solving problems that require large computer resources, e.g., plasma research, weather prediction, ray tracing, seismic analysis, econometric modeling, weapons research, reactor calculation, etc.

rawabstract:
There seems to be a tug-of-war raging between computer procurement technical evaluation committees, computer designers and scholars of computer science and numerical analysis over the issue of parallelism in computations. Caught in the middle seems to be the user community and the compiler writers. For the scope of this paper, the term ``user community'' will be assumed to be Fortran programmers who are involved in solving problems that require large computer resources, e.g., plasma research, weather prediction, ray tracing, seismic analysis, econometric modeling, weapons research, reactor calculation, etc.

entry:
@InProceedings{Cobb:1975:IPS,
  author =       "Gary W. Cobb",
  title =        "The Impact of Parallelism on Software",
  crossref =     "IEEE:1975:SCA",
  pages =        "220--222",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Cobb.pdf",
  abstract =     "There seems to be a tug-of-war raging between computer
                 procurement technical evaluation committees, computer
                 designers and scholars of computer science and
                 numerical analysis over the issue of parallelism in
                 computations. Caught in the middle seems to be the user
                 community and the compiler writers. For the scope of
                 this paper, the term ``user community'' will be assumed
                 to be Fortran programmers who are involved in solving
                 problems that require large computer resources, e.g.,
                 plasma research, weather prediction, ray tracing,
                 seismic analysis, econometric modeling, weapons
                 research, reactor calculation, etc.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: DeMori:1975:MMM
author: Renato De Mori and Michele Elia and Angelo Serra
title: Minimization Methods for Macrocellular Arithmetic Networks
crossref: IEEE:1975:SCA
pages: 232--240
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_DeMori.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Renato {De Mori} and Michele Elia and Angelo Serra
rawtitle: Minimization Methods for Macrocellular Arithmetic Networks
abstract:
This paper presents a new method to study arithmetic combinatorial circuits. Using polynomial associated to the input-output sequences and to the system, it is possible to solve the problem of minimization of the number of the component blocks. Particularly, the important case of the multiple outputs elementary units can be treated.par Applications of the introduced procedures to multiplier and to fast networks for performing convolution are presented.

rawabstract:
This paper presents a new method to study arithmetic combinatorial circuits. Using polynomial associated to the input-output sequences and to the system, it is possible to solve the problem of minimization of the number of the component blocks. Particularly, the important case of the multiple outputs elementary units can be treated.\par Applications of the introduced procedures to multiplier and to fast networks for performing convolution are presented.

entry:
@InProceedings{DeMori:1975:MMM,
  author =       "Renato {De Mori} and Michele Elia and Angelo Serra",
  title =        "Minimization Methods for Macrocellular Arithmetic
                 Networks",
  crossref =     "IEEE:1975:SCA",
  pages =        "232--240",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_DeMori.pdf",
  abstract =     "This paper presents a new method to study arithmetic
                 combinatorial circuits. Using polynomial associated to
                 the input-output sequences and to the system, it is
                 possible to solve the problem of minimization of the
                 number of the component blocks. Particularly, the
                 important case of the multiple outputs elementary units
                 can be treated.\par

                 Applications of the introduced procedures to multiplier
                 and to fast networks for performing convolution are
                 presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Deverell:1975:PIA
author: J. Deverell
title: Pipeline Iterative Arithmetic Arrays
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 3
pages: 317--322
month: mar
monthnumber: 3
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224214
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 18:46:50 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 18:46:50 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. Deverell
rawtitle: Pipeline Iterative Arithmetic Arrays
entry:
@Article{Deverell:1975:PIA,
  author =       "J. Deverell",
  title =        "Pipeline Iterative Arithmetic Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "317--322",
  month =        mar,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224214",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 18:46:50 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Elias:1975:UCS
author: P. Elias
title: Universal codeword sets and representations of the integers
journal: j-IEEE-TRANS-INF-THEORY
volume: 21
number: 2
pages: 194--203
month: mar
monthnumber: 3
year: 1975
CODEN: IETTAW
DOI: https://doi.org/10.1109/tit.1975.1055349
ISSN: 0018-9448 (print), 1557-9654 (electronic) OR 00189448 (print), 15579654 (electronic)
ISSNL: 0018-9448 OR 00189448
bibdate: Fri Dec 15 15:10:16 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 15:10:16 ???
fjournal: IEEE Transactions on Information Theory
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18
rawauthor: P. Elias
rawtitle: Universal codeword sets and representations of the integers
entry:
@Article{Elias:1975:UCS,
  author =       "P. Elias",
  title =        "Universal codeword sets and representations of the
                 integers",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "21",
  number =       "2",
  pages =        "194--203",
  month =        mar,
  year =         "1975",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/tit.1975.1055349",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Fri Dec 15 15:10:16 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}


bibtype: phdthesis
filename: fparith.bib
label: Ercegovac:1975:GMEa
author: Milos Dragutin Ercegovac
title: A General Method for Evaluation of Functions and Computations in a Digital Computer
type: Ph.D. Thesis
school: Department of Computer Science, University of Illinois at Urbana-Champaign
address: Urbana-Champaign, IL, USA
pages: viii + 109
month: jul
monthnumber: 7
year: 1975
bibdate: Mon Feb 10 07:18:12 2020
bibtimestamp: 2020.02.10 07:18:12 ???
URL: https://search.proquest.com/pqdtglobal/docview/302756306
acknowledgement: ack-nhfb
advisor: James E. Robertson
rawauthor: Milo{\v{s}} Dragutin Ercegovac
rawtitle: A General Method for Evaluation of Functions and Computations in a Digital Computer
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@PhdThesis{Ercegovac:1975:GMEa,
  author =       "Milo{\v{s}} Dragutin Ercegovac",
  title =        "A General Method for Evaluation of Functions and
                 Computations in a Digital Computer",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana-Champaign, IL, USA",
  pages =        "viii + 109",
  month =        jul,
  year =         "1975",
  bibdate =      "Mon Feb 10 07:18:12 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://search.proquest.com/pqdtglobal/docview/302756306",
  acknowledgement = ack-nhfb,
  advisor =      "James E. Robertson",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1975:GMEb
author: Milos D. Ercegovac
title: A General Method for Evaluation of Functions in a Digital Computer
crossref: IEEE:1975:SCA
pages: 147--157
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ercegovac.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac
rawtitle: A General Method for Evaluation of Functions in a Digital Computer
abstract:
This paper presents a recently discovered general computational method, amenable for efficient implementation in digital computing systems. The method provides a unique, simple and fast algorithm for solving many computational problems, such as the evaluation of polynomials, rational functions and arithmetic expressions, or solving a class of systems of linear equations, or performing the basic arithmetics. In particular, the method is well suited for fast evaluation of commonly used mathematical functions.

rawabstract:
This paper presents a recently discovered general computational method, amenable for efficient implementation in digital computing systems. The method provides a unique, simple and fast algorithm for solving many computational problems, such as the evaluation of polynomials, rational functions and arithmetic expressions, or solving a class of systems of linear equations, or performing the basic arithmetics. In particular, the method is well suited for fast evaluation of commonly used mathematical functions.

entry:
@InProceedings{Ercegovac:1975:GMEb,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "A General Method for Evaluation of Functions in a
                 Digital Computer",
  crossref =     "IEEE:1975:SCA",
  pages =        "147--157",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ercegovac.pdf",
  abstract =     "This paper presents a recently discovered general
                 computational method, amenable for efficient
                 implementation in digital computing systems. The method
                 provides a unique, simple and fast algorithm for
                 solving many computational problems, such as the
                 evaluation of polynomials, rational functions and
                 arithmetic expressions, or solving a class of systems
                 of linear equations, or performing the basic
                 arithmetics. In particular, the method is well suited
                 for fast evaluation of commonly used mathematical
                 functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: mastersthesis
filename: fparith.bib
label: Fawcett:1975:MCR
author: B. K. Fawcett
title: Maximal Clocking Rates for Pipelined Digital Systems
type: M.S. thesis
school: Department of Electrical Engineering, University of Illinois at Urbana-Champaign
address: Urbana-Champaign, IL, USA
pages: 147--157
year: 1975
bibdate: Fri Nov 09 10:50:56 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:50:56 ???
acknowledgement: ack-nhfb
rawauthor: B. K. Fawcett
rawtitle: Maximal Clocking Rates for Pipelined Digital Systems
entry:
@MastersThesis{Fawcett:1975:MCR,
  author =       "B. K. Fawcett",
  title =        "Maximal Clocking Rates for Pipelined Digital Systems",
  type =         "{M.S.} thesis",
  school =       "Department of Electrical Engineering, University of
                 Illinois at Urbana-Champaign",
  address =      "Urbana-Champaign, IL, USA",
  year =         "1975",
  bibdate =      "Fri Nov 09 10:50:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Foster:1975:CNM
author: Caxton Foster and Edward Riseman and Fred Stockton and Conrad Wogrin
title: CHARGOGGAGGOGGMANCHAUGAGOGGCHAUBUNAGUNGAMAUG: a Novel Multiply-by-Three Circuit
crossref: IEEE:1975:SCA
pages: 185--187
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Foster.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Caxton Foster and Edward Riseman and Fred Stockton and Conrad Wogrin
rawtitle: {CHARGOGGAGGOGGMANCHAUGAGOGGCHAUBUNAGUNGAMAUG}: a Novel Multiply-by-Three Circuit
abstract:
Recently, while considering the connection of a 48 bit word computer to a 16 bit computer, we felt the need for a fast and inexpensive device that would multiply a binary address by a factor of three. Since $ 3 N = N + 2 N $, there is an obvious solution of providing a normal adder circuit and presenting one set of inputs with $N$ and the other with $N$-shifted left one place. But, there is a great deal of redundancy here since knowing one input we have complete knowledge of the other.par Seeking to take advantage of this redundancy, we have spent some twenty man hours and have saved one gate per stage over a conventional full adder. Since the ultimate circuit is to be a ``one-of'' this is scarcely economic, but it has been fun. Before going further, the interested reader may enjoy puzzling over the problem for himself. We make no pretense of minimality, but we have a circuit with 6 gates per stage and a propagation delay of one gate per stage.

remark:
Footnote to title: The title of this paper refers to the Indian name of a lake in Massachusetts which reputedly means ``You fish on your side, I fish on my side, nobody fish in the middle.'

rawabstract:
Recently, while considering the connection of a 48 bit word computer to a 16 bit computer, we felt the need for a fast and inexpensive device that would multiply a binary address by a factor of three. Since $ 3 N = N + 2 N $, there is an obvious solution of providing a normal adder circuit and presenting one set of inputs with $N$ and the other with $N$-shifted left one place. But, there is a great deal of redundancy here since knowing one input we have complete knowledge of the other.\par Seeking to take advantage of this redundancy, we have spent some twenty man hours and have saved one gate per stage over a conventional full adder. Since the ultimate circuit is to be a ``one-of'' this is scarcely economic, but it has been fun. Before going further, the interested reader may enjoy puzzling over the problem for himself. We make no pretense of minimality, but we have a circuit with 6 gates per stage and a propagation delay of one gate per stage.

entry:
@InProceedings{Foster:1975:CNM,
  author =       "Caxton Foster and Edward Riseman and Fred Stockton and
                 Conrad Wogrin",
  title =        "{CHARGOGGAGGOGGMANCHAUGAGOGGCHAUBUNAGUNGAMAUG}: a
                 Novel Multiply-by-Three Circuit",
  crossref =     "IEEE:1975:SCA",
  pages =        "185--187",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Foster.pdf",
  abstract =     "Recently, while considering the connection of a 48 bit
                 word computer to a 16 bit computer, we felt the need
                 for a fast and inexpensive device that would multiply a
                 binary address by a factor of three. Since $ 3 N = N +
                 2 N $, there is an obvious solution of providing a
                 normal adder circuit and presenting one set of inputs
                 with $N$ and the other with $N$-shifted left one place.
                 But, there is a great deal of redundancy here since
                 knowing one input we have complete knowledge of the
                 other.\par

                 Seeking to take advantage of this redundancy, we have
                 spent some twenty man hours and have saved one gate per
                 stage over a conventional full adder. Since the
                 ultimate circuit is to be a ``one-of'' this is scarcely
                 economic, but it has been fun. Before going further,
                 the interested reader may enjoy puzzling over the
                 problem for himself. We make no pretense of minimality,
                 but we have a circuit with 6 gates per stage and a
                 propagation delay of one gate per stage.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
  remark =       "Footnote to title: The title of this paper refers to
                 the Indian name of a lake in Massachusetts which
                 reputedly means ``You fish on your side, I fish on my
                 side, nobody fish in the middle.'",
}


bibtype: inproceedings
filename: fparith.bib
label: Gabrielian:1975:FSN
author: Armen Gabrielian
title: Formal Systems of Numerals
crossref: IEEE:1975:SCA
pages: 76--81
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gabrielian.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Armen Gabrielian
rawtitle: Formal Systems of Numerals
abstract:
A new system of numerals is introduced for representing numbers in base $ 2^N $, for $ N leq 8 $. The new notation greatly simplifies arithmetical operations on numbers. For example, for $ N = 3 (4) $ one obtains a notation for octal (hexadecimal) numbers in which one can perform addition and multiplication much more easily than in the standard notation. For $ N = 8 $ one obtains a practical way of representing numbers to the base 256. A simplification of the decimal notation is also presented.

rawabstract:
A new system of numerals is introduced for representing numbers in base $ 2^N $, for $ N \leq 8 $. The new notation greatly simplifies arithmetical operations on numbers. For example, for $ N = 3 (4) $ one obtains a notation for octal (hexadecimal) numbers in which one can perform addition and multiplication much more easily than in the standard notation. For $ N = 8 $ one obtains a practical way of representing numbers to the base 256. A simplification of the decimal notation is also presented.

entry:
@InProceedings{Gabrielian:1975:FSN,
  author =       "Armen Gabrielian",
  title =        "Formal Systems of Numerals",
  crossref =     "IEEE:1975:SCA",
  pages =        "76--81",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gabrielian.pdf",
  abstract =     "A new system of numerals is introduced for
                 representing numbers in base $ 2^N $, for $ N \leq 8 $.
                 The new notation greatly simplifies arithmetical
                 operations on numbers. For example, for $ N = 3 (4) $
                 one obtains a notation for octal (hexadecimal) numbers
                 in which one can perform addition and multiplication
                 much more easily than in the standard notation. For $ N
                 = 8 $ one obtains a practical way of representing
                 numbers to the base 256. A simplification of the
                 decimal notation is also presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: George:1975:ARR
author: James E. George
title: Algorithms to Reveal the Representation of Characters, Integers, and Floating-Point Numbers
journal: j-TOMS
volume: 1
number: 3
pages: 210--216
month: sep
monthnumber: 9
year: 1975
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355644.355647
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Aug 26 23:44:16 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.26 23:44:16 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: James E. George
rawtitle: Algorithms to Reveal the Representation of Characters, Integers, and Floating-Point Numbers
entry:
@Article{George:1975:ARR,
  author =       "James E. George",
  title =        "Algorithms to Reveal the Representation of Characters,
                 Integers, and Floating-Point Numbers",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "210--216",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355647",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Gibson:1975:SCT
author: J. A. Gibson and R. W. Gibbard
title: Synthesis and Comparison of Two's Complement Parallel Multipliers
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 10
pages: 1020--1027
month: oct
monthnumber: 10
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224117
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:57 MDT 2011
bibtimestamp: 2011.07.12 07:57:57 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672710
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. A. Gibson and R. W. Gibbard
rawtitle: Synthesis and Comparison of Two's Complement Parallel Multipliers
entry:
@Article{Gibson:1975:SCT,
  author =       "J. A. Gibson and R. W. Gibbard",
  title =        "Synthesis and Comparison of Two's Complement Parallel
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "10",
  pages =        "1020--1027",
  month =        oct,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224117",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672710",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Ginsberg:1975:DUFa
author: Myron Ginsberg and Dennis J. Frailey
type: Technical report
number: CP 74028
institution: Department of Computer Science, Institute of Technology, Southern Methodist University
address: Dallas
edition: Revised Oct. 1975.
pages: 26
year: 1975
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: Myron Ginsberg and Dennis J. Frailey
title:
The design and use of a floating-point (software) simulator for testing the arithmetic behavior of mathematical software

keywords:
Computer arithmetic and logic units --- Testing.; Computer programs --- Testing.; Floating-point arithmetic.

rawtitle:
The design and use of a floating-point (software) simulator for testing the arithmetic behavior of mathematical software

entry:
@TechReport{Ginsberg:1975:DUFa,
  author =       "Myron Ginsberg and Dennis J. Frailey",
  title =        "The design and use of a floating-point (software)
                 simulator for testing the arithmetic behavior of
                 mathematical software",
  type =         "Technical report",
  number =       "CP 74028",
  institution =  "Department of Computer Science, Institute of
                 Technology, Southern Methodist University",
  address =      "Dallas",
  edition =      "Revised Oct. 1975.",
  pages =        "26",
  year =         "1975",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units --- Testing.;
                 Computer programs --- Testing.; Floating-point
                 arithmetic.",
}


bibtype: inproceedings
filename: fparith.bib
label: Ginsberg:1975:DUFb
author: Myron Ginsberg and Dennis J. Frailey
crossref: IEEE:1975:SCA
pages: 56--63
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ginsberg.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Myron Ginsberg and Dennis J. Frailey
title:
The Design and Use of a Floating-Point (Software) Simulator for Testing the Arithmetic Behavior of Mathematical Software

abstract:
An important aspect of any evaluative procedure for developing high quality mathematical software is testing the effects of arithmetic behavior on algorithmic implementations. This paper describes a proposed design approach and various applications of a high-level language floating-point simulator which has two inputs: the program to be tested and a description of the floating-point arithmetic under which the routine is to be executed. A brief discussion of the motivation for this approach is given along with a review of existing efforts to study the influences of computer arithmetic on the accuracy and reliability of mathematical. software. An overview of the simulator's structure is presented as well as suggestions for experiments to assist in determining the effects of floating-point behavior across several different computer architectures. Present and future uses of the simulator are also indicated.

rawabstract:
An important aspect of any evaluative procedure for developing high quality mathematical software is testing the effects of arithmetic behavior on algorithmic implementations. This paper describes a proposed design approach and various applications of a high-level language floating-point simulator which has two inputs: the program to be tested and a description of the floating-point arithmetic under which the routine is to be executed. A brief discussion of the motivation for this approach is given along with a review of existing efforts to study the influences of computer arithmetic on the accuracy and reliability of mathematical. software. An overview of the simulator's structure is presented as well as suggestions for experiments to assist in determining the effects of floating-point behavior across several different computer architectures. Present and future uses of the simulator are also indicated.

rawtitle:
The Design and Use of a Floating-Point (Software) Simulator for Testing the Arithmetic Behavior of Mathematical Software

entry:
@InProceedings{Ginsberg:1975:DUFb,
  author =       "Myron Ginsberg and Dennis J. Frailey",
  title =        "The Design and Use of a Floating-Point (Software)
                 Simulator for Testing the Arithmetic Behavior of
                 Mathematical Software",
  crossref =     "IEEE:1975:SCA",
  pages =        "56--63",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ginsberg.pdf",
  abstract =     "An important aspect of any evaluative procedure for
                 developing high quality mathematical software is
                 testing the effects of arithmetic behavior on
                 algorithmic implementations. This paper describes a
                 proposed design approach and various applications of a
                 high-level language floating-point simulator which has
                 two inputs: the program to be tested and a description
                 of the floating-point arithmetic under which the
                 routine is to be executed. A brief discussion of the
                 motivation for this approach is given along with a
                 review of existing efforts to study the influences of
                 computer arithmetic on the accuracy and reliability of
                 mathematical. software. An overview of the simulator's
                 structure is presented as well as suggestions for
                 experiments to assist in determining the effects of
                 floating-point behavior across several different
                 computer architectures. Present and future uses of the
                 simulator are also indicated.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Goodman:1975:REP
author: R. Goodman and A. Feldstein
title: Round-Off Error in Products
journal: j-COMPUTING
volume: 15
number: 3
pages: 263--273
month: sep
monthnumber: 9
year: 1975
CODEN: CMPTA2
DOI: https://doi.org/10.1007/BF02242373
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:52 MST 2001
bibtimestamp: 2001.01.02 17:40:52 MST
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nj
affiliation: Department of Math., University of Miami, Coral Gables, FL, USA
journalURL: http://link.springer.com/journal/607
journalabr: Comput (Vienna/NY)
rawauthor: R. Goodman and A. Feldstein
rawtitle: Round-Off Error in Products
bibsource:
Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date)

keywords:
digit by digit deviation; floating point numbers; fraction; logarithmic distribution; mathematical techniques; mean; multiplication; products; roundoff errors; variance

entry:
@Article{Goodman:1975:REP,
  author =       "R. Goodman and A. Feldstein",
  title =        "Round-Off Error in Products",
  journal =      j-COMPUTING,
  volume =       "15",
  number =       "3",
  pages =        "263--273",
  month =        sep,
  year =         "1975",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/BF02242373",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:52 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Department of Math., University of Miami, Coral
                 Gables, FL, USA",
  classification = "921; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "digit by digit deviation; floating point numbers;
                 fraction; logarithmic distribution; mathematical
                 techniques; mean; multiplication; products; roundoff
                 errors; variance",
}


bibtype: inproceedings
filename: fparith.bib
label: Goyal:1975:DAE
author: Lakshmi N. Goyal
title: Design of an Arithmetic Element for Serial Processing in an Iterative Structure
crossref: IEEE:1975:SCA
pages: 223--231
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Goyal.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Lakshmi N. Goyal
rawtitle: Design of an Arithmetic Element for Serial Processing in an Iterative Structure
abstract:
This paper describes the arithmetic and logic design of the digit processing logic of an arithmetic element. The arithmetic element is used in an iterative structure and arithmetic processing takes place serially on a digit by digit basis with the most significant digit first. Starting from the arithmetic specification of the digit processing logic, the arithmetic design (namely, the choice of number system, number representation and the digit algorithm) is developed. Algebraic and logic designs of the logic necessary to execute the digit algorithm and its implication for LSI implementation are discussed.

rawabstract:
This paper describes the arithmetic and logic design of the digit processing logic of an arithmetic element. The arithmetic element is used in an iterative structure and arithmetic processing takes place serially on a digit by digit basis with the most significant digit first. Starting from the arithmetic specification of the digit processing logic, the arithmetic design (namely, the choice of number system, number representation and the digit algorithm) is developed. Algebraic and logic designs of the logic necessary to execute the digit algorithm and its implication for LSI implementation are discussed.

entry:
@InProceedings{Goyal:1975:DAE,
  author =       "Lakshmi N. Goyal",
  title =        "Design of an Arithmetic Element for Serial Processing
                 in an Iterative Structure",
  crossref =     "IEEE:1975:SCA",
  pages =        "223--231",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Goyal.pdf",
  abstract =     "This paper describes the arithmetic and logic design
                 of the digit processing logic of an arithmetic element.
                 The arithmetic element is used in an iterative
                 structure and arithmetic processing takes place
                 serially on a digit by digit basis with the most
                 significant digit first. Starting from the arithmetic
                 specification of the digit processing logic, the
                 arithmetic design (namely, the choice of number system,
                 number representation and the digit algorithm) is
                 developed. Algebraic and logic designs of the logic
                 necessary to execute the digit algorithm and its
                 implication for LSI implementation are discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Grant:1975:TAS
author: J. A. Grant and G. D. Hitchins
title: Two Algorithms for the Solution of Polynomial Equations to Limiting Machine Precision
journal: j-COMP-J
volume: 18
number: 3
pages: 258--264
month: aug
monthnumber: 8
year: 1975
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/18.3.258
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:56 MST 2012
bibtimestamp: 2012.12.04 14:47:56 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: Department of Math., University of Bradford, Bradford, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: J. A. Grant and G. D. Hitchins
rawtitle: Two Algorithms for the Solution of Polynomial Equations to Limiting Machine Precision
bibsource:
Compendex database; http://comjnl.oxfordjournals.org/content/18/3.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/; https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/18/3/258.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/258.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/259.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/260.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/261.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/262.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/263.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/264.tif

keywords:
algorithms; complex coefficients; computer programming --- Subroutines; limiting machine; mathematical techniques; polynomial equations; polynomials; precision; real coefficients

entry:
@Article{Grant:1975:TAS,
  author =       "J. A. Grant and G. D. Hitchins",
  title =        "Two Algorithms for the Solution of Polynomial
                 Equations to Limiting Machine Precision",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "3",
  pages =        "258--264",
  month =        aug,
  year =         "1975",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/18.3.258",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:56 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/18/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/18/3/258.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/258.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/259.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/260.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/261.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/262.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/263.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/264.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  classification = "723; 921",
  corpsource =   "Department of Math., University of Bradford, Bradford,
                 UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "algorithms; complex coefficients; computer programming
                 --- Subroutines; limiting machine; mathematical
                 techniques; polynomial equations; polynomials;
                 precision; real coefficients",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Gregory:1975:BCR
author: Robert Todd Gregory and David W. Matula
title: Base Conversion in Residue Number Systems
crossref: IEEE:1975:SCA
pages: 117--125
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gregory.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Robert Todd Gregory and David W. Matula
rawtitle: Base Conversion in Residue Number Systems
abstract:
We are concerned in this paper with the representation of an integer in a (multiple-modulus) residue number system and, in particular, with an algorithm for changing the base vector of the residue number system. Szabo and Tanaka [1, p.47] describe such an algorithm when each modulus of the second base vector is relatively prime to each modulus of the first base vector. However, we show that a much simpler algorithm exists if we allow the moduli of the second base vector to have factors in common with the moduli of the first base vector (even though the moduli of the second base vector are pairwise relatively prime among themselves).

rawabstract:
We are concerned in this paper with the representation of an integer in a (multiple-modulus) residue number system and, in particular, with an algorithm for changing the base vector of the residue number system. Szabo and Tanaka [1, p.47] describe such an algorithm when each modulus of the second base vector is relatively prime to each modulus of the first base vector. However, we show that a much simpler algorithm exists if we allow the moduli of the second base vector to have factors in common with the moduli of the first base vector (even though the moduli of the second base vector are pairwise relatively prime among themselves).

entry:
@InProceedings{Gregory:1975:BCR,
  author =       "Robert Todd Gregory and David W. Matula",
  title =        "Base Conversion in Residue Number Systems",
  crossref =     "IEEE:1975:SCA",
  pages =        "117--125",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gregory.pdf",
  abstract =     "We are concerned in this paper with the representation
                 of an integer in a (multiple-modulus) residue number
                 system and, in particular, with an algorithm for
                 changing the base vector of the residue number system.
                 Szabo and Tanaka [1, p.47] describe such an algorithm
                 when each modulus of the second base vector is
                 relatively prime to each modulus of the first base
                 vector. However, we show that a much simpler algorithm
                 exists if we allow the moduli of the second base vector
                 to have factors in common with the moduli of the first
                 base vector (even though the moduli of the second base
                 vector are pairwise relatively prime among
                 themselves).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Hunter:1975:QMP
author: G. Hunter
title: A quantitative measure of precision
journal: j-COMP-J
volume: 18
number: 3
pages: 231--233
month: aug
monthnumber: 8
year: 1975
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Mar 25 13:51:56 MST 1997
bibtimestamp: 1997.03.25 13:51:56 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: York University, Department of Chem., Downsview, Ont., Canada
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: G. Hunter
rawtitle: A quantitative measure of precision
bibsource:
Compendex database; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/231.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/232.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/233.tif

abstract:
The precision $ z_b $ of a real number is defined quantitatively in terms of the fractional error in the number, and the base of the arithmetic in which it is represented. The definition is an extension of the traditional rough measure of precision as the number of signification digits in the number. In binary arithmetic the integral part of $ z_b $ is the number of binary digits required to store the number. Conversion of the precision from one base to another (such as binary/decimal) is discussed, and applied to consideration of the intrinsic precision of input/output routines and floating point arithmetic.

keywords:
binary arithmetic; digital arithmetic; digits; floating; fractional error; input/output routines; mathematical techniques; point arithmetic; precision; real number; significant

rawabstract:
The precision $ z_b $ of a real number is defined quantitatively in terms of the fractional error in the number, and the base of the arithmetic in which it is represented. The definition is an extension of the traditional rough measure of precision as the number of signification digits in the number. In binary arithmetic the integral part of $ z_b $ is the number of binary digits required to store the number. Conversion of the precision from one base to another (such as binary/decimal) is discussed, and applied to consideration of the intrinsic precision of input/output routines and floating point arithmetic.

entry:
@Article{Hunter:1975:QMP,
  author =       "G. Hunter",
  title =        "A quantitative measure of precision",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "3",
  pages =        "231--233",
  month =        aug,
  year =         "1975",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/231.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/232.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/233.tif",
  abstract =     "The precision $ z_b $ of a real number is defined
                 quantitatively in terms of the fractional error in the
                 number, and the base of the arithmetic in which it is
                 represented. The definition is an extension of the
                 traditional rough measure of precision as the number of
                 signification digits in the number. In binary
                 arithmetic the integral part of $ z_b $ is the number
                 of binary digits required to store the number.
                 Conversion of the precision from one base to another
                 (such as binary/decimal) is discussed, and applied to
                 consideration of the intrinsic precision of
                 input/output routines and floating point arithmetic.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723; 921",
  corpsource =   "York University, Department of Chem., Downsview, Ont.,
                 Canada",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary arithmetic; digital arithmetic; digits;
                 floating; fractional error; input/output routines;
                 mathematical techniques; point arithmetic; precision;
                 real number; significant",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Kehl:1975:MMA
author: T. H. Kehl and Kenneth Burkhardt
title: A Minicomputer Microprogrammable, Arithmetic Processor
crossref: IEEE:1975:SCA
pages: 174--178
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kehl.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: T. H. Kehl and Kenneth Burkhardt
rawtitle: A Minicomputer Microprogrammable, Arithmetic Processor
abstract:
Except for a few notable examples, all computers have been designed as ``adder-central'' architectures. ``Adder-central,'' as used here, refers to an organization which places the Arithmetic Logic Unit (ALU) at that junction of the system through which all data must flow --- thus creating a bottleneck. In the early days, when adders were expensive, cost considerations precluded more than one ALU. Nowadays powerful ALU's are available at very low cost and a designer, even of minicomputers, can consider placing more than one ALU in a system.

rawabstract:
Except for a few notable examples, all computers have been designed as ``adder-central'' architectures. ``Adder-central,'' as used here, refers to an organization which places the Arithmetic Logic Unit (ALU) at that junction of the system through which all data must flow --- thus creating a bottleneck. In the early days, when adders were expensive, cost considerations precluded more than one ALU. Nowadays powerful ALU's are available at very low cost and a designer, even of minicomputers, can consider placing more than one ALU in a system.

entry:
@InProceedings{Kehl:1975:MMA,
  author =       "T. H. Kehl and Kenneth Burkhardt",
  title =        "A Minicomputer Microprogrammable, Arithmetic
                 Processor",
  crossref =     "IEEE:1975:SCA",
  pages =        "174--178",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kehl.pdf",
  abstract =     "Except for a few notable examples, all computers have
                 been designed as ``adder-central'' architectures.
                 ``Adder-central,'' as used here, refers to an
                 organization which places the Arithmetic Logic Unit
                 (ALU) at that junction of the system through which all
                 data must flow --- thus creating a bottleneck. In the
                 early days, when adders were expensive, cost
                 considerations precluded more than one ALU. Nowadays
                 powerful ALU's are available at very low cost and a
                 designer, even of minicomputers, can consider placing
                 more than one ALU in a system.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Keir:1975:CNR
author: Roy A. Keir
title: Compatible number representations
crossref: IEEE:1975:SCA
pages: 82--87
year: 1975
bibdate: Fri Nov 28 11:38:18 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:38:18 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_2.pdf
keywords: ARITH-3; decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Roy A. Keir
rawtitle: Compatible number representations
abstract:
A compatible number system for mixed fixed-point and floating-point arithmetic is described in terms of number formats and opcode sequences (for hardwired or microcoded control). This inexpensive system can be as fast as fixed-point arithmetic on integers, is faster than normalized arithmetic in floating point, gets answers identical to those of normalized arithmetic, and automatically satisfies the Algol-60 mixed-mode rules. The central concept is the avoidance of meaningless ``normalization'' following arithmetic operations. Adoption of this system could lead to simpler compilers.

rawabstract:
A compatible number system for mixed fixed-point and floating-point arithmetic is described in terms of number formats and opcode sequences (for hardwired or microcoded control). This inexpensive system can be as fast as fixed-point arithmetic on integers, is faster than normalized arithmetic in floating point, gets answers identical to those of normalized arithmetic, and automatically satisfies the Algol-60 mixed-mode rules. The central concept is the avoidance of meaningless ``normalization'' following arithmetic operations. Adoption of this system could lead to simpler compilers.

entry:
@InProceedings{Keir:1975:CNR,
  author =       "Roy A. Keir",
  title =        "Compatible number representations",
  crossref =     "IEEE:1975:SCA",
  pages =        "82--87",
  year =         "1975",
  bibdate =      "Fri Nov 28 11:38:18 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_2.pdf",
  abstract =     "A compatible number system for mixed fixed-point and
                 floating-point arithmetic is described in terms of
                 number formats and opcode sequences (for hardwired or
                 microcoded control). This inexpensive system can be as
                 fast as fixed-point arithmetic on integers, is faster
                 than normalized arithmetic in floating point, gets
                 answers identical to those of normalized arithmetic,
                 and automatically satisfies the Algol-60 mixed-mode
                 rules. The central concept is the avoidance of
                 meaningless ``normalization'' following arithmetic
                 operations. Adoption of this system could lead to
                 simpler compilers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Keir:1975:PCR
author: Roy A. Keir
title: Programmer-controlled roundoff and the selection of a stable roundoff rule
crossref: IEEE:1975:SCA
pages: 73--76
year: 1975
bibdate: Fri Nov 28 18:11:30 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:11:30 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_1.pdf
keywords: ARITH-3
acknowledgement: ack-mfc
rawauthor: Roy A. Keir
rawtitle: Programmer-controlled roundoff and the selection of a stable roundoff rule
abstract:
The author suggests that every computer with floating-point addition and subtraction should have PSW controllable roundoff facilities. Yohe's catalog should be included. There should also be a stable roundoff mode using the round-to-off [em -odd] or round-to-even rule based on whether the radix is divisible by four or only by two.

rawabstract:
The author suggests that every computer with floating-point addition and subtraction should have PSW controllable roundoff facilities. Yohe's catalog should be included. There should also be a stable roundoff mode using the round-to-off [{\em -odd\/}] or round-to-even rule based on whether the radix is divisible by four or only by two.

entry:
@InProceedings{Keir:1975:PCR,
  author =       "Roy A. Keir",
  title =        "Programmer-controlled roundoff and the selection of a
                 stable roundoff rule",
  crossref =     "IEEE:1975:SCA",
  pages =        "73--76",
  year =         "1975",
  bibdate =      "Fri Nov 28 18:11:30 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_1.pdf",
  abstract =     "The author suggests that every computer with
                 floating-point addition and subtraction should have PSW
                 controllable roundoff facilities. Yohe's catalog should
                 be included. There should also be a stable roundoff
                 mode using the round-to-off [{\em -odd\/}] or
                 round-to-even rule based on whether the radix is
                 divisible by four or only by two.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Keir:1975:SSR
author: R. A. Keir
title: Should the stable rounding rule be radix-dependent?
journal: j-INFO-PROC-LETT
volume: 3
number: 6
pages: 188--189
month: jul
monthnumber: 7
year: 1975
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Tue Nov 17 10:49:43 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.11.17 10:49:43 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
corpsource: Department of Computer Sci., University of Utah, Salt Lake City, UT, USA
journalURL: http://www.sciencedirect.com/science/journal/00200190
treatment: T Theoretical or Mathematical
rawauthor: R. A. Keir
rawtitle: Should the stable rounding rule be radix-dependent?
keywords:
digital arithmetic; drift; floating point addition; radices; round to even rule; round to odd rule; stable rounding rule

entry:
@Article{Keir:1975:SSR,
  author =       "R. A. Keir",
  title =        "Should the stable rounding rule be radix-dependent?",
  journal =      j-INFO-PROC-LETT,
  volume =       "3",
  number =       "6",
  pages =        "188--189",
  day =          "??",
  month =        jul,
  year =         "1975",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Tue Nov 17 10:49:43 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Computer Sci., University of Utah, Salt
                 Lake City, UT, USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "digital arithmetic; drift; floating point addition;
                 radices; round to even rule; round to odd rule; stable
                 rounding rule",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Kent:1975:CSU
author: Jan G. Kent
title: Comparison Sets: a Useful Partitioning of the Space of Floating-Point Operand Pairs
crossref: IEEE:1975:SCA
pages: 36--39
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kent.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Jan G. Kent
rawtitle: Comparison Sets: a Useful Partitioning of the Space of Floating-Point Operand Pairs
abstract:
In this paper the definition of comparison sets and a discussion of their usefulness are presented based on the research work reported in (14). In addition some new results concerning the distribution of floating point (FLP) operand pairs over comparison sets are given.

rawabstract:
In this paper the definition of comparison sets and a discussion of their usefulness are presented based on the research work reported in (14). In addition some new results concerning the distribution of floating point (FLP) operand pairs over comparison sets are given.

entry:
@InProceedings{Kent:1975:CSU,
  author =       "Jan G. Kent",
  title =        "Comparison Sets: a Useful Partitioning of the Space of
                 Floating-Point Operand Pairs",
  crossref =     "IEEE:1975:SCA",
  pages =        "36--39",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kent.pdf",
  abstract =     "In this paper the definition of comparison sets and a
                 discussion of their usefulness are presented based on
                 the research work reported in (14). In addition some
                 new results concerning the distribution of floating
                 point (FLP) operand pairs over comparison sets are
                 given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Klatte:1975:CPI
author: R. Klatte and Ch. Ullrich
title: Consequences of a Properly Implemented Computer Arithmetic for Periodicities of Iterative Methods
crossref: IEEE:1975:SCA
pages: 24--32
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Klatte.pdf
acknowledgement: ack-nhfb
rawauthor: R. Klatte and Ch. Ullrich
rawtitle: Consequences of a Properly Implemented Computer Arithmetic for Periodicities of Iterative Methods
abstract:
In ordered sets it is possible to show under certain assumptions two basic theorems concerning the cycle length of sequences of iterates generated by monotone operators. These results are applied to different iterative methods, where the conclusions are valid for the sequences of iterates produced by the numerical computations only, if the used computer arithmetic is properly implemented.

keywords:
ARITH-3; cycle, weakly cyclic vector function; floating-point arithmetic; Rounding invariant structures

rawabstract:
In ordered sets it is possible to show under certain assumptions two basic theorems concerning the cycle length of sequences of iterates generated by monotone operators. These results are applied to different iterative methods, where the conclusions are valid for the sequences of iterates produced by the numerical computations only, if the used computer arithmetic is properly implemented.

entry:
@InProceedings{Klatte:1975:CPI,
  author =       "R. Klatte and Ch. Ullrich",
  title =        "Consequences of a Properly Implemented Computer
                 Arithmetic for Periodicities of Iterative Methods",
  crossref =     "IEEE:1975:SCA",
  pages =        "24--32",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Klatte.pdf",
  abstract =     "In ordered sets it is possible to show under certain
                 assumptions two basic theorems concerning the cycle
                 length of sequences of iterates generated by monotone
                 operators. These results are applied to different
                 iterative methods, where the conclusions are valid for
                 the sequences of iterates produced by the numerical
                 computations only, if the used computer arithmetic is
                 properly implemented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; cycle, weakly cyclic vector function;
                 floating-point arithmetic; Rounding invariant
                 structures",
}


bibtype: inproceedings
filename: fparith.bib
label: Kornerup:1975:UND
author: Peter Kornerup
title: A Unified Numeric Data Type in Pascal
crossref: IEEE:1975:SCA
pages: 40--47
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kornerup.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Peter Kornerup
rawtitle: A Unified Numeric Data Type in {Pascal}
abstract:
It is proposed to substitute the standard data type em real of a high level language, with a unified data representation which can include a variety of interpretations as well as formats, in order to allow experiments with an environment containing a spectrum of non-standard arithmetics, as well as standard.par The implementation of a system is described where syntactic extensions to a language are made to support a microprogrammed virtual arithmetic unit which can treat variants such as integers, normalized, and unnormalized floating point numbers and intervals, within a unified representation.par More specifically Pascal is chosen as the base language, because it allows the user to define new data types, and the extension then mainly consists in substituting the simple (unstructured) data type em real with a skeletal structured type (which will be called em numeric).par The system is intended to be implemented on a microprogrammable processor (called MATHILDA) with a 64 bit wide datapath. The language Pascal has already been partially implemented based on a stack machine specifically designed for that language, and realized by interpretation in microcode. The present compiler was constructed with the aid of a parser-generator system, which will allow the language extensions to be made with a moderate effort.

rawabstract:
It is proposed to substitute the standard data type {\em real\/} of a high level language, with a unified data representation which can include a variety of interpretations as well as formats, in order to allow experiments with an environment containing a spectrum of non-standard arithmetics, as well as standard.\par The implementation of a system is described where syntactic extensions to a language are made to support a microprogrammed virtual arithmetic unit which can treat variants such as integers, normalized, and unnormalized floating point numbers and intervals, within a unified representation.\par More specifically Pascal is chosen as the base language, because it allows the user to define new data types, and the extension then mainly consists in substituting the simple (unstructured) data type {\em real\/} with a skeletal structured type (which will be called {\em numeric\/}).\par The system is intended to be implemented on a microprogrammable processor (called MATHILDA) with a 64 bit wide datapath. The language Pascal has already been partially implemented based on a stack machine specifically designed for that language, and realized by interpretation in microcode. The present compiler was constructed with the aid of a parser-generator system, which will allow the language extensions to be made with a moderate effort.

entry:
@InProceedings{Kornerup:1975:UND,
  author =       "Peter Kornerup",
  title =        "A Unified Numeric Data Type in {Pascal}",
  crossref =     "IEEE:1975:SCA",
  pages =        "40--47",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kornerup.pdf",
  abstract =     "It is proposed to substitute the standard data type
                 {\em real\/} of a high level language, with a unified
                 data representation which can include a variety of
                 interpretations as well as formats, in order to allow
                 experiments with an environment containing a spectrum
                 of non-standard arithmetics, as well as
                 standard.\par

                 The implementation of a system is described where
                 syntactic extensions to a language are made to support
                 a microprogrammed virtual arithmetic unit which can
                 treat variants such as integers, normalized, and
                 unnormalized floating point numbers and intervals,
                 within a unified representation.\par

                 More specifically Pascal is chosen as the base
                 language, because it allows the user to define new data
                 types, and the extension then mainly consists in
                 substituting the simple (unstructured) data type {\em
                 real\/} with a skeletal structured type (which will be
                 called {\em numeric\/}).\par

                 The system is intended to be implemented on a
                 microprogrammable processor (called MATHILDA) with a 64
                 bit wide datapath. The language Pascal has already been
                 partially implemented based on a stack machine
                 specifically designed for that language, and realized
                 by interpretation in microcode. The present compiler
                 was constructed with the aid of a parser-generator
                 system, which will allow the language extensions to be
                 made with a moderate effort.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Kreifelts:1975:OBF
author: T. Kreifelts
journal: j-COMPUTING
volume: 14
pages: 313--314
year: 1975
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Fri Sep 16 16:30:39 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:39 ???
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/607
rawauthor: T. Kreifelts
title:
Optimale Basiswahl fur eine Gleitkomma-Arithmetik (Berichtigung) toenglish Optimal Basis Choice for a Floating-Point Arithmetic (Correction) endtoenglish 

rawtitle:
{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik (Berichtigung)} \toenglish {Optimal Basis Choice for a Floating-Point Arithmetic (Correction)} \endtoenglish

entry:
@Article{Kreifelts:1975:OBF,
  author =       "T. Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
                 (Berichtigung)} \toenglish {Optimal Basis Choice for a
                 Floating-Point Arithmetic (Correction)} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "??",
  pages =        "313--314",
  month =        "????",
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}


bibtype: inproceedings
filename: fparith.bib
label: Krishnamurthy:1975:MPU
author: E. V. Krishnamurthy
title: Matrix Processors Using $p$-ADIC Arithmetic for Exact Linear Computations
crossref: IEEE:1975:SCA
pages: 92--97
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Krishnamurthy.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: E. V. Krishnamurthy
rawtitle: Matrix Processors Using $p$-{ADIC} Arithmetic for Exact Linear Computations
abstract:
A unique code (called Hensel's code) is derived for a rational number, by truncating its infinite $p$-adic expansion. The four basic arithmetic algorithms for these codes are described and their application to rational matrix computations is demonstrated by solving a system of linear equations exactly, using the Gaussian elimination procedure.par A comparative study of the computational complexity involved in this arithmetic and the multiple prime module arithmetic is made with reference to matrix computations. On this basis, a multiple $p$-adic scheme is suggested for the design of a highly parallel matrix processor.

rawabstract:
A unique code (called Hensel's code) is derived for a rational number, by truncating its infinite $p$-adic expansion. The four basic arithmetic algorithms for these codes are described and their application to rational matrix computations is demonstrated by solving a system of linear equations exactly, using the Gaussian elimination procedure.\par A comparative study of the computational complexity involved in this arithmetic and the multiple prime module arithmetic is made with reference to matrix computations. On this basis, a multiple $p$-adic scheme is suggested for the design of a highly parallel matrix processor.

entry:
@InProceedings{Krishnamurthy:1975:MPU,
  author =       "E. V. Krishnamurthy",
  title =        "Matrix Processors Using $p$-{ADIC} Arithmetic for
                 Exact Linear Computations",
  crossref =     "IEEE:1975:SCA",
  pages =        "92--97",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Krishnamurthy.pdf",
  abstract =     "A unique code (called Hensel's code) is derived for a
                 rational number, by truncating its infinite $p$-adic
                 expansion. The four basic arithmetic algorithms for
                 these codes are described and their application to
                 rational matrix computations is demonstrated by solving
                 a system of linear equations exactly, using the
                 Gaussian elimination procedure.\par

                 A comparative study of the computational complexity
                 involved in this arithmetic and the multiple prime
                 module arithmetic is made with reference to matrix
                 computations. On this basis, a multiple $p$-adic scheme
                 is suggested for the design of a highly parallel matrix
                 processor.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Ku:1975:FPC
author: W. Ku and Siu-Ming Ng
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 22
number: 12
pages: 927--936
month: dec
monthnumber: 12
year: 1975
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: W. Ku and Siu-Ming Ng
title:
Floating-point coefficient sensitivity and roundoff noise of recursive digital filters realized in ladder structures

rawtitle:
Floating-point coefficient sensitivity and roundoff noise of recursive digital filters realized in ladder structures

entry:
@Article{Ku:1975:FPC,
  author =       "W. Ku and Siu-Ming Ng",
  title =        "Floating-point coefficient sensitivity and roundoff
                 noise of recursive digital filters realized in ladder
                 structures",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "22",
  number =       "12",
  pages =        "927--936",
  month =        dec,
  year =         "1975",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Coefficient sensitivity and roundoff error with
                 floating-point rounding have been investigated for
                 several digital ladder filter structures. It is found
                 that in all the cases studied, the ladder structures
                 first proposed by Fettweis show a much lower \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Kuck:1975:RRN
author: D. J. Kuck and D. S. Parker and A. H. Sameh
title: ROM-Rounding: a New Rounding Scheme
crossref: IEEE:1975:SCA
pages: 67--72
year: 1975
bibdate: Thu Sep 01 12:13:06 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 12:13:06 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kuck.pdf
keywords: ARITH-3
acknowledgement: ack-nj
rawauthor: D. J. Kuck and D. S. Parker and A. H. Sameh
rawtitle: {ROM}-Rounding: a New Rounding Scheme
abstract:
ROM-rounding is introduced and is shown to compare favorably with existing floating-point rounding methods on design considerations and on performance over a series of error tests. The error-retarding value of guard digits, of rounding the aligned operand, and of rounding in general are discussed.

rawabstract:
ROM-rounding is introduced and is shown to compare favorably with existing floating-point rounding methods on design considerations and on performance over a series of error tests. The error-retarding value of guard digits, of rounding the aligned operand, and of rounding in general are discussed.

entry:
@InProceedings{Kuck:1975:RRN,
  author =       "D. J. Kuck and D. S. Parker and A. H. Sameh",
  title =        "{ROM}-Rounding: a New Rounding Scheme",
  crossref =     "IEEE:1975:SCA",
  pages =        "67--72",
  year =         "1975",
  bibdate =      "Thu Sep 01 12:13:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kuck.pdf",
  abstract =     "ROM-rounding is introduced and is shown to compare
                 favorably with existing floating-point rounding methods
                 on design considerations and on performance over a
                 series of error tests. The error-retarding value of
                 guard digits, of rounding the aligned operand, and of
                 rounding in general are discussed.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Kulisch:1975:FIF
author: U. Kulisch
title: Formalization and implementation of floating-point arithmetics
journal: j-COMPUTING
volume: 14
number: 4
pages: 323--348
year: 1975
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G05 (68A10)
MRnumber: 53 14897
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: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
reviewer: A. D. Booth
rawauthor: U. Kulisch
rawtitle: Formalization and implementation of floating-point arithmetics
entry:
@Article{Kulisch:1975:FIF,
  author =       "U. Kulisch",
  title =        "Formalization and implementation of floating-point
                 arithmetics",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "4",
  pages =        "323--348",
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05 (68A10)",
  MRnumber =     "53 14897",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "A. D. Booth",
}


bibtype: inproceedings
filename: fparith.bib
label: Kulisch:1975:MFC
author: U. Kulisch
title: Mathematical Foundation of Computer Arithmetic
crossref: IEEE:1975:SCA
pages: 1--13
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kulisch.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: U. Kulisch
rawtitle: Mathematical Foundation of Computer Arithmetic
abstract:
During the last years a number of papers concerning a mathematical foundation of computer arithmetic have been written. Some of these papers are still unpublished. The papers consider the spaces which occur in numerical computations on computers in dependence of a properly defined computer arithmetic. The following treatment gives a summary of the main ideas of these papers. Many of the proofs had to be sketched or completely omitted. In such cases the full information can be found in the references.

rawabstract:
During the last years a number of papers concerning a mathematical foundation of computer arithmetic have been written. Some of these papers are still unpublished. The papers consider the spaces which occur in numerical computations on computers in dependence of a properly defined computer arithmetic. The following treatment gives a summary of the main ideas of these papers. Many of the proofs had to be sketched or completely omitted. In such cases the full information can be found in the references.

entry:
@InProceedings{Kulisch:1975:MFC,
  author =       "U. Kulisch",
  title =        "Mathematical Foundation of Computer Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "1--13",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kulisch.pdf",
  abstract =     "During the last years a number of papers concerning a
                 mathematical foundation of computer arithmetic have
                 been written. Some of these papers are still
                 unpublished. The papers consider the spaces which occur
                 in numerical computations on computers in dependence of
                 a properly defined computer arithmetic. The following
                 treatment gives a summary of the main ideas of these
                 papers. Many of the proofs had to be sketched or
                 completely omitted. In such cases the full information
                 can be found in the references.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Lacroix:1975:PEM
author: Arild Lacroix
title: Limit cycles in floating point digital filters
crossref: Swamy:1975:PEM
pages: 475--479
year: 1975
MRclass: 94A05
MRnumber: 55 12278
bibdate: Fri Dec 08 12:19:10 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 12:19:10 ???
acknowledgement: ack-nhfb
reviewer: Krzysztof Sapiecha
rawauthor: Arild Lacroix
rawtitle: Limit cycles in floating point digital filters
entry:
@InProceedings{Lacroix:1975:PEM,
  author =       "Arild Lacroix",
  title =        "Limit cycles in floating point digital filters",
  crossref =     "Swamy:1975:PEM",
  pages =        "475--479",
  year =         "1975",
  MRclass =      "94A05",
  MRnumber =     "55 12278",
  bibdate =      "Fri Dec 08 12:19:10 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "Krzysztof Sapiecha",
}


bibtype: article
filename: fparith.bib
label: Landauro:1975:ODC
author: A. Landauro and J. Lienard
title: On Overflow Detection and Correction in Digital Filters
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 12
pages: 1226--1228
month: dec
monthnumber: 12
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224168
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:59 MDT 2011
bibtimestamp: 2011.07.12 07:57:59 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672761
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Landauro and J. Lienard
rawtitle: On Overflow Detection and Correction in Digital Filters
entry:
@Article{Landauro:1975:ODC,
  author =       "A. Landauro and J. Lienard",
  title =        "On Overflow Detection and Correction in Digital
                 Filters",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "12",
  pages =        "1226--1228",
  month =        dec,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224168",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672761",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Lang:1975:DPA
author: Allan L. Lang and Bruce D. Shriver
title: The Design of a Polymorphic Arithmetic Unit
crossref: IEEE:1975:SCA
pages: 48--55
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lang.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Allan L. Lang and Bruce D. Shriver
rawtitle: The Design of a Polymorphic Arithmetic Unit
abstract:
This paper presents results which stem from a research effort concerned with the specification and design of arithmetic units which can execute nonstandard integer and floating-point arithmetic. An arithmetic unit is proposed whose characteristics are based on user specifications and subsequently is termed a Polymorphic Arithmetic Unit (PAU). The user binds the identity of the PAU by specifying the contents of various descriptors and semantic interpretation tables which the PAU accesses during its execution. This capability removes several of the restrictions found in commercially available arithmetic units and potentially assists in making mathematically software portable.

rawabstract:
This paper presents results which stem from a research effort concerned with the specification and design of arithmetic units which can execute nonstandard integer and floating-point arithmetic. An arithmetic unit is proposed whose characteristics are based on user specifications and subsequently is termed a Polymorphic Arithmetic Unit (PAU). The user binds the identity of the PAU by specifying the contents of various descriptors and semantic interpretation tables which the PAU accesses during its execution. This capability removes several of the restrictions found in commercially available arithmetic units and potentially assists in making mathematically software portable.

entry:
@InProceedings{Lang:1975:DPA,
  author =       "Allan L. Lang and Bruce D. Shriver",
  title =        "The Design of a Polymorphic Arithmetic Unit",
  crossref =     "IEEE:1975:SCA",
  pages =        "48--55",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lang.pdf",
  abstract =     "This paper presents results which stem from a research
                 effort concerned with the specification and design of
                 arithmetic units which can execute nonstandard integer
                 and floating-point arithmetic. An arithmetic unit is
                 proposed whose characteristics are based on user
                 specifications and subsequently is termed a Polymorphic
                 Arithmetic Unit (PAU). The user binds the identity of
                 the PAU by specifying the contents of various
                 descriptors and semantic interpretation tables which
                 the PAU accesses during its execution. This capability
                 removes several of the restrictions found in
                 commercially available arithmetic units and potentially
                 assists in making mathematically software portable.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Laurie:1975:PIR
author: D. P. Laurie
title: Propagation of Initial Rounding Error in Romberg-Like Quadrature
journal: j-BIT
volume: 15
number: 3
pages: 277--282
month: sep
monthnumber: 9
year: 1975
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01933660
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:14 MST 2006
bibtimestamp: 2006.01.04 18:52:14 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=3&spage=277
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: D. P. Laurie
rawtitle: Propagation of Initial Rounding Error in {Romberg}-Like Quadrature
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=3; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Laurie:1975:PIR,
  author =       "D. P. Laurie",
  title =        "Propagation of Initial Rounding Error in
                 {Romberg}-Like Quadrature",
  journal =      j-BIT,
  volume =       "15",
  number =       "3",
  pages =        "277--282",
  month =        sep,
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933660",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=3&spage=277",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: fparith.bib
label: Lemeire:1975:CEI
author: Frans Lemeire
title: Computation of Equivalent Inherent Rounding Errors in the Solution of a Set of Linear Equations
journal: j-BIT
volume: 15
number: 1
pages: 65--71
month: mar
monthnumber: 3
year: 1975
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01932997
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:14 MST 2006
bibtimestamp: 2006.01.04 18:52:14 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=1&spage=65
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Frans Lemeire
rawtitle: Computation of Equivalent Inherent Rounding Errors in the Solution of a Set of Linear Equations
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Lemeire:1975:CEI,
  author =       "Frans Lemeire",
  title =        "Computation of Equivalent Inherent Rounding Errors in
                 the Solution of a Set of Linear Equations",
  journal =      j-BIT,
  volume =       "15",
  number =       "1",
  pages =        "65--71",
  month =        mar,
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932997",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=1&spage=65",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: fparith.bib
label: Linnainmaa:1975:TAS
author: Seppo Linnainmaa
title: Towards Accurate Statistical Estimation of Rounding Errors in Floating-Point Computations
journal: j-BIT
volume: 15
number: 2
pages: 165--173
month: jun
monthnumber: 6
year: 1975
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01932690
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65G05
MRnumber: 58 19090
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=15&issue=2&spage=165
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Seppo Linnainmaa
rawtitle: Towards Accurate Statistical Estimation of Rounding Errors in Floating-Point Computations
abstract:
A new method of estimating a posteriori the statistical characteristics of the rounding errors of an arbitrary algorithm is presented. This method is based on a discrete model of the distribution of rounding errors which makes more accurate estimates possible. The analysis is given for both rounding and truncating arithmetic. Finally, some experimental results are reported.

rawabstract:
A new method of estimating a posteriori the statistical characteristics of the rounding errors of an arbitrary algorithm is presented. This method is based on a discrete model of the distribution of rounding errors which makes more accurate estimates possible. The analysis is given for both rounding and truncating arithmetic. Finally, some experimental results are reported.

entry:
@Article{Linnainmaa:1975:TAS,
  author =       "Seppo Linnainmaa",
  title =        "Towards Accurate Statistical Estimation of Rounding
                 Errors in Floating-Point Computations",
  journal =      j-BIT,
  volume =       "15",
  number =       "2",
  pages =        "165--173",
  month =        jun,
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932690",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "58 19090",
  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=15&issue=2&spage=165",
  abstract =     "A new method of estimating a posteriori the
                 statistical characteristics of the rounding errors of
                 an arbitrary algorithm is presented. This method is
                 based on a discrete model of the distribution of
                 rounding errors which makes more accurate estimates
                 possible. The analysis is given for both rounding and
                 truncating arithmetic. Finally, some experimental
                 results are reported.",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: inproceedings
filename: fparith.bib
label: Lipovski:1975:RND
author: G. J. Lipovski
title: On Residue Number A/D and D/A Converters
crossref: IEEE:1975:SCA
pages: 197--199
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lipovski.pdf
keywords: ARITH-3; residue number system
acknowledgement: ack-nhfb
rawauthor: G. J. Lipovski
rawtitle: On Residue Number {A/D} and {D/A} Converters
abstract:
A very simple analog to digital converter and digital to analog converter is described for residue number digital processing. These simple devices make it feasible to replace analog components with comparatively inexpensive digital processors that use residue, or modulus, arithmetic capable of operating at very high speeds. Using off-the-shelf integrated circuits, addition, subtraction or multiplication of about 15 bits of accuracy can easily be done in as little as fifty nanoseconds. Any function using these operations (polynomial expansions, linear filters, Fast Fourier Transforms) can be economically implemented in a pipeline or other structure to get very fast systems. Moreover, a stage in the pipeline can correct for nonlinearities in the A/D or D/A converters. The simple devices described herein make residue arithmetic digital processors extremely attractive for use in fast analog systems.

rawabstract:
A very simple analog to digital converter and digital to analog converter is described for residue number digital processing. These simple devices make it feasible to replace analog components with comparatively inexpensive digital processors that use residue, or modulus, arithmetic capable of operating at very high speeds. Using off-the-shelf integrated circuits, addition, subtraction or multiplication of about 15 bits of accuracy can easily be done in as little as fifty nanoseconds. Any function using these operations (polynomial expansions, linear filters, Fast Fourier Transforms) can be economically implemented in a pipeline or other structure to get very fast systems. Moreover, a stage in the pipeline can correct for nonlinearities in the A/D or D/A converters. The simple devices described herein make residue arithmetic digital processors extremely attractive for use in fast analog systems.

entry:
@InProceedings{Lipovski:1975:RND,
  author =       "G. J. Lipovski",
  title =        "On Residue Number {A/D} and {D/A} Converters",
  crossref =     "IEEE:1975:SCA",
  pages =        "197--199",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lipovski.pdf",
  abstract =     "A very simple analog to digital converter and digital
                 to analog converter is described for residue number
                 digital processing. These simple devices make it
                 feasible to replace analog components with
                 comparatively inexpensive digital processors that use
                 residue, or modulus, arithmetic capable of operating at
                 very high speeds. Using off-the-shelf integrated
                 circuits, addition, subtraction or multiplication of
                 about 15 bits of accuracy can easily be done in as
                 little as fifty nanoseconds. Any function using these
                 operations (polynomial expansions, linear filters, Fast
                 Fourier Transforms) can be economically implemented in
                 a pipeline or other structure to get very fast systems.
                 Moreover, a stage in the pipeline can correct for
                 nonlinearities in the A/D or D/A converters. The simple
                 devices described herein make residue arithmetic
                 digital processors extremely attractive for use in fast
                 analog systems.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; residue number system",
}


bibtype: article
filename: fparith.bib
label: Liu:1975:REF
author: B. Liu and T. Kaneko
title: Roundoff error in fast Fourier transforms
journal: j-PROC-IEEE
volume: 63
number: 6
pages: 991--992
month: jun
monthnumber: 6
year: 1975
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: B. Liu and T. Kaneko
rawtitle: Roundoff error in fast {Fourier} transforms
entry:
@Article{Liu:1975:REF,
  author =       "B. Liu and T. Kaneko",
  title =        "Roundoff error in fast {Fourier} transforms",
  journal =      j-PROC-IEEE,
  volume =       "63",
  number =       "6",
  pages =        "991--992",
  month =        jun,
  year =         "1975",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "The finite word length used in the computer causes
                 round-off error in the calculation of Fourier
                 coefficients. When the fast Fourier transform method is
                 used, the statistical mean-square error has been
                 previously determined [3] for the case of the
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lorez:1975:BGB
author: H. Lorez and F. J. Urbanek and H. Will and R. Weiss and W. Baron and others
title: Buchbesprechungen (German) Book Reviews
journal: j-COMPUTING
volume: 14
number: 3
pages: 315--322
month: sep
monthnumber: 9
year: 1975
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Fri Sep 16 16:30:39 1994
bibtimestamp: 1994.09.16 16:30:39 ???
note: See cite Kreifelts:1973:OBG.
fjournal: Computing
language: German
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/607
rawauthor: H. Lorez and F. J. Urbanek and H. Will and R. Weiss and W. Baron and others
rawnote: See \cite{Kreifelts:1973:OBG}.
rawtitle: {Buchbesprechungen} ({German}) {Book Reviews}
bibsource:
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Lorez:1975:BGB,
  author =       "H. Lorez and F. J. Urbanek and H. Will and R. Weiss
                 and W. Baron and others",
  title =        "{Buchbesprechungen} ({German}) {Book Reviews}",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "3",
  pages =        "315--322",
  month =        sep,
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Kreifelts:1973:OBG}.",
  acknowledgement = ack-nj,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}


bibtype: book
filename: fparith.bib
label: Luke:1975:MFT
author: Yudell L. Luke
title: Mathematical Functions and Their Approximations
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xvii + 568
year: 1975
ISBN: 0-12-459950-8, 1-4832-6245-6 (e-book) OR 0124599508, 1483262456 (ebook)
ISBN13: 978-0-12-459950-5, 978-1-4832-6245-1 (e-book) OR 9780124599505, 9781483262451 (ebook)
LCCN: QA55 .L96 1975
bibdate: Fri Jun 30 05:58:16 MDT 2023
bibtimestamp: 2023.06.30 05:58:16 MDT
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawtitle: Mathematical Functions and Their Approximations
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

URL:
https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5

remark:
An updated version of part of Handbook of mathematical functions with formulas, graphs, and mathematical tables, edited by M. Abramowitz and I. A. Stegun. Includes indexes.

subject:
Mathematics; Tables; Fonctions (Matheematiques); Matheematiques; Calculus; Mathematical Analysis; Mathematics; Approximation; Funktion; Mathematik; Spezielle Funktion

TOC:
Preface / xv I. The Gamma Function and Related Functions 1.1 Definitions and Elementary Properties / 1 1.2 Power Series and Other Series Expansions / 1 1.3 Asymptotic Expansions / 7 1.4 Rational Approximations for y (z) / 13 1.5 Inequalities / 17 1.6 Bibliographic and Numerical Data / 20 1.6.1 General References / 20 1.6.2 Description of and References to Tables / 21 1.6.3 Description of and References to Other Approximations and Expansions / 22 II. The Binomial Function 2.1 Power Series / 24 2.2 Expansions in Series of Jacobi and Chebyshev Polynomials / 24 2.3 Expansions in Series of Bessel Functions / 26 2.4 Pade Approximations / 27 24.1 $(1 + 1 / z)^-c$ / 27 2.4.2 The Square Root / 28 2.4.3 Pade Coefficients / 30 2.4.4 The Function $e^-w$ / 31 2.5 Inequalities / 34 III. Elementary Functions 3.1 Logarithmic Functions / 36 3.1.1 Power Series / 36 3.1.2 Expansion in Series of Chebyshev Polynomials / 38 3.1.3 Pade Approximations / 39 3.1.4 Inequalities / 41 3.2 Exponential Function / 42 3.2.1 Series Expansions / 42 3.2.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions / 42 3.2.3 Pade Approximations / 46 3.2.4 Inequalities / 51 3.3 Circular and Hyperbolic Functions / 52 3.3.1 Power Series / 52 3.3.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions / 52 3.3.3 Rational and Pade Approximations / 57 3.3.4 Inequalities / 60 3.4 Inverse Circular and Hyperbolic Functions / 61 3.4.1 Power Series / 61 3.4.2 Expansions in Series of Chebyshev Polynomials / 63 3.4.3 Pade Approximations / 68 3.4.4 Inequalities / 72 3.5 Bibliographic and Numerical Data / 74 3.5.1 Description of and References to Tables / 74 3.5.2 Description of and References to Other Approximations and Expansions / 74 IV. Incomplete Gamma Functions 4.1 Definitions and Series Expansions / 77 4.2 Differential Equations and Difference Equations / 78 4.3 Pade Approximations / 79 4.3.1 $_1F_1(1; nu + 1; -z)$ / 79 4.3.2 $z^1 - nu e^z Gamma (nu , z)$ / 82 4.3.3 The Error $T_n(nu , z)$ for $|rm arg z/k| leq pi $ / 84 4.3.4 The Negative Real Axis and the Zeros of $F_n(nu , z)$ / 89 4.4 Inequalities / 95 4.4.1 $H(nu , z)$ / 95 4.4.2 $Gamma (nu , z)$ / 96 4.5 Notes on the Computation of the Incomplete Gamma Function / 97 4.6 Exponential Integrals / 103 4.6.1 Relation to Incomplete Gamma Function and Other Properties / 103 4.6.2 Expansions in Series of Chebyshev Polynomials / 104 4.6.3 Rational and Pad Approximations / 106 4.7 Cosine and Sine Integrals / 115 4.7.1 Relation to Exponential Integral and Other Properties / 115 4.7.2 Expansions in Series of Chebyshev Polynomials / 116 4.8 Error Functions / 119 4.8.1 Relation to Incomplete Gamma Function and Other Properties / 119 4.8.2 Expansions in Series of Chebyshev Polynomials and Bessel Functions / 122 4.8.3 Pade Approximations / 124 4.8.4 Trapezoidal Rule Approximations / 134 4.8.5 Inequalities / 137 4.9 Fresnel Integrals / 139 4.9.1 Relation to Error Functions and Other Properties / 139 4.9.2 Expansions in Series of Chebyshev Polynomials / 140 4.10 Bibliographic and Numerical Data / 143 4.10.1 References / 143 4.10.2 Description of and References to Tables / 143 4.10.3 Description of and References to Other Approximations and Expansions / 149 V. The Generalized Hypergeometric Function $_pF_g$ and the $G$-Function 5.1 Introduction / 154 5.2 The $_pF_q$ / 155 5.2.1 Power Series / 155 5.2.2 Derivatives and Contiguous Relations / 159 5.2.3 Integral Representations and Integrals Involving the $_pF_q$ / 160 5.2.4 Evaluation for Special Values of the Variable and Parameters / 163 5.3 The $G$-Function / 170 5.3.1 Definition and Relation to the $_pF_q$ / 170 5.3.2 Elementary Properties / 176 5.3.3 Analytic Continuation of $G_p, p^m, n(z)$ / 178 5.4 The Confluence Principle / 179 5.5 Multiplication Theorems / 184 5.6 Integrals Involving $G$-Functions / 186 5.7 Differential Equations / 190 5.7.1 The $_pF_q$ / 190 5.7.2 The $G$-Function / 192 5.8 Series of $G$-Functions / 194 5.8.1 Introduction / 194 5.8.2 Notation / 194 5.8.3 Expansion Theorems / 197 5.9 Asymptotic Expansions / 199 5.9.1 $G_p, q^q, n(z)$, $n = 0, 1$ / 199 5.9.2 $G_p, q^m, n(z)$ / 201 5.9.3 $_pF_q(z)$ / 206 5.10 Expansions in Series of Generalized Jacobi, Generalized Laguerre and Chebyshev Polynomials / 213 5.10.1 Expansions for $G$-Functions / 213 5.10.2 Expansions for $_pF_q$ / 220 5.11 Expansions in Series of Bessel Functions / 223 5.12 Polynomial and Rational Approximations / 224 5.13 Recurrence Formulas for Polynomials and Functions Occurring in Approximations to Generalized Hypergeometric Functions / 234 5.13.1 Introduction / 234 5.13.2 Recursion Formulas for Extended Jacobi and Laguerre Functions / 235 5.13.3 Recursion Formulas for the Numerator and Denominator Polynomials in the Rational Approximations for the Generalized Hypergeometric Function / 244 5.13.4 Recursion Formula for Coefficients in the Expansion of the $G$-Function in Series of Extended Jacobi Polynomials / 247 5.14 Inequalities / 252 VI. The Gaussian Hypergeometric Function $_2F_1$ 6.1 Introduction / 257 6.2 Elementary Properties / 257 6.2.1 Derivatives / 257 6.2.2 Contiguous Relations / 258 6.2.3 Integral Representations / 259 6.3 Differential Equations / 260 6.4 Kummer Solutions and Transformation Formulae / 262 6.5 Analytic Continuation / 263 6.6 The Complete Solution and Wronskians / 265 6.7 Quadratic Transformations / 270 6.8 The $_2F_1$ for Special Values of the Argument / 271 6.9 Expansion in Series of Chebyshev Polynomials / 274 6.10 Pade Approximations for $_2F_1(1, sigma ;rho + 1;-1/z)$ / 274 6.11 Inequalities / 278 6.12 Bibliographic and Numerical Data / 279 6.12.1 References / 279 6.12.2 Description of and References to Tables / 279 VII. The Confluent Hypergeometric Function 7.1 Introduction / 284 7.2 Integral Representations / 284 7.3 Elementary Relations / 285 7.3.1 Derivatives / 285 7.3.2 Contiguous Relations / 285 7.3.3 Products of Confluent Functions / 286 7.4 Differential Equations / 287 7.5 The Complete Solution and Wronskians / 288 7.6 Asymptotic Expansions / 291 7.7 Expansions in Series of Chebyshev Polynomials / 293 7.8 Expansions in Series of Besse! Functions / 294 7.9 Inequalities / 295 7.10 Other Notations and Related Functions / 295 7.11 Bibliographic and Numerical Data / 296 7.11.1 References / 296 7.11.2 Description of and References to Tables and Other Approximations / 296 VIII. Identification of the $_pF_q$, and $G$-Functions with the Special Functions 8.1 Introduction / 298 8.2 Named Special Functions Expressed as $_pF_q$'s / 298 8.2.1 Elementary Functions / 298 8.2.2 The Incomplete Gamma Function and Related Functions / 298 8.2.3 The Gaussian Hypergeometric Function / 298 8.2.4 Legendre Functions / 299 8.2.5 Orthogonal Polynomials / 299 8.2.6 Complete Elliptic Integrals / 299 8.2.7 Confluent Hypergeometric Functions, Whittaker Functions and Bessel Functions / 300 8.3 Named Functions Expressed in Terms of the $G$-Function / 300 8.4 The $G$-Function Expressed as a Named Function / 306 IX. Bessel Functions and Their Integrals 9.1 Introduction / 311 9.2 Definitions, Connecting Relations and Power Series / 311 9.3 Difference--Differential Formulas / 313 9.4 Products of Bessel Functions / 314 9.5 Asymptotic Expansions for Large Variable / 315 9.6 Integrals of Bessel Functions / 315 9.7 Expansions in Series of Chebyshev Polynomials / 316 9.8 Expansions in Series of Bessel Functions / 360 9.9 Rational Approximations / 361 9.9.1 Introduction / 361 9.9.2 $I_nu (z)$, $z$ Small / 361 9.9.3 $K_nu (z)$, $z$ Large / 366 9.10 Computation of Bessel Functions by Use of Recurrence Formulas / 380 9.10.1 Introduction / 380 9.10.2 Backward Recurrence Schemata for Generating $I_nu (z)$ / 380 9.10.3 Closed Form Expressions / 382 9.10.4 Expressions for $J_nu (z)$ / 389 9.10.5 Numerical Examples / 392 9.11 Evaluation of Bessel Functions by Application of Trapezoidal Type Integration Formulas / 395 9.12 Inequalities / 399 9.13 Bibliographic and Numerical Data / 403 9.13.1 References / 403 9.13.2 Description of and References to Tables / 404 9.13.3 Description of and References to Other Approximations and Expansions / 410 X. Lommel Functions, Struve Functions, and Associated Bessel Functions 10.1 Definitions, Connecting Relations and Power Series / 413 10.2 Asymptotic Expansions / 415 10.3 Expansions in Series of Chebyshev Polynomials and Bessel Functions / 415 10.4 Rational Approximations for $H_nu (z) - Y_nu (z)$ and the Errors in These Approximations / 422 10.5 Bibliographic and Numerical Data / 426 10.5.1 References / 426 10.5.2 Description of and References to Tables / 426 XI. Orthogonal Polynomials 11.1 Introduction / 428 11.2 Orthogonal Properties / 428 11.3 Jacobi Polynomials / 436 11.3.1 Expansion Formulae / 436 11.3.2 Difference--Differential Formulae / 439 11.3.3 Integrals / 439 11.3.4 Expansion of $x^rho $ in Series of Jacobi Polynomials / 440 11.3.5 Convergence Theorems for the Expansion of Arbitrary Functions in Series of Jacobi Polynomials / 442 11.3.6 Evaluation and Estimation of the Coefficients in the Expansion of a Given Function $f(x)$ in Series of Jacobi Polynomials / 443 11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ / 453 11.5 The Chebyshev Polynomials $T_n^*(x)$ and $U_n^*(x)$ / 459 11.6 Coefficients for Expansion of Integrals of Functions in Series of Chebyshev Polynomials of the First Kind / 464 11.6.1 Introduction / 464 11.6.2 Series of Shifted Chebyshev Polynomials / 464 11.6.3 Series of Chebyshev Polynomials of Even Order / 468 11.6.4 Series of Chebyshev Polynomials of Odd Order / 468 11.7 Orthogonality Properties of Chebyshev Polynomials with Respect to Summation / 469 11.8 A Nesting Procedure for the Computation of Expansions in Series of Functions Where the Functions Satisfy a Linear Finite Difference Equation / 475 XII. Computation by Use of Recurrence Formulas 12.1 Introduction / 483 12.2 Homogeneous Difference Equations / 483 12.3 Inhomogeneous Difference Equations / 487 XIII. Some Aspects of Rational and Polynomial Approximations 13.1 Introduction / 490 13.2 Approximations in Series of Chebyshev Polynomials of the First Kind / 490 13.3 The Pade Table / 493 13.4 Approximation of Functions Defined by a Differential Equation --- The $tau $-Method / 495 13.5 Approximations of Functions Defined by a Series / 499 13.6 Solution of Differential Equations in Series of Chebyshev Polynomials of the First Kind / 500 XIV. Miscellaneous Topics 14.1 Introduction / 505 14.2 Bernoulli Polynomials and Numbers / 505 14.3 $D$ and $delta $ Operators / 507 14.4 Computation and Check of the Tables / 509 14.5 Mathematical Constants / 512 14.6 Late Bibliography / 516 Bibliography / 517 Notation Index / 545 Subject Index / 551

rawTOC:
Preface / xv \\ \\ I. The Gamma Function and Related Functions \\ \\ 1.1 Definitions and Elementary Properties / 1 \\ 1.2 Power Series and Other Series Expansions / 1 \\ 1.3 Asymptotic Expansions / 7 \\ 1.4 Rational Approximations for y (z) / 13 \\ 1.5 Inequalities / 17 \\ 1.6 Bibliographic and Numerical Data / 20 \\ 1.6.1 General References / 20 \\ 1.6.2 Description of and References to Tables / 21 \\ 1.6.3 Description of and References to Other Approximations and Expansions / 22 \\ \\ II. The Binomial Function \\ \\ 2.1 Power Series / 24 \\ 2.2 Expansions in Series of Jacobi and Chebyshev Polynomials / 24 \\ 2.3 Expansions in Series of Bessel Functions / 26 \\ 2.4 Pad{\'e} Approximations / 27 \\ 24.1 $(1 + 1 / z)^{-c}$ / 27 \\ 2.4.2 The Square Root / 28 \\ 2.4.3 Pad{\'e} Coefficients / 30 \\ 2.4.4 The Function $e^{-w}$ / 31 \\ 2.5 Inequalities / 34 \\ \\ III. Elementary Functions \\ \\ 3.1 Logarithmic Functions / 36 \\ 3.1.1 Power Series / 36 \\ 3.1.2 Expansion in Series of Chebyshev Polynomials / 38 \\ 3.1.3 Pad{\'e} Approximations / 39 \\ 3.1.4 Inequalities / 41 \\ 3.2 Exponential Function / 42 \\ 3.2.1 Series Expansions / 42 \\ 3.2.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions / 42 \\ 3.2.3 Pad{\'e} Approximations / 46 \\ 3.2.4 Inequalities / 51 \\ 3.3 Circular and Hyperbolic Functions / 52 \\ 3.3.1 Power Series / 52 \\ 3.3.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions / 52 \\ 3.3.3 Rational and Pad{\'e} Approximations / 57 \\ 3.3.4 Inequalities / 60 \\ 3.4 Inverse Circular and Hyperbolic Functions / 61 \\ 3.4.1 Power Series / 61 \\ 3.4.2 Expansions in Series of Chebyshev Polynomials / 63 \\ 3.4.3 Pad{\'e} Approximations / 68 \\ 3.4.4 Inequalities / 72 \\ 3.5 Bibliographic and Numerical Data / 74 \\ 3.5.1 Description of and References to Tables / 74 \\ 3.5.2 Description of and References to Other Approximations and Expansions / 74 \\ \\ IV. Incomplete Gamma Functions \\ \\ 4.1 Definitions and Series Expansions / 77 \\ 4.2 Differential Equations and Difference Equations / 78 \\ 4.3 Pad{\'e} Approximations / 79 \\ 4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\ 4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\ 4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq \pi$ / 84 \\ 4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu, z)$ / 89 \\ 4.4 Inequalities / 95 \\ 4.4.1 $H(\nu, z)$ / 95 \\ 4.4.2 $\Gamma(\nu, z)$ / 96 \\ 4.5 Notes on the Computation of the Incomplete Gamma Function / 97 \\ 4.6 Exponential Integrals / 103 \\ 4.6.1 Relation to Incomplete Gamma Function and Other Properties / 103 \\ 4.6.2 Expansions in Series of Chebyshev Polynomials / 104 \\ 4.6.3 Rational and Pad Approximations / 106 \\ 4.7 Cosine and Sine Integrals / 115 \\ 4.7.1 Relation to Exponential Integral and Other Properties / 115 \\ 4.7.2 Expansions in Series of Chebyshev Polynomials / 116 \\ 4.8 Error Functions / 119 \\ 4.8.1 Relation to Incomplete Gamma Function and Other Properties / 119 \\ 4.8.2 Expansions in Series of Chebyshev Polynomials and Bessel Functions / 122 \\ 4.8.3 Pad{\'e} Approximations / 124 \\ 4.8.4 Trapezoidal Rule Approximations / 134 \\ 4.8.5 Inequalities / 137 \\ 4.9 Fresnel Integrals / 139 \\ 4.9.1 Relation to Error Functions and Other Properties / 139 \\ 4.9.2 Expansions in Series of Chebyshev Polynomials / 140 \\ 4.10 Bibliographic and Numerical Data / 143 \\ 4.10.1 References / 143 \\ 4.10.2 Description of and References to Tables / 143 \\ 4.10.3 Description of and References to Other Approximations and Expansions / 149 \\ \\ V. The Generalized Hypergeometric Function $_pF_g$ and the $G$-Function \\ \\ 5.1 Introduction / 154 \\ 5.2 The $_pF_q$ / 155 \\ 5.2.1 Power Series / 155 \\ 5.2.2 Derivatives and Contiguous Relations / 159 \\ 5.2.3 Integral Representations and Integrals Involving the $_pF_q$ / 160 \\ 5.2.4 Evaluation for Special Values of the Variable and Parameters / 163 \\ 5.3 The $G$-Function / 170 \\ 5.3.1 Definition and Relation to the $_pF_q$ / 170 \\ 5.3.2 Elementary Properties / 176 \\ 5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ / 178 \\ 5.4 The Confluence Principle / 179 \\ 5.5 Multiplication Theorems / 184 \\ 5.6 Integrals Involving $G$-Functions / 186 \\ 5.7 Differential Equations / 190 \\ 5.7.1 The $_pF_q$ / 190 \\ 5.7.2 The $G$-Function / 192 \\ 5.8 Series of $G$-Functions / 194 \\ 5.8.1 Introduction / 194 \\ 5.8.2 Notation / 194 \\ 5.8.3 Expansion Theorems / 197 \\ 5.9 Asymptotic Expansions / 199 \\ 5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\ 5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\ 5.9.3 $_pF_q(z)$ / 206 \\ 5.10 Expansions in Series of Generalized Jacobi, Generalized Laguerre and Chebyshev Polynomials / 213 \\ 5.10.1 Expansions for $G$-Functions / 213 \\ 5.10.2 Expansions for $_pF_q$ / 220 \\ 5.11 Expansions in Series of Bessel Functions / 223 \\ 5.12 Polynomial and Rational Approximations / 224 \\ 5.13 Recurrence Formulas for Polynomials and Functions Occurring in Approximations to Generalized Hypergeometric Functions / 234 \\ 5.13.1 Introduction / 234 \\ 5.13.2 Recursion Formulas for Extended Jacobi and Laguerre Functions / 235 \\ 5.13.3 Recursion Formulas for the Numerator and Denominator Polynomials in the Rational Approximations for the Generalized Hypergeometric Function / 244 \\ 5.13.4 Recursion Formula for Coefficients in the Expansion of the $G$-Function in Series of Extended Jacobi Polynomials / 247 \\ 5.14 Inequalities / 252 \\ \\ VI. The Gaussian Hypergeometric Function $_2F_1$ \\ \\ 6.1 Introduction / 257 \\ 6.2 Elementary Properties / 257 \\ 6.2.1 Derivatives / 257 \\ 6.2.2 Contiguous Relations / 258 \\ 6.2.3 Integral Representations / 259 \\ 6.3 Differential Equations / 260 \\ 6.4 Kummer Solutions and Transformation Formulae / 262 \\ 6.5 Analytic Continuation / 263 \\ 6.6 The Complete Solution and Wronskians / 265 \\ 6.7 Quadratic Transformations / 270 \\ 6.8 The $_2F_1$ for Special Values of the Argument / 271 \\ 6.9 Expansion in Series of Chebyshev Polynomials / 274 \\ 6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho + 1;-1/z)$ / 274 \\ 6.11 Inequalities / 278 \\ 6.12 Bibliographic and Numerical Data / 279 \\ 6.12.1 References / 279 \\ 6.12.2 Description of and References to Tables / 279 \\ \\ VII. The Confluent Hypergeometric Function \\ \\ 7.1 Introduction / 284 \\ 7.2 Integral Representations / 284 \\ 7.3 Elementary Relations / 285 \\ 7.3.1 Derivatives / 285 \\ 7.3.2 Contiguous Relations / 285 \\ 7.3.3 Products of Confluent Functions / 286 \\ 7.4 Differential Equations / 287 \\ 7.5 The Complete Solution and Wronskians / 288 \\ 7.6 Asymptotic Expansions / 291 \\ 7.7 Expansions in Series of Chebyshev Polynomials / 293 \\ 7.8 Expansions in Series of Besse! Functions / 294 \\ 7.9 Inequalities / 295 \\ 7.10 Other Notations and Related Functions / 295 \\ 7.11 Bibliographic and Numerical Data / 296 \\ 7.11.1 References / 296 \\ 7.11.2 Description of and References to Tables and Other Approximations / 296 \\ \\ VIII. Identification of the $_pF_q$, and $G$-Functions with the Special Functions \\ \\ 8.1 Introduction / 298 \\ 8.2 Named Special Functions Expressed as $_pF_q$'s / 298 \\ 8.2.1 Elementary Functions / 298 \\ 8.2.2 The Incomplete Gamma Function and Related Functions / 298 \\ 8.2.3 The Gaussian Hypergeometric Function / 298 \\ 8.2.4 Legendre Functions / 299 \\ 8.2.5 Orthogonal Polynomials / 299 \\ 8.2.6 Complete Elliptic Integrals / 299 \\ 8.2.7 Confluent Hypergeometric Functions, Whittaker Functions and Bessel Functions / 300 \\ 8.3 Named Functions Expressed in Terms of the $G$-Function / 300 \\ 8.4 The $G$-Function Expressed as a Named Function / 306 \\ \\ IX. Bessel Functions and Their Integrals \\ \\ 9.1 Introduction / 311 \\ 9.2 Definitions, Connecting Relations and Power Series / 311 \\ 9.3 Difference--Differential Formulas / 313 \\ 9.4 Products of Bessel Functions / 314 \\ 9.5 Asymptotic Expansions for Large Variable / 315 \\ 9.6 Integrals of Bessel Functions / 315 \\ 9.7 Expansions in Series of Chebyshev Polynomials / 316 \\ 9.8 Expansions in Series of Bessel Functions / 360 \\ 9.9 Rational Approximations / 361 \\ 9.9.1 Introduction / 361 \\ 9.9.2 $I_\nu(z)$, $z$ Small / 361 \\ 9.9.3 $K_\nu(z)$, $z$ Large / 366 \\ 9.10 Computation of Bessel Functions by Use of Recurrence Formulas / 380 \\ 9.10.1 Introduction / 380 \\ 9.10.2 Backward Recurrence Schemata for Generating $I_\nu(z)$ / 380 \\ 9.10.3 Closed Form Expressions / 382 \\ 9.10.4 Expressions for $J_\nu(z)$ / 389 \\ 9.10.5 Numerical Examples / 392 \\ 9.11 Evaluation of Bessel Functions by Application of Trapezoidal Type Integration Formulas / 395 \\ 9.12 Inequalities / 399 \\ 9.13 Bibliographic and Numerical Data / 403 \\ 9.13.1 References / 403 \\ 9.13.2 Description of and References to Tables / 404 \\ 9.13.3 Description of and References to Other Approximations and Expansions / 410 \\ \\ X. Lommel Functions, Struve Functions, and Associated Bessel Functions \\ \\ 10.1 Definitions, Connecting Relations and Power Series / 413 \\ 10.2 Asymptotic Expansions / 415 \\ 10.3 Expansions in Series of Chebyshev Polynomials and Bessel Functions / 415 \\ 10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$ and the Errors in These Approximations / 422 \\ 10.5 Bibliographic and Numerical Data / 426 \\ 10.5.1 References / 426 \\ 10.5.2 Description of and References to Tables / 426 \\ \\ XI. Orthogonal Polynomials \\ \\ 11.1 Introduction / 428 \\ 11.2 Orthogonal Properties / 428 \\ 11.3 Jacobi Polynomials / 436 \\ 11.3.1 Expansion Formulae / 436 \\ 11.3.2 Difference--Differential Formulae / 439 \\ 11.3.3 Integrals / 439 \\ 11.3.4 Expansion of $x^\rho$ in Series of Jacobi Polynomials / 440 \\ 11.3.5 Convergence Theorems for the Expansion of Arbitrary Functions in Series of Jacobi Polynomials / 442 \\ 11.3.6 Evaluation and Estimation of the Coefficients in the Expansion of a Given Function $f(x)$ in Series of Jacobi Polynomials / 443 \\ 11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ / 453 \\ 11.5 The Chebyshev Polynomials $T_n^*(x)$ and $U_n^*(x)$ / 459 \\ 11.6 Coefficients for Expansion of Integrals of Functions in Series of Chebyshev Polynomials of the First Kind / 464 \\ 11.6.1 Introduction / 464 \\ 11.6.2 Series of Shifted Chebyshev Polynomials / 464 \\ 11.6.3 Series of Chebyshev Polynomials of Even Order / 468 \\ 11.6.4 Series of Chebyshev Polynomials of Odd Order / 468 \\ 11.7 Orthogonality Properties of Chebyshev Polynomials with Respect to Summation / 469 \\ 11.8 A Nesting Procedure for the Computation of Expansions in Series of Functions Where the Functions Satisfy a Linear Finite Difference Equation / 475 \\ \\ XII. Computation by Use of Recurrence Formulas \\ \\ 12.1 Introduction / 483 \\ 12.2 Homogeneous Difference Equations / 483 \\ 12.3 Inhomogeneous Difference Equations / 487 \\ \\ XIII. Some Aspects of Rational and Polynomial Approximations \\ \\ 13.1 Introduction / 490 \\ 13.2 Approximations in Series of Chebyshev Polynomials of the First Kind / 490 \\ 13.3 The Pad{\'e} Table / 493 \\ 13.4 Approximation of Functions Defined by a Differential Equation --- The $\tau$-Method / 495 \\ 13.5 Approximations of Functions Defined by a Series / 499 \\ 13.6 Solution of Differential Equations in Series of Chebyshev Polynomials of the First Kind / 500 \\ \\ XIV. Miscellaneous Topics \\ \\ 14.1 Introduction / 505 \\ 14.2 Bernoulli Polynomials and Numbers / 505 \\ 14.3 $D$ and $\delta$ Operators / 507 \\ 14.4 Computation and Check of the Tables / 509 \\ 14.5 Mathematical Constants / 512 \\ 14.6 Late Bibliography / 516 \\ \\ Bibliography / 517 \\ \\ Notation Index / 545 \\ \\ Subject Index / 551

entry:
@Book{Luke:1975:MFT,
  author =       "Yudell L. Luke",
  title =        "Mathematical Functions and Their Approximations",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 568",
  year =         "1975",
  ISBN =         "0-12-459950-8, 1-4832-6245-6 (e-book)",
  ISBN-13 =      "978-0-12-459950-5, 978-1-4832-6245-1 (e-book)",
  LCCN =         "QA55 .L96 1975",
  bibdate =      "Fri Jun 30 05:58:16 MDT 2023",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  URL =          "https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5",
  acknowledgement = ack-nhfb,
  libnote =      "Not in my library.",
  remark =       "An updated version of part of Handbook of mathematical
                 functions with formulas, graphs, and mathematical
                 tables, edited by M. Abramowitz and I. A. Stegun.
                 Includes indexes.",
  subject =      "Mathematics; Tables; Fonctions (Math{\'e}ematiques);
                 Math{\'e}ematiques; Calculus; Mathematical Analysis;
                 Mathematics; Approximation; Funktion; Mathematik;
                 Spezielle Funktion",
  tableofcontents = "Preface / xv \\
                 \\
                 I. The Gamma Function and Related Functions \\
                 \\
                 1.1 Definitions and Elementary Properties / 1 \\
                 1.2 Power Series and Other Series Expansions / 1 \\
                 1.3 Asymptotic Expansions / 7 \\
                 1.4 Rational Approximations for y (z) / 13 \\
                 1.5 Inequalities / 17 \\
                 1.6 Bibliographic and Numerical Data / 20 \\
                 1.6.1 General References / 20 \\
                 1.6.2 Description of and References to Tables / 21 \\
                 1.6.3 Description of and References to Other
                 Approximations and Expansions / 22 \\
                 \\
                 II. The Binomial Function \\
                 \\
                 2.1 Power Series / 24 \\
                 2.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials / 24 \\
                 2.3 Expansions in Series of Bessel Functions / 26 \\
                 2.4 Pad{\'e} Approximations / 27 \\
                 24.1 $(1 + 1 / z)^{-c}$ / 27 \\
                 2.4.2 The Square Root / 28 \\
                 2.4.3 Pad{\'e} Coefficients / 30 \\
                 2.4.4 The Function $e^{-w}$ / 31 \\
                 2.5 Inequalities / 34 \\
                 \\
                 III. Elementary Functions \\
                 \\
                 3.1 Logarithmic Functions / 36 \\
                 3.1.1 Power Series / 36 \\
                 3.1.2 Expansion in Series of Chebyshev Polynomials / 38
                 \\
                 3.1.3 Pad{\'e} Approximations / 39 \\
                 3.1.4 Inequalities / 41 \\
                 3.2 Exponential Function / 42 \\
                 3.2.1 Series Expansions / 42 \\
                 3.2.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials and Bessel Functions / 42 \\
                 3.2.3 Pad{\'e} Approximations / 46 \\
                 3.2.4 Inequalities / 51 \\
                 3.3 Circular and Hyperbolic Functions / 52 \\
                 3.3.1 Power Series / 52 \\
                 3.3.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials and Bessel Functions / 52 \\
                 3.3.3 Rational and Pad{\'e} Approximations / 57 \\
                 3.3.4 Inequalities / 60 \\
                 3.4 Inverse Circular and Hyperbolic Functions / 61 \\
                 3.4.1 Power Series / 61 \\
                 3.4.2 Expansions in Series of Chebyshev Polynomials /
                 63 \\
                 3.4.3 Pad{\'e} Approximations / 68 \\
                 3.4.4 Inequalities / 72 \\
                 3.5 Bibliographic and Numerical Data / 74 \\
                 3.5.1 Description of and References to Tables / 74 \\
                 3.5.2 Description of and References to Other
                 Approximations and Expansions / 74 \\
                 \\
                 IV. Incomplete Gamma Functions \\
                 \\
                 4.1 Definitions and Series Expansions / 77 \\
                 4.2 Differential Equations and Difference Equations /
                 78 \\
                 4.3 Pad{\'e} Approximations / 79 \\
                 4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\
                 4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\
                 4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq
                 \pi$ / 84 \\
                 4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu,
                 z)$ / 89 \\
                 4.4 Inequalities / 95 \\
                 4.4.1 $H(\nu, z)$ / 95 \\
                 4.4.2 $\Gamma(\nu, z)$ / 96 \\
                 4.5 Notes on the Computation of the Incomplete Gamma
                 Function / 97 \\
                 4.6 Exponential Integrals / 103 \\
                 4.6.1 Relation to Incomplete Gamma Function and Other
                 Properties / 103 \\
                 4.6.2 Expansions in Series of Chebyshev Polynomials /
                 104 \\
                 4.6.3 Rational and Pad Approximations / 106 \\
                 4.7 Cosine and Sine Integrals / 115 \\
                 4.7.1 Relation to Exponential Integral and Other
                 Properties / 115 \\
                 4.7.2 Expansions in Series of Chebyshev Polynomials /
                 116 \\
                 4.8 Error Functions / 119 \\
                 4.8.1 Relation to Incomplete Gamma Function and Other
                 Properties / 119 \\
                 4.8.2 Expansions in Series of Chebyshev Polynomials and
                 Bessel Functions / 122 \\
                 4.8.3 Pad{\'e} Approximations / 124 \\
                 4.8.4 Trapezoidal Rule Approximations / 134 \\
                 4.8.5 Inequalities / 137 \\
                 4.9 Fresnel Integrals / 139 \\
                 4.9.1 Relation to Error Functions and Other Properties
                 / 139 \\
                 4.9.2 Expansions in Series of Chebyshev Polynomials /
                 140 \\
                 4.10 Bibliographic and Numerical Data / 143 \\
                 4.10.1 References / 143 \\
                 4.10.2 Description of and References to Tables / 143
                 \\
                 4.10.3 Description of and References to Other
                 Approximations and Expansions / 149 \\
                 \\
                 V. The Generalized Hypergeometric Function $_pF_g$ and
                 the $G$-Function \\
                 \\
                 5.1 Introduction / 154 \\
                 5.2 The $_pF_q$ / 155 \\
                 5.2.1 Power Series / 155 \\
                 5.2.2 Derivatives and Contiguous Relations / 159 \\
                 5.2.3 Integral Representations and Integrals Involving
                 the $_pF_q$ / 160 \\
                 5.2.4 Evaluation for Special Values of the Variable and
                 Parameters / 163 \\
                 5.3 The $G$-Function / 170 \\
                 5.3.1 Definition and Relation to the $_pF_q$ / 170 \\
                 5.3.2 Elementary Properties / 176 \\
                 5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ /
                 178 \\
                 5.4 The Confluence Principle / 179 \\
                 5.5 Multiplication Theorems / 184 \\
                 5.6 Integrals Involving $G$-Functions / 186 \\
                 5.7 Differential Equations / 190 \\
                 5.7.1 The $_pF_q$ / 190 \\
                 5.7.2 The $G$-Function / 192 \\
                 5.8 Series of $G$-Functions / 194 \\
                 5.8.1 Introduction / 194 \\
                 5.8.2 Notation / 194 \\
                 5.8.3 Expansion Theorems / 197 \\
                 5.9 Asymptotic Expansions / 199 \\
                 5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\
                 5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\
                 5.9.3 $_pF_q(z)$ / 206 \\
                 5.10 Expansions in Series of Generalized Jacobi,
                 Generalized Laguerre and Chebyshev Polynomials / 213
                 \\
                 5.10.1 Expansions for $G$-Functions / 213 \\
                 5.10.2 Expansions for $_pF_q$ / 220 \\
                 5.11 Expansions in Series of Bessel Functions / 223 \\
                 5.12 Polynomial and Rational Approximations / 224 \\
                 5.13 Recurrence Formulas for Polynomials and Functions
                 Occurring in Approximations to Generalized
                 Hypergeometric Functions / 234 \\
                 5.13.1 Introduction / 234 \\
                 5.13.2 Recursion Formulas for Extended Jacobi and
                 Laguerre Functions / 235 \\
                 5.13.3 Recursion Formulas for the Numerator and
                 Denominator Polynomials in the Rational Approximations
                 for the Generalized Hypergeometric Function / 244 \\
                 5.13.4 Recursion Formula for Coefficients in the
                 Expansion of the $G$-Function in Series of Extended
                 Jacobi Polynomials / 247 \\
                 5.14 Inequalities / 252 \\
                 \\
                 VI. The Gaussian Hypergeometric Function $_2F_1$ \\
                 \\
                 6.1 Introduction / 257 \\
                 6.2 Elementary Properties / 257 \\
                 6.2.1 Derivatives / 257 \\
                 6.2.2 Contiguous Relations / 258 \\
                 6.2.3 Integral Representations / 259 \\
                 6.3 Differential Equations / 260 \\
                 6.4 Kummer Solutions and Transformation Formulae / 262
                 \\
                 6.5 Analytic Continuation / 263 \\
                 6.6 The Complete Solution and Wronskians / 265 \\
                 6.7 Quadratic Transformations / 270 \\
                 6.8 The $_2F_1$ for Special Values of the Argument /
                 271 \\
                 6.9 Expansion in Series of Chebyshev Polynomials / 274
                 \\
                 6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho
                 + 1;-1/z)$ / 274 \\
                 6.11 Inequalities / 278 \\
                 6.12 Bibliographic and Numerical Data / 279 \\
                 6.12.1 References / 279 \\
                 6.12.2 Description of and References to Tables / 279
                 \\
                 \\
                 VII. The Confluent Hypergeometric Function \\
                 \\
                 7.1 Introduction / 284 \\
                 7.2 Integral Representations / 284 \\
                 7.3 Elementary Relations / 285 \\
                 7.3.1 Derivatives / 285 \\
                 7.3.2 Contiguous Relations / 285 \\
                 7.3.3 Products of Confluent Functions / 286 \\
                 7.4 Differential Equations / 287 \\
                 7.5 The Complete Solution and Wronskians / 288 \\
                 7.6 Asymptotic Expansions / 291 \\
                 7.7 Expansions in Series of Chebyshev Polynomials / 293
                 \\
                 7.8 Expansions in Series of Besse! Functions / 294 \\
                 7.9 Inequalities / 295 \\
                 7.10 Other Notations and Related Functions / 295 \\
                 7.11 Bibliographic and Numerical Data / 296 \\
                 7.11.1 References / 296 \\
                 7.11.2 Description of and References to Tables and
                 Other Approximations / 296 \\
                 \\
                 VIII. Identification of the $_pF_q$, and $G$-Functions
                 with the Special Functions \\
                 \\
                 8.1 Introduction / 298 \\
                 8.2 Named Special Functions Expressed as $_pF_q$'s /
                 298 \\
                 8.2.1 Elementary Functions / 298 \\
                 8.2.2 The Incomplete Gamma Function and Related
                 Functions / 298 \\
                 8.2.3 The Gaussian Hypergeometric Function / 298 \\
                 8.2.4 Legendre Functions / 299 \\
                 8.2.5 Orthogonal Polynomials / 299 \\
                 8.2.6 Complete Elliptic Integrals / 299 \\
                 8.2.7 Confluent Hypergeometric Functions, Whittaker
                 Functions and Bessel Functions / 300 \\
                 8.3 Named Functions Expressed in Terms of the
                 $G$-Function / 300 \\
                 8.4 The $G$-Function Expressed as a Named Function /
                 306 \\
                 \\
                 IX. Bessel Functions and Their Integrals \\
                 \\
                 9.1 Introduction / 311 \\
                 9.2 Definitions, Connecting Relations and Power Series
                 / 311 \\
                 9.3 Difference--Differential Formulas / 313 \\
                 9.4 Products of Bessel Functions / 314 \\
                 9.5 Asymptotic Expansions for Large Variable / 315 \\
                 9.6 Integrals of Bessel Functions / 315 \\
                 9.7 Expansions in Series of Chebyshev Polynomials / 316
                 \\
                 9.8 Expansions in Series of Bessel Functions / 360 \\
                 9.9 Rational Approximations / 361 \\
                 9.9.1 Introduction / 361 \\
                 9.9.2 $I_\nu(z)$, $z$ Small / 361 \\
                 9.9.3 $K_\nu(z)$, $z$ Large / 366 \\
                 9.10 Computation of Bessel Functions by Use of
                 Recurrence Formulas / 380 \\
                 9.10.1 Introduction / 380 \\
                 9.10.2 Backward Recurrence Schemata for Generating
                 $I_\nu(z)$ / 380 \\
                 9.10.3 Closed Form Expressions / 382 \\
                 9.10.4 Expressions for $J_\nu(z)$ / 389 \\
                 9.10.5 Numerical Examples / 392 \\
                 9.11 Evaluation of Bessel Functions by Application of
                 Trapezoidal Type Integration Formulas / 395 \\
                 9.12 Inequalities / 399 \\
                 9.13 Bibliographic and Numerical Data / 403 \\
                 9.13.1 References / 403 \\
                 9.13.2 Description of and References to Tables / 404
                 \\
                 9.13.3 Description of and References to Other
                 Approximations and Expansions / 410 \\
                 \\
                 X. Lommel Functions, Struve Functions, and Associated
                 Bessel Functions \\
                 \\
                 10.1 Definitions, Connecting Relations and Power Series
                 / 413 \\
                 10.2 Asymptotic Expansions / 415 \\
                 10.3 Expansions in Series of Chebyshev Polynomials and
                 Bessel Functions / 415 \\
                 10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$
                 and the Errors in These Approximations / 422 \\
                 10.5 Bibliographic and Numerical Data / 426 \\
                 10.5.1 References / 426 \\
                 10.5.2 Description of and References to Tables / 426
                 \\
                 \\
                 XI. Orthogonal Polynomials \\
                 \\
                 11.1 Introduction / 428 \\
                 11.2 Orthogonal Properties / 428 \\
                 11.3 Jacobi Polynomials / 436 \\
                 11.3.1 Expansion Formulae / 436 \\
                 11.3.2 Difference--Differential Formulae / 439 \\
                 11.3.3 Integrals / 439 \\
                 11.3.4 Expansion of $x^\rho$ in Series of Jacobi
                 Polynomials / 440 \\
                 11.3.5 Convergence Theorems for the Expansion of
                 Arbitrary Functions in Series of Jacobi Polynomials /
                 442 \\
                 11.3.6 Evaluation and Estimation of the Coefficients in
                 the Expansion of a Given Function $f(x)$ in Series of
                 Jacobi Polynomials / 443 \\
                 11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
                 453 \\
                 11.5 The Chebyshev Polynomials $T_n^*(x)$ and
                 $U_n^*(x)$ / 459 \\
                 11.6 Coefficients for Expansion of Integrals of
                 Functions in Series of Chebyshev Polynomials of the
                 First Kind / 464 \\
                 11.6.1 Introduction / 464 \\
                 11.6.2 Series of Shifted Chebyshev Polynomials / 464
                 \\
                 11.6.3 Series of Chebyshev Polynomials of Even Order /
                 468 \\
                 11.6.4 Series of Chebyshev Polynomials of Odd Order /
                 468 \\
                 11.7 Orthogonality Properties of Chebyshev Polynomials
                 with Respect to Summation / 469 \\
                 11.8 A Nesting Procedure for the Computation of
                 Expansions in Series of Functions Where the Functions
                 Satisfy a Linear Finite Difference Equation / 475 \\
                 \\
                 XII. Computation by Use of Recurrence Formulas \\
                 \\
                 12.1 Introduction / 483 \\
                 12.2 Homogeneous Difference Equations / 483 \\
                 12.3 Inhomogeneous Difference Equations / 487 \\
                 \\
                 XIII. Some Aspects of Rational and Polynomial
                 Approximations \\
                 \\
                 13.1 Introduction / 490 \\
                 13.2 Approximations in Series of Chebyshev Polynomials
                 of the First Kind / 490 \\
                 13.3 The Pad{\'e} Table / 493 \\
                 13.4 Approximation of Functions Defined by a
                 Differential Equation --- The $\tau$-Method / 495 \\
                 13.5 Approximations of Functions Defined by a Series /
                 499 \\
                 13.6 Solution of Differential Equations in Series of
                 Chebyshev Polynomials of the First Kind / 500 \\
                 \\
                 XIV. Miscellaneous Topics \\
                 \\
                 14.1 Introduction / 505 \\
                 14.2 Bernoulli Polynomials and Numbers / 505 \\
                 14.3 $D$ and $\delta$ Operators / 507 \\
                 14.4 Computation and Check of the Tables / 509 \\
                 14.5 Mathematical Constants / 512 \\
                 14.6 Late Bibliography / 516 \\
                 \\
                 Bibliography / 517 \\
                 \\
                 Notation Index / 545 \\
                 \\
                 Subject Index / 551",
}


bibtype: article
filename: fparith.bib
label: Martinson:1975:DMF
author: L. Martinson and R. Smith
title: Digital matched filtering with pipelined floating point fast Fourier transforms (FFT's)
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 23
number: 2
pages: 222--234
month: apr
monthnumber: 4
year: 1975
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: L. Martinson and R. Smith
rawtitle: Digital matched filtering with pipelined floating point fast {Fourier} transforms ({FFT}'s)
entry:
@Article{Martinson:1975:DMF,
  author =       "L. Martinson and R. Smith",
  title =        "Digital matched filtering with pipelined floating
                 point fast {Fourier} transforms ({FFT}'s)",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "23",
  number =       "2",
  pages =        "222--234",
  month =        apr,
  year =         "1975",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A special floating point arithmetic technique for fast
                 Fourier transform (FFT) processors has been developed.
                 The implementation of a high-speed pipeline FFT matched
                 filter using the method employs significantly fewer
                 components than a fixed-point \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1975:FSF
author: D. W. Matula
title: Fixed-Slash and Floating-Slash Arithmetic
crossref: IEEE:1975:SCA
pages: 90--91
year: 1975
bibdate: Wed Nov 14 17:45:51 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:45:51 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Matula.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: D. W. Matula
rawtitle: Fixed-Slash and Floating-Slash Arithmetic
abstract:
A finite precision rational number system provides for representation of a collection of rational numbers subject to limitations on numerator and denominator magnitude. In fixed-point and floating-point radix number systems, only rationals of the form $ i / beta ^j $, where $ beta $ is the base, can be realized. In contrast, a finite precision rational number system will allow representation of practically all simple fractions encountered in applications.

rawabstract:
A finite precision rational number system provides for representation of a collection of rational numbers subject to limitations on numerator and denominator magnitude. In fixed-point and floating-point radix number systems, only rationals of the form $ i / \beta^j $, where $ \beta $ is the base, can be realized. In contrast, a finite precision rational number system will allow representation of practically all simple fractions encountered in applications.

entry:
@InProceedings{Matula:1975:FSF,
  author =       "D. W. Matula",
  title =        "Fixed-Slash and Floating-Slash Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "90--91",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:45:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Matula.pdf",
  abstract =     "A finite precision rational number system provides for
                 representation of a collection of rational numbers
                 subject to limitations on numerator and denominator
                 magnitude. In fixed-point and floating-point radix
                 number systems, only rationals of the form $ i /
                 \beta^j $, where $ \beta $ is the base, can be
                 realized. In contrast, a finite precision rational
                 number system will allow representation of practically
                 all simple fractions encountered in applications.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: McDonald:1975:TCQ
author: T. G. McDonald and R. K. Guha
title: The Two's Complement Quasi-Serial Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 12
pages: 1233--1235
month: dec
monthnumber: 12
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224170
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:59 MDT 2011
bibtimestamp: 2011.07.12 07:57:59 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672763
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. G. McDonald and R. K. Guha
rawtitle: The Two's Complement Quasi-Serial Multiplier
entry:
@Article{McDonald:1975:TCQ,
  author =       "T. G. McDonald and R. K. Guha",
  title =        "The Two's Complement Quasi-Serial Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "12",
  pages =        "1233--1235",
  month =        dec,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224170",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672763",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Meo:1975:ANT
author: A. R. Meo
title: Arithmetic Networks and Their Minimization Using a New Line of Elementary Units
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 3
pages: 258--280
month: mar
monthnumber: 3
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224207
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:51 MDT 2011
bibtimestamp: 2011.07.12 07:57:51 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672800
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. R. Meo
rawtitle: Arithmetic Networks and Their Minimization Using a New Line of Elementary Units
entry:
@Article{Meo:1975:ANT,
  author =       "A. R. Meo",
  title =        "Arithmetic Networks and Their Minimization Using a New
                 Line of Elementary Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "258--280",
  month =        mar,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224207",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672800",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Miller:1975:SRA
author: Webb Miller
title: Software for Roundoff Analysis
journal: j-TOMS
volume: 1
number: 2
pages: 108--128
month: jun
monthnumber: 6
year: 1975
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355637.355639
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65G05
MRnumber: 53 \#9622
bibdate: Fri Aug 26 23:44:16 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.26 23:44:16 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
reviewer: James H. Wilkinson
rawauthor: Webb Miller
rawtitle: Software for Roundoff Analysis
entry:
@Article{Miller:1975:SRA,
  author =       "Webb Miller",
  title =        "Software for Roundoff Analysis",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "108--128",
  month =        jun,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355637.355639",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05",
  MRnumber =     "53 \#9622",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "James H. Wilkinson",
}


bibtype: article
filename: fparith.bib
label: Nance:1975:IFR
author: Richard E. Nance and Claude Overstreet, Jr.
title: Implementation of Fortran Random Number Generators on Computers with One's Complement Arithmetic
journal: j-J-STAT-COMPUT-SIMUL
volume: 4
number: 3
pages: 235--243
year: 1975
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949657508810126
ISSNL: 0094-9655 OR 00949655
bibdate: Thu Jan 05 10:58:18 2012
bibtimestamp: 2012.01.05 10:58:18 ???
URL: http://www.tandfonline.com/doi/abs/10.1080/00949657508810126
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
onlinedate: 20 Mar 2007
rawauthor: Richard E. Nance and Claude {Overstreet, Jr.}
rawtitle: Implementation of {Fortran} Random Number Generators on Computers with One's Complement Arithmetic
ISSN:
0094-9655 (print), 1026-7778 (electronic), 1563-5163 OR 00949655 (print), 10267778 (electronic), 15635163

bibsource:
https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib

abstract:
Random number generators can be programmed in FORTRAN using several methods on 1's complement machines. We have presented several methods for the SRU 1107--1108 and CDC 6000 and CYBER series, the two most popular that utilize 1's complement arithmetic. We believe the logical mask method to be the most efficient technique based on execution time on both machines. This method requires only a little more than one-half the time of the signed residue method on the SRU 1107--1108 and a little more than two thirds the time of the unsigned residue method on the CDC 6000--CYBER. A fast composite generator in FORTRAN uses the logical mask method combined with the FLD function to implement the table approach of MacLaren and Marsaglia (1965). This generator proves to be more than twice as fast as a previous one for the SRU 1108, Marsaglia and Bray (1968)

rawabstract:
Random number generators can be programmed in FORTRAN using several methods on 1's complement machines. We have presented several methods for the SRU 1107--1108 and CDC 6000 and CYBER series, the two most popular that utilize 1's complement arithmetic. We believe the logical mask method to be the most efficient technique based on execution time on both machines. This method requires only a little more than one-half the time of the signed residue method on the SRU 1107--1108 and a little more than two thirds the time of the unsigned residue method on the CDC 6000--CYBER. A fast composite generator in FORTRAN uses the logical mask method combined with the FLD function to implement the table approach of MacLaren and Marsaglia (1965). This generator proves to be more than twice as fast as a previous one for the SRU 1108, Marsaglia and Bray (1968)

entry:
@Article{Nance:1975:IFR,
  author =       "Richard E. Nance and Claude {Overstreet, Jr.}",
  title =        "Implementation of {Fortran} Random Number Generators
                 on Computers with One's Complement Arithmetic",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "4",
  number =       "3",
  pages =        "235--243",
  month =        "????",
  year =         "1975",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657508810126",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Thu Jan 05 10:58:18 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00949657508810126",
  abstract =     "Random number generators can be programmed in FORTRAN
                 using several methods on 1's complement machines. We
                 have presented several methods for the SRU 1107--1108
                 and CDC 6000 and CYBER series, the two most popular
                 that utilize 1's complement arithmetic. We believe the
                 logical mask method to be the most efficient technique
                 based on execution time on both machines. This method
                 requires only a little more than one-half the time of
                 the signed residue method on the SRU 1107--1108 and a
                 little more than two thirds the time of the unsigned
                 residue method on the CDC 6000--CYBER. A fast composite
                 generator in FORTRAN uses the logical mask method
                 combined with the FLD function to implement the table
                 approach of MacLaren and Marsaglia (1965). This
                 generator proves to be more than twice as fast as a
                 previous one for the SRU 1108, Marsaglia and Bray
                 (1968)",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
  onlinedate =   "20 Mar 2007",
}


bibtype: article
filename: fparith.bib
label: Nelson:1975:PPF
author: James M. Nelson and Charles E. Cohn
title: Parallel Processing in FORTRAN with Floating-Point Hardware
journal: j-SPE
volume: 5
number: 1
pages: 65--68
month: jan
monthnumber: 1
year: 1975
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Sat May 31 13:36:16 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/spe.bib
bibtimestamp: 1997.05.31 13:36:16 MDT
fjournal: Software---Practice and Experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: James M. Nelson and Charles E. Cohn
rawtitle: Parallel Processing in {FORTRAN} with Floating-Point Hardware
entry:
@Article{Nelson:1975:PPF,
  author =       "James M. Nelson and Charles E. Cohn",
  title =        "Parallel Processing in {FORTRAN} with Floating-Point
                 Hardware",
  journal =      j-SPE,
  volume =       "5",
  number =       "1",
  pages =        "65--68",
  month =        jan # "\slash " # mar,
  year =         "1975",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}


bibtype: article
filename: fparith.bib
label: Newbery:1975:PES
author: A. C. R. Newbery
title: Polynomial Evaluation Schemes
journal: j-MATH-COMPUT
volume: 29
number: 132
pages: 1046--1050
month: oct
monthnumber: 10
year: 1975
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.
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Department of Computer Sci., University of Kentucky, Lexington, KY, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: A. C. R. Newbery
rawtitle: Polynomial Evaluation Schemes
keywords:
floating; function evaluation; point arithmetic; polynomial evaluation algorithm; polynomials; round off error

entry:
@Article{Newbery:1975:PES,
  author =       "A. C. R. Newbery",
  title =        "Polynomial Evaluation Schemes",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "132",
  pages =        "1046--1050",
  month =        oct,
  year =         "1975",
  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.",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Department of Computer Sci., University of Kentucky,
                 Lexington, KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "floating; function evaluation; point arithmetic;
                 polynomial evaluation algorithm; polynomials; round off
                 error",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: manual
filename: fparith.bib
label: NSC:1975:IFP
author: National Semiconductor Corporation
title: IMP-16F / 400 floating point firmware technical description
type: Publication - National Semiconductor Corporation no. 4200072A
organization: National Semiconductor Corporation
address: Santa Clara, CA, USA
pages: 16
year: 1975
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: Microprocessors --- Handbooks, manuals, etc.; Microprogramming --- Handbooks, manuals, etc.
remark: At head of title: Integrated microprocessor-16.
acknowledgement: ack-nhfb
rawauthor: {National Semiconductor Corporation}
rawtitle: {IMP-16F\slash 400} floating point firmware technical description
entry:
@Manual{NSC:1975:IFP,
  author =       "{National Semiconductor Corporation}",
  title =        "{IMP-16F\slash 400} floating point firmware technical
                 description",
  type =         "Publication - National Semiconductor Corporation no.
                 4200072A",
  organization = "National Semiconductor Corporation",
  address =      "Santa Clara, CA, USA",
  pages =        "16",
  year =         "1975",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microprocessors --- Handbooks, manuals, etc.;
                 Microprogramming --- Handbooks, manuals, etc.",
  remark =       "At head of title: Integrated microprocessor-16.",
}


bibtype: article
filename: fparith.bib
label: OKeefe:1975:NFB
author: K. H. O'Keefe
title: A Note on Fast Base Extension for Residue Number Systems with Three Moduli
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 11
pages: 1132--1133
month: nov
monthnumber: 11
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1975.224147
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:58 MDT 2011
bibtimestamp: 2011.07.12 07:57:58 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: K. H. O'Keefe
rawtitle: A Note on Fast Base Extension for Residue Number Systems with Three Moduli
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672740; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35091

entry:
@Article{OKeefe:1975:NFB,
  author =       "K. H. O'Keefe",
  title =        "A Note on Fast Base Extension for Residue Number
                 Systems with Three Moduli",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "11",
  pages =        "1132--1133",
  month =        nov,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1975.224147",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672740;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35091",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "An algorithm is given for the base-extension (BE)
                 computation in residue number systems that requires the
                 standard four steps (for systems with three moduli) but
                 which saves hardware. Furthermore, for the particular
                 moduli m-1, m, and m+1 it is \ldots{}",
}


bibtype: incollection
filename: fparith.bib
label: Phillips:1975:BC
author: E. William Phillips
title: Binary Calculation
crossref: Randell:1975:ODC
pages: 293--304
year: 1975
bibdate: Wed Oct 13 09:51:37 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 09:51:37 ???
acknowledgement: ack-nhfb
rawauthor: E. William Phillips
rawtitle: Binary Calculation
remark:
The 1936 epigraph credited to this author in cite [Chapter 7]Coonen:1984:CPS says: ``The ultimate aim is to persuade all of the civilized world to abandon the decimal numeration and to use octonal in its place; to discontinue counting in tens and to count in eights instead. However, it seems unlikely that the whole civilized world will be persuaded to complete this change during the next twelve months, having previously declined similar invitations.''

entry:
@InCollection{Phillips:1975:BC,
  author =       "E. William Phillips",
  title =        "Binary Calculation",
  crossref =     "Randell:1975:ODC",
  pages =        "293--304",
  year =         "1975",
  bibdate =      "Wed Oct 13 09:51:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "The 1936 epigraph credited to this author in
                 \cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
                 aim is to persuade all of the civilized world to
                 abandon the decimal numeration and to use octonal in
                 its place; to discontinue counting in tens and to count
                 in eights instead. However, it seems unlikely that the
                 whole civilized world will be persuaded to complete
                 this change during the next twelve months, having
                 previously declined similar invitations.''",
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1975:TIS
author: T. R. N. Rao and D. W. Matula
title: The Third IEEE Symposium on Computer Arithmetic: Foreword
crossref: IEEE:1975:SCA
pages: v--v
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: T. R. N. Rao and D. W. Matula
rawtitle: The {Third IEEE Symposium on Computer Arithmetic}: Foreword
URL:
http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_contents.pdf; http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_foreword.pdf; http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_preface.pdf

entry:
@InProceedings{Rao:1975:TIS,
  author =       "T. R. N. Rao and D. W. Matula",
  title =        "The {Third IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "IEEE:1975:SCA",
  pages =        "v--v",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Reiser:1975:EDF
author: John F. Reiser and Donald E. Knuth
title: Evading the Drift in Floating-Point Addition
journal: j-INFO-PROC-LETT
volume: 3
number: 3
pages: 84--87
month: jan
monthnumber: 1
year: 1975
CODEN: IFPLAT
DOI: https://doi.org/10.1016/0020-0190(75)90022-8
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Sun Dec 04 12:21:37 1994
bibtimestamp: 1994.12.04 12:21:37 ???
note: See erratum cite Reiser:1975:EED.
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: John F. Reiser and Donald E. Knuth
rawnote: See erratum \cite{Reiser:1975:EED}.
rawtitle: Evading the Drift in Floating-Point Addition
bibsource:
Compendex database; 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/infoproc1970.bib

remark:
From p. 87: ``Actually Tannery's and Scarborough's contradictory arguments [round-up and round-to-even] are both incorrect; for example, the logarithmic law of distribution of leading digits [3] [Benford's Law] implies that the least significant digit of a floating-point number will be odd slightly less often than it will be even, assuming that $b$ is even and $ p > 1$. The real justification for stable rounding is that it eliminates drift.''

entry:
@Article{Reiser:1975:EDF,
  author =       "John F. Reiser and Donald E. Knuth",
  title =        "Evading the Drift in Floating-Point Addition",
  journal =      j-INFO-PROC-LETT,
  volume =       "3",
  number =       "3",
  pages =        "84--87",
  month =        jan,
  year =         "1975",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/0020-0190(75)90022-8",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sun Dec 04 12:21:37 1994",
  bibsource =    "Compendex database;
                 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/infoproc1970.bib",
  note =         "See erratum \cite{Reiser:1975:EED}.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  remark =       "From p. 87: ``Actually Tannery's and Scarborough's
                 contradictory arguments [round-up and round-to-even]
                 are both incorrect; for example, the logarithmic law of
                 distribution of leading digits [3] [Benford's Law]
                 implies that the least significant digit of a
                 floating-point number will be odd slightly less often
                 than it will be even, assuming that $b$ is even and $ p
                 > 1$. The real justification for stable rounding is
                 that it eliminates drift.''",
}


bibtype: article
filename: fparith.bib
label: Reiser:1975:EED
author: John F. Reiser and Donald E. Knuth
title: Erratum: ``Evading the Drift in Floating-Point Addition''
journal: j-INFO-PROC-LETT
volume: 3
number: 5
pages: 164--164
month: may
monthnumber: 5
year: 1975
CODEN: IFPLAT
DOI: https://doi.org/10.1016/0020-0190(75)90031-9
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Sun Dec 04 12:21:42 1994
bibtimestamp: 1994.12.04 12:21:42 ???
note: See cite Reiser:1975:EDF.
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: John F. Reiser and Donald E. Knuth
rawnote: See \cite{Reiser:1975:EDF}.
rawtitle: Erratum: {``Evading the Drift in Floating-Point Addition''}
bibsource:
Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Reiser:1975:EED,
  author =       "John F. Reiser and Donald E. Knuth",
  title =        "Erratum: {``Evading the Drift in Floating-Point
                 Addition''}",
  journal =      j-INFO-PROC-LETT,
  volume =       "3",
  number =       "5",
  pages =        "164--164",
  month =        may,
  year =         "1975",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/0020-0190(75)90031-9",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sun Dec 04 12:21:42 1994",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Reiser:1975:EDF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: article
filename: fparith.bib
label: Rokne:1975:ACI
author: J. Rokne and P. Lancaster
title: Algorithm 86. Complex Interval Arithmetic
journal: j-COMP-J
volume: 18
number: 1
pages: 83--85
month: feb
monthnumber: 2
year: 1975
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Mar 25 13:51:56 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.03.25 13:51:56 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods); C7310 (Mathematics computing)
corpsource: Univ. Calgary, Alta., Canada
journalURL: http://comjnl.oxfordjournals.org/
treatment: A Application; T Theoretical or Mathematical
rawauthor: J. Rokne and P. Lancaster
rawtitle: Algorithm 86. Complex Interval Arithmetic
keywords:
algorithm; complex interval arithmetic; digital arithmetic; floating point; real numbers; subroutines

entry:
@Article{Rokne:1975:ACI,
  author =       "J. Rokne and P. Lancaster",
  title =        "Algorithm 86. Complex Interval Arithmetic",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "1",
  pages =        "83--85",
  month =        feb,
  year =         "1975",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C7310 (Mathematics
                 computing)",
  corpsource =   "Univ. Calgary, Alta., Canada",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "algorithm; complex interval arithmetic; digital
                 arithmetic; floating point; real numbers; subroutines",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Rubinfield:1975:PMB
author: L. P. Rubinfield
title: A Proof of the Modified Booth's Algorithm for Multiplication
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 10
pages: 1014--1015
month: oct
monthnumber: 10
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224114
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:57 MDT 2011
bibtimestamp: 2011.07.12 07:57:57 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672707
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. P. Rubinfield
rawtitle: A Proof of the Modified {Booth}'s Algorithm for Multiplication
entry:
@Article{Rubinfield:1975:PMB,
  author =       "L. P. Rubinfield",
  title =        "A Proof of the Modified {Booth}'s Algorithm for
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "10",
  pages =        "1014--1015",
  month =        oct,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224114",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672707",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Senzig:1975:CA
author: Don Senzig
title: Calculator Algorithms
journal: IEEE Compcon Reader Digest
pages: 139--141
year: 1975
bibdate: Fri Nov 28 19:19:40 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 19:19:40 ???
note: IEEE catalog number 75CH0920-9C.
acknowledgement: ack-mfc
rawauthor: Don Senzig
rawnote: IEEE catalog number 75CH0920-9C.
rawtitle: Calculator Algorithms
abstract:
This paper discusses algorithms for generating the trigonometric, exponential, and hyperbolic functions and their inverses. No invention is claimed here. The algorithm for logarithm was used by Briggs in compiling his table of logarithms in the 1600's. Other earlier references are [cited]. The development presented here is, perhaps, more direct than those given in the above references but leads to the same result.

rawabstract:
This paper discusses algorithms for generating the trigonometric, exponential, and hyperbolic functions and their inverses. No invention is claimed here. The algorithm for logarithm was used by Briggs in compiling his table of logarithms in the 1600's. Other earlier references are [cited]. The development presented here is, perhaps, more direct than those given in the above references but leads to the same result.

entry:
@Article{Senzig:1975:CA,
  author =       "Don Senzig",
  title =        "Calculator Algorithms",
  journal =      "IEEE Compcon Reader Digest",
  pages =        "139--141",
  year =         "1975",
  bibdate =      "Fri Nov 28 19:19:40 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 75CH0920-9C.",
  abstract =     "This paper discusses algorithms for generating the
                 trigonometric, exponential, and hyperbolic functions
                 and their inverses. No invention is claimed here. The
                 algorithm for logarithm was used by Briggs in compiling
                 his table of logarithms in the 1600's. Other earlier
                 references are [cited]. The development presented here
                 is, perhaps, more direct than those given in the above
                 references but leads to the same result.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Shimizu:1975:REF
author: Tatsujiro Shimizu and Tsunemichi Oohashi
title: Rounding errors in floating point addition
journal: TRU Math.
volume: 11
pages: 41--50
year: 1975
MRclass: 65G05
MRnumber: 55 4646
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: R. P. Brent
rawauthor: Tatsujiro Shimizu and Tsunemichi Oohashi
rawtitle: Rounding errors in floating point addition
entry:
@Article{Shimizu:1975:REF,
  author =       "Tatsujiro Shimizu and Tsunemichi Oohashi",
  title =        "Rounding errors in floating point addition",
  journal =      "TRU Math.",
  volume =       "11",
  pages =        "41--50",
  year =         "1975",
  MRclass =      "65G05",
  MRnumber =     "55 4646",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "R. P. Brent",
}


bibtype: inproceedings
filename: fparith.bib
label: Shriver:1975:BCA
author: B. D. Shriver and E. K. Reuter
title: A Bibliography on Computer Arithmetic
crossref: IEEE:1975:SCA
pages: 241--249
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Biography.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: B. D. Shriver and E. K. Reuter
rawtitle: A Bibliography on Computer Arithmetic
abstract:
This bibliography on computer arithmetic uses, by and large, the format and abbreviations employed by Computing Reviews. It is presented in alphabetical order only and not by individual topics. The topics included, however, span the abstract and implementation problems associated with finite precision computer arithmetic.

rawabstract:
This bibliography on computer arithmetic uses, by and large, the format and abbreviations employed by Computing Reviews. It is presented in alphabetical order only and not by individual topics. The topics included, however, span the abstract and implementation problems associated with finite precision computer arithmetic.

entry:
@InProceedings{Shriver:1975:BCA,
  author =       "B. D. Shriver and E. K. Reuter",
  title =        "A Bibliography on Computer Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "241--249",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Biography.pdf",
  abstract =     "This bibliography on computer arithmetic uses, by and
                 large, the format and abbreviations employed by
                 Computing Reviews. It is presented in alphabetical
                 order only and not by individual topics. The topics
                 included, however, span the abstract and implementation
                 problems associated with finite precision computer
                 arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Shriver:1975:UUN
author: Bruce D. Shriver and Peter Kornerup
title: The UNRAU --- a Unified Numeric Representation Arithmetic Unit
crossref: IEEE:1975:SCA
pages: 179--184
year: 1975
bibdate: Wed Nov 14 17:46:23 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:46:23 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Shriver.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Bruce D. Shriver and Peter Kornerup
rawtitle: The {UNRAU} --- a {Unified Numeric Representation Arithmetic Unit}
abstract:
A companion paper entitled, ``A Unified Numeric Data Type in Pascal'', proposes the substitution of the standard data type em real of the language Pascal with a unified data representation termed em numeric. The em numeric data type can represent a variety of arithmetic operands such as integers, normalized floating point numbers, and centered-radius intervals.par This paper describes an arithmetic unit which is capable of executing the standard arithmetic operations (addition, subtraction, multiplication, and division) on pairs of operands specified to be of the em numeric data type. This arithmetic unit, called the UNRAU --- Unified Numeric Representation Arithmetic Unit, supports operations on operands externally represented as 5-tuples $ (t, a, e, f, r) $. The UNRAU provides for automatic conversion among the various data types and can also be used to perform an explicit conversion on a single operand.par It is intended to implement the UNRAU on a dynamically microprogrammable microprocessor to determine what host facilities are required to efficiently realize such an arithmetic unit and to experiment with the high level language support of such a unit.

rawabstract:
A companion paper entitled, ``A Unified Numeric Data Type in Pascal'', proposes the substitution of the standard data type {\em real\/} of the language Pascal with a unified data representation termed {\em numeric}. The {\em numeric\/} data type can represent a variety of arithmetic operands such as integers, normalized floating point numbers, and centered-radius intervals.\par This paper describes an arithmetic unit which is capable of executing the standard arithmetic operations (addition, subtraction, multiplication, and division) on pairs of operands specified to be of the {\em numeric\/} data type. This arithmetic unit, called the UNRAU --- Unified Numeric Representation Arithmetic Unit, supports operations on operands externally represented as 5-tuples $ (t, a, e, f, r) $. The UNRAU provides for automatic conversion among the various data types and can also be used to perform an explicit conversion on a single operand.\par It is intended to implement the UNRAU on a dynamically microprogrammable microprocessor to determine what host facilities are required to efficiently realize such an arithmetic unit and to experiment with the high level language support of such a unit.

entry:
@InProceedings{Shriver:1975:UUN,
  author =       "Bruce D. Shriver and Peter Kornerup",
  title =        "The {UNRAU} --- a {Unified Numeric Representation
                 Arithmetic Unit}",
  crossref =     "IEEE:1975:SCA",
  pages =        "179--184",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:46:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Shriver.pdf",
  abstract =     "A companion paper entitled, ``A Unified Numeric Data
                 Type in Pascal'', proposes the substitution of the
                 standard data type {\em real\/} of the language Pascal
                 with a unified data representation termed {\em
                 numeric}. The {\em numeric\/} data type can represent a
                 variety of arithmetic operands such as integers,
                 normalized floating point numbers, and centered-radius
                 intervals.\par

                 This paper describes an arithmetic unit which is
                 capable of executing the standard arithmetic operations
                 (addition, subtraction, multiplication, and division)
                 on pairs of operands specified to be of the {\em
                 numeric\/} data type. This arithmetic unit, called the
                 UNRAU --- Unified Numeric Representation Arithmetic
                 Unit, supports operations on operands externally
                 represented as 5-tuples $ (t, a, e, f, r) $. The UNRAU
                 provides for automatic conversion among the various
                 data types and can also be used to perform an explicit
                 conversion on a single operand.\par

                 It is intended to implement the UNRAU on a dynamically
                 microprogrammable microprocessor to determine what host
                 facilities are required to efficiently realize such an
                 arithmetic unit and to experiment with the high level
                 language support of such a unit.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Smith:1975:CPC
author: Alan Jay Smith
title: Comments on a paper by T. C. Chen and I. T. Ho
journal: j-CACM
volume: 18
number: 8
pages: 463--463
month: aug
monthnumber: 8
year: 1975
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:22:40 MST 2001
bibtimestamp: 2001.01.22 07:22:40 MST
note: See cite Chen:1975:SER.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C6130 (Data handling techniques)
corpsource: University of California, Berkeley, CA, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: G General Review; T Theoretical or Mathematical
rawauthor: Alan Jay Smith
rawnote: See \cite{Chen:1975:SER}.
rawtitle: Comments on a paper by {T. C. Chen} and {I. T. Ho}
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Smith75a; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
advantages; alternatives; binary coded decimal; codes; coding; compression of numbers; data handling; decimal data; decimal floating-point arithmetic; decoding; deletions; Huffman codes; insertions; permutations; storage efficient representation; variable length codes

entry:
@Article{Smith:1975:CPC,
  author =       "Alan Jay Smith",
  title =        "Comments on a paper by {T. C. Chen} and {I. T. Ho}",
  journal =      j-CACM,
  volume =       "18",
  number =       "8",
  pages =        "463--463",
  month =        aug,
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:22:40 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Smith75a;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Chen:1975:SER}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6130 (Data handling techniques)",
  corpsource =   "University of California, Berkeley, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "advantages; alternatives; binary coded decimal; codes;
                 coding; compression of numbers; data handling; decimal
                 data; decimal floating-point arithmetic; decoding;
                 deletions; Huffman codes; insertions; permutations;
                 storage efficient representation; variable length
                 codes",
  oldlabel =     "Smith75a",
  treatment =    "G General Review; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Smith75a",
}


bibtype: article
filename: fparith.bib
label: Smith:1975:SCO
author: Cyril Stanley Smith
title: A Seventeenth-Century Octonary Arithmetic
journal: j-ISIS
volume: 66
number: 3
pages: 390--394
month: sep
monthnumber: 9
year: 1975
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:29:19 MDT 2013
bibtimestamp: 2013.07.30 21:29:19 MDT
URL: http://www.jstor.org/stable/228846
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: Cyril Stanley Smith
rawtitle: A {Seventeenth-Century} Octonary Arithmetic
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302314; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1970.bib

entry:
@Article{Smith:1975:SCO,
  author =       "Cyril Stanley Smith",
  title =        "A {Seventeenth-Century} Octonary Arithmetic",
  journal =      j-ISIS,
  volume =       "66",
  number =       "3",
  pages =        "390--394",
  month =        sep,
  year =         "1975",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:29:19 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302314;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
  URL =          "http://www.jstor.org/stable/228846",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: book
filename: fparith.bib
label: Smith:1975:SAP
author: Jon M. Smith
title: Scientific Analysis on the Pocket Calculator
publisher: pub-Wiley
address: pub-Wiley:adr
pages: xii + 380
year: 1975
ISBN: 0-471-79997-1 OR 0471799971
ISBN13: 978-0-471-79997-9 OR 9780471799979
LCCN: QA75 .S555
bibdate: Wed Jun 12 16:56:02 2024
bibtimestamp: 2024.06.12 16:56:02 ???
acknowledgement: ack-nhfb
rawauthor: Jon M. Smith
rawtitle: Scientific Analysis on the Pocket Calculator
bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

TOC:
Part I: Introduction to Pocket Calculator Analysis 1: The Pocket Calculator / 3 2: Difference Tables, Data Analysis, and Function Evaluation / 53 Part II: Numerical Evaluation of Functions on the Pocket Calculator 3: Elementary Analysis with the Pocket Calculator / 81 4: Numerical Evaluation of Advanced Functions / 114 Part III: Advanced Analysis on the Pocket Calculator 5: Fourier Analysis / 139 6: Numerical Integration / 154 7: Linear Systems Simulation / 180 8: Chebyshev and Rational Polynomial Approximations for Analytic Substitution / 198 9: Determining the Roots of a Function / 224 10: Statistics and Probability / 242 Part IV: The Programmable Pocket Calculator 11: The Programmable Pocket Calculator / 283 12: Optimization / 300 Appendix 1: Some Tricks of the Pocket Calculator Trade / 323 Appendix 2: Matrix Analysis on the Pocket Calculator / 333 Appendix 3: Complex Numbers and Functions / 336 Appendix 4: Key Stroke Sequences for Complex Variable Analysis and Hyperbolic Inverse Functions / 340 Index

rawTOC:
Part I: Introduction to Pocket Calculator Analysis \\ 1: The Pocket Calculator / 3 \\ 2: Difference Tables, Data Analysis, and Function Evaluation / 53 \\ Part II: Numerical Evaluation of Functions on the Pocket Calculator \\ 3: Elementary Analysis with the Pocket Calculator / 81 \\ 4: Numerical Evaluation of Advanced Functions / 114 \\ Part III: Advanced Analysis on the Pocket Calculator \\ 5: Fourier Analysis / 139 \\ 6: Numerical Integration / 154 \\ 7: Linear Systems Simulation / 180 \\ 8: Chebyshev and Rational Polynomial Approximations for Analytic Substitution / 198 \\ 9: Determining the Roots of a Function / 224 \\ 10: Statistics and Probability / 242 \\ Part IV: The Programmable Pocket Calculator \\ 11: The Programmable Pocket Calculator / 283 \\ 12: Optimization / 300 \\ Appendix 1: Some Tricks of the Pocket Calculator Trade / 323 \\ Appendix 2: Matrix Analysis on the Pocket Calculator / 333 \\ Appendix 3: Complex Numbers and Functions / 336 \\ Appendix 4: Key Stroke Sequences for Complex Variable Analysis and Hyperbolic Inverse Functions / 340 \\ Index

entry:
@Book{Smith:1975:SAP,
  author =       "Jon M. Smith",
  title =        "Scientific Analysis on the Pocket Calculator",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xii + 380",
  year =         "1975",
  ISBN =         "0-471-79997-1",
  ISBN-13 =      "978-0-471-79997-9",
  LCCN =         "QA75 .S555",
  bibdate =      "Wed Jun 12 16:56:02 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I: Introduction to Pocket Calculator Analysis
                 \\
                 1: The Pocket Calculator / 3 \\
                 2: Difference Tables, Data Analysis, and Function
                 Evaluation / 53 \\
                 Part II: Numerical Evaluation of Functions on the
                 Pocket Calculator \\
                 3: Elementary Analysis with the Pocket Calculator / 81
                 \\
                 4: Numerical Evaluation of Advanced Functions / 114 \\
                 Part III: Advanced Analysis on the Pocket Calculator
                 \\
                 5: Fourier Analysis / 139 \\
                 6: Numerical Integration / 154 \\
                 7: Linear Systems Simulation / 180 \\
                 8: Chebyshev and Rational Polynomial Approximations for
                 Analytic Substitution / 198 \\
                 9: Determining the Roots of a Function / 224 \\
                 10: Statistics and Probability / 242 \\
                 Part IV: The Programmable Pocket Calculator \\
                 11: The Programmable Pocket Calculator / 283 \\
                 12: Optimization / 300 \\
                 Appendix 1: Some Tricks of the Pocket Calculator Trade
                 / 323 \\
                 Appendix 2: Matrix Analysis on the Pocket Calculator /
                 333 \\
                 Appendix 3: Complex Numbers and Functions / 336 \\
                 Appendix 4: Key Stroke Sequences for Complex Variable
                 Analysis and Hyperbolic Inverse Functions / 340 \\
                 Index",
}


bibtype: article
filename: fparith.bib
label: Soule:1975:AAB
author: Stephen Soule
title: Addition in an Arbitrary Base Without Radix Conversion
journal: j-CACM
volume: 18
number: 6
pages: 344--346
month: jun
monthnumber: 6
year: 1975
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:23:30 MST 2001
bibtimestamp: 2001.01.22 07:23:30 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods); C6130 (Data handling techniques)
corpsource: University of Calgary, Calgary, Alta., Canada
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
treatment: A Application; T Theoretical or Mathematical
rawauthor: Stephen Soule
rawtitle: Addition in an Arbitrary Base Without Radix Conversion
bibsource:
Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Theory/Seiferas/1975.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Soule75; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
This paper presents a generalization of an old programming technique; using it, one may add and subtract numbers represented in any radix, including a mixed radix, and stored one digit per byte in bytes of sufficient size. Radix conversion is unnecessary, no looping is required, and numbers may even be stored in a display (I/O) format. Applications to Cobol, MIX, and hexadecimal sums are discussed.

keywords:
add; addition; arbitrary base; arbitrary radix arithmetic; Cobol display arithmetic; computer systems programming; data handling; decimal arithmetic; decimal floating-point arithmetic; digital arithmetic; mathematical techniques --- Digital Arithmetic; MIX arithmetic; mixed radix arithmetic; numbers; programming; radix conversion; subtract; subtraction; without radix conversion

rawabstract:
This paper presents a generalization of an old programming technique; using it, one may add and subtract numbers represented in any radix, including a mixed radix, and stored one digit per byte in bytes of sufficient size. Radix conversion is unnecessary, no looping is required, and numbers may even be stored in a display (I/O) format. Applications to Cobol, MIX, and hexadecimal sums are discussed.

entry:
@Article{Soule:1975:AAB,
  author =       "Stephen Soule",
  title =        "Addition in an Arbitrary Base Without Radix
                 Conversion",
  journal =      j-CACM,
  volume =       "18",
  number =       "6",
  pages =        "344--346",
  month =        jun,
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:23:30 MST 2001",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Theory/Seiferas/1975.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Soule75;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a generalization of an old
                 programming technique; using it, one may add and
                 subtract numbers represented in any radix, including a
                 mixed radix, and stored one digit per byte in bytes of
                 sufficient size. Radix conversion is unnecessary, no
                 looping is required, and numbers may even be stored in
                 a display (I/O) format. Applications to Cobol, MIX, and
                 hexadecimal sums are discussed.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  classification = "723; 921",
  corpsource =   "University of Calgary, Calgary, Alta., Canada",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "add; addition; arbitrary base; arbitrary radix
                 arithmetic; Cobol display arithmetic; computer systems
                 programming; data handling; decimal arithmetic; decimal
                 floating-point arithmetic; digital arithmetic;
                 mathematical techniques --- Digital Arithmetic; MIX
                 arithmetic; mixed radix arithmetic; numbers;
                 programming; radix conversion; subtract; subtraction;
                 without radix conversion",
  oldlabel =     "Soule75",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Soule75",
}


bibtype: inproceedings
filename: fparith.bib
label: Stephenson:1975:CSP
author: Charles Stephenson
title: Case Study of the Pipelined Arithmetic Unit for the TI Advanced Scientific Computer
crossref: IEEE:1975:SCA
pages: 168--173
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Stephenson.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Charles Stephenson
rawtitle: Case Study of the Pipelined Arithmetic Unit for the {TI Advanced Scientific Computer}
abstract:
Many scientific applications today require computers which are very fast and capable of processing large amounts of data. Some advances in scientific processing have been slowed due to the lack of supercomputer capabilities which are required primarily in the area of Central Processor speed and the availability of large amounts of high speed memory. Particularly in the fields of modeling and simulation, additional speed and memory capacity are desired to allow increased resolution of the experiment. Technological developments: In such things as integrated circuits, multilayer printed circuit boards, memory speeds, and others have contributed to the ability of computer manufacturers to serve this market. In addition to these developments, however, large advances had to be realized from the standpoint of the basic computer architecture. The concept of pipelining has provided an answer to the large data execution rate required. Pipelined capabilities in the form of arithmetic units and special purpose functional units are included in machines such as the CDC 7600, IBM 360/195, CDC STAR-100, etc. The Texas Instruments Advanced Scientific Computer (ASC) uses the pipeline concept throughout the Central Processor and carries the concept throughout the Central Processor and carries the concept further to include vector instructions in response to the high execution rates required. 3

rawabstract:
Many scientific applications today require computers which are very fast and capable of processing large amounts of data. Some advances in scientific processing have been slowed due to the lack of supercomputer capabilities which are required primarily in the area of Central Processor speed and the availability of large amounts of high speed memory. Particularly in the fields of modeling and simulation, additional speed and memory capacity are desired to allow increased resolution of the experiment. Technological developments: In such things as integrated circuits, multilayer printed circuit boards, memory speeds, and others have contributed to the ability of computer manufacturers to serve this market. In addition to these developments, however, large advances had to be realized from the standpoint of the basic computer architecture. The concept of pipelining has provided an answer to the large data execution rate required. Pipelined capabilities in the form of arithmetic units and special purpose functional units are included in machines such as the CDC 7600, IBM 360/195, CDC STAR-100, etc. The Texas Instruments Advanced Scientific Computer (ASC) uses the pipeline concept throughout the Central Processor and carries the concept throughout the Central Processor and carries the concept further to include vector instructions in response to the high execution rates required. 3

entry:
@InProceedings{Stephenson:1975:CSP,
  author =       "Charles Stephenson",
  title =        "Case Study of the Pipelined Arithmetic Unit for the
                 {TI Advanced Scientific Computer}",
  crossref =     "IEEE:1975:SCA",
  pages =        "168--173",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Stephenson.pdf",
  abstract =     "Many scientific applications today require computers
                 which are very fast and capable of processing large
                 amounts of data. Some advances in scientific processing
                 have been slowed due to the lack of supercomputer
                 capabilities which are required primarily in the area
                 of Central Processor speed and the availability of
                 large amounts of high speed memory. Particularly in the
                 fields of modeling and simulation, additional speed and
                 memory capacity are desired to allow increased
                 resolution of the experiment. Technological
                 developments: In such things as integrated circuits,
                 multilayer printed circuit boards, memory speeds, and
                 others have contributed to the ability of computer
                 manufacturers to serve this market. In addition to
                 these developments, however, large advances had to be
                 realized from the standpoint of the basic computer
                 architecture. The concept of pipelining has provided an
                 answer to the large data execution rate required.
                 Pipelined capabilities in the form of arithmetic units
                 and special purpose functional units are included in
                 machines such as the CDC 7600, IBM 360/195, CDC
                 STAR-100, etc. The Texas Instruments Advanced
                 Scientific Computer (ASC) uses the pipeline concept
                 throughout the Central Processor and carries the
                 concept throughout the Central Processor and carries
                 the concept further to include vector instructions in
                 response to the high execution rates required. 3",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Sterbenz:1975:UA
author: Pat H. Sterbenz
title: Understandable Arithmetic
crossref: IEEE:1975:SCA
pages: 33--35
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Sterbenz.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Pat H. Sterbenz
rawtitle: Understandable Arithmetic
abstract:
Since the floating-point operations form the basic steps in our programs, the programmer has to understand the results that will be produced by these operations. This paper discusses operations which have been or might be implemented in the hardware. The emphasis is on making the results easy for the user to understand.

rawabstract:
Since the floating-point operations form the basic steps in our programs, the programmer has to understand the results that will be produced by these operations. This paper discusses operations which have been or might be implemented in the hardware. The emphasis is on making the results easy for the user to understand.

entry:
@InProceedings{Sterbenz:1975:UA,
  author =       "Pat H. Sterbenz",
  title =        "Understandable Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "33--35",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Sterbenz.pdf",
  abstract =     "Since the floating-point operations form the basic
                 steps in our programs, the programmer has to understand
                 the results that will be produced by these operations.
                 This paper discusses operations which have been or
                 might be implemented in the hardware. The emphasis is
                 on making the results easy for the user to
                 understand.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: book
filename: fparith.bib
label: Stone:1975:ICA
editor: Harold S. Stone and Tien Chi Chen and Michael J. Flynn and Samuel H. Fuller and others
title: Introduction to computer architecture
publisher: Science Research Associates
address: Chicago, IL, USA
pages: x + 565
year: 1975
ISBN: 0-574-18405-8 OR 0574184058
ISBN13: 978-0-574-18405-4 OR 9780574184054
LCCN: QA76.5 .I7; QA76.9.A73 I57; QA76.5 .I63; QA76.9.A73 I57 1975
bibdate: Fri Nov 9 19:22:07 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.11.09 19:22:07 MST
series: SRA computer science series
subject: Electronic digital computers
acknowledgement: ack-nhfb
raweditor: Harold S. Stone and Tien Chi Chen and Michael J. Flynn and Samuel H. Fuller and others
rawtitle: Introduction to computer architecture
entry:
@Book{Stone:1975:ICA,
  editor =       "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
                 and Samuel H. Fuller and others",
  title =        "Introduction to computer architecture",
  publisher =    "Science Research Associates",
  address =      "Chicago, IL, USA",
  pages =        "x + 565",
  year =         "1975",
  ISBN =         "0-574-18405-8",
  ISBN-13 =      "978-0-574-18405-4",
  LCCN =         "QA76.5 .I7; QA76.9.A73 I57; QA76.5 .I63; QA76.9.A73
                 I57 1975",
  bibdate =      "Fri Nov 9 19:22:07 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "SRA computer science series",
  acknowledgement = ack-nhfb,
  subject =      "Electronic digital computers",
}


bibtype: inproceedings
filename: fparith.bib
label: Svoboda:1975:SCA
author: Antonin Svoboda
title: Self-Checking Adder for Large Scale Integration
crossref: IEEE:1975:SCA
pages: 108--112
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Svoboda.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Antonin Svoboda
rawtitle: Self-Checking Adder for Large Scale Integration
abstract:
The testing of LSI chips is expensive and unsatisfactory. On the other hand there are cases (as in space ship computers) where a damaged chip must be localized and replaced. The use of self-checking chips seems to be one of several possible solutions of this problem. The theory of the structure of self-checking logical circuit is covered by literature at least at the fundamental form (see References). However, even when the design principles are supposed to be known, their application to the actual creation of a self-checking circuit of an average complexity is and will remain an art. The reason is quite simple and fundamental optimization of design criteria (engineering qualifications, performance and physical properties of components of the circuits are entities possessing different physical dimensions --- it is impossible to qualify, for instance, two circuits A, B designed for the same task by comparing their speeds and costs if A is faster than B but B is cheaper than A) will never be objective and independent of the talent or whim of the circuit designer.

rawabstract:
The testing of LSI chips is expensive and unsatisfactory. On the other hand there are cases (as in space ship computers) where a damaged chip must be localized and replaced. The use of self-checking chips seems to be one of several possible solutions of this problem. The theory of the structure of self-checking logical circuit is covered by literature at least at the fundamental form (see References). However, even when the design principles are supposed to be known, their application to the actual creation of a self-checking circuit of an average complexity is and will remain an art. The reason is quite simple and fundamental optimization of design criteria (engineering qualifications, performance and physical properties of components of the circuits are entities possessing different physical dimensions --- it is impossible to qualify, for instance, two circuits A, B designed for the same task by comparing their speeds and costs if A is faster than B but B is cheaper than A) will never be objective and independent of the talent or whim of the circuit designer.

entry:
@InProceedings{Svoboda:1975:SCA,
  author =       "Antonin Svoboda",
  title =        "Self-Checking Adder for Large Scale Integration",
  crossref =     "IEEE:1975:SCA",
  pages =        "108--112",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Svoboda.pdf",
  abstract =     "The testing of LSI chips is expensive and
                 unsatisfactory. On the other hand there are cases (as
                 in space ship computers) where a damaged chip must be
                 localized and replaced. The use of self-checking chips
                 seems to be one of several possible solutions of this
                 problem. The theory of the structure of self-checking
                 logical circuit is covered by literature at least at
                 the fundamental form (see References). However, even
                 when the design principles are supposed to be known,
                 their application to the actual creation of a
                 self-checking circuit of an average complexity is and
                 will remain an art. The reason is quite simple and
                 fundamental optimization of design criteria
                 (engineering qualifications, performance and physical
                 properties of components of the circuits are entities
                 possessing different physical dimensions --- it is
                 impossible to qualify, for instance, two circuits A, B
                 designed for the same task by comparing their speeds
                 and costs if A is faster than B but B is cheaper than
                 A) will never be objective and independent of the
                 talent or whim of the circuit designer.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Swartzlander:1975:SLN
author: E. E. Swartzlander, Jr. and A. G. Alexopoulos
title: The Sign / Logarithm Number System
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 12
pages: 1238--1242
month: dec
monthnumber: 12
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224172
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:59 MDT 2011
bibtimestamp: 2011.07.12 07:57:59 MDT
note: See cite Hongyuan:1986:CSL.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672765
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. E. {Swartzlander, Jr.} and A. G. Alexopoulos
rawnote: See \cite{Hongyuan:1986:CSL}.
rawtitle: The Sign\slash Logarithm Number System
entry:
@Article{Swartzlander:1975:SLN,
  author =       "E. E. {Swartzlander, Jr.} and A. G. Alexopoulos",
  title =        "The Sign\slash Logarithm Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "12",
  pages =        "1238--1242",
  month =        dec,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224172",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Hongyuan:1986:CSL}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672765",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Toma:1975:CLA
author: C. I. Toma
title: Cellular Logic Array for High-Speed Signed Binary Number Multiplication
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 9
pages: 932--935
month: sep
monthnumber: 9
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224340
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:57 MDT 2011
bibtimestamp: 2011.07.12 07:57:57 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672933
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. I. Toma
rawtitle: Cellular Logic Array for High-Speed Signed Binary Number Multiplication
entry:
@Article{Toma:1975:CLA,
  author =       "C. I. Toma",
  title =        "Cellular Logic Array for High-Speed Signed Binary
                 Number Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "9",
  pages =        "932--935",
  month =        sep,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224340",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672933",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Trivedi:1975:LAD
author: Kishor S. Trivedi and Milos D. Ercegovac
title: On-Line Algorithms for Division and Multiplication
crossref: IEEE:1975:SCA
pages: 161--177
year: 1975
bibdate: Fri Dec 08 10:45:59 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.12.08 10:45:59 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_2.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac
rawtitle: On-Line Algorithms for Division and Multiplication
abstract:
In this paper we are considering problems of division and multiplication in a computational environment in which all but basic arithmetic operations satisfy ``on-line'' property: to generate $ j^mbox th $ digits of the result it is necessary and sufficient to have argument(s) available up to the $ (j + delta )^mbox th $ digit, where the index difference $ delta $ is a small positive constant. Such an environment, due to its potential to perform a sequence of operations in an overlapped fashion, could conveniently speed up an arithmetic multiprocessor structure it could be useful in certain real-time applications, with inherent on-line properties. The on-line property implies a left-to-right digit-by-digit type of algorithm and consequently, a redundant representation, at least of the results. For addition and subtraction such algorithms satisfying on-line property can be easily specified. Multiplication requires a somewhat more elaborate approach and there are several possible ways of defining an on-line algorithm. However, the existence of an on-line division algorithm is not obvious and its analysis appears interesting.

rawabstract:
In this paper we are considering problems of division and multiplication in a computational environment in which all but basic arithmetic operations satisfy ``on-line'' property: to generate $ j^{\mbox {th}} $ digits of the result it is necessary and sufficient to have argument(s) available up to the $ (j + \delta)^{\mbox {th}} $ digit, where the index difference $ \delta $ is a small positive constant. Such an environment, due to its potential to perform a sequence of operations in an overlapped fashion, could conveniently speed up an arithmetic multiprocessor structure it could be useful in certain real-time applications, with inherent on-line properties. The on-line property implies a left-to-right digit-by-digit type of algorithm and consequently, a redundant representation, at least of the results. For addition and subtraction such algorithms satisfying on-line property can be easily specified. Multiplication requires a somewhat more elaborate approach and there are several possible ways of defining an on-line algorithm. However, the existence of an on-line division algorithm is not obvious and its analysis appears interesting.

entry:
@InProceedings{Trivedi:1975:LAD,
  author =       "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
  title =        "On-Line Algorithms for Division and Multiplication",
  crossref =     "IEEE:1975:SCA",
  pages =        "161--177",
  year =         "1975",
  bibdate =      "Fri Dec 08 10:45:59 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_2.pdf",
  abstract =     "In this paper we are considering problems of division
                 and multiplication in a computational environment in
                 which all but basic arithmetic operations satisfy
                 ``on-line'' property: to generate $ j^{\mbox {th}} $
                 digits of the result it is necessary and sufficient to
                 have argument(s) available up to the $ (j +
                 \delta)^{\mbox {th}} $ digit, where the index
                 difference $ \delta $ is a small positive
                 constant.

                 Such an environment, due to its potential to perform a
                 sequence of operations in an overlapped fashion, could
                 conveniently speed up an arithmetic multiprocessor
                 structure it could be useful in certain real-time
                 applications, with inherent on-line properties. The
                 on-line property implies a left-to-right digit-by-digit
                 type of algorithm and consequently, a redundant
                 representation, at least of the results. For addition
                 and subtraction such algorithms satisfying on-line
                 property can be easily specified. Multiplication
                 requires a somewhat more elaborate approach and there
                 are several possible ways of defining an on-line
                 algorithm. However, the existence of an on-line
                 division algorithm is not obvious and its analysis
                 appears interesting.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Trivedi:1975:UCF
author: Kishor S. Trivedi
title: On the Use of Continued Fractions for Digital Computer Arithmetic
crossref: IEEE:1975:SCA
pages: 137--146
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_1.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Kishor S. Trivedi
rawtitle: On the Use of Continued Fractions for Digital Computer Arithmetic
abstract:
Recently, there has been some interest in the use of continued fractions for digital hardware calculations. We require that the coefficients of the continued fractions be integral powers of two. As a result well known continued fraction expansions of functions cannot be used. Methods of expansion of a large number of functions are presented.par We show that the problem of selection of coefficients of the continued fractions does not have practical solution in most of the cases we have considered. We conjecture that the solution of a polynomial equation is the only problem that can be solved in our formulation.

rawabstract:
Recently, there has been some interest in the use of continued fractions for digital hardware calculations. We require that the coefficients of the continued fractions be integral powers of two. As a result well known continued fraction expansions of functions cannot be used. Methods of expansion of a large number of functions are presented.\par We show that the problem of selection of coefficients of the continued fractions does not have practical solution in most of the cases we have considered. We conjecture that the solution of a polynomial equation is the only problem that can be solved in our formulation.

entry:
@InProceedings{Trivedi:1975:UCF,
  author =       "Kishor S. Trivedi",
  title =        "On the Use of Continued Fractions for Digital Computer
                 Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "137--146",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_1.pdf",
  abstract =     "Recently, there has been some interest in the use of
                 continued fractions for digital hardware calculations.
                 We require that the coefficients of the continued
                 fractions be integral powers of two. As a result well
                 known continued fraction expansions of functions cannot
                 be used. Methods of expansion of a large number of
                 functions are presented.\par

                 We show that the problem of selection of coefficients
                 of the continued fractions does not have practical
                 solution in most of the cases we have considered. We
                 conjecture that the solution of a polynomial equation
                 is the only problem that can be solved in our
                 formulation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: mastersthesis
filename: fparith.bib
label: Tzaferos:1975:EBD
author: Konstantina Tzaferos
type: Thesis (M.S.)
school: California State University, Chico
address: Chico, CA, USA
pages: vi + 43
year: 1975
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 --- Programming.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Konstantina Tzaferos
title:
Error bounds due to index of significance specifications in floating-point operations with encoded mantissa lengths

rawtitle:
Error bounds due to index of significance specifications in floating-point operations with encoded mantissa lengths

entry:
@MastersThesis{Tzaferos:1975:EBD,
  author =       "Konstantina Tzaferos",
  title =        "Error bounds due to index of significance
                 specifications in floating-point operations with
                 encoded mantissa lengths",
  type =         "Thesis ({M.S.})",
  school =       "California State University, Chico",
  address =      "Chico, CA, USA",
  pages =        "vi + 43",
  year =         "1975",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.",
}


bibtype: manual
filename: fparith.bib
label: Wadsworth:1975:MLP
author: Nat Wadsworth
title: Machine Language Programming for the 8008 (and Similar Microcomputers)
organization: Scelbi Computer Consulting. Inc.
address: 1322 Rear --- Boston Post Road, Milford, CT 0646, USA
pages: 172 (chapter numbering)
year: 1975
bibdate: Fri Dec 01 15:53:00 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.01 15:53:00 ???
URL: http://www.scelbi.com/files/docs/books/Machine%20Language%20Programming%20For%20The%208008.pdf
keywords: floating-point arithmetic; multiple-precision arithmetic
acknowledgement: ack-nhfb
rawauthor: Nat Wadsworth
rawtitle: Machine Language Programming for the 8008 (and Similar Microcomputers)
remark:
Chapter 5 discusses implementation of floating-point arithmetic in software on the Intel 8008, with assembly-code routines for each operation.

entry:
@Manual{Wadsworth:1975:MLP,
  author =       "Nat Wadsworth",
  title =        "Machine Language Programming for the 8008 (and Similar
                 Microcomputers)",
  organization = "Scelbi Computer Consulting. Inc.",
  address =      "1322 Rear --- Boston Post Road, Milford, CT 0646,
                 USA",
  pages =        "172 (chapter numbering)",
  year =         "1975",
  bibdate =      "Fri Dec 01 15:53:00 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.scelbi.com/files/docs/books/Machine%20Language%20Programming%20For%20The%208008.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; multiple-precision
                 arithmetic",
  remark =       "Chapter 5 discusses implementation of floating-point
                 arithmetic in software on the Intel 8008, with
                 assembly-code routines for each operation.",
}


bibtype: article
filename: fparith.bib
label: Wakerly:1975:DUM
author: J. F. Wakerly
title: Detection of Unidirectional Multiple Errors Using Low-Cost Arithmetic Codes
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 2
pages: 210--212
month: feb
monthnumber: 2
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224187
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:37 MDT 2011
bibtimestamp: 2011.07.12 07:57:37 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672780
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. F. Wakerly
rawtitle: Detection of Unidirectional Multiple Errors Using Low-Cost Arithmetic Codes
entry:
@Article{Wakerly:1975:DUM,
  author =       "J. F. Wakerly",
  title =        "Detection of Unidirectional Multiple Errors Using
                 Low-Cost Arithmetic Codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "2",
  pages =        "210--212",
  month =        feb,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224187",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672780",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Weinberger:1975:HSZ
author: Arnold Weinberger
title: High-Speed Zero-Sum Detection
crossref: IEEE:1975:SCA
pages: 200--207
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Weinberger.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Arnold Weinberger
rawtitle: High-Speed Zero-Sum Detection
abstract:
A common requirement accompanying high-speed parallel addition is the early detection that the sum is equal to zero. Normally, this condition is detected from the sum, generally at least two logic gate levels after the sum.par This paper derives expressions for detecting a zero-sum condition concurrently with or even earlier than the determination of the sum digits proper. As a result, a branch operation based on detecting a zero-sum can be executed earlier.

rawabstract:
A common requirement accompanying high-speed parallel addition is the early detection that the sum is equal to zero. Normally, this condition is detected from the sum, generally at least two logic gate levels after the sum.\par This paper derives expressions for detecting a zero-sum condition concurrently with or even earlier than the determination of the sum digits proper. As a result, a branch operation based on detecting a zero-sum can be executed earlier.

entry:
@InProceedings{Weinberger:1975:HSZ,
  author =       "Arnold Weinberger",
  title =        "High-Speed Zero-Sum Detection",
  crossref =     "IEEE:1975:SCA",
  pages =        "200--207",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Weinberger.pdf",
  abstract =     "A common requirement accompanying high-speed parallel
                 addition is the early detection that the sum is equal
                 to zero. Normally, this condition is detected from the
                 sum, generally at least two logic gate levels after the
                 sum.\par

                 This paper derives expressions for detecting a zero-sum
                 condition concurrently with or even earlier than the
                 determination of the sum digits proper. As a result, a
                 branch operation based on detecting a zero-sum can be
                 executed earlier.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Wilkinson:1975:PAA
author: J. H. Wilkinson
title: The Pilot ACE at the NPL
journal: j-RADIO-ELECTRON-ENG
volume: 45
number: 7
pages: 336--340
month: jul
monthnumber: 7
year: 1975
CODEN: RDEEA4
ISSN: 0033-7722 OR 00337722
bibdate: Mon Nov 1 18:34:26 2010
bibtimestamp: 2010.11.01 18:34:26 ???
fjournal: The Radio and Electronic Engineer
acknowledgement: ack-nhfb
rawauthor: J. H. Wilkinson
rawtitle: The {Pilot ACE at the NPL}
entry:
@Article{Wilkinson:1975:PAA,
  author =       "J. H. Wilkinson",
  title =        "The {Pilot ACE at the NPL}",
  journal =      j-RADIO-ELECTRON-ENG,
  volume =       "45",
  number =       "7",
  pages =        "336--340",
  month =        jul,
  year =         "1975",
  CODEN =        "RDEEA4",
  ISSN =         "0033-7722",
  bibdate =      "Mon Nov 1 18:34:26 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 =     "The Radio and Electronic Engineer",
}


bibtype: techreport
filename: fparith.bib
label: Wozniakowski:1975:NSI
author: H. Wozniakowski
title: Numerical stability of iterations for solution of nonlinear equations and large linear systems
institution: Department of Computer Science, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 16
year: 1975
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: H. Wozniakowski
rawtitle: Numerical stability of iterations for solution of nonlinear equations and large linear systems
keywords:
Differential equations, Nonlinear.; Floating-point arithmetic.; Iterative methods (Mathematics); Linear systems.

entry:
@TechReport{Wozniakowski:1975:NSI,
  author =       "H. Wozniakowski",
  title =        "Numerical stability of iterations for solution of
                 nonlinear equations and large linear systems",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "16",
  year =         "1975",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Differential equations, Nonlinear.; Floating-point
                 arithmetic.; Iterative methods (Mathematics); Linear
                 systems.",
}


bibtype: article
filename: fparith.bib
label: Yamashita:1975:EEF
author: Shin-ichiro Yamashita
title: On the error estimation in floating-point arithmetic
journal: Information Processing in Japan
volume: 15
pages: 64--69
year: 1975
MRclass: 65G05
MRnumber: 54 4081
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: Artenio De Matteis
rawauthor: Shin-ichiro Yamashita
rawtitle: On the error estimation in floating-point arithmetic
entry:
@Article{Yamashita:1975:EEF,
  author =       "Shin-ichiro Yamashita",
  title =        "On the error estimation in floating-point arithmetic",
  journal =      "Information Processing in Japan",
  volume =       "15",
  pages =        "64--69",
  year =         "1975",
  MRclass =      "65G05",
  MRnumber =     "54 4081",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "Artenio De Matteis",
}


bibtype: article
filename: fparith.bib
label: Yuen:1975:FPR
author: C. K. Yuen
title: On the Floating Point Representation of Complex Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 8
pages: 846--848
month: aug
monthnumber: 8
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224321
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:56 MDT 2011
bibtimestamp: 2011.07.12 07:57:56 MDT
note: See comments cite Bauer:1977:CFP.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672914
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. K. Yuen
rawnote: See comments \cite{Bauer:1977:CFP}.
rawtitle: On the Floating Point Representation of Complex Numbers
entry:
@Article{Yuen:1975:FPR,
  author =       "C. K. Yuen",
  title =        "On the Floating Point Representation of Complex
                 Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "8",
  pages =        "846--848",
  month =        aug,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224321",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Bauer:1977:CFP}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672914",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Yuen:1975:NBA
author: C. K. Yuen
title: A Note on Base $ - 2 $ Arithmetic Logic
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 3
pages: 325--329
month: mar
monthnumber: 3
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224216
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:51 MDT 2011
bibtimestamp: 2011.07.12 07:57:51 MDT
note: See comments cite Agrawal:1977:CNB.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672809
fjournal: IEEE Transactions on Computers
keywords: negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. K. Yuen
rawnote: See comments \cite{Agrawal:1977:CNB}.
rawtitle: A Note on Base $ - 2 $ Arithmetic Logic
entry:
@Article{Yuen:1975:NBA,
  author =       "C. K. Yuen",
  title =        "A Note on Base $ - 2 $ Arithmetic Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "325--329",
  month =        mar,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224216",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Agrawal:1977:CNB}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672809",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
  received =     "25 January 1974; revised 3 June 1978",
  remark-1 =     "From page 328: ``[In base $-2$,] the product of two
                 $n$-bit numbers may have $2 n + 1$ bits.''",
  remark-2 =     "From page 329: ``In general circumstances, however, it
                 is at present difficult to see base $-2$ as a strong
                 competitor against positive base arithmetic. We have
                 seen that arithmetic operations are usually more
                 complex, and fast adders are difficult to design. The
                 range of base $-2$ numbers is not symmetrical: either
                 there are twice as many positive numbers as negative
                 ones, or vice versa.''",
  remark-3 =     "The appendix on page 329 shows a simple algorithm for
                 converting between numbers with base $b$ and base
                 $-b$.",
}


bibtype: article
filename: fparith.bib
label: Asai:1976:RRC
author: H. Asai
title: A recursive radix conversion formula and its application to multiplication and division
journal: j-COMPUT-MATH-APPL
volume: 2
number: 3--4
pages: 255--265
year: 1976
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:13 MST 2017
bibtimestamp: 2017.03.01 18:51:13 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122176900183
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: H. Asai
rawtitle: A recursive radix conversion formula and its application to multiplication and division
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Asai:1976:RRC,
  author =       "H. Asai",
  title =        "A recursive radix conversion formula and its
                 application to multiplication and division",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "2",
  number =       "3--4",
  pages =        "255--265",
  month =        "????",
  year =         "1976",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:13 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122176900183",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Assmus:1976:NFS
author: E. F. Assmus, Jr. and H. F. Mattson, Jr. and Howard E. Sachar
title: A New Form of the Square Root Bound
journal: j-SIAM-J-APPL-MATH
volume: 30
number: 2
pages: 352--354
month: mar
monthnumber: 3
year: 1976
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Thu Oct 15 18:16:06 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.15 18:16:06 MDT
fjournal: SIAM Journal on Applied Mathematics
keywords: combinatorial mathematics; linear codes; square root bound; sufficient combinatorial conditions
acknowledgement: ack-nhfb
corpsource: Department of Math., Lehigh University, Bethlehem, PA, USA
journalURL: http://epubs.siam.org/siap
treatment: T Theoretical or Mathematical
rawauthor: E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and Howard E. Sachar
rawtitle: A New Form of the Square Root Bound
entry:
@Article{Assmus:1976:NFS,
  author =       "E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and
                 Howard E. Sachar",
  title =        "A New Form of the Square Root Bound",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "30",
  number =       "2",
  pages =        "352--354",
  month =        mar,
  year =         "1976",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0250 (Combinatorial mathematics); C1160
                 (Combinatorial mathematics)",
  corpsource =   "Department of Math., Lehigh University, Bethlehem, PA,
                 USA",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  keywords =     "combinatorial mathematics; linear codes; square root
                 bound; sufficient combinatorial conditions",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Baker:1976:SFB
author: P. W. Baker
title: Suggestion for a fast binary sine / cosine generator
journal: j-IEEE-TRANS-COMPUT
volume: C-25
pages: 1134--1137
month: nov
monthnumber: 11
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674566
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon May 20 05:24:26 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.20 05:24:26 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. W. Baker
rawtitle: Suggestion for a fast binary sine\slash cosine generator
entry:
@Article{Baker:1976:SFB,
  author =       "P. W. Baker",
  title =        "Suggestion for a fast binary sine\slash cosine
                 generator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "??",
  pages =        "1134--1137",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674566",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 05:24:26 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Brent:1976:FMP
author: Richard P. Brent
title: Fast Multiple-Precision Evaluation of Elementary Functions
journal: j-J-ACM
volume: 23
number: 2
pages: 242--251
month: apr
monthnumber: 4
year: 1976
CODEN: JACOAH
DOI: https://doi.org/10.1145/321941.321944
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 68A20 (68A10)
MRnumber: 52 \#16111
MRreviewer: Amnon Barak
bibdate: Wed Jan 15 18:12:53 MST 1997
bibtimestamp: 1997.01.15 18:12:53 MST
fjournal: Journal of the ACM
keywords: computational complexity; computer arithmetic; computer programming
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
journalabr: J Assoc Comput Mach
rawauthor: Richard P. Brent
rawtitle: Fast Multiple-Precision Evaluation of Elementary Functions
bibsource:
Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Let $ f(x) $ be one of the usual elementary functions ($ exp $, $ log $, $ artan $, $ sin $, $ cosh $, etc.), and let $ M(n) $ be the number of single-precision operations required to multiply $n$-bit integers. It is shown that $ f(x) $ can be evaluated, with relative error $ O(2 - n) $, in $ O(M(n)l o g (n)) $ operations as $ n rightarrow infty $, for any floating-point number $x$ (with an $n$-bit fraction) in a suitable finite interval. From the Schonhage--Strassen bound on $ M(n) $, it follows that an $n$-bit approximation to $ f(x) $ may be evaluated in $ O(n log _(n) log log (n)) $ operations. Special cases include the evaluation of constants such as $ pi $ $e$, and $ e^pi $. The algorithms depend on the theory of elliptic integrals, using the arithmetic-geometric mean iteration and ascending Landen transformations.

rawabstract:
Let $ f(x) $ be one of the usual elementary functions ($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $, etc.), and let $ M(n) $ be the number of single-precision operations required to multiply $n$-bit integers. It is shown that $ f(x) $ can be evaluated, with relative error $ O(2 - n) $, in $ O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty $, for any floating-point number $x$ (with an $n$-bit fraction) in a suitable finite interval. From the Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows that an $n$-bit approximation to $ f(x) $ may be evaluated in $ O(n \log_(n) \log \log (n)) $ operations. Special cases include the evaluation of constants such as $ \pi $ $e$, and $ e^\pi $. The algorithms depend on the theory of elliptic integrals, using the arithmetic-geometric mean iteration and ascending Landen transformations.

entry:
@Article{Brent:1976:FMP,
  author =       "Richard P. Brent",
  title =        "Fast Multiple-Precision Evaluation of Elementary
                 Functions",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "242--251",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321941.321944",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "68A20 (68A10)",
  MRnumber =     "52 \#16111",
  MRreviewer =   "Amnon Barak",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply
                 $n$-bit integers. It is shown that $ f(x) $ can be
                 evaluated, with relative error $ O(2 - n) $, in $
                 O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
                 $, for any floating-point number $x$ (with an $n$-bit
                 fraction) in a suitable finite interval. From the
                 Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
                 that an $n$-bit approximation to $ f(x) $ may be
                 evaluated in $ O(n \log_(n) \log \log (n)) $
                 operations. Special cases include the evaluation of
                 constants such as $ \pi $ $e$, and $ e^\pi $. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic-geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
  classification = "723",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "computational complexity; computer arithmetic;
                 computer programming",
}


bibtype: inproceedings
filename: fparith.bib
label: Brent:1976:MPZ
author: Richard P. Brent
title: Multiple-precision zero-finding methods and the complexity of elementary function evaluation
crossref: Traub:1976:ACC
pages: 151--176
year: 1976
MRclass: 68A20
MRnumber: 54 \#11843
MRreviewer: Claus-Peter Schnorr
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Richard P. Brent
rawtitle: Multiple-precision zero-finding methods and the complexity of elementary function evaluation
entry:
@InProceedings{Brent:1976:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  crossref =     "Traub:1976:ACC",
  pages =        "151--176",
  year =         "1976",
  MRclass =      "68A20",
  MRnumber =     "54 \#11843",
  MRreviewer =   "Claus-Peter Schnorr",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Carter:1976:ANT
author: Allison Birchard Carter
title: Applications of number theory to the avoidance of round-off in digital computer systems
type: Thesis (M.S.)
school: University of Florida
address: Gainesville, FL, USA
pages: v + 74
year: 1976
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.; Floating-point arithmetic.; Number theory.
acknowledgement: ack-nhfb
rawauthor: Allison Birchard Carter
rawtitle: Applications of number theory to the avoidance of round-off in digital computer systems
entry:
@MastersThesis{Carter:1976:ANT,
  author =       "Allison Birchard Carter",
  title =        "Applications of number theory to the avoidance of
                 round-off in digital computer systems",
  type =         "Thesis ({M.S.})",
  school =       "University of Florida",
  address =      "Gainesville, FL, USA",
  pages =        "v + 74",
  year =         "1976",
  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.; Floating-point
                 arithmetic.; Number theory.",
}


bibtype: article
filename: fparith.bib
label: Cohen:1976:EFD
author: Daniel I. A. Cohen
title: An explanation of the first digit phenomenon
journal: j-J-COMB-THEORY-A
volume: 20
number: 3
pages: 367--370
month: may
monthnumber: 5
year: 1976
CODEN: JCBTA7
ISSN: 0097-3165 (print), 1096-0899 (electronic) OR 00973165 (print), 10960899 (electronic)
ISSNL: 0097-3165 OR 00973165
bibdate: Thu Feb 15 16:29:51 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 16:29:51 ???
fjournal: Journal of Combinatorial Theory. Series A
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00973165
rawauthor: Daniel I. A. Cohen
rawtitle: An explanation of the first digit phenomenon
entry:
@Article{Cohen:1976:EFD,
  author =       "Daniel I. A. Cohen",
  title =        "An explanation of the first digit phenomenon",
  journal =      j-J-COMB-THEORY-A,
  volume =       "20",
  number =       "3",
  pages =        "367--370",
  month =        may,
  year =         "1976",
  CODEN =        "JCBTA7",
  ISSN =         "0097-3165 (print), 1096-0899 (electronic)",
  ISSN-L =       "0097-3165",
  bibdate =      "Thu Feb 15 16:29:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory. Series A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00973165",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Davies:1976:IPS
author: M. Davies and B. Dawson
title: The incrementation parameter in square root iteration
journal: j-J-INST-MATH-APPL
volume: 17
number: 2
pages: 219--223
year: 1976
CODEN: JMTAA8
ISSN: 0020-2932 OR 00202932
MRclass: 65H05
MRnumber: 55 \#9514
MRreviewer: Luciano Biasini
bibdate: Fri Apr 5 07:38:01 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.04.05 07:38:01 MST
fjournal: Journal of the Institute of Mathematics and its Applications
ZMnumber: 0319.65039
acknowledgement: ack-nhfb
journalURL: http://imamat.oxfordjournals.org/content/by/year
rawauthor: M. Davies and B. Dawson
rawtitle: The incrementation parameter in square root iteration
entry:
@Article{Davies:1976:IPS,
  author =       "M. Davies and B. Dawson",
  title =        "The incrementation parameter in square root
                 iteration",
  journal =      j-J-INST-MATH-APPL,
  volume =       "17",
  number =       "2",
  pages =        "219--223",
  year =         "1976",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  MRclass =      "65H05",
  MRnumber =     "55 \#9514",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Fri Apr 5 07:38:01 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0319.65039",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
}


bibtype: book
filename: fparith.bib
label: DEC:1976:DHM
author: Digital Equipment Corporation
title: DECsystem-10 / 20 Hardware Manual
publisher: pub-DP
address: pub-DP:adr
edition: Fourth
pages: various
month: mar
monthnumber: 3
year: 1976
bibdate: Fri Dec 08 13:03:19 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:03:19 ???
note: Also published as Stanford Artificial Intelligence Laboratory Operating Note 75, November 1976.
acknowledgement: ack-nhfb
rawauthor: {Digital Equipment Corporation}
rawnote: Also published as Stanford Artificial Intelligence Laboratory Operating Note 75, November 1976.
rawtitle: {DECsystem}-10\slash 20 Hardware Manual
entry:
@Book{DEC:1976:DHM,
  author =       "{Digital Equipment Corporation}",
  title =        "{DECsystem}-10\slash 20 Hardware Manual",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  edition =      "Fourth",
  pages =        "various",
  month =        mar,
  year =         "1976",
  bibdate =      "Fri Dec 08 13:03:19 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also published as Stanford Artificial Intelligence
                 Laboratory Operating Note 75, November 1976.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: DeSandre:1976:FPF
author: Giovanni De Sandre and Angelo Subrizi and Franco Bretti
title: Fixed point to floating point conversion in an electronic computer
pages: various
day: 1
month: jun
monthnumber: 6
year: 1976
bibdate: Sat Mar 24 06:14:58 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.03.24 06:14:58 ???
note: Patent filed 17 April 1974.
URL: https://patents.google.com/patent/US3961170A; https://tinyurl.com/ybz9rrqy
acknowledgement: ack-nhfb
howpublished: US Patent US3961170.
rawauthor: Giovanni {De Sandre} and Angelo Subrizi and Franco Bretti
rawnote: Patent filed 17 April 1974.
rawtitle: Fixed point to floating point conversion in an electronic computer
abstract:
In a digital electronic computer which comprises a memory including a first and a second register, the first register is receptive of a number to be converted from fixed to floating point notation and the second register is receptive of a significant zero digit with an associated decimal point. Shifting means including a register is operable to shift the contents of either register and aligning means is operable to cause shifting of the second register until the decimal point stored therein is aligned with the decimal point in the first register. Indicating means indicates whether the number stored in the first register is greater or less than one and the shifting means next begins shifting the contents of one or the other of the registers when the number is indicated greater or less than one respectively. A control means includes a detecting means for stopping the shifting means when the decimal point of the second register becomes aligned with the location of the next higher order with respect to the highest significant digit of the first register. The control means also includes counting means which is incremented or decremented by one for each shifting operation in dependence on the direction of shifting. The resultant numbers in the first and second registers represent the mantissa and exponent respectively, of the desired floating point number.

rawabstract:
In a digital electronic computer which comprises a memory including a first and a second register, the first register is receptive of a number to be converted from fixed to floating point notation and the second register is receptive of a significant zero digit with an associated decimal point. Shifting means including a register is operable to shift the contents of either register and aligning means is operable to cause shifting of the second register until the decimal point stored therein is aligned with the decimal point in the first register. Indicating means indicates whether the number stored in the first register is greater or less than one and the shifting means next begins shifting the contents of one or the other of the registers when the number is indicated greater or less than one respectively. A control means includes a detecting means for stopping the shifting means when the decimal point of the second register becomes aligned with the location of the next higher order with respect to the highest significant digit of the first register. The control means also includes counting means which is incremented or decremented by one for each shifting operation in dependence on the direction of shifting. The resultant numbers in the first and second registers represent the mantissa and exponent respectively, of the desired floating point number.

entry:
@Misc{DeSandre:1976:FPF,
  author =       "Giovanni {De Sandre} and Angelo Subrizi and Franco
                 Bretti",
  title =        "Fixed point to floating point conversion in an
                 electronic computer",
  howpublished = "US Patent US3961170.",
  day =          "1",
  month =        jun,
  year =         "1976",
  bibdate =      "Sat Mar 24 06:14:58 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Patent filed 17 April 1974.",
  URL =          "https://patents.google.com/patent/US3961170A;
                 https://tinyurl.com/ybz9rrqy",
  abstract =     "In a digital electronic computer which comprises a
                 memory including a first and a second register, the
                 first register is receptive of a number to be converted
                 from fixed to floating point notation and the second
                 register is receptive of a significant zero digit with
                 an associated decimal point. Shifting means including a
                 register is operable to shift the contents of either
                 register and aligning means is operable to cause
                 shifting of the second register until the decimal point
                 stored therein is aligned with the decimal point in the
                 first register. Indicating means indicates whether the
                 number stored in the first register is greater or less
                 than one and the shifting means next begins shifting
                 the contents of one or the other of the registers when
                 the number is indicated greater or less than one
                 respectively. A control means includes a detecting
                 means for stopping the shifting means when the decimal
                 point of the second register becomes aligned with the
                 location of the next higher order with respect to the
                 highest significant digit of the first register. The
                 control means also includes counting means which is
                 incremented or decremented by one for each shifting
                 operation in dependence on the direction of shifting.
                 The resultant numbers in the first and second registers
                 represent the mantissa and exponent respectively, of
                 the desired floating point number.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Detlefsen:1976:CRN
author: Michael Detlefsen and Douglas K. Erlandson and J. Clark Heston and Charles M. Young
title: Computation with Roman numerals
journal: j-ARCH-HIST-EXACT-SCI
volume: 15
number: 2
pages: 141--148
month: jun
monthnumber: 6
year: 1976
CODEN: AHESAN
DOI: https://doi.org/10.1007/BF00348497
ISSN: 0003-9519 (print), 1432-0657 (electronic) OR 00039519 (print), 14320657 (electronic)
ISSNL: 0003-9519 OR 00039519
MRclass: 00A05 (01A20)
MRnumber: 0453407 (56 \#11671)
MRreviewer: Richard L. Francis
bibdate: Fri Feb 4 21:50:12 MST 2011
bibtimestamp: 2011.02.04 21:50:12 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=15&issue=2&spage=141
fjournal: Archive for History of Exact Sciences
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/407
rawauthor: Michael Detlefsen and Douglas K. Erlandson and J. Clark Heston and Charles M. Young
rawtitle: Computation with {Roman} numerals
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=15&issue=2; https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Detlefsen:1976:CRN,
  author =       "Michael Detlefsen and Douglas K. Erlandson and J.
                 Clark Heston and Charles M. Young",
  title =        "Computation with {Roman} numerals",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "15",
  number =       "2",
  pages =        "141--148",
  month =        jun,
  year =         "1976",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/BF00348497",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "00A05 (01A20)",
  MRnumber =     "0453407 (56 \#11671)",
  MRreviewer =   "Richard L. Francis",
  bibdate =      "Fri Feb 4 21:50:12 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=15&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=15&issue=2&spage=141",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  MRtitle =      "Computation with {Roman} numerals",
}


bibtype: mastersthesis
filename: fparith.bib
label: Dickinson:1976:PAA
author: Fred Kenneth Dickinson
title: Pseudo-round: an alternative approach for floating-point representation
type: Thesis (M.S.)
school: Southwest Texas State University
address: San Marcos, TX, USA
pages: vi + 53
year: 1976
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: Floating-point arithmetic.; Numerical calculations --- Computer programs.
acknowledgement: ack-nhfb
rawauthor: Fred Kenneth Dickinson
rawtitle: Pseudo-round: an alternative approach for floating-point representation
entry:
@MastersThesis{Dickinson:1976:PAA,
  author =       "Fred Kenneth Dickinson",
  title =        "Pseudo-round: an alternative approach for
                 floating-point representation",
  type =         "Thesis ({M.S.})",
  school =       "Southwest Texas State University",
  address =      "San Marcos, TX, USA",
  pages =        "vi + 53",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Numerical calculations ---
                 Computer programs.",
}


bibtype: article
filename: fparith.bib
label: Fateman:1976:MAP
author: R. J. Fateman
journal: j-SIAM-REVIEW
volume: 18
number: 4
pages: 802--802
year: 1976
CODEN: SIREAD
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: R. J. Fateman
title:
Macsyma Arbitrary Precision Floating Point Arithmetic Package --- Philosophy and an Overview of its Implementation

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

rawtitle:
{Macsyma} Arbitrary Precision Floating Point Arithmetic Package --- Philosophy and an Overview of its Implementation

entry:
@Article{Fateman:1976:MAP,
  author =       "R. J. Fateman",
  title =        "{Macsyma} Arbitrary Precision Floating Point
                 Arithmetic Package --- Philosophy and an Overview of
                 its Implementation",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "802--802",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "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",
}


bibtype: article
filename: fparith.bib
label: Feldstein:1976:CED
author: Alan Feldstein and Richard Goodman
title: Convergence Estimates for the Distribution of Trailing Digits
journal: j-J-ACM
volume: 23
number: 2
pages: 287--297
month: apr
monthnumber: 4
year: 1976
CODEN: JACOAH
DOI: https://doi.org/10.1145/321941.321948
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Wed Jan 15 18:12:53 MST 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.01.15 18:12:53 MST
fjournal: Journal of the ACM
keywords: Benford's Law; computer arithmetic; computer programming; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
journalabr: J Assoc Comput Mach
rawauthor: Alan Feldstein and Richard Goodman
rawtitle: Convergence Estimates for the Distribution of Trailing Digits
abstract:
An analysis is made of the distribution of trailing digits (tail end digits) of positive real floating-point numbers represented in arbitrary base $ beta $ and randomly chosen from a logarithmic distribution. The analysis shows that the $n$ th digit for $ n geq 2 $ is actually approximately uniformly distributed. The approximation depends upon both $n$ and the base beta. It becomes better as $n$ increases, and it is exact in the limit as $ n rightarrow infty $. A table of this distribution is presented for various $ beta $ and $n$, along with a table of the maximum digit by digit deviation $ Delta $ of the logarithmic distribution from the uniform distribution. Various asymptotic results for $ Delta $ are included.

rawabstract:
An analysis is made of the distribution of trailing digits (tail end digits) of positive real floating-point numbers represented in arbitrary base $ \beta $ and randomly chosen from a logarithmic distribution. The analysis shows that the $n$ th digit for $ n \geq 2 $ is actually approximately uniformly distributed. The approximation depends upon both $n$ and the base beta. It becomes better as $n$ increases, and it is exact in the limit as $ n \rightarrow \infty $. A table of this distribution is presented for various $ \beta $ and $n$, along with a table of the maximum digit by digit deviation $ \Delta $ of the logarithmic distribution from the uniform distribution. Various asymptotic results for $ \Delta $ are included.

entry:
@Article{Feldstein:1976:CED,
  author =       "Alan Feldstein and Richard Goodman",
  title =        "Convergence Estimates for the Distribution of Trailing
                 Digits",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "287--297",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321941.321948",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An analysis is made of the distribution of trailing
                 digits (tail end digits) of positive real
                 floating-point numbers represented in arbitrary base $
                 \beta $ and randomly chosen from a logarithmic
                 distribution. The analysis shows that the $n$ th digit
                 for $ n \geq 2 $ is actually approximately uniformly
                 distributed. The approximation depends upon both $n$
                 and the base beta. It becomes better as $n$ increases,
                 and it is exact in the limit as $ n \rightarrow \infty
                 $. A table of this distribution is presented for
                 various $ \beta $ and $n$, along with a table of the
                 maximum digit by digit deviation $ \Delta $ of the
                 logarithmic distribution from the uniform distribution.
                 Various asymptotic results for $ \Delta $ are
                 included.",
  acknowledgement = ack-nhfb,
  classification = "723",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "Benford's Law; computer arithmetic; computer
                 programming; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Garner:1976:SSR
author: H. L. Garner
title: A Survey of Some Recent Contributions to Computer Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 12
pages: 1277--1282
month: dec
monthnumber: 12
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674595
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:14:15 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 10:14:15 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. L. Garner
rawtitle: A Survey of Some Recent Contributions to Computer Arithmetic
entry:
@Article{Garner:1976:SSR,
  author =       "H. L. Garner",
  title =        "A Survey of Some Recent Contributions to Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "12",
  pages =        "1277--1282",
  month =        dec,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674595",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Goldstein:1976:FCF
author: M. J. Goldstein
title: Further Comparison of Floating Point Summation Methods
journal: j-SIAM-REVIEW
volume: 18
number: 4
pages: 805--805
year: 1976
CODEN: SIREAD
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: M. J. Goldstein
rawtitle: Further Comparison of Floating Point Summation Methods
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Goldstein:1976:FCF,
  author =       "M. J. Goldstein",
  title =        "Further Comparison of Floating Point Summation
                 Methods",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "805--805",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "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",
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: Goodman:1976:EGD
author: R. Goodman and A. Feldstein
title: Effect of Guard Digits and Normalization Options on Floating Point Multiplication
journal: j-SIAM-REVIEW
volume: 18
number: 4
pages: 806--806
year: 1976
CODEN: SIREAD
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: R. Goodman and A. Feldstein
rawtitle: Effect of Guard Digits and Normalization Options on Floating Point Multiplication
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Goodman:1976:EGD,
  author =       "R. Goodman and A. Feldstein",
  title =        "Effect of Guard Digits and Normalization Options on
                 Floating Point Multiplication",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "806--806",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "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",
}


bibtype: article
filename: fparith.bib
label: Goodman:1976:REF
author: Richard Goodman
title: On round-off error in fixed-point multiplication
journal: j-BIT
volume: 16
number: 1
pages: 41--51
month: mar
monthnumber: 3
year: 1976
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01940776
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:14 MST 2006
bibtimestamp: 2006.01.04 18:52:14 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=1&spage=41
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: fixed-point arithmetic; floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Richard Goodman
rawtitle: On round-off error in fixed-point multiplication
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Goodman:1976:REF,
  author =       "Richard Goodman",
  title =        "On round-off error in fixed-point multiplication",
  journal =      j-BIT,
  volume =       "16",
  number =       "1",
  pages =        "41--51",
  month =        mar,
  year =         "1976",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01940776",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=1&spage=41",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "fixed-point arithmetic; floating-point arithmetic;
                 rounding errors",
}


bibtype: article
filename: fparith.bib
label: Goyal:1976:NAR
author: L. N. Goyal
title: A Note on Atrubin's Real-Time Iterative Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 5
pages: 546--548
month: may
monthnumber: 5
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674646
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:51 MDT 2011
bibtimestamp: 2011.07.12 06:24:51 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674646
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. N. Goyal
rawtitle: A Note on {Atrubin}'s Real-Time Iterative Multiplier
entry:
@Article{Goyal:1976:NAR,
  author =       "L. N. Goyal",
  title =        "A Note on {Atrubin}'s Real-Time Iterative Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "5",
  pages =        "546--548",
  month =        may,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674646",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674646",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Hannington:1976:FPM
author: G. Hannington and D. G. Whitehead
title: A Floating-Point Multiplexed DDA System
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 11
pages: 1074--1077
month: nov
monthnumber: 11
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674557
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:54 MDT 2011
bibtimestamp: 2011.07.12 06:24:54 MDT
note: See comments cite McCrea:1978:CFP.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674557
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. Hannington and D. G. Whitehead
rawnote: See comments \cite{McCrea:1978:CFP}.
rawtitle: A Floating-Point Multiplexed {DDA} System
entry:
@Article{Hannington:1976:FPM,
  author =       "G. Hannington and D. G. Whitehead",
  title =        "A Floating-Point Multiplexed {DDA} System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "11",
  pages =        "1074--1077",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674557",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{McCrea:1978:CFP}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674557",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Higbie:1976:VFP
author: L. C. Higbie
title: Vector Floating-Point Data Format
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 1
pages: 25--32
month: jan
monthnumber: 1
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.5009201
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:20 MDT 2011
bibtimestamp: 2011.07.12 06:24:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009201
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. C. Higbie
rawtitle: Vector Floating-Point Data Format
entry:
@Article{Higbie:1976:VFP,
  author =       "L. C. Higbie",
  title =        "Vector Floating-Point Data Format",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "1",
  pages =        "25--32",
  month =        jan,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.5009201",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009201",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: IBM:1976:ISP
author: IBM Corporation
title: IBM System / 370: Principles of Operation: Systems
publisher: pub-IBM
address: pub-IBM:adr
pages: 326
year: 1976
LCCN: QA76.8.I122 I57 1976
bibdate: Fri Sep 16 16:30:13 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:13 ???
acknowledgement: ack-nhfb
rawauthor: {IBM Corporation}
rawtitle: {IBM System}\slash 370: Principles of Operation: Systems
entry:
@Book{IBM:1976:ISP,
  author =       "{IBM Corporation}",
  title =        "{IBM System}\slash 370: Principles of Operation:
                 Systems",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "326",
  year =         "1976",
  LCCN =         "QA76.8.I122 I57 1976",
  bibdate =      "Fri Sep 16 16:30:13 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Jayashree:1976:BMU
author: T. Jayashree and D. Basu
title: On Binary Multiplication Using the Quarter Square Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 9
pages: 957--960
month: sep
monthnumber: 9
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674723
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:54 MDT 2011
bibtimestamp: 2011.07.12 06:24:54 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674723
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Jayashree and D. Basu
rawtitle: On Binary Multiplication Using the Quarter Square Algorithm
entry:
@Article{Jayashree:1976:BMU,
  author =       "T. Jayashree and D. Basu",
  title =        "On Binary Multiplication Using the Quarter Square
                 Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "9",
  pages =        "957--960",
  month =        sep,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674723",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674723",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Kulisch:1976:FIF
author: U. Kulisch and G. Bohlender
title: Formalization and implementation of floating-point matrix operations
journal: j-COMPUTING
volume: 16
number: 3
pages: 239--261
year: 1976
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G05 (68A10)
MRnumber: 53 7010
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: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
reviewer: F. Szidarovszky
rawauthor: U. Kulisch and G. Bohlender
rawtitle: Formalization and implementation of floating-point matrix operations
entry:
@Article{Kulisch:1976:FIF,
  author =       "U. Kulisch and G. Bohlender",
  title =        "Formalization and implementation of floating-point
                 matrix operations",
  journal =      j-COMPUTING,
  volume =       "16",
  number =       "3",
  pages =        "239--261",
  year =         "1976",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05 (68A10)",
  MRnumber =     "53 7010",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "F. Szidarovszky",
}


bibtype: book
filename: fparith.bib
label: Kulisch:1976:GNR
author: Ulrich W. Kulisch
volume: 19
publisher: pub-BIB-INST
address: pub-BIB-INST:adr
pages: 467
year: 1976
ISBN: 3-411-01517-9 OR 3411015179
ISBN13: 978-3-411-01517-7 OR 9783411015177
LCCN: QA162 .K85
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
series: Reihe Informatik
keywords: Algebra, Abstract.; Floating-point arithmetic.; Mathematics --- Data processing.
acknowledgement: ack-nhfb
rawauthor: Ulrich W. Kulisch
title:
Grundlagen des numerischen Rechnens: mathematische Begrundung der Rechnerarithmetik toenglish Fundamental Principles of Numerical Computation: Mathematical Foundations of Computer Arithmetic endtoenglish 

rawtitle:
{Grundlagen des numerischen Rechnens: mathematische Begr{\"u}ndung der Rechnerarithmetik} \toenglish {Fundamental Principles of Numerical Computation: Mathematical Foundations of Computer Arithmetic} \endtoenglish

entry:
@Book{Kulisch:1976:GNR,
  author =       "Ulrich W. Kulisch",
  title =        "{Grundlagen des numerischen Rechnens: mathematische
                 Begr{\"u}ndung der Rechnerarithmetik} \toenglish
                 {Fundamental Principles of Numerical Computation:
                 Mathematical Foundations of Computer Arithmetic}
                 \endtoenglish",
  volume =       "19",
  publisher =    pub-BIB-INST,
  address =      pub-BIB-INST:adr,
  pages =        "467",
  year =         "1976",
  ISBN =         "3-411-01517-9",
  ISBN-13 =      "978-3-411-01517-7",
  LCCN =         "QA162 .K85",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Reihe Informatik",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra, Abstract.; Floating-point arithmetic.;
                 Mathematics --- Data processing.",
}


bibtype: article
filename: fparith.bib
label: Lacroix:1976:LCF
author: Arild Lacroix
title: Limit cycles in floating point digital filters
journal: AEU---Arch. Elektron. Ubertragungstech.
volume: 30
number: 7/8
pages: 277--284
year: 1976
MRclass: 94A05
MRnumber: 56 15123
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
acknowledgement: ack-nhfb
rawauthor: Arild Lacroix
rawtitle: Limit cycles in floating point digital filters
entry:
@Article{Lacroix:1976:LCF,
  author =       "Arild Lacroix",
  title =        "Limit cycles in floating point digital filters",
  journal =      "AE{\"U}---Arch. Elektron. {\"U}bertragungstech.",
  volume =       "30",
  number =       "7/8",
  pages =        "277--284",
  year =         "1976",
  MRclass =      "94A05",
  MRnumber =     "56 15123",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Linnainmaa:1976:TEA
author: Seppo Linnainmaa
title: Taylor expansion of the accumulated rounding error
journal: j-BIT
volume: 16
number: 2
pages: 146--160
month: jun
monthnumber: 6
year: 1976
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01931367
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:14 MST 2006
bibtimestamp: 2006.01.04 18:52:14 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=146
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Seppo Linnainmaa
rawtitle: {Taylor} expansion of the accumulated rounding error
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The article describes analytic and algorithmic methods for determining the coefficients of the Taylor expansion of an accumulated rounding error with respect to the local rounding errors, and hence determining the influence of the local errors on the accumulated error. Second and higher order coefficients are also discussed, and some possible methods of reducing the extensive storage requirements are analyzed.

rawabstract:
The article describes analytic and algorithmic methods for determining the coefficients of the Taylor expansion of an accumulated rounding error with respect to the local rounding errors, and hence determining the influence of the local errors on the accumulated error. Second and higher order coefficients are also discussed, and some possible methods of reducing the extensive storage requirements are analyzed.

entry:
@Article{Linnainmaa:1976:TEA,
  author =       "Seppo Linnainmaa",
  title =        "{Taylor} expansion of the accumulated rounding error",
  journal =      j-BIT,
  volume =       "16",
  number =       "2",
  pages =        "146--160",
  month =        jun,
  year =         "1976",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01931367",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=146",
  abstract =     "The article describes analytic and algorithmic methods
                 for determining the coefficients of the Taylor
                 expansion of an accumulated rounding error with respect
                 to the local rounding errors, and hence determining the
                 influence of the local errors on the accumulated error.
                 Second and higher order coefficients are also
                 discussed, and some possible methods of reducing the
                 extensive storage requirements are analyzed.",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: mastersthesis
filename: fparith.bib
label: Lipschutz:1976:OPS
author: David Lipschutz
title: Optimization of a practical system for high fidelity digital audio
type: Thesis (M.S.)
school: Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science
address: Cambridge, MA, USA
pages: 53
year: 1976
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
note: Supervised by Francis F. Lee.
acknowledgement: ack-nhfb
rawauthor: David Lipschutz
rawnote: Supervised by Francis F. Lee.
rawtitle: Optimization of a practical system for high fidelity digital audio
keywords:
Computer sound processing.; Digital electronics.; Floating-point arithmetic.; High-fidelity sound systems.; Noise --- Psychological aspects.

entry:
@MastersThesis{Lipschutz:1976:OPS,
  author =       "David Lipschutz",
  title =        "Optimization of a practical system for high fidelity
                 digital audio",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "53",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Francis F. Lee.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer sound processing.; Digital electronics.;
                 Floating-point arithmetic.; High-fidelity sound
                 systems.; Noise --- Psychological aspects.",
}


bibtype: article
filename: fparith.bib
label: Majithia:1976:SCC
author: J. C. Majithia
title: Some Comments Concerning Design of Pipeline Arithmetic Arrays
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 11
pages: 1132--1134
month: nov
monthnumber: 11
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674565
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:06:10 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:06:10 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. C. Majithia
rawtitle: Some Comments Concerning Design of Pipeline Arithmetic Arrays
entry:
@Article{Majithia:1976:SCC,
  author =       "J. C. Majithia",
  title =        "Some Comments Concerning Design of Pipeline Arithmetic
                 Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "11",
  pages =        "1132--1134",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674565",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:06:10 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Maples:1976:FPI
author: Michael D. Maples
title: Floating-point package for INTEL 8008 and 8080 microprocessors
address: Livermore, CA, USA
pages: 8 + A-33
year: 1976
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: Floating-point arithmetic.; Intel 8080 (Microprocessor); Microprocessors.
acknowledgement: ack-nhfb
rawauthor: Michael D. Maples
rawtitle: Floating-point package for {INTEL} 8008 and 8080 microprocessors
institution:
Lawrence Livermore Laboratory, University of California/Livermore; National Technical Information Service [distributor]

remark:
Prepared for U.S. Energy Research and Development Administration, under Contract No. W-7405-Eng-43. Microfiche reproduction: Springfield, Va.: National Technical Information Service, 1976. --- 1 microfiche; 10 x 15 cm.

entry:
@TechReport{Maples:1976:FPI,
  author =       "Michael D. Maples",
  title =        "Floating-point package for {INTEL} 8008 and 8080
                 microprocessors",
  institution =  "Lawrence Livermore Laboratory, University of
                 California/Livermore; National Technical Information
                 Service [distributor]",
  address =      "Livermore, CA, USA",
  pages =        "8 + A-33",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Intel 8080
                 (Microprocessor); Microprocessors.",
  remark =       "Prepared for U.S. Energy Research and Development
                 Administration, under Contract No. W-7405-Eng-43.
                 Microfiche reproduction: Springfield, Va.: National
                 Technical Information Service, 1976. --- 1 microfiche;
                 10 x 15 cm.",
}


bibtype: phdthesis
filename: fparith.bib
label: Martinez:1976:SSS
author: Ralph Martinez
title: A semi-portable simulation system using both fixed and floating point derivative blocks
type: Thesis (Ph.D. - Electrical Engineering)
school: University of Arizona
address: Tucson, AZ, USA
pages: xii + 169
year: 1976
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: Digital computer simulation.; Dynamics --- Data processing.
acknowledgement: ack-nhfb
rawauthor: Ralph Martinez
rawtitle: A semi-portable simulation system using both fixed and floating point derivative blocks
entry:
@PhdThesis{Martinez:1976:SSS,
  author =       "Ralph Martinez",
  title =        "A semi-portable simulation system using both fixed and
                 floating point derivative blocks",
  type =         "Thesis ({Ph.D.} - Electrical Engineering)",
  school =       "University of Arizona",
  address =      "Tucson, AZ, USA",
  pages =        "xii + 169",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital computer simulation.; Dynamics --- Data
                 processing.",
}


bibtype: techreport
filename: fparith.bib
label: Metropolis:1976:MSA
author: N. Metropolis
title: Methods of significance arithmetic
type: Technical report
number: LA-UR-76-661;CONF-760428-1
institution: inst-LASL
address: inst-LASL:adr
pages: xii + 169
day: 1
month: jan
monthnumber: 1
year: 1976
bibdate: Tue Mar 20 11:16:47 2007
bibtimestamp: 2007.03.20 11:16:47 ???
URL: http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=7189580&query_id=0
remark: OSTI ID: 7189580
acknowledgement: ack-nhfb
rawauthor: N. Metropolis
rawtitle: Methods of significance arithmetic
note:
Presented at the Conference on the state of the art in numerical analysis, 12 April 1976, University of York, England, UK

abstract:
A preliminary report is given of two applications of the methods of significance arithmetic. These are a simple nonlinear partial differential equation and matrix inversion.

rawabstract:
A preliminary report is given of two applications of the methods of significance arithmetic. These are a simple nonlinear partial differential equation and matrix inversion.

rawnote:
Presented at the Conference on the state of the art in numerical analysis, 12 April 1976, University of York, England, UK

entry:
@TechReport{Metropolis:1976:MSA,
  author =       "N. Metropolis",
  title =        "Methods of significance arithmetic",
  type =         "Technical report",
  number =       "LA-UR-76-661;CONF-760428-1",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  day =          "1",
  month =        jan,
  year =         "1976",
  bibdate =      "Tue Mar 20 11:16:47 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Presented at the Conference on the state of the art in
                 numerical analysis, 12 April 1976, University of York,
                 England, UK",
  URL =          "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=7189580&query_id=0",
  abstract =     "A preliminary report is given of two applications of
                 the methods of significance arithmetic. These are a
                 simple nonlinear partial differential equation and
                 matrix inversion.",
  acknowledgement = ack-nhfb,
  remark =       "OSTI ID: 7189580",
}


bibtype: article
filename: fparith.bib
label: Miller:1976:AGF
author: Webb Miller and David L. Spooner
title: Automatic Generation of Floating-Point Test Data
journal: j-IEEE-TRANS-SOFTW-ENG
volume: SE-2
number: 3
pages: 223--226
month: sep
monthnumber: 9
year: 1976
CODEN: IESEDJ
DOI: https://doi.org/10.1109/TSE.1976.233818
ISSN: 0098-5589 (print), 1939-3520 (electronic) OR 00985589 (print), 19393520 (electronic)
ISSNL: 0098-5589 OR 00985589
MRclass: 68A05
MRnumber: 55 1787
bibdate: Thu Feb 1 08:07:37 MST 2018
bibtimestamp: 2018.02.01 08:07:37 MST
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1702369
fjournal: IEEE Transactions on Software Engineering
keywords: floating-point testing
remark: Special section on testing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32
reviewer: George Marsaglia
rawauthor: Webb Miller and David L. Spooner
rawtitle: Automatic Generation of Floating-Point Test Data
bibsource:
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/ieeetranssoftweng1970.bib

entry:
@Article{Miller:1976:AGF,
  author =       "Webb Miller and David L. Spooner",
  title =        "Automatic Generation of Floating-Point Test Data",
  journal =      j-IEEE-TRANS-SOFTW-ENG,
  volume =       "SE-2",
  number =       "3",
  pages =        "223--226",
  month =        sep,
  year =         "1976",
  CODEN =        "IESEDJ",
  DOI =          "https://doi.org/10.1109/TSE.1976.233818",
  ISSN =         "0098-5589 (print), 1939-3520 (electronic)",
  ISSN-L =       "0098-5589",
  MRclass =      "68A05",
  MRnumber =     "55 1787",
  bibdate =      "Thu Feb 1 08:07:37 MST 2018",
  bibsource =    "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/ieeetranssoftweng1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1702369",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Software Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
  keywords =     "floating-point testing",
  remark =       "Special section on testing",
  reviewer =     "George Marsaglia",
}


bibtype: article
filename: fparith.bib
label: Mohn:1976:IPA
author: K. Mohn and R. V. Roman
title: An interactive polynomial approximation algorithm
journal: j-COMP-J
volume: 19
number: 1
pages: 74--78
month: feb
monthnumber: 2
year: 1976
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Thu Sep 15 18:39:43 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 18:39:43 ???
fjournal: The Computer Journal
acknowledgement: ack-nj
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: K. Mohn and R. V. Roman
rawtitle: An interactive polynomial approximation algorithm
entry:
@Article{Mohn:1976:IPA,
  author =       "K. Mohn and R. V. Roman",
  title =        "An interactive polynomial approximation algorithm",
  journal =      j-COMP-J,
  volume =       "19",
  number =       "1",
  pages =        "74--78",
  month =        feb,
  year =         "1976",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Sep 15 18:39:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Ni:1976:EAT
author: Ming Duenn Ni and J. K. Aggarwal
title: Error analysis of two-dimensional recursive digital filters employing floating-point arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 7
pages: 755--759
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674684
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65D99 (93E10)
MRnumber: 55 6802
bibdate: Sat Dec 16 16:45:24 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.16 16:45:24 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
reviewer: Sven-AA ke Gustafson
rawauthor: Ming Duenn Ni and J. K. Aggarwal
rawtitle: Error analysis of two-dimensional recursive digital filters employing floating-point arithmetic
entry:
@Article{Ni:1976:EAT,
  author =       "Ming Duenn Ni and J. K. Aggarwal",
  title =        "Error analysis of two-dimensional recursive digital
                 filters employing floating-point arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "7",
  pages =        "755--759",
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674684",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65D99 (93E10)",
  MRnumber =     "55 6802",
  bibdate =      "Sat Dec 16 16:45:24 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  reviewer =     "Sven-{\AA}ke Gustafson",
}


bibtype: techreport
filename: fparith.bib
label: Paoni:1976:PFI
author: C. Paoni and M. Maples
title: A PLM floating-point interface program
institution: Lawrence Livermore Laboratory; National Technical Information Service
address: Livermore, CA, USA
pages: iii + 39
year: 1976
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: C. Paoni and M. Maples
rawtitle: A {PLM} floating-point interface program
entry:
@TechReport{Paoni:1976:PFI,
  author =       "C. Paoni and M. Maples",
  title =        "A {PLM} floating-point interface program",
  institution =  "Lawrence Livermore Laboratory; National Technical
                 Information Service",
  address =      "Livermore, CA, USA",
  pages =        "iii + 39",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Parker:1976:STR
author: Douglass Stott Parker
title: The statistical theory of relative errors in floating-point computation
type: Thesis (M.S.)
school: Department of Computer Science, University of Illinois at Urbana-Champaign
address: Urbana, IL, USA
pages: 62
year: 1976
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
series: Report no. UIUCDCS-R-76-787
keywords: Floating-point arithmetic.; Roundoff errors.
acknowledgement: ack-nhfb
rawauthor: Douglass Stott Parker
rawtitle: The statistical theory of relative errors in floating-point computation
entry:
@MastersThesis{Parker:1976:STR,
  author =       "Douglass Stott Parker",
  title =        "The statistical theory of relative errors in
                 floating-point computation",
  type =         "Thesis ({M.S.})",
  school =       "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, IL, USA",
  pages =        "62",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Report no. UIUCDCS-R-76-787",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Roundoff errors.",
}


bibtype: article
filename: fparith.bib
label: Patel:1976:ASB
author: M. R. Patel and K. H. Bennett
title: Analysis of Speed of a Binary Multiplier Using a Variable Number of Shifts Per Cycle
journal: j-COMP-J
volume: 19
number: 3
pages: 254--257
month: aug
monthnumber: 8
year: 1976
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/19.3.254
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:58 MST 2012
bibtimestamp: 2012.12.04 14:47:58 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C5210 (Logic design methods); C5230 (Digital arithmetic methods)
corpsource: Department of Computer Sci., University of Keele, Keele, UK
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: M. R. Patel and K. H. Bennett
rawtitle: Analysis of Speed of a Binary Multiplier Using a Variable Number of Shifts Per Cycle
bibsource:
Compendex database; http://comjnl.oxfordjournals.org/content/19/3.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/; https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/19/3/254.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/254.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/255.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/256.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/257.tif

keywords:
binary multiplication; binary multiplier; computers, digital; digital arithmetic; logic design; multiplication; multiplying circuits; shift per cycle; speed

entry:
@Article{Patel:1976:ASB,
  author =       "M. R. Patel and K. H. Bennett",
  title =        "Analysis of Speed of a Binary Multiplier Using a
                 Variable Number of Shifts Per Cycle",
  journal =      j-COMP-J,
  volume =       "19",
  number =       "3",
  pages =        "254--257",
  month =        aug,
  year =         "1976",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/19.3.254",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:58 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/19/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/19/3/254.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/254.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/255.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/256.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/257.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5210 (Logic design methods); C5230 (Digital
                 arithmetic methods)",
  classification = "723",
  corpsource =   "Department of Computer Sci., University of Keele,
                 Keele, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary multiplication; binary multiplier; computers,
                 digital; digital arithmetic; logic design;
                 multiplication; multiplying circuits; shift per cycle;
                 speed",
}


bibtype: article
filename: fparith.bib
label: Paul:1976:SEF
author: George Paul and M. Wayne Wilson
title: Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?
journal: j-TOMS
volume: 2
number: 2
pages: 132--142
month: jun
monthnumber: 6
year: 1976
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355681.355684
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 27 00:30:21 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.27 00:30:21 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: George Paul and M. Wayne Wilson
rawtitle: Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?
entry:
@Article{Paul:1976:SEF,
  author =       "George Paul and M. Wayne Wilson",
  title =        "Should the Elementary Function Library Be Incorporated
                 Into Computer Instruction Sets?",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "132--142",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355684",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: phdthesis
filename: fparith.bib
label: Pichat:1976:CEE
author: Michele Pichat
type: These
school: Universite de Grenoble 1
address: Grenoble, France
pages: 132--142
year: 1976
bibdate: Thu May 27 07:44:27 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.05.27 07:44:27 ???
URL: https://tel.archives-ouvertes.fr/tel-00287209/
language: French
acknowledgement: ack-nhfb
rawauthor: Mich{\`e}le Pichat
title:
Contributions a l'etude des erreurs d'arrondi en arithmetique a virgule flottante. (French) [Contributions to the error analysis of rounding errors in floating-point arithmetic]

rawtitle:
Contributions {\`a} l'{\`e}tude des erreurs d'arrondi en arithm{\`e}tique {\`a} virgule flottante. ({French}) [Contributions to the error analysis of rounding errors in floating-point arithmetic]

entry:
@PhdThesis{Pichat:1976:CEE,
  author =       "Mich{\`e}le Pichat",
  title =        "Contributions {\`a} l'{\`e}tude des erreurs d'arrondi
                 en arithm{\`e}tique {\`a} virgule flottante. ({French})
                 [Contributions to the error analysis of rounding errors
                 in floating-point arithmetic]",
  type =         "Th{\`e}se",
  school =       "Universit{\'e} de Grenoble 1",
  address =      "Grenoble, France",
  year =         "1976",
  bibdate =      "Thu May 27 07:44:27 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://tel.archives-ouvertes.fr/tel-00287209/",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: techreport
filename: fparith.bib
label: Randell:1976:ODC
author: Brian Randell
type: Technical report
number: 91
institution: Computing Laboratory, University of Newcastle upon Tyne
address: Newcastle upon Tyne, UK
pages: 3 + 37
year: 1976
LCCN: Z5642.2 .R36 1979
bibdate: Wed Oct 13 09:24:25 MDT 2010
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 09:24:25 MDT
subject: electronic digital computers; history; calculators
acknowledgement: ack-nhfb
rawauthor: Brian Randell
title:
The origins of digital computers: supplementary bibliography to ``Origins of digital computers: selected papers''

rawtitle:
The origins of digital computers: supplementary bibliography to {``Origins of digital computers: selected papers''}

entry:
@TechReport{Randell:1976:ODC,
  author =       "Brian Randell",
  title =        "The origins of digital computers: supplementary
                 bibliography to {``Origins of digital computers:
                 selected papers''}",
  type =         "Technical report",
  number =       "91",
  institution =  "Computing Laboratory, University of Newcastle upon
                 Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "3 + 37",
  year =         "1976",
  LCCN =         "Z5642.2 .R36 1979",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "electronic digital computers; history; calculators",
}


bibtype: article
filename: fparith.bib
label: Rankin:1976:FPR
author: Roy Rankin and Steve Wozniak
title: Floating Point Routines for the 6502
journal: j-DDJ
volume: 1
pages: 17--19
month: aug
monthnumber: 8
year: 1976
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Sat Jan 15 06:04:06 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.01.15 06:04:06 ???
URL: http://www.6502.org/source/floats/wozfp1.txt
fjournal: Dr. Dobb's Journal of Software Tools
keywords: HP 2100; MOS Technology
acknowledgement: ack-nhfb
rawauthor: Roy Rankin and Steve Wozniak
rawtitle: Floating Point Routines for the 6502
entry:
@Article{Rankin:1976:FPR,
  author =       "Roy Rankin and Steve Wozniak",
  title =        "Floating Point Routines for the 6502",
  journal =      j-DDJ,
  volume =       "1",
  number =       "??",
  pages =        "17--19",
  month =        aug,
  year =         "1976",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Sat Jan 15 06:04:06 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.6502.org/source/floats/wozfp1.txt",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "HP 2100; MOS Technology",
}


bibtype: article
filename: fparith.bib
label: Riesel:1976:FPU
author: Zvi H. Riesel
title: The floating point unit of the Golem B computer
journal: j-RADIO-ELECTRON-ENG
volume: 46
number: 7
pages: 355--359
month: jul
monthnumber: 7
year: 1976
CODEN: RDEEA4
DOI: https://doi.org/10.1049/ree.1976.0057
ISSN: 0033-7722 OR 00337722
bibdate: Fri Dec 03 15:11:57 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.12.03 15:11:57 ???
fjournal: The Radio and Electronic Engineer
acknowledgement: ack-nhfb
rawauthor: Zvi H. Riesel
rawtitle: The floating point unit of the {Golem B} computer
abstract:
The Golem B computer is a fast machine using emitter-coupled logic and multi-layer circuits. The autonomous floating point arithmetic unit obtains its instructions and operands from buffers loaded ahead of need. Its main part, for 56-bit fractions, uses two 4-operand adder complexes with stored carries. In multiplication instructions, 4 bits of the multiplier are used to form a new partial product in each pass through an adder complex. Division instructions use a base-4 non-restoring algorithm. Addition favours the case of equal or nearly equal exponents, but 112 sum bits are accumulated for all exponent differences. An effort has been made to provide instructions and number formats that will aid the writing of compilers and operating systems.

keywords:
adder complex; autonomous floating point arithmetic unit; buffers; division instructions; emitter coupled logic; exponent differences; Golem B computer; multi layer circuits; multiplication instructions; partial product

rawabstract:
The Golem B computer is a fast machine using emitter-coupled logic and multi-layer circuits. The autonomous floating point arithmetic unit obtains its instructions and operands from buffers loaded ahead of need. Its main part, for 56-bit fractions, uses two 4-operand adder complexes with stored carries. In multiplication instructions, 4 bits of the multiplier are used to form a new partial product in each pass through an adder complex. Division instructions use a base-4 non-restoring algorithm. Addition favours the case of equal or nearly equal exponents, but 112 sum bits are accumulated for all exponent differences. An effort has been made to provide instructions and number formats that will aid the writing of compilers and operating systems.

entry:
@Article{Riesel:1976:FPU,
  author =       "Zvi H. Riesel",
  title =        "The floating point unit of the {Golem B} computer",
  journal =      j-RADIO-ELECTRON-ENG,
  volume =       "46",
  number =       "7",
  pages =        "355--359",
  month =        jul,
  year =         "1976",
  CODEN =        "RDEEA4",
  DOI =          "https://doi.org/10.1049/ree.1976.0057",
  ISSN =         "0033-7722",
  bibdate =      "Fri Dec 03 15:11:57 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Golem B computer is a fast machine using
                 emitter-coupled logic and multi-layer circuits. The
                 autonomous floating point arithmetic unit obtains its
                 instructions and operands from buffers loaded ahead of
                 need. Its main part, for 56-bit fractions, uses two
                 4-operand adder complexes with stored carries. In
                 multiplication instructions, 4 bits of the multiplier
                 are used to form a new partial product in each pass
                 through an adder complex. Division instructions use a
                 base-4 non-restoring algorithm. Addition favours the
                 case of equal or nearly equal exponents, but 112 sum
                 bits are accumulated for all exponent differences. An
                 effort has been made to provide instructions and number
                 formats that will aid the writing of compilers and
                 operating systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Radio and Electronic Engineer",
  keywords =     "adder complex; autonomous floating point arithmetic
                 unit; buffers; division instructions; emitter coupled
                 logic; exponent differences; Golem B computer; multi
                 layer circuits; multiplication instructions; partial
                 product",
}


bibtype: article
filename: fparith.bib
label: Ris:1976:UDF
author: Frederic N. Ris
title: A Unified Decimal Floating-Point Architecture For the Support of High-Level Languages
journal: j-SIGNUM
volume: 11
number: 3
pages: 18--23
month: oct
monthnumber: 10
year: 1976
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:03 MDT 2005
bibtimestamp: 2005.04.12 07:50:03 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods); C6120 (File organisation)C6140D (High level languages)
corpsource: IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical; T Theoretical or Mathematical
rawauthor: Frederic N. Ris
rawtitle: A Unified Decimal Floating-Point Architecture For the Support of High-Level Languages
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
This paper summarizes a proposal for a decimal floating-point arithmetic interface for the support of high-level languages, consisting both of the arithmetic operations observed by application programs and facilities to produce subroutine libraries accessible from these programs. What is not included here are the detailed motivations, examinations of alternatives, and implementation considerations which will appear in the full work.

keywords:
arithmetic operations; decimal floating point arithmetic; digital arithmetic; high level languages; one level store

remark:
Normalized decimal floating-point arithmetic with a fractional coefficient, three directed rounding modes, and a trap mechanism. Three precisions are provided, with up to 31 decimal digits, and an exponent range of $ pm 9999 $. Cowlishaw cite Cowlishaw:2003:DFP says that this is the first implementation of the Chen-Ho cite Chen:1975:SER compressed format, allowing storage of 31 digits and 4 exponent digits in a 128-bit value. More modern encodings get 34 digits in the same number of bits, at somewhat reduced exponent range ($ [ - 6143, 6144] $).

rawabstract:
This paper summarizes a proposal for a decimal floating-point arithmetic interface for the support of high-level languages, consisting both of the arithmetic operations observed by application programs and facilities to produce subroutine libraries accessible from these programs. What is not included here are the detailed motivations, examinations of alternatives, and implementation considerations which will appear in the full work.

entry:
@Article{Ris:1976:UDF,
  author =       "Frederic N. Ris",
  title =        "A Unified Decimal Floating-Point Architecture For the
                 Support of High-Level Languages",
  journal =      j-SIGNUM,
  volume =       "11",
  number =       "3",
  pages =        "18--23",
  month =        oct,
  year =         "1976",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:03 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper summarizes a proposal for a decimal
                 floating-point arithmetic interface for the support of
                 high-level languages, consisting both of the arithmetic
                 operations observed by application programs and
                 facilities to produce subroutine libraries accessible
                 from these programs. What is not included here are the
                 detailed motivations, examinations of alternatives, and
                 implementation considerations which will appear in the
                 full work.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods); C6120 (File
                 organisation)C6140D (High level languages)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic operations; decimal floating point
                 arithmetic; digital arithmetic; high level languages;
                 one level store",
  remark =       "Normalized decimal floating-point arithmetic with a
                 fractional coefficient, three directed rounding modes,
                 and a trap mechanism. Three precisions are provided,
                 with up to 31 decimal digits, and an exponent range of
                 $ \pm 9999 $. Cowlishaw \cite{Cowlishaw:2003:DFP} says
                 that this is the first implementation of the Chen-Ho
                 \cite{Chen:1975:SER} compressed format, allowing
                 storage of 31 digits and 4 exponent digits in a 128-bit
                 value. More modern encodings get 34 digits in the same
                 number of bits, at somewhat reduced exponent range ($ [
                 - 6143, 6144] $).",
  treatment =    "P Practical; T Theoretical or Mathematical",
}


bibtype: techreport
filename: fparith.bib
label: Rosser:1976:CRE
author: J. Barkley Rosser and J. Michael Yohe
title: Cancellation and Rounding Errors
type: Technical Summary Report
number: 1588
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: 18--23
month: apr
monthnumber: 4
year: 1976
bibdate: Sun Dec 30 21:30:27 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.30 21:30:27 ???
acknowledgement: ack-nhfb
rawauthor: J. Barkley Rosser and J. Michael Yohe
rawtitle: Cancellation and Rounding Errors
abstract:
The fact that a calculating machine can usually hold only an approximation to the number that one is concerned with leads to cancellation errors and rounding errors. These concepts are defined precisely and examples are given. Suggestions are given for reducing (when possible) the size of errors arising from these two effects.

rawabstract:
The fact that a calculating machine can usually hold only an approximation to the number that one is concerned with leads to cancellation errors and rounding errors. These concepts are defined precisely and examples are given. Suggestions are given for reducing (when possible) the size of errors arising from these two effects.

entry:
@TechReport{Rosser:1976:CRE,
  author =       "J. Barkley Rosser and J. Michael Yohe",
  title =        "Cancellation and Rounding Errors",
  type =         "Technical Summary Report",
  number =       "1588",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        apr,
  year =         "1976",
  bibdate =      "Sun Dec 30 21:30:27 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The fact that a calculating machine can usually hold
                 only an approximation to the number that one is
                 concerned with leads to cancellation errors and
                 rounding errors. These concepts are defined precisely
                 and examples are given. Suggestions are given for
                 reducing (when possible) the size of errors arising
                 from these two effects.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Rowland:1976:BRB
author: John H. Rowland
title: Book Review: booktitle Floating-Point Computation (Pat H. Sterbenz)
journal: j-SIAM-REVIEW
volume: 18
number: 1
pages: 138--139
year: 1976
CODEN: SIREAD
DOI: https://doi.org/10.1137/1018026
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Sat Mar 29 09:52:30 MDT 2014
bibtimestamp: 2014.03.29 09:52:30 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1976
rawauthor: John H. Rowland
rawtitle: Book Review: {{\booktitle{Floating-Point Computation}} (Pat H. Sterbenz)}
bibsource:
http://epubs.siam.org/toc/siread/18/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Rowland:1976:BRB,
  author =       "John H. Rowland",
  title =        "Book Review: {{\booktitle{Floating-Point Computation}}
                 (Pat H. Sterbenz)}",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "1",
  pages =        "138--139",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1018026",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:52:30 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/18/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1976",
}


bibtype: article
filename: fparith.bib
label: Rudeanu:1976:SRF
author: S. Rudeanu
title: Square Roots and Functional Decompositions of Boolean Functions
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 5
pages: 528--532
month: may
monthnumber: 5
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674641
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:51 MDT 2011
bibtimestamp: 2011.07.12 06:24:51 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674641
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Rudeanu
rawtitle: Square Roots and Functional Decompositions of {Boolean} Functions
entry:
@Article{Rudeanu:1976:SRF,
  author =       "S. Rudeanu",
  title =        "Square Roots and Functional Decompositions of
                 {Boolean} Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "5",
  pages =        "528--532",
  month =        may,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674641",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674641",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: phdthesis
filename: fparith.bib
label: Sanderson:1976:PCT
author: James George Sanderson
title: A proof of convergence for the tridiagonal QL algorithm in floating-point arithmetic
type: Thesis (Ph.D.)
school: University of New Mexico
address: Albuquerque, NM, USA
pages: vi + 69
year: 1976
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: Algorithms.; Arithmetic --- Foundations.
acknowledgement: ack-nhfb
rawauthor: James George Sanderson
rawtitle: A proof of convergence for the tridiagonal {QL} algorithm in floating-point arithmetic
entry:
@PhdThesis{Sanderson:1976:PCT,
  author =       "James George Sanderson",
  title =        "A proof of convergence for the tridiagonal {QL}
                 algorithm in floating-point arithmetic",
  type =         "Thesis ({Ph.D.})",
  school =       "University of New Mexico",
  address =      "Albuquerque, NM, USA",
  pages =        "vi + 69",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Arithmetic --- Foundations.",
}


bibtype: article
filename: fparith.bib
label: Shi:1976:SLC
author: S.-Y. Shi
title: Shortcut to Logarithms Combines Table Lookup and Computation
journal: j-COMP-DESIGN
volume: 15
number: 5
pages: 184--186
month: may
monthnumber: 5
year: 1976
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
bibdate: Thu Sep 08 08:07:38 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:07:38 ???
fjournal: Computer Design
acknowledgement: ack-nj
rawauthor: S.-Y. Shi
rawtitle: Shortcut to Logarithms Combines Table Lookup and Computation
entry:
@Article{Shi:1976:SLC,
  author =       "S.-Y. Shi",
  title =        "Shortcut to Logarithms Combines Table Lookup and
                 Computation",
  journal =      j-COMP-DESIGN,
  volume =       "15",
  number =       "5",
  pages =        "184--186",
  month =        may,
  year =         "1976",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Thu Sep 08 08:07:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Design",
}


bibtype: phdthesis
filename: fparith.bib
label: Slekys:1976:DCN
author: Arunas George Slekys
title: Design of complex number digital arithmetic units based on a modified bi-imaginary number system
type: Ph.D. thesis
school: University of California, Los Angeles
address: Los Angeles, CA, USA
pages: 223
year: 1976
bibdate: Sat Aug 22 09:03:47 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 09:03:47 ???
remark: ProQuest order number AAI7707685.
acknowledgement: ack-nhfb
rawauthor: Arunas George Slekys
rawtitle: Design of complex number digital arithmetic units based on a modified bi-imaginary number system
entry:
@PhdThesis{Slekys:1976:DCN,
  author =       "Arunas George Slekys",
  title =        "Design of complex number digital arithmetic units
                 based on a modified bi-imaginary number system",
  type =         "{Ph.D. thesis}",
  school =       "University of California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "223",
  year =         "1976",
  bibdate =      "Sat Aug 22 09:03:47 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "ProQuest order number AAI7707685.",
}


bibtype: book
filename: fparith.bib
label: Spaniol:1976:AR
author: Otto Spaniol
publisher: pub-TEUBNER
address: pub-TEUBNER:adr
pages: 208
year: 1976
ISBN: 3-519-02332-6 OR 3519023326
ISBN13: 978-3-519-02332-6 OR 9783519023326
LCCN: QA76.6 .S66
bibdate: Fri Sep 16 16:30:39 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:39 ???
note: For an English translation, see cite Spaniol:1981:CAL.
acknowledgement: ack-nj
rawauthor: Otto Spaniol
rawnote: For an English translation, see \cite{Spaniol:1981:CAL}.
title:
Arithmetik in Rechenanlagen: Logik und Entwurf toenglish Computer Arithmetic: Logic and Design endtoenglish 

rawtitle:
{Arithmetik in Rechenanlagen: Logik und Entwurf} \toenglish {Computer Arithmetic: Logic and Design} \endtoenglish

entry:
@Book{Spaniol:1976:AR,
  author =       "Otto Spaniol",
  title =        "{Arithmetik in Rechenanlagen: Logik und Entwurf}
                 \toenglish {Computer Arithmetic: Logic and Design}
                 \endtoenglish",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  pages =        "208",
  year =         "1976",
  ISBN =         "3-519-02332-6",
  ISBN-13 =      "978-3-519-02332-6",
  LCCN =         "QA76.6 .S66",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "For an English translation, see
                 \cite{Spaniol:1981:CAL}.",
  price =        "DM24.80",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: fparith.bib
label: Warren:1976:MDT
author: H. S. Warren, Jr. and A. S. Fox and P. W. Markstein
title: Modulus Division on a Two's Complement Machine
type: Research Report
number: RC7712
institution: IBM
address: Yorktown Heights, NY, USA
pages: 208
month: jun
monthnumber: 6
year: 1976
bibdate: Fri Nov 09 19:32:44 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:32:44 ???
acknowledgement: ack-nhfb
rawauthor: H. S. {Warren, Jr.} and A. S. Fox and P. W. Markstein
rawtitle: Modulus Division on a Two's Complement Machine
entry:
@TechReport{Warren:1976:MDT,
  author =       "H. S. {Warren, Jr.} and A. S. Fox and P. W.
                 Markstein",
  title =        "Modulus Division on a Two's Complement Machine",
  type =         "Research Report",
  number =       "RC7712",
  institution =  "IBM",
  address =      "Yorktown Heights, NY, USA",
  month =        jun,
  year =         "1976",
  bibdate =      "Fri Nov 09 19:32:44 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Check: Waser/Flynn book dates this as 1979.",
}


bibtype: article
filename: fparith.bib
label: Wyatt:1976:PEP
author: W. T. Wyatt Jr. and D. W. Lozier and D. J. Orser
title: A Portable Extended Precision Arithmetic Package and Library With Fortran Precompiler
journal: j-TOMS
volume: 2
number: 3
pages: 209--231
month: sep
monthnumber: 9
year: 1976
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Sep 12 08:07:55 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 08:07:55 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1976-2-3/p209-lozier/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. T. {Wyatt Jr.} and D. W. Lozier and D. J. Orser
rawtitle: A Portable Extended Precision Arithmetic Package and Library With {Fortran} Precompiler
entry:
@Article{Wyatt:1976:PEP,
  author =       "W. T. {Wyatt Jr.} and D. W. Lozier and D. J. Orser",
  title =        "A Portable Extended Precision Arithmetic Package and
                 Library With {Fortran} Precompiler",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "209--231",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 12 08:07:55 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1976-2-3/p209-lozier/",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Yau:1976:DMA
author: S. S. Yau and J. Chung
title: On the Design of Modulo Arithmetic Units Based on Cyclic Groups
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 11
pages: 1057--1067
month: nov
monthnumber: 11
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674555
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:54 MDT 2011
bibtimestamp: 2011.07.12 06:24:54 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674555
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. S. Yau and J. Chung
rawtitle: On the Design of Modulo Arithmetic Units Based on Cyclic Groups
entry:
@Article{Yau:1976:DMA,
  author =       "S. S. Yau and J. Chung",
  title =        "On the Design of Modulo Arithmetic Units Based on
                 Cyclic Groups",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "11",
  pages =        "1057--1067",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674555",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674555",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Zohar:1976:RTR
author: S. Zohar
title: Rounding and Truncation in Radix (-2) Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 5
pages: 464--469
month: may
monthnumber: 5
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674634
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:51 MDT 2011
bibtimestamp: 2011.07.12 06:24:51 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674634
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Zohar
rawtitle: Rounding and Truncation in Radix (-2) Systems
entry:
@Article{Zohar:1976:RTR,
  author =       "S. Zohar",
  title =        "Rounding and Truncation in Radix (-2) Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "5",
  pages =        "464--469",
  month =        may,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674634",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674634",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Agrawal:1977:CNB
author: D. P. Agrawal
title: Comments on ``A Note on Base-$2$ Arithmetic Logic''
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 5
pages: 511--511
month: may
monthnumber: 5
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674869
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:54 MDT 2011
bibtimestamp: 2011.07.11 21:56:54 MDT
note: See cite Yuen:1975:NBA.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674869
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. P. Agrawal
rawnote: See \cite{Yuen:1975:NBA}.
rawtitle: Comments on {``A Note on Base-$2$ Arithmetic Logic''}
entry:
@Article{Agrawal:1977:CNB,
  author =       "D. P. Agrawal",
  title =        "Comments on {``A Note on Base-$2$ Arithmetic
                 Logic''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "5",
  pages =        "511--511",
  month =        may,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674869",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Yuen:1975:NBA}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674869",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


