# bibtab

bibtype: inproceedings
filename: fparith.bib
label: Trivedi:1978:HRL
author: Kishor S. Trivedi and Joseph G. Rusnak
title: Higher Radix On-Line Division
crossref: IEEE:1978:PSC
pages: 164--174
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Trivedi.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Kishor S. Trivedi and Joseph G. Rusnak
rawtitle: Higher Radix On-Line Division
abstract:
We present a formal proof of correctness of the on-line division algorithm specified in an earlier paper [1]. We also derive two radix 4 on-line division algorithms, with non-redundant and redundant operands respectively.

rawabstract:
We present a formal proof of correctness of the on-line division algorithm specified in an earlier paper [1]. We also derive two radix 4 on-line division algorithms, with non-redundant and redundant operands respectively.

entry:
@InProceedings{Trivedi:1978:HRL,
  author =       "Kishor S. Trivedi and Joseph G. Rusnak",
  title =        "Higher Radix On-Line Division",
  crossref =     "IEEE:1978:PSC",
  pages =        "164--174",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Trivedi.pdf",
  abstract =     "We present a formal proof of correctness of the
                 on-line division algorithm specified in an earlier
                 paper [1]. We also derive two radix 4 on-line division
                 algorithms, with non-redundant and redundant operands
                 respectively.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Tseng:1978:EAF
author: B. Tseng and W. Miller and G. Jullien and J. Soltis and A. Baraniecka
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '78
title: An error analysis of a FFT implementation using the residue number system
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 800--803
year: 1978
DOI: https://doi.org/10.1049/el:19780088
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: B. Tseng and W. Miller and G. Jullien and J. Soltis and A. Baraniecka
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '78}
rawtitle: An error analysis of a {FFT} implementation using the residue number system
entry:
@InProceedings{Tseng:1978:EAF,
  author =       "B. Tseng and W. Miller and G. Jullien and J. Soltis
                 and A. Baraniecka",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '78}",
  title =        "An error analysis of a {FFT} implementation using the
                 residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "800--803",
  year =         "1978",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19780088",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper considers an implementation of the FFT
                 based upon the residue number system. This system
                 offers the advantages of using integer based arithmetic
                 operations and a simple hardware realization involving
                 table look-up arrays. The proposed \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Wang:1978:EPF
author: J. Y. Wang
title: The Evaluation of Periodic Functions with Large Input Arguments
journal: j-SIGNUM
volume: 13
number: 4
pages: 7--9
month: dec
monthnumber: 12
year: 1978
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:15:56 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:56 ???
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: J. Y. Wang
rawtitle: The Evaluation of Periodic Functions with Large Input Arguments
entry:
@Article{Wang:1978:EPF,
  author =       "J. Y. Wang",
  title =        "The Evaluation of Periodic Functions with Large Input
                 Arguments",
  journal =      j-SIGNUM,
  volume =       "13",
  number =       "4",
  pages =        "7--9",
  month =        dec,
  year =         "1978",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: fparith.bib
label: Waser:1978:HMM
author: Shlomo Waser
title: High-speed monolithic multipliers for real-time digital signal processing
journal: j-COMPUTER
volume: 11
number: 10
pages: 19--29
month: oct
monthnumber: 10
year: 1978
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Thu Dec 12 07:20:54 MST 1996
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.12.12 07:20:54 MST
fjournal: Computer
keywords: signal processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
journalabr: Computer
rawauthor: Shlomo Waser
rawtitle: High-speed monolithic multipliers for real-time digital signal processing
abstract:
An analysis is made of arithmetic requirements for signal processing and monolithic multipliers are characterized. It is shown that real-time digital signal processing requires very fast multiplication, which is now becoming possible using mathematical techniques to take advantage of single-chip multipliers.

rawabstract:
An analysis is made of arithmetic requirements for signal processing and monolithic multipliers are characterized. It is shown that real-time digital signal processing requires very fast multiplication, which is now becoming possible using mathematical techniques to take advantage of single-chip multipliers.

entry:
@Article{Waser:1978:HMM,
  author =       "Shlomo Waser",
  title =        "High-speed monolithic multipliers for real-time
                 digital signal processing",
  journal =      j-COMPUTER,
  volume =       "11",
  number =       "10",
  pages =        "19--29",
  month =        oct,
  year =         "1978",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Dec 12 07:20:54 MST 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An analysis is made of arithmetic requirements for
                 signal processing and monolithic multipliers are
                 characterized. It is shown that real-time digital
                 signal processing requires very fast multiplication,
                 which is now becoming possible using mathematical
                 techniques to take advantage of single-chip
                 multipliers.",
  acknowledgement = ack-nhfb,
  classification = "713; 721; 723",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabr =   "Computer",
  keywords =     "signal processing",
}


bibtype: article
filename: fparith.bib
label: Waser:1978:SAH
author: S. Waser
title: State of the Art in High-Spped Arithmetic ICs
journal: j-COMP-DESIGN
pages: ??--??
month: jul
monthnumber: 7
year: 1978
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
bibdate: Fri Nov 09 19:34:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:34:34 ???
fjournal: Computer Design
acknowledgement: ack-nhfb
rawauthor: S. Waser
rawtitle: State of the Art in High-Spped Arithmetic {ICs}
entry:
@Article{Waser:1978:SAH,
  author =       "S. Waser",
  title =        "State of the Art in High-Spped Arithmetic {ICs}",
  journal =      j-COMP-DESIGN,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jul,
  year =         "1978",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Fri Nov 09 19:34:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Design",
}


bibtype: inproceedings
filename: fparith.bib
label: Waser:1978:SAI
author: Shlomo Waser
title: Survey of Arithmetic Integrated Circuits
crossref: IEEE:1978:PSC
pages: 257--266
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Waser.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Shlomo Waser
rawtitle: Survey of Arithmetic Integrated Circuits
abstract:
The purpose of this report is to provide the state-of-the-art of high performance arithmetic integrated circuits (ICs). The survey concentrates on arithmetic ICs that are designed to improve execution speed over software techniques, therefore, no calculator chips are surveyed.par In order to understand the difficulties encountered in fabricating high speed arithmetic ICs, we start the article with a discussion on semiconductor technology. Next, we survey the various arithmetic elements that are available in monolithic form: ALUs, Data Slices, Multipliers, Floating Point Processors, and ROMs. Finally, we conclude with a comment on digital signal processing and a discussion of the future trends in arithmetic ICs.

rawabstract:
The purpose of this report is to provide the state-of-the-art of high performance arithmetic integrated circuits (ICs). The survey concentrates on arithmetic ICs that are designed to improve execution speed over software techniques, therefore, no calculator chips are surveyed.\par In order to understand the difficulties encountered in fabricating high speed arithmetic ICs, we start the article with a discussion on semiconductor technology. Next, we survey the various arithmetic elements that are available in monolithic form: ALUs, Data Slices, Multipliers, Floating Point Processors, and ROMs. Finally, we conclude with a comment on digital signal processing and a discussion of the future trends in arithmetic ICs.

entry:
@InProceedings{Waser:1978:SAI,
  author =       "Shlomo Waser",
  title =        "Survey of Arithmetic Integrated Circuits",
  crossref =     "IEEE:1978:PSC",
  pages =        "257--266",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Waser.pdf",
  abstract =     "The purpose of this report is to provide the
                 state-of-the-art of high performance arithmetic
                 integrated circuits (ICs). The survey concentrates on
                 arithmetic ICs that are designed to improve execution
                 speed over software techniques, therefore, no
                 calculator chips are surveyed.\par

                 In order to understand the difficulties encountered in
                 fabricating high speed arithmetic ICs, we start the
                 article with a discussion on semiconductor technology.
                 Next, we survey the various arithmetic elements that
                 are available in monolithic form: ALUs, Data Slices,
                 Multipliers, Floating Point Processors, and ROMs.
                 Finally, we conclude with a comment on digital signal
                 processing and a discussion of the future trends in
                 arithmetic ICs.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Weinberger:1978:PAU
author: Arnold Weinberger
title: Parallel Adders Using Standard PLAs
crossref: IEEE:1978:PSC
pages: 116--124
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Weinberger.pdf
acknowledgement: ack-nhfb
rawauthor: Arnold Weinberger
rawtitle: Parallel Adders Using Standard {PLAs}
abstract:
PLA adders are described that add in one cycle and require a reasonable number of product terms for an 8, 16, or even a 32-bit adder. A procedure is also described for minimizing the number of product terms for any size adder.

keywords:
adder; ARITH-4; carry-look-ahead; input decoders; output exclusive-ors; product term minimization; Programmable Logic Array (PLA)

rawabstract:
PLA adders are described that add in one cycle and require a reasonable number of product terms for an 8, 16, or even a 32-bit adder. A procedure is also described for minimizing the number of product terms for any size adder.

entry:
@InProceedings{Weinberger:1978:PAU,
  author =       "Arnold Weinberger",
  title =        "Parallel Adders Using Standard {PLAs}",
  crossref =     "IEEE:1978:PSC",
  pages =        "116--124",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Weinberger.pdf",
  abstract =     "PLA adders are described that add in one cycle and
                 require a reasonable number of product terms for an 8,
                 16, or even a 32-bit adder. A procedure is also
                 described for minimizing the number of product terms
                 for any size adder.",
  acknowledgement = ack-nhfb,
  keywords =     "adder; ARITH-4; carry-look-ahead; input decoders;
                 output exclusive-ors; product term minimization;
                 Programmable Logic Array (PLA)",
}


bibtype: article
filename: fparith.bib
label: Wittmayer:1978:APP
author: W. R. Wittmayer
title: Array Processor Provides High Throughput Rate
journal: j-COMP-DESIGN
pages: 93--100
month: mar
monthnumber: 3
year: 1978
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
bibdate: Fri Nov 09 19:45:09 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:45:09 ???
fjournal: Computer Design
acknowledgement: ack-nhfb
rawauthor: W. R. Wittmayer
rawtitle: Array Processor Provides High Throughput Rate
entry:
@Article{Wittmayer:1978:APP,
  author =       "W. R. Wittmayer",
  title =        "Array Processor Provides High Throughput Rate",
  journal =      j-COMP-DESIGN,
  volume =       "??",
  number =       "??",
  pages =        "93--100",
  month =        mar,
  year =         "1978",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Fri Nov 09 19:45:09 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Design",
}


bibtype: article
filename: fparith.bib
label: Wozniakowski:1978:REA
author: H. Wozniakowski
title: Round-off error analysis of iterations for large linear systems
journal: j-NUM-MATH
volume: 30
number: 3
pages: 301--314
year: 1978
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Department of Computer Sci., Carnegie-Mellon University, Pittsburgh, PA, USA
journalURL: http://link.springer.com/journal/211
treatment: A Application; T Theoretical or Mathematical
rawauthor: H. Wo{\'z}niakowski
rawtitle: Round-off error analysis of iterations for large linear systems
keywords:
equations; error analysis; floating point arithmetic; Gauss Seidel iteration; iteration round off error analysis; iterative methods; residual vector; sparse linear systems

entry:
@Article{Wozniakowski:1978:REA,
  author =       "H. Wo{\'z}niakowski",
  title =        "Round-off error analysis of iterations for large
                 linear systems",
  journal =      j-NUM-MATH,
  volume =       "30",
  number =       "3",
  pages =        "301--314",
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Department of Computer Sci., Carnegie-Mellon
                 University, Pittsburgh, PA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "equations; error analysis; floating point arithmetic;
                 Gauss Seidel iteration; iteration round off error
                 analysis; iterative methods; residual vector; sparse
                 linear systems",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Wrathall:1978:CGI
author: Celia Wrathall and Tien Chi Chen
crossref: IEEE:1978:PSC
pages: 175--182
year: 1978
bibdate: Thu Sep 01 11:46:12 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 11:46:12 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Wrathall.pdf
keywords: ARITH-4
acknowledgement: ack-nj
rawauthor: Celia Wrathall and Tien Chi Chen
title:
Convergence Guarantee and Improvements for a fast Hardware Exponential and Logarithm Evaluation Scheme

abstract:
In one iteration, Chen's algorithm for evaluating exponentials and logarithms advances by 2 bits on the average, yet may not advance at all. Analysis reveals that the no-advance situation actually paves the way for sizable advance in the next iteration, and the guaranteed advance, after a one iteration overhead, is one bit per iteration.par Two new schemes raise the guaranteed advance to 1.5 bits per iteration, after a two-iteration overhead, while maintaining the original requirement of one stored constant per operand bit.par Adopting as a figure of merit the following quantitypar $$ Q = textrm advance per iteration over textrm memory words per operand hit $$ par for the steady-state iterations, the new schemes appears to be better than other methods heretofore proposed.

rawabstract:
In one iteration, Chen's algorithm for evaluating exponentials and logarithms advances by 2 bits on the average, yet may not advance at all. Analysis reveals that the no-advance situation actually paves the way for sizable advance in the next iteration, and the guaranteed advance, after a one iteration overhead, is one bit per iteration.\par Two new schemes raise the guaranteed advance to 1.5 bits per iteration, after a two-iteration overhead, while maintaining the original requirement of one stored constant per operand bit.\par Adopting as a figure of merit the following quantity\par $$ Q = \textrm {advance per iteration} \over \textrm {memory words per operand hit} $$ \par for the steady-state iterations, the new schemes appears to be better than other methods heretofore proposed.

rawtitle:
Convergence Guarantee and Improvements for a fast Hardware Exponential and Logarithm Evaluation Scheme

entry:
@InProceedings{Wrathall:1978:CGI,
  author =       "Celia Wrathall and Tien Chi Chen",
  title =        "Convergence Guarantee and Improvements for a fast
                 Hardware Exponential and Logarithm Evaluation Scheme",
  crossref =     "IEEE:1978:PSC",
  pages =        "175--182",
  year =         "1978",
  bibdate =      "Thu Sep 01 11:46:12 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/arith4/papers/ARITH4_Wrathall.pdf",
  abstract =     "In one iteration, Chen's algorithm for evaluating
                 exponentials and logarithms advances by 2 bits on the
                 average, yet may not advance at all. Analysis reveals
                 that the no-advance situation actually paves the way
                 for sizable advance in the next iteration, and the
                 guaranteed advance, after a one iteration overhead, is
                 one bit per iteration.\par

                 Two new schemes raise the guaranteed advance to 1.5
                 bits per iteration, after a two-iteration overhead,
                 while maintaining the original requirement of one
                 stored constant per operand bit.\par

                 Adopting as a figure of merit the following
                 quantity\par

                  $$ Q = \textrm {advance per iteration} \over \textrm
                 {memory words per operand hit} $$ \par

                 for the steady-state iterations, the new schemes
                 appears to be better than other methods heretofore
                 proposed.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4",
}


bibtype: article
filename: fparith.bib
label: Abu-El-Haija:1979:AER
author: A. Abu-El-Haija and A. Peterson
title: An approach to eliminate roundoff errors in digital filters
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 27
number: 2
pages: 195--198
month: apr
monthnumber: 4
year: 1979
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
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: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: A. Abu-El-Haija and A. Peterson
rawtitle: An approach to eliminate roundoff errors in digital filters
entry:
@Article{Abu-El-Haija:1979:AER,
  author =       "A. Abu-El-Haija and A. Peterson",
  title =        "An approach to eliminate roundoff errors in digital
                 filters",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "27",
  number =       "2",
  pages =        "195--198",
  month =        apr,
  year =         "1979",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 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 =      "``Second-order quantizers'' are introduced which can
                 be used for implementing recursive digital filters with
                 practically no roundoff errors or limit-cycle
                 oscillations. Based on the idea of changing the
                 transfer function used to compute roundoff \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Aggarwal:1979:REM
author: Vijay B. Aggarwal and James W. Burgmeier
title: A round-off error model with applications to arithmetic expressions
journal: j-SIAM-J-COMPUT
volume: 8
number: 1
pages: 60--72
year: 1979
CODEN: SMJCAT
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
MRclass: 68C01 (65G05)
MRnumber: 81b:68031
bibdate: Mon Nov 29 10:58:59 MST 2010
bibtimestamp: 2010.11.29 10:58:59 MST
fjournal: SIAM Journal on Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
rawauthor: Vijay B. Aggarwal and James W. Burgmeier
rawtitle: A round-off error model with applications to arithmetic expressions
bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Aggarwal:1979:REM,
  author =       "Vijay B. Aggarwal and James W. Burgmeier",
  title =        "A round-off error model with applications to
                 arithmetic expressions",
  journal =      j-SIAM-J-COMPUT,
  volume =       "8",
  number =       "1",
  pages =        "60--72",
  month =        "????",
  year =         "1979",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68C01 (65G05)",
  MRnumber =     "81b:68031",
  bibdate =      "Mon Nov 29 10:58:59 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}


bibtype: article
filename: fparith.bib
label: Agrawal:1979:HSA
author: D. P. Agrawal
title: High-Speed Arithmetic Arrays
journal: j-IEEE-TRANS-COMPUT
volume: C-28
number: 3
pages: 215--224
month: mar
monthnumber: 3
year: 1979
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1979.1675322
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 06:49:36 MDT 2011
bibtimestamp: 2011.07.11 06:49:36 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675322
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
rawtitle: High-Speed Arithmetic Arrays
entry:
@Article{Agrawal:1979:HSA,
  author =       "D. P. Agrawal",
  title =        "High-Speed Arithmetic Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "3",
  pages =        "215--224",
  month =        mar,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675322",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:36 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=1675322",
  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: Alt:1979:SRD
author: H. Alt
title: Square Rooting Is as Difficult as Multiplication
journal: j-COMPUTING
volume: 21
number: 3
pages: 221--232
year: 1979
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 68C25
MRnumber: 82m:68081
bibdate: Tue Jan 2 17:40:54 MST 2001
bibtimestamp: 2001.01.02 17:40:54 MST
fjournal: Computing: Archiv fur informatik und numerik
keywords: algorithm; computer programming; square rooting
acknowledgement: ack-nj
affiliation: Math. & Information, University of Saarlandes, Saarbrucken, West Germany
journalURL: http://link.springer.com/journal/607
journalabr: Computing (Vienna/New York)
rawauthor: H. Alt
rawtitle: Square Rooting Is as Difficult as Multiplication
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); MathSciNet database

entry:
@Article{Alt:1979:SRD,
  author =       "H. Alt",
  title =        "Square Rooting Is as Difficult as Multiplication",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  year =         "1979",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68C25",
  MRnumber =     "82m:68081",
  bibdate =      "Tue Jan 2 17:40:54 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); MathSciNet
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Math. \& Information, University of Saarlandes,
                 Saarbrucken, West Germany",
  classification = "723; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "algorithm; computer programming; square rooting",
}


bibtype: article
filename: fparith.bib
label: Atkins:1979:FSC
author: D. E. Atkins
title: Fourth Symposium on Computer Arithmetic: crunching with quality and LSI
journal: j-COMPUTER
volume: 12
number: 4
pages: 94--97
month: apr
monthnumber: 4
year: 1979
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Thu Dec 12 07:20:54 MST 1996
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.12.12 07:20:54 MST
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
journalabr: Computer
rawauthor: D. E. Atkins
rawtitle: {Fourth Symposium on Computer Arithmetic}: crunching with quality and {LSI}
abstract:
Computer arithmetic problems --- faster computation rates and more efficient representations of real numbers --- are considered in the paper. Floating-point arithmetic standardization, novel implementation of basic arithmetic operators, evaluation of elementary functions --- these are the main considerations of the conference review.

keywords:
computer arithmetic; computer systems, digital; data processing --- data description; mathematical techniques --- digital arithmetic

rawabstract:
Computer arithmetic problems --- faster computation rates and more efficient representations of real numbers --- are considered in the paper. Floating-point arithmetic standardization, novel implementation of basic arithmetic operators, evaluation of elementary functions --- these are the main considerations of the conference review.

entry:
@Article{Atkins:1979:FSC,
  author =       "D. E. Atkins",
  title =        "{Fourth Symposium on Computer Arithmetic}: crunching
                 with quality and {LSI}",
  journal =      j-COMPUTER,
  volume =       "12",
  number =       "4",
  pages =        "94--97",
  month =        apr,
  year =         "1979",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Dec 12 07:20:54 MST 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Computer arithmetic problems --- faster computation
                 rates and more efficient representations of real
                 numbers --- are considered in the paper. Floating-point
                 arithmetic standardization, novel implementation of
                 basic arithmetic operators, evaluation of elementary
                 functions --- these are the main considerations of the
                 conference review.",
  acknowledgement = ack-nhfb,
  classification = "722; 723",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabr =   "Computer",
  keywords =     "computer arithmetic; computer systems, digital; data
                 processing --- data description; mathematical
                 techniques --- digital arithmetic",
}


bibtype: mastersthesis
filename: fparith.bib
label: Barlow:1979:PEA
author: Jesse Louis Barlow
title: Probabilistic error analysis of computer arithmetics
type: M.S. (Computer Science)
school: Northwestern University
address: Evanston, IL, USA
year: 1979
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: Jesse Louis Barlow
rawtitle: Probabilistic error analysis of computer arithmetics
keywords:
Electronic digital computers --- Programming.; Floating-point arithmetic.; Numbers, Real.; Numerical calculations --- Computer programs.

entry:
@MastersThesis{Barlow:1979:PEA,
  author =       "Jesse Louis Barlow",
  title =        "Probabilistic error analysis of computer arithmetics",
  type =         "{M.S. (Computer Science)}",
  school =       "Northwestern University",
  address =      "Evanston, IL, USA",
  pages =        "????",
  year =         "1979",
  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.; Numbers, Real.; Numerical
                 calculations --- Computer programs.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Biddulph:1979:MFC
author: Thomas P. Biddulph
type: Master of Science, Plan II
school: Department of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
year: 1979
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: Thomas P. Biddulph
title:
A modified FORTRAN / 77 compiler that will implement the proposed IEEE / KCS floating point standard via calls to emulation routines

rawtitle:
A modified {FORTRAN\slash 77} compiler that will implement the proposed {IEEE\slash KCS} floating point standard via calls to emulation routines

entry:
@MastersThesis{Biddulph:1979:MFC,
  author =       "Thomas P. Biddulph",
  title =        "A modified {FORTRAN\slash 77} compiler that will
                 implement the proposed {IEEE\slash KCS} floating point
                 standard via calls to emulation routines",
  type =         "{Master of Science, Plan II}",
  school =       "Department of Electrical Engineering and Computer
                 Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "????",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Brent:1979:RLP
author: R. P. Brent and H. T. Kung
title: A regular layout for parallel adders
institution: Computer Science Department, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 20
year: 1979
bibdate: Thu Nov 18 09:31:44 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:31:44 ???
URL: http://books.google.com/books?id=mutgGwAACAAJ
acknowledgement: ack-nhfb
rawauthor: R. P. Brent and H. T. Kung
rawtitle: A regular layout for parallel adders
abstract:
With VLSI architecture the chip area is a better measure of cost than the conventional gate count. We show that addition of n-bit binary numbers can be performed on a chip in time proportional to $ log n $ and with area proportional to $ n log n $.

rawabstract:
With VLSI architecture the chip area is a better measure of cost than the conventional gate count. We show that addition of n-bit binary numbers can be performed on a chip in time proportional to $ \log n $ and with area proportional to $ n \log n $.

entry:
@TechReport{Brent:1979:RLP,
  author =       "R. P. Brent and H. T. Kung",
  title =        "A regular layout for parallel adders",
  institution =  "Computer Science Department, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "20",
  year =         "1979",
  bibdate =      "Thu Nov 18 09:31:44 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://books.google.com/books?id=mutgGwAACAAJ",
  abstract =     "With VLSI architecture the chip area is a better
                 measure of cost than the conventional gate count. We
                 show that addition of n-bit binary numbers can be
                 performed on a chip in time proportional to $ \log n $
                 and with area proportional to $ n \log n $.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Brent:1979:RMF
author: R. P. Brent
title: Remark on ``Algorithm 524: MP, A Fortran Multiple-Precision Arithmetic Package [A1]''
journal: j-TOMS
volume: 5
number: 4
pages: 518--519
month: dec
monthnumber: 12
year: 1979
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355853.355868
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Sep 05 22:49:18 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.05 22:49:18 ???
note: See cite Brent:1978:AMF,Brent:1980:AIB.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: R. P. Brent
rawnote: See \cite{Brent:1978:AMF,Brent:1980:AIB}.
rawtitle: Remark on ``{Algorithm} 524: {MP}, {A Fortran} Multiple-Precision Arithmetic Package [{A1}]''
entry:
@Article{Brent:1979:RMF,
  author =       "R. P. Brent",
  title =        "Remark on ``{Algorithm} 524: {MP}, {A Fortran}
                 Multiple-Precision Arithmetic Package [{A1}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "518--519",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355868",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 22:49:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Brent:1978:AMF,Brent:1980:AIB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: fparith.bib
label: Brown:1979:EPB
author: W. S. Brown and S. I. Feldman
title: Environment parameters and basic functions for floating-point computation
crossref: ACM:1979:PSC
pages: 42--45
year: 1979
bibdate: Fri Nov 28 17:31:00 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:31:00 ???
acknowledgement: ack-nhfb
rawauthor: W. S. Brown and S. I. Feldman
rawtitle: Environment parameters and basic functions for floating-point computation
entry:
@InProceedings{Brown:1979:EPB,
  author =       "W. S. Brown and S. I. Feldman",
  title =        "Environment parameters and basic functions for
                 floating-point computation",
  crossref =     "ACM:1979:PSC",
  pages =        "42--45",
  year =         "1979",
  bibdate =      "Fri Nov 28 17:31:00 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Bustoz:1979:ITD
author: Joaquin Bustoz and Alan Feldstein and Richard Goodman and Seppo Linnainmaa
title: Improved Trailing Digits Estimates Applied to Optimal Computer Arithmetic
journal: j-J-ACM
volume: 26
number: 4
pages: 716--730
month: oct
monthnumber: 10
year: 1979
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Wed Oct 26 23:35:40 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.10.26 23:35:40 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Joaqu{\'i}n Bustoz and Alan Feldstein and Richard Goodman and Seppo Linnainmaa
rawtitle: Improved Trailing Digits Estimates Applied to Optimal Computer Arithmetic
abstract:
New results are given on the distribution of trailing digits for logarithmically distributed numbers and on error in floating-point multiplication. Some of the results have application to computer design. In particular, there are certain values of the base (indeed, $ beta = 2, 4, 6 $, and sometimes, $8$, but em not $ 16 $) which, when carefully balanced with other design parameters, minimize the mean multiplicative error. For these special minimizing situations, it suffices to have only one guard $ beta $ it provided that postnormalization occurs after symmetric rounding.

keywords:
computer arithmetic; floating-point multiplication; floating-point numbers; floating-point precision and significance; fraction error; guard digits; logarithmically distributed numbers; mean and standard deviation of error; nonleading digits; normalization options; roundoff error; trailing digits; uniformly distributed numbers

rawabstract:
New results are given on the distribution of trailing digits for logarithmically distributed numbers and on error in floating-point multiplication. Some of the results have application to computer design. In particular, there are certain values of the base (indeed, $ \beta = 2, 4, 6 $, and sometimes, $8$, but {\em not} $ 16 $) which, when carefully balanced with other design parameters, minimize the mean multiplicative error. For these special minimizing situations, it suffices to have only one guard $ \beta $ it provided that postnormalization occurs after symmetric rounding.

entry:
@Article{Bustoz:1979:ITD,
  author =       "Joaqu{\'i}n Bustoz and Alan Feldstein and Richard
                 Goodman and Seppo Linnainmaa",
  title =        "Improved Trailing Digits Estimates Applied to Optimal
                 Computer Arithmetic",
  journal =      j-J-ACM,
  volume =       "26",
  number =       "4",
  pages =        "716--730",
  month =        oct,
  year =         "1979",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Oct 26 23:35:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "New results are given on the distribution of trailing
                 digits for logarithmically distributed numbers and on
                 error in floating-point multiplication. Some of the
                 results have application to computer design. In
                 particular, there are certain values of the base
                 (indeed, $ \beta = 2, 4, 6 $, and sometimes, $8$, but
                 {\em not} $ 16 $) which, when carefully balanced with
                 other design parameters, minimize the mean
                 multiplicative error. For these special minimizing
                 situations, it suffices to have only one guard $ \beta
                 $ it provided that postnormalization occurs after
                 symmetric rounding.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "computer arithmetic; floating-point multiplication;
                 floating-point numbers; floating-point precision and
                 significance; fraction error; guard digits;
                 logarithmically distributed numbers; mean and standard
                 deviation of error; nonleading digits; normalization
                 options; roundoff error; trailing digits; uniformly
                 distributed numbers",
}


bibtype: article
filename: fparith.bib
label: Chen:1979:PMB
author: I-Ngo Chen and R. Willoner
title: An $ O(n) $ Parallel Multiplier with Bit-Sequential Input and Output
journal: j-IEEE-TRANS-COMPUT
volume: C-28
number: 10
pages: 721--727
month: oct
monthnumber: 10
year: 1979
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1979.1675239
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 06:49:41 MDT 2011
bibtimestamp: 2011.07.11 06:49:41 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675239
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: I-Ngo Chen and R. Willoner
rawtitle: An {$ O(n) $} Parallel Multiplier with Bit-Sequential Input and Output
entry:
@Article{Chen:1979:PMB,
  author =       "I-Ngo Chen and R. Willoner",
  title =        "An {$ O(n) $} Parallel Multiplier with Bit-Sequential
                 Input and Output",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "10",
  pages =        "721--727",
  month =        oct,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675239",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:41 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=1675239",
  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: Cody:1979:IPI
author: W. J. Cody
title: Impact of The Proposed IEEE Floating Point Standard on Numerical Software
journal: j-SIGNUM
volume: 14
number: 3S (Special issue)
pages: 29--30
month: oct
monthnumber: 10
year: 1979
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:07 MDT 2005
bibtimestamp: 2005.04.12 07:50:07 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
classcodes: C4100 (Numerical analysis); C5230 (Digital arithmetic methods); C7310 (Mathematics computing)
corpsource: Appl. Math. Div., Argonne Nat. Lab., Argonne, IL, USA
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical
rawauthor: W. J. Cody
rawtitle: Impact of The Proposed {IEEE} Floating Point Standard on Numerical Software
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
digital arithmetic; floating point; IEEE; numerical analysis; numerical software; standard; standards

entry:
@Article{Cody:1979:IPI,
  author =       "W. J. Cody",
  title =        "Impact of The Proposed {IEEE} Floating Point Standard
                 on Numerical Software",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "29--30",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C4100 (Numerical analysis); C5230 (Digital arithmetic
                 methods); C7310 (Mathematics computing)",
  corpsource =   "Appl. Math. Div., Argonne Nat. Lab., Argonne, IL,
                 USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "digital arithmetic; floating point; IEEE; numerical
                 analysis; numerical software; standard; standards",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}


bibtype: article
filename: fparith.bib
label: Coonen:1979:PSB
author: Jerome Coonen and William Kahan and John Palmer and Tom Pittman and David Stevenson
title: A Proposed Standard for Binary Floating Point Arithmetic: Draft 5.11
journal: j-SIGNUM
volume: 14
number: 3S (Special issue)
pages: 4--12
month: oct
monthnumber: 10
year: 1979
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1057520.1057521
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:07 MDT 2005
bibtimestamp: 2005.04.12 07:50:07 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical
rawauthor: Jerome Coonen and William Kahan and John Palmer and Tom Pittman and David Stevenson
rawtitle: A Proposed Standard for Binary Floating Point Arithmetic: Draft 5.11
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib

keywords:
arithmetic; binary; digital arithmetic; floating point; IEEE Computer Society; Microprocessor; standard; standards; Standards Subcommittee

entry:
@Article{Coonen:1979:PSB,
  author =       "Jerome Coonen and William Kahan and John Palmer and
                 Tom Pittman and David Stevenson",
  title =        "A Proposed Standard for Binary Floating Point
                 Arithmetic: Draft 5.11",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "4--12",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057520.1057521",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic; binary; digital arithmetic; floating
                 point; IEEE Computer Society; Microprocessor; standard;
                 standards; Standards Subcommittee",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}


bibtype: techreport
filename: fparith.bib
label: Coonen:1979:SPS
author: Jerome T. Coonen
title: Specifications for a Proposed Standard for Floating-Point Arithmetic
type: Memorandum
number: {UCB\slash ERL M78\slash 72}
institution: University of California, Berkeley
address: Berkeley, CA, USA
pages: 4--12
day: 25
month: jan
monthnumber: 1
year: 1979
bibdate: Mon Dec 24 08:33:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 08:33:07 ???
acknowledgement: ack-nhfb
rawauthor: Jerome T. Coonen
rawtitle: Specifications for a Proposed Standard for Floating-Point Arithmetic
entry:
@TechReport{Coonen:1979:SPS,
  author =       "Jerome T. Coonen",
  title =        "Specifications for a Proposed Standard for
                 Floating-Point Arithmetic",
  type =         "Memorandum",
  number =       "{UCB\slash ERL M78\slash 72}",
  institution =  "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "25",
  month =        jan,
  year =         "1979",
  bibdate =      "Mon Dec 24 08:33:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Cybenko:1979:REP
author: G. Cybenko
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '79
title: Round-off error propagation in Durbin's, Levinson's, and Trench's algorithms
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 498--501
year: 1979
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: G. Cybenko
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '79}
rawtitle: Round-off error propagation in {Durbin}'s, {Levinson}'s, and {Trench}'s algorithms
entry:
@InProceedings{Cybenko:1979:REP,
  author =       "G. Cybenko",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '79}",
  title =        "Round-off error propagation in {Durbin}'s,
                 {Levinson}'s, and {Trench}'s algorithms",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "498--501",
  year =         "1979",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The subject matter of this paper concerns the
                 round-off error propagation in order $n^2$ algorithms
                 for solving problems involving Toeplitz matrices. Since
                 linear predictive techniques owe much of their appeal
                 to the computational efficiency \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Diaconis:1979:RP
author: Persi Diaconis and David Freedman
title: On Rounding Percentages
journal: j-J-AM-STAT-ASSOC
volume: 74
number: 366
pages: 359--364
month: jun
monthnumber: 6
year: 1979
CODEN: JSTNAL
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
bibdate: Wed Nov 23 11:24:59 2011
bibtimestamp: 2011.11.23 11:24:59 ???
URL: http://www.jstor.org/stable/2284288
fjournal: Journal of the American Statistical Association
keywords: Benford's Law; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uasa20
rawauthor: Persi Diaconis and David Freedman
rawtitle: On Rounding Percentages
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib; 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/jamstatassoc.bib

note:
The authors extend prior work on correctness of sums of rounded percentages cite Mosteller:1967:DSR, and criticize biased rounding practices in cite Benford:1938:LAN.

remark:
When percentage-column entries are rounded, their sum may differ from 100%. The authors use a prior proof cite Mosteller:1967:DSR that for $ n gg 2 $ rounded values, the probability of a correct sum is $ sqrt 6 / (pi n) approx 1.382 / sqrt n $. They show that rounding may produce large changes in computed chi-squared values, and they conclude their article with this recommendation: ``it is important to calculate with many-digit accuracy when computing $ chi ^2 $ for large sample sizes.''

rawnote:
The authors extend prior work on correctness of sums of rounded percentages \cite{Mosteller:1967:DSR}, and criticize biased rounding practices in \cite{Benford:1938:LAN}.

entry:
@Article{Diaconis:1979:RP,
  author =       "Persi Diaconis and David Freedman",
  title =        "On Rounding Percentages",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "74",
  number =       "366",
  pages =        "359--364",
  month =        jun,
  year =         "1979",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Nov 23 11:24:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 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/jamstatassoc.bib",
  note =         "The authors extend prior work on correctness of sums
                 of rounded percentages \cite{Mosteller:1967:DSR}, and
                 criticize biased rounding practices in
                 \cite{Benford:1938:LAN}.",
  URL =          "http://www.jstor.org/stable/2284288",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "Benford's Law; correct rounding; floating-point
                 arithmetic",
  remark =       "When percentage-column entries are rounded, their sum
                 may differ from 100\%. The authors use a prior proof
                 \cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded
                 values, the probability of a correct sum is $ \sqrt {6
                 / (\pi n)} \approx 1.382 / \sqrt {n} $. They show that
                 rounding may produce large changes in computed
                 chi-squared values, and they conclude their article
                 with this recommendation: ``it is important to
                 calculate with many-digit accuracy when computing $
                 \chi^2 $ for large sample sizes.''",
}


bibtype: article
filename: fparith.bib
label: Edgar:1979:FMN
author: Albert D. Edgar and Samuel C. Lee
title: FOCUS Microcomputer Number System
journal: j-CACM
volume: 22
number: 3
pages: 166--177
month: mar
monthnumber: 3
year: 1979
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:37:26 MST 2001
bibtimestamp: 2001.01.22 06:37:26 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods); C5250 (Microcomputer techniques)
corpsource: University of Oklahoma, Norman, OK, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
treatment: P Practical
rawauthor: Albert D. Edgar and Samuel C. Lee
rawtitle: {FOCUS} Microcomputer Number System
bibsource:
Compendex database; http://dblp.uni-trier.de/db/journals/cacm/cacm22.html#EdgarL79; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
FOCUS is a number system and supporting computational algorithms especially useful for microcomputer control and other signal processing applications. FOCUS has the wide-ranging character of floating-point numbers with a uniformity of state distributions that give FOCUS better than a twofold accuracy advantage over an equal word length floating-point system. FOCUS computations are typically five times faster than single precision fixed-point or integer arithmetic for a mixture of operations, comparable in speed with hardware arithmetic for many applications. Algorithms for 8-bit and 16-bit implementations of FOCUS are included.

keywords:
algorithms; arithmetic; computational; computers, microprocessor; digital arithmetic; floating point numbers; FOCUS; microcomputer; microcomputer control; microcomputers; number system; signal processing

rawabstract:
FOCUS is a number system and supporting computational algorithms especially useful for microcomputer control and other signal processing applications. FOCUS has the wide-ranging character of floating-point numbers with a uniformity of state distributions that give FOCUS better than a twofold accuracy advantage over an equal word length floating-point system. FOCUS computations are typically five times faster than single precision fixed-point or integer arithmetic for a mixture of operations, comparable in speed with hardware arithmetic for many applications. Algorithms for 8-bit and 16-bit implementations of FOCUS are included.

entry:
@Article{Edgar:1979:FMN,
  author =       "Albert D. Edgar and Samuel C. Lee",
  title =        "{FOCUS} Microcomputer Number System",
  journal =      j-CACM,
  volume =       "22",
  number =       "3",
  pages =        "166--177",
  month =        mar,
  year =         "1979",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:37:26 MST 2001",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm22.html#EdgarL79;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "FOCUS is a number system and supporting computational
                 algorithms especially useful for microcomputer control
                 and other signal processing applications. FOCUS has the
                 wide-ranging character of floating-point numbers with a
                 uniformity of state distributions that give FOCUS
                 better than a twofold accuracy advantage over an equal
                 word length floating-point system. FOCUS computations
                 are typically five times faster than single precision
                 fixed-point or integer arithmetic for a mixture of
                 operations, comparable in speed with hardware
                 arithmetic for many applications. Algorithms for 8-bit
                 and 16-bit implementations of FOCUS are included.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C5250
                 (Microcomputer techniques)",
  classification = "723",
  corpsource =   "University of Oklahoma, Norman, OK, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "algorithms; arithmetic; computational; computers,
                 microprocessor; digital arithmetic; floating point
                 numbers; FOCUS; microcomputer; microcomputer control;
                 microcomputers; number system; signal processing",
  oldlabel =     "EdgarL79",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/EdgarL79",
}


bibtype: inproceedings
filename: fparith.bib
label: Eggers:1979:HFP
author: Thomas W. Eggers and Judson S. Leonard and Mary H. Payne
title: Handling of floating point exceptions
crossref: ACM:1979:PSC
pages: 100--108
year: 1979
bibdate: Fri Nov 28 17:31:00 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:31:00 ???
acknowledgement: ack-nhfb
rawauthor: Thomas W. Eggers and Judson S. Leonard and Mary H. Payne
rawtitle: Handling of floating point exceptions
entry:
@InProceedings{Eggers:1979:HFP,
  author =       "Thomas W. Eggers and Judson S. Leonard and Mary H.
                 Payne",
  title =        "Handling of floating point exceptions",
  crossref =     "ACM:1979:PSC",
  pages =        "100--108",
  year =         "1979",
  bibdate =      "Fri Nov 28 17:31:00 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Feldman:1979:IPS
author: Stuart I. Feldman
title: The Impact of the Proposed Standard for Floating Point Arithmetic on Languages and Systems
journal: j-SIGNUM
volume: 14
number: 3S (Special issue)
pages: 31--32
month: oct
monthnumber: 10
year: 1979
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:07 MDT 2005
bibtimestamp: 2005.04.12 07:50:07 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods); C6140D (High level languages)
corpsource: Bell Labs., Murray Hill, NJ, USA
journalURL: https://dl.acm.org/loi/signum
rawauthor: Stuart I. Feldman
rawtitle: The Impact of the Proposed Standard for Floating Point Arithmetic on Languages and Systems
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
arithmetic; digital arithmetic; floating point; languages; programming languages; proposed; standard; standards; systems

entry:
@Article{Feldman:1979:IPS,
  author =       "Stuart I. Feldman",
  title =        "The Impact of the Proposed Standard for Floating Point
                 Arithmetic on Languages and Systems",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "31--32",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods); C6140D (High level
                 languages)",
  corpsource =   "Bell Labs., Murray Hill, NJ, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic; digital arithmetic; floating point;
                 languages; programming languages; proposed; standard;
                 standards; systems",
  xxnumber =     "si-2",
}


bibtype: mastersthesis
filename: fparith.bib
label: Fogler:1979:BFP
author: Robert Joseph Fogler
title: On a block floating point implementation of an intrusion-detection algorithm
type: Thesis (M.S.)
school: Kansas State University
address: Manhattan, KS, USA
pages: 71
year: 1979
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 alarm systems.; Signal processing.
acknowledgement: ack-nhfb
rawauthor: Robert Joseph Fogler
rawtitle: On a block floating point implementation of an intrusion-detection algorithm
entry:
@MastersThesis{Fogler:1979:BFP,
  author =       "Robert Joseph Fogler",
  title =        "On a block floating point implementation of an
                 intrusion-detection algorithm",
  type =         "Thesis ({M.S.})",
  school =       "Kansas State University",
  address =      "Manhattan, KS, USA",
  pages =        "71",
  year =         "1979",
  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 alarm systems.; Signal processing.",
}


bibtype: article
filename: fparith.bib
label: Fox:1979:RFP
author: Phyllis Fox
title: Remark on ``Algorithm 528: Framework for a Portable Library [Z]''
journal: j-TOMS
volume: 5
number: 4
pages: 524--524
month: dec
monthnumber: 12
year: 1979
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355853.355871
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Aug 30 00:28:06 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.30 00:28:06 ???
note: See cite Fox:1978:AFP.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Phyllis Fox
rawnote: See \cite{Fox:1978:AFP}.
rawtitle: Remark on ``{Algorithm} 528: Framework for a Portable Library [{Z}]''
entry:
@Article{Fox:1979:RFP,
  author =       "Phyllis Fox",
  title =        "Remark on ``{Algorithm} 528: Framework for a Portable
                 Library [{Z}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "524--524",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355871",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fox:1978:AFP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Fraley:1979:PED
author: Bob Fraley and Steve Walther
title: Proposal to Eliminate Denormalized Numbers
journal: j-SIGNUM
volume: 14
number: 3S (Special issue)
pages: 22--23
month: oct
monthnumber: 10
year: 1979
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:07 MDT 2005
bibtimestamp: 2005.04.12 07:50:07 MDT
fjournal: ACM SIGNUM Newsletter
keywords: denormalized numbers; digital arithmetic; expense; floating point
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Hewlett--Packard Labs., Palo Alto, CA, USA
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical
rawauthor: Bob Fraley and Steve Walther
rawtitle: Proposal to Eliminate Denormalized Numbers
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Fraley:1979:PED,
  author =       "Bob Fraley and Steve Walther",
  title =        "Proposal to Eliminate Denormalized Numbers",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "22--23",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Hewlett--Packard Labs., Palo Alto, CA, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "denormalized numbers; digital arithmetic; expense;
                 floating point",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}


bibtype: article
filename: fparith.bib
label: Gargantini:1979:NSS
author: Irene Gargantini
title: The Numerical Stability of Simultaneous Iterations Via Square-Rooting
journal: j-COMPUT-MATH-APPL
volume: 5
number: 1
pages: 25--31
year: 1979
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(81)90136-X
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:16 MST 2017
bibtimestamp: 2017.03.01 18:51:16 MST
URL: http://www.sciencedirect.com/science/article/pii/089812218190136X
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-jr
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Irene Gargantini
rawtitle: The Numerical Stability of Simultaneous Iterations Via Square-Rooting
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Gargantini:1979:NSS,
  author =       "Irene Gargantini",
  title =        "The Numerical Stability of Simultaneous Iterations Via
                 Square-Rooting",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "5",
  number =       "1",
  pages =        "25--31",
  month =        "????",
  year =         "1979",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(81)90136-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812218190136X",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: techreport
filename: fparith.bib
label: Ginsberg:1979:MFE
author: Myron Ginsberg
title: Monitoring floating-point error propagation in scientific computation
type: Technical report
number: CSE 7910
institution: Department of Computer Science and Engineering, Southern Methodist University
address: Dallas, TX, USA
pages: 32
year: 1979
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.
acknowledgement: ack-nhfb
rawauthor: Myron Ginsberg
rawtitle: Monitoring floating-point error propagation in scientific computation
entry:
@TechReport{Ginsberg:1979:MFE,
  author =       "Myron Ginsberg",
  title =        "Monitoring floating-point error propagation in
                 scientific computation",
  type =         "Technical report",
  number =       "CSE 7910",
  institution =  "Department of Computer Science and Engineering,
                 Southern Methodist University",
  address =      "Dallas, TX, USA",
  pages =        "32",
  year =         "1979",
  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.",
}


bibtype: article
filename: fparith.bib
label: Gregory:1979:EFC
author: Robert Todd Gregory
title: Error-free computation with finite number systems
journal: j-SIGNUM
volume: 14
number: 3
pages: 9--16
month: sep
monthnumber: 9
year: 1979
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:07 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:07 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: University of Tennessee, Knoxville, TN, USA
journalURL: https://dl.acm.org/loi/signum
treatment: T Theoretical or Mathematical
rawauthor: Robert Todd Gregory
rawtitle: Error-free computation with finite number systems
keywords:
automatic digital computer; computer-representable numbers; error free computation; finite; finite number systems; floating point numbers; machine; numerical methods; real numbers

entry:
@Article{Gregory:1979:EFC,
  author =       "Robert Todd Gregory",
  title =        "Error-free computation with finite number systems",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3",
  pages =        "9--16",
  month =        sep,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "University of Tennessee, Knoxville, TN, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "automatic digital computer; computer-representable
                 numbers; error free computation; finite; finite number
                 systems; floating point numbers; machine; numerical
                 methods; real numbers",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: phdthesis
filename: fparith.bib
label: Gruener:1979:ARD
author: K. Gruner
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1979
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 ???
acknowledgement: ack-nj
rawauthor: K. Gr{\"u}ner
title:
Allgemeine Rechnerarithmetik und deren Implementierung mit optimaler Genauigkeit toenglish General Computer Arithmetic and its Implementation with Optimal Accuracy endtoenglish 

rawtitle:
{Allgemeine Rechnerarithmetik und deren Implementierung mit optimaler Genauigkeit} \toenglish {General Computer Arithmetic and its Implementation with Optimal Accuracy} \endtoenglish

entry:
@PhdThesis{Gruener:1979:ARD,
  author =       "K. Gr{\"u}ner",
  title =        "{Allgemeine Rechnerarithmetik und deren
                 Implementierung mit optimaler Genauigkeit} \toenglish
                 {General Computer Arithmetic and its Implementation
                 with Optimal Accuracy} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1979",
  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,
}


bibtype: book
filename: fparith.bib
label: Hardy:1979:ITN
author: G. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) Wright
title: An Introduction to the Theory of Numbers
publisher: pub-OXFORD
address: pub-OXFORD:adr
edition: Fifth
pages: xvi + 426
year: 1979
ISBN: 0-19-853170-2, 0-19-853171-0 (paperback) OR 0198531702, 0198531710 (paperback)
ISBN13: 978-0-19-853170-8, 978-0-19-853171-5 (paperback) OR 9780198531708, 9780198531715 (paperback)
LCCN: A241 .H28 1979
bibdate: Fri Nov 30 06:49:15 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.30 06:49:15 ???
remark: Reprinted in 1988 and 1998 with corrections.
acknowledgement: ack-nhfb
rawauthor: G. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) Wright
rawtitle: An Introduction to the Theory of Numbers
entry:
@Book{Hardy:1979:ITN,
  author =       "G. H. (Godfrey Harold) Hardy and E. M. (Edward
                 Maitland) Wright",
  title =        "An Introduction to the Theory of Numbers",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  edition =      "Fifth",
  pages =        "xvi + 426",
  year =         "1979",
  ISBN =         "0-19-853170-2, 0-19-853171-0 (paperback)",
  ISBN-13 =      "978-0-19-853170-8, 978-0-19-853171-5 (paperback)",
  LCCN =         "A241 .H28 1979",
  bibdate =      "Fri Nov 30 06:49:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted in 1988 and 1998 with corrections.",
}


bibtype: inproceedings
filename: fparith.bib
label: Hastings:1979:SMM
author: C. Hastings
title: Shift Matrices: The Missing Teeth in the Number Cruncher
crossref: Anonymous:1979:WCR
pages: ??--??
year: 1979
bibdate: Fri Nov 09 18:59:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 18:59:11 ???
note: Paper number 18/3.
acknowledgement: ack-nhfb
rawauthor: C. Hastings
rawnote: Paper number 18/3.
rawtitle: Shift Matrices: The Missing Teeth in the Number Cruncher
entry:
@InProceedings{Hastings:1979:SMM,
  author =       "C. Hastings",
  title =        "Shift Matrices: The Missing Teeth in the Number
                 Cruncher",
  crossref =     "Anonymous:1979:WCR",
  pages =        "??--??",
  year =         "1979",
  bibdate =      "Fri Nov 09 18:59:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Paper number 18/3.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Heath:1979:RDF
author: J. Heath and H. Nagle, Jr. and S. Shiva
title: Realization of digital filters using input-scaled floating-point arithmetic
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 27
number: 5
pages: 469--477
month: oct
monthnumber: 10
year: 1979
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
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
note: See note cite Heath:1986:NRD.
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: J. Heath and H. {Nagle, Jr.} and S. Shiva
rawnote: See note \cite{Heath:1986:NRD}.
rawtitle: Realization of digital filters using input-scaled floating-point arithmetic
entry:
@Article{Heath:1979:RDF,
  author =       "J. Heath and H. {Nagle, Jr.} and S. Shiva",
  title =        "Realization of digital filters using input-scaled
                 floating-point arithmetic",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "27",
  number =       "5",
  pages =        "469--477",
  month =        oct,
  year =         "1979",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See note \cite{Heath:1986:NRD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "Fixed-point and floating-point realizations of digital
                 filters are abundant in the literature of digital
                 signal processing. A block-floating-point realization
                 which has some advantages of both fixed-point and
                 floating-point has been reported and \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Hehner:1979:NRR
author: E. C. R. Hehner and R. N. S. Horspool
title: A new representation of the rational numbers for fast easy arithmetic
journal: j-SIAM-J-COMPUT
volume: 8
number: 2
pages: 124--134
year: 1979
CODEN: SMJCAT
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
MRclass: 68C05 (10A30 68A05)
MRnumber: 80h:68027
MRreviewer: P. J. Weinberger
bibdate: Mon Nov 29 10:59:01 MST 2010
bibtimestamp: 2010.11.29 10:59:01 MST
note: See corrigendum cite Hehner:1980:CNR.
fjournal: SIAM Journal on Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
rawauthor: E. C. R. Hehner and R. N. S. Horspool
rawnote: See corrigendum \cite{Hehner:1980:CNR}.
rawtitle: A new representation of the rational numbers for fast easy arithmetic
bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/2; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Hehner:1979:NRR,
  author =       "E. C. R. Hehner and R. N. S. Horspool",
  title =        "A new representation of the rational numbers for fast
                 easy arithmetic",
  journal =      j-SIAM-J-COMPUT,
  volume =       "8",
  number =       "2",
  pages =        "124--134",
  month =        "????",
  year =         "1979",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68C05 (10A30 68A05)",
  MRnumber =     "80h:68027",
  MRreviewer =   "P. J. Weinberger",
  bibdate =      "Mon Nov 29 10:59:01 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See corrigendum \cite{Hehner:1980:CNR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}


bibtype: inproceedings
filename: fparith.bib
label: Hull:1979:DFP
author: T. E. Hull
title: Desirable floating-point arithmetic and elementary functions for numerical computation
crossref: ACM:1979:PSC
pages: 96--99
year: 1979
bibdate: Mon Jan 08 11:06:31 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.01.08 11:06:31 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: T. E. Hull
rawtitle: Desirable floating-point arithmetic and elementary functions for numerical computation
abstract:
The purpose of this talk is to summarize proposed specifications for floating-polar arithmetic and elementary functions. The topics considered are: the base of the number system, precision control, number representation, arithmetic operations, ocher basic operations, elementary functions, and exception handling. The possibility of doing without fixed-point arithmetic is also mentioned. The specifications are intended to be entirely at the level of a programming language such as Fortran. The emphasis is on convenience and simplicity from the user's point of view. Conforming to such specifications would have obvious beneficial implications for the portability of numerical software, and for proving programs correct, as well as attempting to provide facilities which are most suitable for the user. The specifications are not complete in every detail, but it is intended that they be complete ``in spirit'' --- some further details, especially syntactic details, would have to be provided, but the proposals are otherwise relatively complete.

rawabstract:
The purpose of this talk is to summarize proposed specifications for floating-polar arithmetic and elementary functions. The topics considered are: the base of the number system, precision control, number representation, arithmetic operations, ocher basic operations, elementary functions, and exception handling. The possibility of doing without fixed-point arithmetic is also mentioned. The specifications are intended to be entirely at the level of a programming language such as Fortran. The emphasis is on convenience and simplicity from the user's point of view. Conforming to such specifications would have obvious beneficial implications for the portability of numerical software, and for proving programs correct, as well as attempting to provide facilities which are most suitable for the user. The specifications are not complete in every detail, but it is intended that they be complete ``in spirit'' --- some further details, especially syntactic details, would have to be provided, but the proposals are otherwise relatively complete.

entry:
@InProceedings{Hull:1979:DFP,
  author =       "T. E. Hull",
  title =        "Desirable floating-point arithmetic and elementary
                 functions for numerical computation",
  crossref =     "ACM:1979:PSC",
  pages =        "96--99",
  year =         "1979",
  bibdate =      "Mon Jan 08 11:06:31 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The purpose of this talk is to summarize proposed
                 specifications for floating-polar arithmetic and
                 elementary functions. The topics considered are: the
                 base of the number system, precision control, number
                 representation, arithmetic operations, ocher basic
                 operations, elementary functions, and exception
                 handling. The possibility of doing without fixed-point
                 arithmetic is also mentioned. The specifications are
                 intended to be entirely at the level of a programming
                 language such as Fortran. The emphasis is on
                 convenience and simplicity from the user's point of
                 view. Conforming to such specifications would have
                 obvious beneficial implications for the portability of
                 numerical software, and for proving programs correct,
                 as well as attempting to provide facilities which are
                 most suitable for the user. The specifications are not
                 complete in every detail, but it is intended that they
                 be complete ``in spirit'' --- some further details,
                 especially syntactic details, would have to be
                 provided, but the proposals are otherwise relatively
                 complete.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: book
filename: fparith.bib
label: Hwang:1979:CAP
author: Kai Hwang
title: Computer Arithmetic: Principles, Architecture, and Design
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xiii + 423
year: 1979
ISBN: 0-471-03496-7 OR 0471034967
ISBN13: 978-0-471-03496-4 OR 9780471034964
LCCN: TK7888.3 .H9
bibdate: Sat May 18 14:15:19 2002
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:15:19 ???
acknowledgement: ack-nj
rawauthor: Kai Hwang
rawtitle: Computer Arithmetic: Principles, Architecture, and Design
entry:
@Book{Hwang:1979:CAP,
  author =       "Kai Hwang",
  title =        "Computer Arithmetic: Principles, Architecture, and
                 Design",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 423",
  year =         "1979",
  ISBN =         "0-471-03496-7",
  ISBN-13 =      "978-0-471-03496-4",
  LCCN =         "TK7888.3 .H9",
  bibdate =      "Sat May 18 14:15:19 2002",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Hwang:1979:GMT
author: Kai Hwang
title: Global and Modular Two's Complement Cellular Array Multipliers
journal: j-IEEE-TRANS-COMPUT
volume: C-28
number: 4
pages: 300--306
month: apr
monthnumber: 4
year: 1979
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1979.1675350
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 06:49:37 MDT 2011
bibtimestamp: 2011.07.11 06:49:37 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675350
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Kai Hwang
rawtitle: Global and Modular Two's Complement Cellular Array Multipliers
entry:
@Article{Hwang:1979:GMT,
  author =       "Kai Hwang",
  title =        "Global and Modular Two's Complement Cellular Array
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "4",
  pages =        "300--306",
  month =        apr,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675350",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:37 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=1675350",
  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: IEEE:1979:PIF
author: Anonymous
title: The Proposed IEEE floating-point standard
journal: j-SIGNUM
pages: 32
month: oct
monthnumber: 10
year: 1979
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
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
fjournal: ACM SIGNUM Newsletter
keywords: Floating-point arithmetic --- Standards.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Anonymous
rawtitle: The Proposed {IEEE} floating-point standard
entry:
@Article{IEEE:1979:PIF,
  author =       "Anonymous",
  title =        "The Proposed {IEEE} floating-point standard",
  journal =      j-SIGNUM,
  pages =        "32",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Floating-point arithmetic --- Standards.",
}


bibtype: manual
filename: fparith.bib
label: IntelCorporation:1979:FAL
author: Intel Corporation
title: 8080 / 8085 floating-point arithmetic library user's manual
organization: The Corporation
address: Santa Clara, CA, USA
pages: v + 20
year: 1979
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
remark: ``Manual Order Number: 9800452-03''.
acknowledgement: ack-nhfb
rawauthor: Intel Corporation
rawtitle: 8080\slash 8085 floating-point arithmetic library user's manual
keywords:
Assembly language (Computer program language).; Intel 8080 (Microprocessor) --- Programming.; INTEL 8085 (Computer) --- Programming.; PL/M-80 (Computer program language).

entry:
@Manual{IntelCorporation:1979:FAL,
  author =       "Intel Corporation",
  title =        "8080\slash 8085 floating-point arithmetic library
                 user's manual",
  organization = "The Corporation",
  address =      "Santa Clara, CA, USA",
  pages =        "v + 20",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Assembly language (Computer program language).; Intel
                 8080 (Microprocessor) --- Programming.; INTEL 8085
                 (Computer) --- Programming.; PL/M-80 (Computer program
                 language).",
  remark =       "``Manual Order Number: 9800452-03''.",
}


bibtype: article
filename: fparith.bib
label: Jenkins:1979:RAR
author: W. Jenkins
title: Recent advances in residue number techniques for recursive digital filtering
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 27
number: 1
pages: 19--30
month: feb
monthnumber: 2
year: 1979
CODEN: IETABA
DOI: https://doi.org/10.1049/el:19780088
ISSN: 0096-3518 OR 00963518
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26137
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: W. Jenkins
rawtitle: Recent advances in residue number techniques for recursive digital filtering
entry:
@Article{Jenkins:1979:RAR,
  author =       "W. Jenkins",
  title =        "Recent advances in residue number techniques for
                 recursive digital filtering",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "27",
  number =       "1",
  pages =        "19--30",
  month =        feb,
  year =         "1979",
  CODEN =        "IETABA",
  DOI =          "https://doi.org/10.1049/el:19780088",
  ISSN =         "0096-3518",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26137",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new algorithm for scaling in residue number systems
                 (RNS's) is presented for applying residue number theory
                 to recursive digital filtering. The algorithm provides
                 an efficient method for scaling the output of each
                 recursive filter section for use \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Johnson:1979:RAF
author: Donald B. Johnson and Webb Miller and Brian Minnihan and Celia Wrathall
title: Reducibility Among Floating-Point Graphs
journal: j-J-ACM
volume: 26
number: 4
pages: 739--760
month: oct
monthnumber: 10
year: 1979
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 65G05
MRnumber: 80i:65045
bibdate: Fri Dec 08 11:55:10 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 11:55:10 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Donald B. Johnson and Webb Miller and Brian Minnihan and Celia Wrathall
rawtitle: Reducibility Among Floating-Point Graphs
abstract:
The graph-theoretic models of this paper can be used to compare the rounding-error behavior of numerical programs. The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors in each arithmetic operation. Models constructed on this assumption are more tractable than would be the case under more realistic assumptions. There are identified two easily tested conditions on programs which guarantee that error analyses are relatively insensitive to the particular graph model employed. The development has the additional benefit of sometimes providing an elementary proof that one program is comparable in stability to another. Examples of such results are given.

rawabstract:
The graph-theoretic models of this paper can be used to compare the rounding-error behavior of numerical programs. The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors in each arithmetic operation. Models constructed on this assumption are more tractable than would be the case under more realistic assumptions. There are identified two easily tested conditions on programs which guarantee that error analyses are relatively insensitive to the particular graph model employed. The development has the additional benefit of sometimes providing an elementary proof that one program is comparable in stability to another. Examples of such results are given.

entry:
@Article{Johnson:1979:RAF,
  author =       "Donald B. Johnson and Webb Miller and Brian Minnihan
                 and Celia Wrathall",
  title =        "Reducibility Among Floating-Point Graphs",
  journal =      j-J-ACM,
  volume =       "26",
  number =       "4",
  pages =        "739--760",
  month =        oct,
  year =         "1979",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "80i:65045",
  bibdate =      "Fri Dec 08 11:55:10 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The graph-theoretic models of this paper can be used
                 to compare the rounding-error behavior of numerical
                 programs. The models follow the approach, popularized
                 by Wilkinson, of assuming independent rounding errors
                 in each arithmetic operation. Models constructed on
                 this assumption are more tractable than would be the
                 case under more realistic assumptions. There are
                 identified two easily tested conditions on programs
                 which guarantee that error analyses are relatively
                 insensitive to the particular graph model employed. The
                 development has the additional benefit of sometimes
                 providing an elementary proof that one program is
                 comparable in stability to another. Examples of such
                 results are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}


bibtype: article
filename: fparith.bib
label: Kahan:1979:PCK
author: William M. Kahan
title: Personal Calculator Has Key to Solve Any Equation $ f(x) = 0 $
journal: j-HEWLETT-PACKARD-J
volume: 30
number: 12
pages: 20--26
month: dec
monthnumber: 12
year: 1979
CODEN: HPJOAX
ISSN: 0018-1153 OR 00181153
MRclass: 65-01 (65G05 65H05)
MRnumber: MR574853 (81k:65002)
MRreviewer: R. P. Brent
bibdate: Tue Mar 25 14:12:15 MST 1997
bibtimestamp: 1997.03.25 14:12:15 MST
note: Lecture notes for Math 128.
URL: http://www.cs.berkeley.edu/~wkahan/Math128/SOLVEkey.pdf
fjournal: Hewlett--Packard Journal
acknowledgement: ack-nhfb
classcodes: C5420 (Mainframes and minicomputers); C7310 (Mathematics computing)
corpsource: Univ. of California, Berkeley, CA, USA
reviewer: R. P. Brent
treatment: P Practical
rawauthor: William M. Kahan
rawnote: Lecture notes for Math 128.
rawtitle: Personal Calculator Has Key to Solve Any Equation $ f(x) = 0 $
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/hpj.bib

keywords:
electronic calculators; equation solving; finding; handheld calculator; HP 34C; linear algebra; personal calculator; root; SOLVE

entry:
@Article{Kahan:1979:PCK,
  author =       "William M. Kahan",
  title =        "Personal Calculator Has Key to Solve Any Equation $
                 f(x) = 0 $",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "30",
  number =       "12",
  pages =        "20--26",
  month =        dec,
  year =         "1979",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  MRclass =      "65-01 (65G05 65H05)",
  MRnumber =     "MR574853 (81k:65002)",
  MRreviewer =   "R. P. Brent",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hpj.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/SOLVEkey.pdf",
  acknowledgement = ack-nhfb,
  classcodes =   "C5420 (Mainframes and minicomputers); C7310
                 (Mathematics computing)",
  corpsource =   "Univ. of California, Berkeley, CA, USA",
  fjournal =     "Hewlett--Packard Journal",
  keywords =     "electronic calculators; equation solving; finding;
                 handheld calculator; HP 34C; linear algebra; personal
                 calculator; root; SOLVE",
  reviewer =     "R. P. Brent",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Kahan:1979:PFP
author: W. Kahan and J. Palmer
title: On a Proposed Floating-Point Standard
journal: j-SIGNUM
volume: 14
number: 3S (Special issue)
pages: 13--21
month: oct
monthnumber: 10
year: 1979
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1057520.1057522
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Wed Mar 19 23:00:11 MST 1997
bibtimestamp: 1997.03.19 23:00:11 MST
fjournal: ACM SIGNUM Newsletter
keywords: arithmetic; digital arithmetic; floating point; proposal; standard; standards
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: University of California, Berkeley, CA, USA
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical
rawauthor: W. Kahan and J. Palmer
rawtitle: On a Proposed Floating-Point Standard
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib

abstract:
A standard for binary floating-point arithmetic is being proposed and there is a very real possibility that it will be adopted by many manufacturers and implemented on a wide range of computers. This development matters to all of us concerned with numerical software. One of the principal motivations for the standard is to distribute more evenly the burden of portability between hardware and software. At present, any program intended to be portable must be designed for a mythical computer that enjoys no capability not supported by every computer on which the program will be run. That mythical computer is so much grubbier than almost any real computer that a portable program will frequently be denigrated as ``suboptimal'' and then supplanted by another program supposedly ``optimal'' for the real computer in question but often inferior in critical respects like reliability. A standard --- almost any reasonable standard --- will surely improve the situation. A standard environment for numerical programs will promote fair comparisons and sharing of numerical codes, thereby lowering costs and prices. Furthermore, we have chosen repeatedly to enrich that environment in order that applications programs be simpler and more reliable. Thus will the onus of portability be shared among hardware manufacturers and software producers.

rawabstract:
A standard for binary floating-point arithmetic is being proposed and there is a very real possibility that it will be adopted by many manufacturers and implemented on a wide range of computers. This development matters to all of us concerned with numerical software. One of the principal motivations for the standard is to distribute more evenly the burden of portability between hardware and software. At present, any program intended to be portable must be designed for a mythical computer that enjoys no capability not supported by every computer on which the program will be run. That mythical computer is so much grubbier than almost any real computer that a portable program will frequently be denigrated as ``suboptimal'' and then supplanted by another program supposedly ``optimal'' for the real computer in question but often inferior in critical respects like reliability. A standard --- almost any reasonable standard --- will surely improve the situation. A standard environment for numerical programs will promote fair comparisons and sharing of numerical codes, thereby lowering costs and prices. Furthermore, we have chosen repeatedly to enrich that environment in order that applications programs be simpler and more reliable. Thus will the onus of portability be shared among hardware manufacturers and software producers.

entry:
@Article{Kahan:1979:PFP,
  author =       "W. Kahan and J. Palmer",
  title =        "On a Proposed Floating-Point Standard",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "13--21",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057520.1057522",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Wed Mar 19 23:00:11 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  abstract =     "A standard for binary floating-point arithmetic is
                 being proposed and there is a very real possibility
                 that it will be adopted by many manufacturers and
                 implemented on a wide range of computers. This
                 development matters to all of us concerned with
                 numerical software. One of the principal motivations
                 for the standard is to distribute more evenly the
                 burden of portability between hardware and software. At
                 present, any program intended to be portable must be
                 designed for a mythical computer that enjoys no
                 capability not supported by every computer on which the
                 program will be run. That mythical computer is so much
                 grubbier than almost any real computer that a portable
                 program will frequently be denigrated as ``suboptimal''
                 and then supplanted by another program supposedly
                 ``optimal'' for the real computer in question but often
                 inferior in critical respects like reliability. A
                 standard --- almost any reasonable standard --- will
                 surely improve the situation. A standard environment
                 for numerical programs will promote fair comparisons
                 and sharing of numerical codes, thereby lowering costs
                 and prices. Furthermore, we have chosen repeatedly to
                 enrich that environment in order that applications
                 programs be simpler and more reliable. Thus will the
                 onus of portability be shared among hardware
                 manufacturers and software producers.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "University of California, Berkeley, CA, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic; digital arithmetic; floating point;
                 proposal; standard; standards",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}


bibtype: phdthesis
filename: fparith.bib
label: Kent:1979:TPS
author: Jan Kent
type: Dr. Avhandling
school: Universitetet i Oslo
address: Oslo, Norway
pages: 13--21
year: 1979
bibdate: Thu May 09 08:05:31 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:05:31 ???
acknowledgement: ack-nhfb
rawauthor: Jan Kent
title:
The theoretical and practical study of floating point instructions: Consisting of Theoretical definition, analysis and comparison of floating point instruction, and procedures for the description and simulation of floating point instructions

rawtitle:
The theoretical and practical study of floating point instructions: Consisting of Theoretical definition, analysis and comparison of floating point instruction, and procedures for the description and simulation of floating point instructions

entry:
@PhdThesis{Kent:1979:TPS,
  author =       "Jan Kent",
  title =        "The theoretical and practical study of floating point
                 instructions: Consisting of Theoretical definition,
                 analysis and comparison of floating point instruction,
                 and procedures for the description and simulation of
                 floating point instructions",
  type =         "{Dr. Avhandling}",
  school =       "Universitetet i Oslo",
  address =      "Oslo, Norway",
  year =         "1979",
  bibdate =      "Thu May 09 08:05:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Bibsys library catalog gave both 1977 and 1979 as
                 year??",
}


bibtype: techreport
filename: fparith.bib
label: Kolze:1979:BFP
author: Thomas Joseph Kolze
title: Block floating point FFT statistical noise analysis program
type: Technical report
number: CSR-79-2
institution: Department of Electrical Engineering, University of Missouri--Rolla
address: Rolla, MO, USA
pages: vii + 180
year: 1979
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: Communications and signal processing research.
keywords: Radio noise --- Computer programs.; Signals and signaling --- Computer programs.
acknowledgement: ack-nhfb
rawauthor: Thomas Joseph Kolze
rawtitle: Block floating point {FFT} statistical noise analysis program
entry:
@TechReport{Kolze:1979:BFP,
  author =       "Thomas Joseph Kolze",
  title =        "Block floating point {FFT} statistical noise analysis
                 program",
  type =         "Technical report",
  number =       "CSR-79-2",
  institution =  "Department of Electrical Engineering, University of
                 Missouri--Rolla",
  address =      "Rolla, MO, USA",
  pages =        "vii + 180",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Communications and signal processing research.",
  acknowledgement = ack-nhfb,
  keywords =     "Radio noise --- Computer programs.; Signals and
                 signaling --- Computer programs.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Kolze:1979:SNA
author: Thomas Joseph Kolze
title: Statistical noise analysis of a block floating point FFT and an example application
type: Electrical Engineering Thesis (M.S.)
school: University of Missouri--Rolla
address: Rolla, MO, USA
pages: viii + 88
year: 1979
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: Thomas Joseph Kolze
rawtitle: Statistical noise analysis of a block floating point {FFT} and an example application
entry:
@MastersThesis{Kolze:1979:SNA,
  author =       "Thomas Joseph Kolze",
  title =        "Statistical noise analysis of a block floating point
                 {FFT} and an example application",
  type =         "Electrical Engineering Thesis ({M.S.})",
  school =       "University of Missouri--Rolla",
  address =      "Rolla, MO, USA",
  pages =        "viii + 88",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kornerup:1979:NRA
author: Peter Kornerup
title: A note on rational arithmetic
journal: j-SIGMICRO
volume: 10
number: 2
pages: 28--28
month: jun
monthnumber: 6
year: 1979
CODEN: SIGMDJ
DOI: https://doi.org/10.1145/1218003.1218004
ISSN: 0163-5751, 1050-916X OR 01635751, 1050916X
ISSNL: 0163-5751 OR 01635751
bibdate: Fri Apr 16 10:27:24 MDT 2021
bibtimestamp: 2021.04.16 10:27:24 MDT
note: See cite Thacker:1979:MPR,Thacker:1979:R.
URL: https://dl.acm.org/doi/10.1145/1218003.1218004
fjournal: ACM SIGMICRO Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigmicro
rawauthor: Peter Kornerup
rawnote: See \cite{Thacker:1979:MPR,Thacker:1979:R}.
rawtitle: A note on rational arithmetic
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/sigmicro.bib

abstract:
A recent paper in SIGMICRO [1] contained a comparison of the accuracy of floating point vs. rational representations, which is very unfair to the latter. The format chosen for rational numbers utilizes 16 bits for numerators and 16 bits for denominators. This implies that the spacing between consecutive numbers in the system is in most cases of the order $ 2 -32 $. Only around simple rational numbers (e.g. 1/1, 2/3) is the spacing of the order $ 2 -16. $ However the rounding algorithm presented in [1] will almost certainly introduce a rounding error of the order $ 2 -16 $, i.e. introduce an error which in most cases is of the order $ 2^16 $ larger than necessary.

rawabstract:
A recent paper in SIGMICRO [1] contained a comparison of the accuracy of floating point vs. rational representations, which is very unfair to the latter. The format chosen for rational numbers utilizes 16 bits for numerators and 16 bits for denominators. This implies that the spacing between consecutive numbers in the system is in most cases of the order $ 2 {-32} $. Only around simple rational numbers (e.g. 1/1, 2/3) is the spacing of the order $ 2 {-16}. $ However the rounding algorithm presented in [1] will almost certainly introduce a rounding error of the order $ 2 {-16} $, i.e. introduce an error which in most cases is of the order $ 2^{16} $ larger than necessary.

entry:
@Article{Kornerup:1979:NRA,
  author =       "Peter Kornerup",
  title =        "A note on rational arithmetic",
  journal =      j-SIGMICRO,
  volume =       "10",
  number =       "2",
  pages =        "28--28",
  month =        jun,
  year =         "1979",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1218003.1218004",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:24 MDT 2021",
  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/sigmicro.bib",
  note =         "See \cite{Thacker:1979:MPR,Thacker:1979:R}.",
  URL =          "https://dl.acm.org/doi/10.1145/1218003.1218004",
  abstract =     "A recent paper in SIGMICRO [1] contained a comparison
                 of the accuracy of floating point vs. rational
                 representations, which is very unfair to the latter.
                 The format chosen for rational numbers utilizes 16 bits
                 for numerators and 16 bits for denominators. This
                 implies that the spacing between consecutive numbers in
                 the system is in most cases of the order $ 2 {-32} $.
                 Only around simple rational numbers (e.g. 1/1, 2/3) is
                 the spacing of the order $ 2 {-16}. $ However the
                 rounding algorithm presented in [1] will almost
                 certainly introduce a rounding error of the order $ 2
                 {-16} $, i.e. introduce an error which in most cases is
                 of the order $ 2^{16} $ larger than necessary.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}


bibtype: article
filename: fparith.bib
label: Kusterer:1979:SEP
author: Roland Kusterer and Manfred Reimer
title: Stable Evaluation of Polynomials in Time $ log n $
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1019--1031
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1979-0528054-X; https://doi.org/10.2307/2006075
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65G05 (68C25)
MRnumber: 80d:65050 (528054)
MRreviewer: C. W. Clenshaw
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: algorithm; approximation theory; number of multiplications to evaluate a polynomial; polynomials
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4130 (Interpolation and function approximation)
corpsource: Math. Inst., University of Dortmund, Dortmund, West Germany
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Roland Kusterer and Manfred Reimer
rawtitle: Stable Evaluation of Polynomials in Time $ \log n $
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database

entry:
@Article{Kusterer:1979:SEP,
  author =       "Roland Kusterer and Manfred Reimer",
  title =        "Stable Evaluation of Polynomials in Time $ \log n $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1019--1031",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1979-0528054-X;
                 https://doi.org/10.2307/2006075",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G05 (68C25)",
  MRnumber =     "80d:65050 (528054)",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Math. Inst., University of Dortmund, Dortmund, West
                 Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm; approximation theory; number of
                 multiplications to evaluate a polynomial; polynomials",
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Lautz:1979:JLD
author: Gunter Lautz
title: 300 Jahre leibnizsches dualzahlensystem. (German) [300 years of the Leibniz binary number system]
journal: j-BIOL-CYBERN
volume: 35
number: 3
pages: 175--181
month: dec
monthnumber: 12
year: 1979
CODEN: BICYAF
DOI: https://doi.org/10.1007/bf00337062
ISSN: 0340-1200 (print), 1432-0770 (electronic) OR 03401200 (print), 14320770 (electronic)
ISSNL: 0340-1200 OR 03401200
bibdate: Fri Mar 17 08:46:29 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.03.17 08:46:29 ???
fjournal: Biological cybernetics
language: German
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/422
rawauthor: G{\"u}nter Lautz
abstract:
300 years ago G. W. Leibniz has invented his binary number system, now widely used in computer sciences. The paper recapitulates some informations about the contents of the first private notes from 1679, partly reproduced in facsimiles, and the scientific background of that time. The circumstances and the genesis of the first treatise on this matter, published in 1703/5 by Leibniz at the Academy of Sciences, Paris, are discussed in detail.

rawabstract:
300 years ago G. W. Leibniz has invented his binary number system, now widely used in computer sciences. The paper recapitulates some informations about the contents of the first private notes from 1679, partly reproduced in facsimiles, and the scientific background of that time. The circumstances and the genesis of the first treatise on this matter, published in 1703/5 by Leibniz at the Academy of Sciences, Paris, are discussed in detail.

rawtitle:
{300 Jahre leibnizsches dualzahlensystem}. ({German}) [300 years of the {Leibniz} binary number system]

entry:
@Article{Lautz:1979:JLD,
  author =       "G{\"u}nter Lautz",
  title =        "{300 Jahre leibnizsches dualzahlensystem}. ({German})
                 [300 years of the {Leibniz} binary number system]",
  journal =      j-BIOL-CYBERN,
  volume =       "35",
  number =       "3",
  pages =        "175--181",
  month =        dec,
  year =         "1979",
  CODEN =        "BICYAF",
  DOI =          "https://doi.org/10.1007/bf00337062",
  ISSN =         "0340-1200 (print), 1432-0770 (electronic)",
  ISSN-L =       "0340-1200",
  bibdate =      "Fri Mar 17 08:46:29 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "300 years ago G. W. Leibniz has invented his binary
                 number system, now widely used in computer sciences.
                 The paper recapitulates some informations about the
                 contents of the first private notes from 1679, partly
                 reproduced in facsimiles, and the scientific background
                 of that time. The circumstances and the genesis of the
                 first treatise on this matter, published in 1703/5 by
                 Leibniz at the Academy of Sciences, Paris, are
                 discussed in detail.",
  acknowledgement = ack-nhfb,
  fjournal =     "Biological cybernetics",
  journal-URL =  "http://link.springer.com/journal/422",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Lee:1979:AFN
author: S. C. Lee and A. D. Edgar
title: Addendum to ``The Focus Number System''
journal: j-IEEE-TRANS-COMPUT
volume: C-28
number: 9
pages: 693--693
month: sep
monthnumber: 9
year: 1979
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1979.1675442
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 06:49:40 MDT 2011
bibtimestamp: 2011.07.11 06:49:40 MDT
note: See cite Lee:1977:FNS,Swartzlander:1979:CFN.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675442
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. C. Lee and A. D. Edgar
rawnote: See \cite{Lee:1977:FNS,Swartzlander:1979:CFN}.
rawtitle: Addendum to {``The Focus Number System''}
abstract:
In 1971 Kingsbury and Rayner, publishing under the title ``Digital Filtering Using Logarithmic Arithmetic'' disclosed a sign-plus-logarithm number system, and a means of performing addition through single dimensional lookup using the formula $ c = b + F(a b) $. The system was demonstrated on a computer. In 1975 Swartzlander and Alexopoulos disclosed Kingsbury's logarithmic arithmetic as ``The Sign / Logarithm Number System''. In 1977, without knowledge of prior art, we reinvented the wheel a third time, dubbing it ``Focus,'' after the focus of resolution around the zero origin [3]. We wish now to acknowledge Kingsbury and Rayner as the pioneer authors, and also Swartzlander and Alexopoulos as prior to our publication.

rawabstract:
In 1971 Kingsbury and Rayner, publishing under the title ``Digital Filtering Using Logarithmic Arithmetic'' disclosed a sign-plus-logarithm number system, and a means of performing addition through single dimensional lookup using the formula $ c = b + F(a b) $. The system was demonstrated on a computer. In 1975 Swartzlander and Alexopoulos disclosed Kingsbury's logarithmic arithmetic as ``The Sign\slash Logarithm Number System''. In 1977, without knowledge of prior art, we reinvented the wheel a third time, dubbing it ``Focus,'' after the focus of resolution around the zero origin [3]. We wish now to acknowledge Kingsbury and Rayner as the pioneer authors, and also Swartzlander and Alexopoulos as prior to our publication.

entry:
@Article{Lee:1979:AFN,
  author =       "S. C. Lee and A. D. Edgar",
  title =        "Addendum to {``The Focus Number System''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "9",
  pages =        "693--693",
  month =        sep,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675442",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:40 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{Lee:1977:FNS,Swartzlander:1979:CFN}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675442",
  abstract =     "In 1971 Kingsbury and Rayner, publishing under the
                 title ``Digital Filtering Using Logarithmic
                 Arithmetic'' disclosed a sign-plus-logarithm number
                 system, and a means of performing addition through
                 single dimensional lookup using the formula $ c = b +
                 F(a b) $. The system was demonstrated on a computer. In
                 1975 Swartzlander and Alexopoulos disclosed Kingsbury's
                 logarithmic arithmetic as ``The Sign\slash Logarithm
                 Number System''. In 1977, without knowledge of prior
                 art, we reinvented the wheel a third time, dubbing it
                 ``Focus,'' after the focus of resolution around the
                 zero origin [3]. We wish now to acknowledge Kingsbury
                 and Rayner as the pioneer authors, and also
                 Swartzlander and Alexopoulos as prior to our
                 publication.",
  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: McDonnell:1979:FR
author: Eugene McDonnell
title: Fuzzy residue
journal: j-APL-QUOTE-QUAD
volume: 9
number: 4
pages: 42--46
year: 1979
CODEN: APLQD9
DOI: https://doi.org/10.1145/390009.804437
ISSN: 0163-6006 (print), 1558-3392 (electronic) OR 01636006 (print), 15583392 (electronic)
ISSNL: 0163-6006 OR 01636006
bibdate: Thu Aug 07 19:13:11 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 19:13:11 ???
fjournal: APL Quote Quad
acknowledgement: ack-nhfb
rawauthor: Eugene McDonnell
rawtitle: Fuzzy residue
abstract:
Certain pairs of arguments to the residue function, as implemented on many APL systems, give results which make it seem as if the ordinary decimal relationships we remember from grade school no longer hold. As far as we can tell, it looks as if a given modulus should divide the right argument, but the implementation tells us it doesn't. A definition for a fuzzed residue function is proposed which resolves the difficulties users have complained of. However, certain points of continuing difficulty remain, where the limitations of machine arithmetic continue to defeat the attempt to model the real number system. The representation function is defined in terms of the residue function, and so is affected by the change in residue. The nature of this effect is also discussed in this paper.

rawabstract:
Certain pairs of arguments to the residue function, as implemented on many APL systems, give results which make it seem as if the ordinary decimal relationships we remember from grade school no longer hold. As far as we can tell, it looks as if a given modulus should divide the right argument, but the implementation tells us it doesn't. A definition for a fuzzed residue function is proposed which resolves the difficulties users have complained of. However, certain points of continuing difficulty remain, where the limitations of machine arithmetic continue to defeat the attempt to model the real number system. The representation function is defined in terms of the residue function, and so is affected by the change in residue. The nature of this effect is also discussed in this paper.

entry:
@Article{McDonnell:1979:FR,
  author =       "Eugene McDonnell",
  title =        "Fuzzy residue",
  journal =      j-APL-QUOTE-QUAD,
  volume =       "9",
  number =       "4",
  pages =        "42--46",
  year =         "1979",
  CODEN =        "APLQD9",
  DOI =          "https://doi.org/10.1145/390009.804437",
  ISSN =         "0163-6006 (print), 1558-3392 (electronic)",
  ISSN-L =       "0163-6006",
  bibdate =      "Thu Aug 07 19:13:11 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Certain pairs of arguments to the residue function, as
                 implemented on many APL systems, give results which
                 make it seem as if the ordinary decimal relationships
                 we remember from grade school no longer hold. As far as
                 we can tell, it looks as if a given modulus should
                 divide the right argument, but the implementation tells
                 us it doesn't. A definition for a fuzzed residue
                 function is proposed which resolves the difficulties
                 users have complained of. However, certain points of
                 continuing difficulty remain, where the limitations of
                 machine arithmetic continue to defeat the attempt to
                 model the real number system. The representation
                 function is defined in terms of the residue function,
                 and so is affected by the change in residue. The nature
                 of this effect is also discussed in this paper.",
  acknowledgement = ack-nhfb,
  fjournal =     "APL Quote Quad",
}


bibtype: book
filename: fparith.bib
label: Oberman:1979:DCB
author: R. M. M. (Roelof Maarten Marie) Oberman
title: Digital circuits for binary arithmetic
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xii + 340
year: 1979
ISBN: 0-470-26373-3 OR 0470263733
ISBN13: 978-0-470-26373-0 OR 9780470263730
LCCN: TK7868.L6 O23 1979
bibdate: Wed Nov 14 17:33:15 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.11.14 17:33:15 MST
remark: A Halsted Press book.
subject: logic circuits; digital integrated circuits; switching theory
acknowledgement: ack-nhfb
rawauthor: R. M. M. (Roelof Maarten Marie) Oberman
rawtitle: Digital circuits for binary arithmetic
entry:
@Book{Oberman:1979:DCB,
  author =       "R. M. M. (Roelof Maarten Marie) Oberman",
  title =        "Digital circuits for binary arithmetic",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 340",
  year =         "1979",
  ISBN =         "0-470-26373-3",
  ISBN-13 =      "978-0-470-26373-0",
  LCCN =         "TK7868.L6 O23 1979",
  bibdate =      "Wed Nov 14 17:33:15 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "A Halsted Press book.",
  subject =      "logic circuits; digital integrated circuits; switching
                 theory",
}


bibtype: article
filename: fparith.bib
label: Oliver:1979:REP
author: J. Oliver
title: Rounding error propagation in polynomial evaluation schemes
journal: j-J-COMPUT-APPL-MATH
volume: 5
number: 2
pages: 85--97
month: jun
monthnumber: 6
year: 1979
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:18 MST 2017
bibtimestamp: 2017.02.25 11:59:18 MST
URL: http://www.sciencedirect.com/science/article/pii/0771050X79900020
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: J. Oliver
rawtitle: Rounding error propagation in polynomial evaluation schemes
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib

entry:
@Article{Oliver:1979:REP,
  author =       "J. Oliver",
  title =        "Rounding error propagation in polynomial evaluation
                 schemes",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "5",
  number =       "2",
  pages =        "85--97",
  month =        jun,
  year =         "1979",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X79900020",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: fparith.bib
label: Payne:1979:DPB
author: Mary Payne and William Strecker
title: Draft Proposal for a Binary Normalized Floating Point Standard
journal: j-SIGNUM
volume: 14
number: 3S (Special issue)
pages: 24--28
month: oct
monthnumber: 10
year: 1979
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:07 MDT 2005
bibtimestamp: 2005.04.12 07:50:07 MDT
fjournal: ACM SIGNUM Newsletter
keywords: binary; digital arithmetic; floating point; normalized; proposal; standard; standards
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Digital Equipment Corp., Maynard, MA, USA
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical
rawauthor: Mary Payne and William Strecker
rawtitle: Draft Proposal for a Binary Normalized Floating Point Standard
entry:
@Article{Payne:1979:DPB,
  author =       "Mary Payne and William Strecker",
  title =        "Draft Proposal for a Binary Normalized Floating Point
                 Standard",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "24--28",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Digital Equipment Corp., Maynard, MA, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "binary; digital arithmetic; floating point;
                 normalized; proposal; standard; standards",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}


bibtype: techreport
filename: fparith.bib
label: Randell:1979:ABO
author: Brian Randell
title: An annotated bibliography on the origins of digital computers
type: Technical report
number: 140
institution: Computing Laboratory, University of Newcastle upon Tyne
address: Newcastle upon Tyne, UK
pages: 146
year: 1979
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; Bibliography; Calculators
acknowledgement: ack-nhfb
rawauthor: Brian Randell
rawtitle: An annotated bibliography on the origins of digital computers
entry:
@TechReport{Randell:1979:ABO,
  author =       "Brian Randell",
  title =        "An annotated bibliography on the origins of digital
                 computers",
  type =         "Technical report",
  number =       "140",
  institution =  "Computing Laboratory, University of Newcastle upon
                 Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "146",
  year =         "1979",
  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; Bibliography;
                 Calculators",
}


bibtype: incollection
filename: fparith.bib
label: Rauch:1979:EAA
author: E. Rauch
crossref: Meinardus:1979:ATP
pages: ??--??
year: 1979
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 ???
acknowledgement: ack-nj
rawauthor: E. Rauch
title:
Einige Aspekte der Auswahl und Realisierung numerischer Verfahren in anwendungsorientierten Systemen toenglish Several Aspects of the Choice and Realisation of Numerical Procedures in Application-Oriented Systems endtoenglish 

rawtitle:
{Einige Aspekte der Auswahl und Realisierung numerischer Verfahren in anwendungsorientierten Systemen} \toenglish {Several Aspects of the Choice and Realisation of Numerical Procedures in Application-Oriented Systems} \endtoenglish

entry:
@InCollection{Rauch:1979:EAA,
  author =       "E. Rauch",
  title =        "{Einige Aspekte der Auswahl und Realisierung
                 numerischer Verfahren in anwendungsorientierten
                 Systemen} \toenglish {Several Aspects of the Choice and
                 Realisation of Numerical Procedures in
                 Application-Oriented Systems} \endtoenglish",
  crossref =     "Meinardus:1979:ATP",
  pages =        "??--??",
  year =         "1979",
  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,
}


bibtype: article
filename: fparith.bib
label: Redinbo:1979:FFA
author: G. R. Redinbo
title: Finite Field Arithmetic on an Array Processor
journal: j-IEEE-TRANS-COMPUT
volume: C-28
number: 7
pages: 461--471
month: jul
monthnumber: 7
year: 1979
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1979.1675390
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 06:49:39 MDT 2011
bibtimestamp: 2011.07.11 06:49:39 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675390
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. R. Redinbo
rawtitle: Finite Field Arithmetic on an Array Processor
entry:
@Article{Redinbo:1979:FFA,
  author =       "G. R. Redinbo",
  title =        "Finite Field Arithmetic on an Array Processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "7",
  pages =        "461--471",
  month =        jul,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675390",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:39 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=1675390",
  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: Reid:1979:FMF
author: John Reid
title: Functions for Manipulating Floating-Point Numbers
journal: j-SIGNUM
volume: 14
number: 4
pages: 11--13
month: dec
monthnumber: 12
year: 1979
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:08 MDT 2005
bibtimestamp: 2005.04.12 07:50:08 MDT
fjournal: ACM SIGNUM Newsletter
keywords: complex numbers; digital arithmetic; floating; FORTRAN; point arithmetic; portability; precision
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Computer Sci. and Systems Div., AERE, Harwell, UK
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical
rawauthor: John Reid
rawtitle: Functions for Manipulating Floating-Point Numbers
entry:
@Article{Reid:1979:FMF,
  author =       "John Reid",
  title =        "Functions for Manipulating Floating-Point Numbers",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "4",
  pages =        "11--13",
  month =        dec,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:08 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Computer Sci. and Systems Div., AERE, Harwell, UK",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "complex numbers; digital arithmetic; floating;
                 FORTRAN; point arithmetic; portability; precision",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Reinsch:1979:PPC
author: Christian H. Reinsch
title: Principles and Preferences for Computer Arithmetic
journal: j-SIGNUM
volume: 14
number: 1
pages: 12--27
month: mar
monthnumber: 3
year: 1979
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:06 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:06 MDT
fjournal: ACM SIGNUM Newsletter
keywords: computer arithmetic; digital arithmetic
acknowledgement: ack-nhfb
authordates: Christian H. Reinsch (?? ?? 1932--8 October 2022)
classcodes: C5230 (Digital arithmetic methods)
corpsource: Leibniz-Rechenzentrum, Munich, West Germany
journalURL: https://dl.acm.org/loi/signum
treatment: T Theoretical or Mathematical
rawauthor: Christian H. Reinsch
rawtitle: Principles and Preferences for Computer Arithmetic
entry:
@Article{Reinsch:1979:PPC,
  author =       "Christian H. Reinsch",
  title =        "Principles and Preferences for Computer Arithmetic",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "1",
  pages =        "12--27",
  month =        mar,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:06 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Leibniz-Rechenzentrum, Munich, West Germany",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "computer arithmetic; digital arithmetic",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Rink:1979:CEF
author: R. Rink and H. Chong
title: Covariance equation for a floating-point regulator system
journal: j-IEEE-TRANS-AUTOMAT-CONTR
volume: 24
number: 6
pages: 980--982
month: dec
monthnumber: 12
year: 1979
CODEN: IETAA9
ISSN: 0018-9286 (print), 1558-2523 (electronic) OR 00189286 (print), 15582523 (electronic)
ISSNL: 0018-9286 OR 00189286
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 Automatic Control
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
rawauthor: R. Rink and H. Chong
rawtitle: Covariance equation for a floating-point regulator system
entry:
@Article{Rink:1979:CEF,
  author =       "R. Rink and H. Chong",
  title =        "Covariance equation for a floating-point regulator
                 system",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "24",
  number =       "6",
  pages =        "980--982",
  month =        dec,
  year =         "1979",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  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 Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "Derived are linear equations that can be solved for
                 the steady-state covariance matrix of the plant and
                 observer states of a closed-loop regulator system which
                 employs finite wordlength A/D conversion and
                 floating-point computation in the observer/ \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Rink:1979:PSR
author: R. Rink and Hoi Chong
title: Performance of state regulator systems with floating-point computation
journal: j-IEEE-TRANS-AUTOMAT-CONTR
volume: 24
number: 3
pages: 411--421
month: jun
monthnumber: 6
year: 1979
CODEN: IETAA9
ISSN: 0018-9286 (print), 1558-2523 (electronic) OR 00189286 (print), 15582523 (electronic)
ISSNL: 0018-9286 OR 00189286
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
note: See correction cite Rink:1980:CPS.
fjournal: IEEE Transactions on Automatic Control
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
rawauthor: R. Rink and Hoi Chong
rawnote: See correction \cite{Rink:1980:CPS}.
rawtitle: Performance of state regulator systems with floating-point computation
entry:
@Article{Rink:1979:PSR,
  author =       "R. Rink and Hoi Chong",
  title =        "Performance of state regulator systems with
                 floating-point computation",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "24",
  number =       "3",
  pages =        "411--421",
  month =        jun,
  year =         "1979",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Rink:1980:CPS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "The performance of a digital state regulator system
                 having an A/D converter of finite wordlength and a
                 floating-point estimator/ controller computer of finite
                 mantissa-length is analyzed. An upper bound on the
                 mean-square state error, as a function \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Robertson:1979:VPA
author: D. A. Robertson
title: Variable precision arithmetic on CDC 6000 / 7000 machines
journal: j-SPE
volume: 9
number: 3
pages: 247--248
month: mar
monthnumber: 3
year: 1979
CODEN: SPEXBL
DOI: https://doi.org/10.1002/spe.4380090310
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Wed Sep 10 12:36:39 MDT 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/spe.bib
bibtimestamp: 2014.09.10 12:36:39 MDT
fjournal: Software --- Practice and Experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
onlinedate: 27 Oct 2006
rawauthor: D. A. Robertson
rawtitle: Variable precision arithmetic on {CDC 6000\slash 7000} machines
entry:
@Article{Robertson:1979:VPA,
  author =       "D. A. Robertson",
  title =        "Variable precision arithmetic on {CDC 6000\slash 7000}
                 machines",
  journal =      j-SPE,
  volume =       "9",
  number =       "3",
  pages =        "247--248",
  month =        mar,
  year =         "1979",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380090310",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Wed Sep 10 12:36:39 MDT 2014",
  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",
  onlinedate =   "27 Oct 2006",
}


bibtype: mastersthesis
filename: fparith.bib
label: Scharf:1979:HRW
author: Stuart Lee Scharf
title: A hardware realization of the Winograd Fourier Transform Algorithm
type: Thesis (M.S.)
school: Massachusetts Institute of Technology. Dept. of Electrical and Engineering and Computer Science
address: Cambridge, MA, USA
pages: 109
year: 1979
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 James H. McClellan.
acknowledgement: ack-nhfb
rawauthor: Stuart Lee Scharf
rawnote: Supervised by James H. McClellan.
rawtitle: A hardware realization of the {Winograd Fourier} Transform Algorithm
keywords:
Algorithms.; Computer engineering.; Floating-point arithmetic.; Fourier transformations --- Computer programs.

entry:
@MastersThesis{Scharf:1979:HRW,
  author =       "Stuart Lee Scharf",
  title =        "A hardware realization of the {Winograd Fourier}
                 Transform Algorithm",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical and Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "109",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by James H. McClellan.",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Computer engineering.; Floating-point
                 arithmetic.; Fourier transformations --- Computer
                 programs.",
}


bibtype: inproceedings
filename: fparith.bib
label: Shapiro:1979:ELM
author: G. Shapiro
title: Exploit LSI Memory Components Today, Instead of Waiting for Arithmetic Devices
crossref: Anonymous:1979:WCR
pages: ??--??
year: 1979
bibdate: Fri Nov 09 19:15:35 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:15:35 ???
note: Paper 18/5.
acknowledgement: ack-nhfb
rawauthor: G. Shapiro
rawnote: Paper 18/5.
rawtitle: Exploit {LSI} Memory Components Today, Instead of Waiting for Arithmetic Devices
entry:
@InProceedings{Shapiro:1979:ELM,
  author =       "G. Shapiro",
  title =        "Exploit {LSI} Memory Components Today, Instead of
                 Waiting for Arithmetic Devices",
  crossref =     "Anonymous:1979:WCR",
  pages =        "??--??",
  year =         "1979",
  bibdate =      "Fri Nov 09 19:15:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Paper 18/5.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Shauman:1979:OMA
author: Aleksandr Mikhailovich Shauman
title: Osnovy mashinnoi arifmetiki toenglish Principles of Machine Arithmetic endtoenglish
publisher: Izd-vo LGU (Leningrad State University Publishers)
address: Leningrad, USSR
pages: 311
year: 1979
LCCN: QA76.6 .S516
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: Aleksandr Mikhailovich Shauman
rawtitle: Osnovy mashinnoi arifmetiki \toenglish {Principles of Machine Arithmetic} \endtoenglish
keywords:
Computer arithmetic and logic units.; Electronic digital computers --- Programming.; Floating-point arithmetic.

remark:
At head of title: Leningradskii Gosudarstvennyi universitet imeni A. A. Zhdanova. Bibliography: p. 306-[309]

entry:
@Book{Shauman:1979:OMA,
  author =       "Aleksandr Mikhailovich Shauman",
  title =        "Osnovy mashinnoi arifmetiki \toenglish {Principles of
                 Machine Arithmetic} \endtoenglish",
  publisher =    "Izd-vo LGU (Leningrad State University Publishers)",
  address =      "Leningrad, USSR",
  pages =        "311",
  year =         "1979",
  LCCN =         "QA76.6 .S516",
  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.; Electronic
                 digital computers --- Programming.; Floating-point
                 arithmetic.",
  remark =       "At head of title: Leningradskii Gosudarstvennyi
                 universitet imeni A. A. Zhdanova. Bibliography: p.
                 306-[309]",
}


bibtype: article
filename: fparith.bib
label: Sheue:1979:TCM
author: A. E. Sheue
title: Two's-Complement Multiplication
journal: j-SIGMICRO
volume: 10
number: 1
pages: 21--23
month: mar
monthnumber: 3
year: 1979
CODEN: SIGMDJ
ISSN: 0163-5751, 1050-916X OR 01635751, 1050916X
ISSNL: 0163-5751 OR 01635751
bibdate: Thu Sep 1 10:15:07 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:07 ???
fjournal: ACM SIG Micro Newsletter
acknowledgement: ack-nj
rawauthor: A. E. Sheue
rawtitle: Two's-Complement Multiplication
entry:
@Article{Sheue:1979:TCM,
  author =       "A. E. Sheue",
  title =        "Two's-Complement Multiplication",
  journal =      j-SIGMICRO,
  volume =       "10",
  number =       "1",
  pages =        "21--23",
  month =        mar,
  year =         "1979",
  CODEN =        "SIGMDJ",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIG Micro Newsletter",
}


bibtype: article
filename: fparith.bib
label: Swartzlander:1979:CFN
author: E. E. Swartzlander, Jr.
title: Comment on ``The Focus Number System''
journal: j-IEEE-TRANS-COMPUT
volume: C-28
number: 9
pages: 693--693
month: sep
monthnumber: 9
year: 1979
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1979.1675441
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 06:49:40 MDT 2011
bibtimestamp: 2011.07.11 06:49:40 MDT
note: See cite Lee:1977:FNS,Lee:1979:AFN.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675441
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.}
rawnote: See \cite{Lee:1977:FNS,Lee:1979:AFN}.
rawtitle: Comment on {``The Focus Number System''}
entry:
@Article{Swartzlander:1979:CFN,
  author =       "E. E. {Swartzlander, Jr.}",
  title =        "Comment on {``The Focus Number System''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "9",
  pages =        "693--693",
  month =        sep,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675441",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:40 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{Lee:1977:FNS,Lee:1979:AFN}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675441",
  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: Thacker:1979:MPR
author: William I. Thacker and G. W. Gorsline
title: Micro programming rational arithmetic operations
journal: j-SIGMICRO
volume: 10
number: 1
pages: 10--13
month: mar
monthnumber: 3
year: 1979
CODEN: SIGMDJ
DOI: https://doi.org/10.1145/1217236.1217238
ISSN: 0163-5751, 1050-916X OR 01635751, 1050916X
ISSNL: 0163-5751 OR 01635751
bibdate: Fri Apr 16 10:27:24 MDT 2021
bibtimestamp: 2021.04.16 10:27:24 MDT
note: See critical comments cite Kornerup:1979:NRA and response cite Thacker:1979:R.
URL: https://dl.acm.org/doi/10.1145/1217236.1217238
fjournal: ACM SIGMICRO Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigmicro
rawauthor: William I. Thacker and G. W. Gorsline
rawnote: See critical comments \cite{Kornerup:1979:NRA} and response \cite{Thacker:1979:R}.
rawtitle: Micro programming rational arithmetic operations
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/sigmicro.bib

abstract:
For many years, real number arithmetic, whether accomplished in hardware, software, or firmware, has utilized a floating point scheme. This paper summarizes the results of a study assessing rational representation as a possible replacement for floating point representation. The Hewlett-Packard 2100A microprogrammable computer was used as the test vehicle. Both accuracy and speed comparisons were used to judge the usefulness of the substitution.

rawabstract:
For many years, real number arithmetic, whether accomplished in hardware, software, or firmware, has utilized a floating point scheme. This paper summarizes the results of a study assessing rational representation as a possible replacement for floating point representation. The Hewlett-Packard 2100A microprogrammable computer was used as the test vehicle. Both accuracy and speed comparisons were used to judge the usefulness of the substitution.

entry:
@Article{Thacker:1979:MPR,
  author =       "William I. Thacker and G. W. Gorsline",
  title =        "Micro programming rational arithmetic operations",
  journal =      j-SIGMICRO,
  volume =       "10",
  number =       "1",
  pages =        "10--13",
  month =        mar,
  year =         "1979",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1217236.1217238",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:24 MDT 2021",
  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/sigmicro.bib",
  note =         "See critical comments \cite{Kornerup:1979:NRA} and
                 response \cite{Thacker:1979:R}.",
  URL =          "https://dl.acm.org/doi/10.1145/1217236.1217238",
  abstract =     "For many years, real number arithmetic, whether
                 accomplished in hardware, software, or firmware, has
                 utilized a floating point scheme. This paper summarizes
                 the results of a study assessing rational
                 representation as a possible replacement for floating
                 point representation. The Hewlett-Packard 2100A
                 microprogrammable computer was used as the test
                 vehicle. Both accuracy and speed comparisons were used
                 to judge the usefulness of the substitution.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}


bibtype: article
filename: fparith.bib
label: Thacker:1979:R
author: W. I. Thacker and G. W. Gorsline
title: Response
journal: j-SIGMICRO
volume: 10
number: 2
pages: 29--29
month: jun
monthnumber: 6
year: 1979
CODEN: SIGMDJ
DOI: https://doi.org/10.1145/1218003.1218005
ISSN: 0163-5751, 1050-916X OR 01635751, 1050916X
ISSNL: 0163-5751 OR 01635751
bibdate: Fri Apr 16 10:27:24 MDT 2021
bibtimestamp: 2021.04.16 10:27:24 MDT
note: See cite Thacker:1979:MPR,Kornerup:1979:NRA.
URL: https://dl.acm.org/doi/10.1145/1218003.1218005
fjournal: ACM SIGMICRO Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigmicro
rawauthor: W. I. Thacker and G. W. Gorsline
rawnote: See \cite{Thacker:1979:MPR,Kornerup:1979:NRA}.
rawtitle: Response
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/sigmicro.bib

abstract:
Within the context of our study; that is, the direct substitution of a pure rational scheme for a floating point scheme of arithmetic and storage within an extant FORTRAN system with no changes to the compiler (and thus to the storage space available for a single numerical quantity), we continue to claim that our results are valid. We again wish to note that our investigation was limited to the pure rational scheme using the same storage space available to a floating point scheme.

rawabstract:
Within the context of our study; that is, the direct substitution of a pure rational scheme for a floating point scheme of arithmetic and storage within an extant FORTRAN system with no changes to the compiler (and thus to the storage space available for a single numerical quantity), we continue to claim that our results are valid. We again wish to note that our investigation was limited to the pure rational scheme using the same storage space available to a floating point scheme.

entry:
@Article{Thacker:1979:R,
  author =       "W. I. Thacker and G. W. Gorsline",
  title =        "Response",
  journal =      j-SIGMICRO,
  volume =       "10",
  number =       "2",
  pages =        "29--29",
  month =        jun,
  year =         "1979",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1218003.1218005",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:24 MDT 2021",
  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/sigmicro.bib",
  note =         "See \cite{Thacker:1979:MPR,Kornerup:1979:NRA}.",
  URL =          "https://dl.acm.org/doi/10.1145/1218003.1218005",
  abstract =     "Within the context of our study; that is, the direct
                 substitution of a pure rational scheme for a floating
                 point scheme of arithmetic and storage within an extant
                 FORTRAN system with no changes to the compiler (and
                 thus to the storage space available for a single
                 numerical quantity), we continue to claim that our
                 results are valid. We again wish to note that our
                 investigation was limited to the pure rational scheme
                 using the same storage space available to a floating
                 point scheme.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}


bibtype: article
filename: fparith.bib
label: Tseng:1979:IFS
author: Ben-Dau Tseng and G. A. Jullien and W. C. Miller
title: Implementation of FFT Structures Using the Residue Number System
journal: j-IEEE-TRANS-COMPUT
volume: C-28
number: 11
pages: 831--845
month: nov
monthnumber: 11
year: 1979
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1979.1675263
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 06:49:41 MDT 2011
bibtimestamp: 2011.07.11 06:49:41 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: Ben-Dau Tseng and G. A. Jullien and W. C. Miller
rawtitle: Implementation of {FFT} Structures Using the Residue Number System
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675263; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35176

entry:
@Article{Tseng:1979:IFS,
  author =       "Ben-Dau Tseng and G. A. Jullien and W. C. Miller",
  title =        "Implementation of {FFT} Structures Using the Residue
                 Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "11",
  pages =        "831--845",
  month =        nov,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675263",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:41 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=1675263;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35176",
  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 =      "This paper considers the implementation of a fast
                 Fourier transform (FFT) structure using arrays of
                 read-only memories. The arithmetic operations are based
                 entirely on the residue number system. The most
                 important aspect of the structure relates to \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Ukkonen:1979:AER
author: Esko Ukkonen
title: An analysis of the effect of rounding errors on the flow of control in numerical processes
journal: j-BIT
volume: 19
number: 1
pages: 116--133
month: mar
monthnumber: 3
year: 1979
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01931229
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65G05
MRnumber: 81a:65048
bibdate: Wed Jan 4 18:52:16 MST 2006
bibtimestamp: 2006.01.04 18:52:16 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=1&spage=116
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Esko Ukkonen
rawtitle: An analysis of the effect of rounding errors on the flow of control in numerical processes
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Ukkonen:1979:AER,
  author =       "Esko Ukkonen",
  title =        "An analysis of the effect of rounding errors on the
                 flow of control in numerical processes",
  journal =      j-BIT,
  volume =       "19",
  number =       "1",
  pages =        "116--133",
  month =        mar,
  year =         "1979",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01931229",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "81a:65048",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&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=19&issue=1&spage=116",
  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: vanHulzen:1979:NMS
author: J. A. van Hulzen
title: A note on methods for solving systems of polynomial equations with floating point coefficients
crossref: Ng:1979:SAC
pages: 346--357
year: 1979
MRclass: 65H10
MRnumber: 81h:65049
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: Frederick N. Fritsch
rawauthor: J. A. {van Hulzen}
rawtitle: A note on methods for solving systems of polynomial equations with floating point coefficients
entry:
@InProceedings{vanHulzen:1979:NMS,
  author =       "J. A. {van Hulzen}",
  title =        "A note on methods for solving systems of polynomial
                 equations with floating point coefficients",
  crossref =     "Ng:1979:SAC",
  pages =        "346--357",
  year =         "1979",
  MRclass =      "65H10",
  MRnumber =     "81h:65049",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "Frederick N. Fritsch",
}


bibtype: article
filename: fparith.bib
label: Wichmann:1979:ID
author: B. A. Wichmann
title: Integer division
journal: j-SPE
volume: 9
number: 6
pages: 507--508
month: jun
monthnumber: 6
year: 1979
CODEN: SPEXBL
DOI: https://doi.org/10.1002/spe.4380090610
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Wed Sep 10 12:36:39 MDT 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/spe.bib
bibtimestamp: 2014.09.10 12:36:39 MDT
fjournal: Software --- Practice and Experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
onlinedate: 27 Oct 2006
rawauthor: B. A. Wichmann
rawtitle: Integer division
entry:
@Article{Wichmann:1979:ID,
  author =       "B. A. Wichmann",
  title =        "Integer division",
  journal =      j-SPE,
  volume =       "9",
  number =       "6",
  pages =        "507--508",
  month =        jun,
  year =         "1979",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380090610",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Wed Sep 10 12:36:39 MDT 2014",
  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",
  onlinedate =   "27 Oct 2006",
}


bibtype: article
filename: fparith.bib
label: Wichmann:1979:PCG
author: B. A. Wichmann and J. Du Croz
title: A program to calculate the GAMM measure
journal: j-COMP-J
volume: 22
number: 4
pages: 317--322
month: nov
monthnumber: 11
year: 1979
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: Compendex database; 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: C4240 (Programming and algorithm theory); C7430 (Computer engineering)
corpsource: Computing Services Unit, Nat. Phys. Lab., Teddington, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: B. A. Wichmann and J. {Du Croz}
rawtitle: A program to calculate the {GAMM} measure
keywords:
analysis; complete computer programs; computer performance; computer programs; computer selection and; confidence check; error; evaluation; floating point calculation; FORTRAN program; GAMM measure; performance evaluation

entry:
@Article{Wichmann:1979:PCG,
  author =       "B. A. Wichmann and J. {Du Croz}",
  title =        "A program to calculate the {GAMM} measure",
  journal =      j-COMP-J,
  volume =       "22",
  number =       "4",
  pages =        "317--322",
  month =        nov,
  year =         "1979",
  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;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C4240 (Programming and algorithm theory); C7430
                 (Computer engineering)",
  classification = "723",
  corpsource =   "Computing Services Unit, Nat. Phys. Lab., Teddington,
                 UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "analysis; complete computer programs; computer
                 performance; computer programs; computer selection and;
                 confidence check; error; evaluation; floating point
                 calculation; FORTRAN program; GAMM measure; performance
                 evaluation",
  treatment =    "P Practical",
}


bibtype: mastersthesis
filename: fparith.bib
label: Wilbanks:1979:MFI
author: Thomas D. Wilbanks
title: Microcoding floating-point instructions for a bit-slice processor
type: Thesis (M.S.)
school: University of South Carolina
address: Columbia, SC, USA
pages: vi + 131
year: 1979
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: Bit slice microprocessors.; Microprocessors --- Programming.
acknowledgement: ack-nhfb
rawauthor: Thomas D. Wilbanks
rawtitle: Microcoding floating-point instructions for a bit-slice processor
entry:
@MastersThesis{Wilbanks:1979:MFI,
  author =       "Thomas D. Wilbanks",
  title =        "Microcoding floating-point instructions for a
                 bit-slice processor",
  type =         "Thesis ({M.S.})",
  school =       "University of South Carolina",
  address =      "Columbia, SC, USA",
  pages =        "vi + 131",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bit slice microprocessors.; Microprocessors ---
                 Programming.",
}


bibtype: inproceedings
filename: fparith.bib
label: Winnigstad:1979:ULC
author: C. N. Winnigstad
title: Using LSI to Crunch Numbers at High Speed: An Overview
crossref: Anonymous:1979:WCR
pages: ??--??
year: 1979
bibdate: Fri Nov 09 19:43:13 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:43:13 ???
acknowledgement: ack-nhfb
rawauthor: C. N. Winnigstad
rawtitle: Using {LSI} to Crunch Numbers at High Speed: An Overview
entry:
@InProceedings{Winnigstad:1979:ULC,
  author =       "C. N. Winnigstad",
  title =        "Using {LSI} to Crunch Numbers at High Speed: An
                 Overview",
  crossref =     "Anonymous:1979:WCR",
  pages =        "??--??",
  year =         "1979",
  bibdate =      "Fri Nov 09 19:43:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Yohe:1979:INA
author: J. M. Yohe
title: Implementing Nonstandard Arithmetics
journal: j-SIAM-REVIEW
volume: 21
number: 1
pages: 34--56
year: 1979
CODEN: SIREAD
DOI: https://doi.org/10.1137/1021003
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: J. M. Yohe
rawtitle: Implementing Nonstandard Arithmetics
entry:
@Article{Yohe:1979:INA,
  author =       "J. M. Yohe",
  title =        "Implementing Nonstandard Arithmetics",
  journal =      j-SIAM-REVIEW,
  volume =       "21",
  number =       "1",
  pages =        "34--56",
  month =        "????",
  year =         "1979",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1021003",
  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 # " and " # ack-jr,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}


bibtype: article
filename: fparith.bib
label: Agrawal:1980:NBA
author: D. P. Agrawal
title: On Negabinary-Binary Arithmetic Relationships and Their Hardware Reciprocity
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 11
pages: 1032--1035
month: nov
monthnumber: 11
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675502
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 19:15:30 MDT 2011
bibtimestamp: 2011.07.10 19:15:30 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675502
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
rawtitle: On Negabinary-Binary Arithmetic Relationships and Their Hardware Reciprocity
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib

entry:
@Article{Agrawal:1980:NBA,
  author =       "D. P. Agrawal",
  title =        "On Negabinary-Binary Arithmetic Relationships and
                 Their Hardware Reciprocity",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "11",
  pages =        "1032--1035",
  month =        nov,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675502",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675502",
  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: Albrecht:1980:RAO
author: R. Albrecht
title: Roundings and Approximations in Ordered Sets
crossref: Alefeld:1980:FNC
pages: 17--31
year: 1980
bibdate: Tue Oct 23 08:17:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.23 08:17:48 ???
keywords: interval arithmetic; rounding error
acknowledgement: ack-nhfb
rawauthor: R. Albrecht
rawtitle: Roundings and Approximations in Ordered Sets
entry:
@InProceedings{Albrecht:1980:RAO,
  author =       "R. Albrecht",
  title =        "Roundings and Approximations in Ordered Sets",
  crossref =     "Alefeld:1980:FNC",
  pages =        "17--31",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rounding error",
}


bibtype: article
filename: fparith.bib
label: Ambikairajah:1980:TPM
author: E. Ambikairajah and M. J. Carey
journal: j-ELECT-LETTERS
volume: 16
number: 2
pages: 53--54
month: jan
monthnumber: 1
year: 1980
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Thu Sep 1 10:15:07 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:07 ???
fjournal: Electronics Letters
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: E. Ambikairajah and M. J. Carey
title:
Technique for Performing Multiplication on a 16-bit Microprocessor Using an Extension of Booth's Algorithm

rawtitle:
Technique for Performing Multiplication on a 16-bit Microprocessor Using an Extension of {Booth}'s Algorithm

entry:
@Article{Ambikairajah:1980:TPM,
  author =       "E. Ambikairajah and M. J. Carey",
  title =        "Technique for Performing Multiplication on a 16-bit
                 Microprocessor Using an Extension of {Booth}'s
                 Algorithm",
  journal =      j-ELECT-LETTERS,
  volume =       "16",
  number =       "2",
  pages =        "53--54",
  month =        jan,
  year =         "1980",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}


bibtype: article
filename: fparith.bib
label: Baraniecka:1980:RNS
author: A. Baraniecka and G. Jullien
title: Residue number system implementations of number theoretic transforms in complex residue rings
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 28
number: 3
pages: 285--291
month: jun
monthnumber: 6
year: 1980
CODEN: IETABA
DOI: https://doi.org/10.1109/TC.1979.1675263
ISSN: 0096-3518 OR 00963518
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26146
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: A. Baraniecka and G. Jullien
rawtitle: Residue number system implementations of number theoretic transforms in complex residue rings
entry:
@Article{Baraniecka:1980:RNS,
  author =       "A. Baraniecka and G. Jullien",
  title =        "Residue number system implementations of number
                 theoretic transforms in complex residue rings",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "28",
  number =       "3",
  pages =        "285--291",
  month =        jun,
  year =         "1980",
  CODEN =        "IETABA",
  DOI =          "https://doi.org/10.1109/TC.1979.1675263",
  ISSN =         "0096-3518",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26146",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper discusses the implementation of number
                 theoretic transforms defined in complex residue rings.
                 A selection of transform parameters for lookup table
                 and microprocessor realizations are discussed. When the
                 length of the convolution is \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Bareiss:1980:RED
author: E. H. Bareiss and J. L. Barlow
title: Roundoff error distribution in fixed point multiplication
journal: j-BIT
volume: 20
number: 2
pages: 247--250
month: jun
monthnumber: 6
year: 1980
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01933198
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65G05
MRnumber: 81j:65066
MRreviewer: Seppo Linnainmaa
bibdate: Wed Jan 4 18:52:16 MST 2006
bibtimestamp: 2006.01.04 18:52:16 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=2&spage=247
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: E. H. Bareiss and J. L. Barlow
rawtitle: Roundoff error distribution in fixed point multiplication
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Bareiss:1980:RED,
  author =       "E. H. Bareiss and J. L. Barlow",
  title =        "Roundoff error distribution in fixed point
                 multiplication",
  journal =      j-BIT,
  volume =       "20",
  number =       "2",
  pages =        "247--250",
  month =        jun,
  year =         "1980",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933198",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "81j:65066",
  MRreviewer =   "Seppo Linnainmaa",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&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=20&issue=2&spage=247",
  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: Barsi:1980:ECC
author: Ferruccio Barsi and Piero Maestrini
title: Error codes constructed in residue number systems with non-pairwise-prime moduli
journal: j-INF-CONTROL
volume: 46
number: 1
pages: 16--25
month: jul
monthnumber: 7
year: 1980
CODEN: IFCNA4
DOI: https://doi.org/10.1016/S0019-9958(80)90471-4
ISSN: 0019-9958 (print), 1878-2981 (electronic) OR 00199958 (print), 18782981 (electronic)
ISSNL: 0019-9958 OR 00199958
bibdate: Thu Nov 18 09:54:38 2010
bibtimestamp: 2010.11.18 09:54:38 ???
fjournal: Information and Control
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00199958
rawauthor: Ferruccio Barsi and Piero Maestrini
rawtitle: Error codes constructed in residue number systems with non-pairwise-prime moduli
bibsource:
http://www.sciencedirect.com/science/journal/00199958; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Codes constructed in a Residue Number System (RNS) of moduli $ m_1, m_2, ldots , m_n $ are non-binary, arithmetic codes whose codewords are vectors where the $i$ th component is $ m_i $-valued $ (1 leq i leq n) $. A new class of codes in RNS is described, where redundancy is introduced by removing the constraint that the moduli of the RNS be pairwise prime. The error-detecting and correcting capabilities of such codes are discussed and a simple approach to error detection, localization and correction is presented. Although the codes under consideration are quite inefficient in some respects, it is shown that codes is examined in more detail. Codes in this subclass, besides correcting all single errors, also correct almost all of double errors and localize some errors of higher multiplicity, with less redundancy than required to construct optimal 2-correcting codes in RNS.

rawabstract:
Codes constructed in a Residue Number System (RNS) of moduli $ m_1, m_2, \ldots {}, m_n $ are non-binary, arithmetic codes whose codewords are vectors where the $i$ th component is $ m_i $-valued $ (1 \leq i \leq n) $. A new class of codes in RNS is described, where redundancy is introduced by removing the constraint that the moduli of the RNS be pairwise prime. The error-detecting and correcting capabilities of such codes are discussed and a simple approach to error detection, localization and correction is presented. Although the codes under consideration are quite inefficient in some respects, it is shown that codes is examined in more detail. Codes in this subclass, besides correcting all single errors, also correct almost all of double errors and localize some errors of higher multiplicity, with less redundancy than required to construct optimal 2-correcting codes in RNS.

entry:
@Article{Barsi:1980:ECC,
  author =       "Ferruccio Barsi and Piero Maestrini",
  title =        "Error codes constructed in residue number systems with
                 non-pairwise-prime moduli",
  journal =      j-INF-CONTROL,
  volume =       "46",
  number =       "1",
  pages =        "16--25",
  month =        jul,
  year =         "1980",
  CODEN =        "IFCNA4",
  DOI =          "https://doi.org/10.1016/S0019-9958(80)90471-4",
  ISSN =         "0019-9958 (print), 1878-2981 (electronic)",
  ISSN-L =       "0019-9958",
  bibdate =      "Thu Nov 18 09:54:38 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/00199958;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Codes constructed in a Residue Number System (RNS) of
                 moduli $ m_1, m_2, \ldots {}, m_n $ are non-binary,
                 arithmetic codes whose codewords are vectors where the
                 $i$ th component is $ m_i $-valued $ (1 \leq i \leq n)
                 $. A new class of codes in RNS is described, where
                 redundancy is introduced by removing the constraint
                 that the moduli of the RNS be pairwise prime. The
                 error-detecting and correcting capabilities of such
                 codes are discussed and a simple approach to error
                 detection, localization and correction is presented.
                 Although the codes under consideration are quite
                 inefficient in some respects, it is shown that codes is
                 examined in more detail. Codes in this subclass,
                 besides correcting all single errors, also correct
                 almost all of double errors and localize some errors of
                 higher multiplicity, with less redundancy than required
                 to construct optimal 2-correcting codes in RNS.",
  acknowledgement = ack-nhfb,
  fjournal =     "Information and Control",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00199958",
}


bibtype: article
filename: fparith.bib
label: Brent:1980:AIB
author: Richard P. Brent and Judith A. Hooper and J. Michael Yohe
title: An AUGMENT Interface for Brent's Multiple Precision Arithmetic Package
journal: j-TOMS
volume: 6
number: 2
pages: 146--149
month: jun
monthnumber: 6
year: 1980
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355887.355889
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Sep 05 22:49:19 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.05 22:49:19 ???
note: See cite Brent:1978:AMF,Brent:1979:RMF.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Richard P. Brent and Judith A. Hooper and J. Michael Yohe
rawnote: See \cite{Brent:1978:AMF,Brent:1979:RMF}.
rawtitle: An {AUGMENT} Interface for {Brent}'s Multiple Precision Arithmetic Package
keywords:
arithmetic, multiple precision, extended precision, floating point, portable software, software package, precompiler interface, AUGMENT interface

entry:
@Article{Brent:1980:AIB,
  author =       "Richard P. Brent and Judith A. Hooper and J. Michael
                 Yohe",
  title =        "An {AUGMENT} Interface for {Brent}'s Multiple
                 Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "146--149",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355889",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 22:49:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Brent:1978:AMF,Brent:1979:RMF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic, multiple precision, extended precision,
                 floating point, portable software, software package,
                 precompiler interface, AUGMENT interface",
}


bibtype: inproceedings
filename: fparith.bib
label: Brent:1980:UAE
author: R. P. Brent
title: Unrestricted Algorithms for Elementary and Special Functions
crossref: Lavington:1980:IPP
pages: 613--619
year: 1980
bibdate: Thu Sep 01 11:55:31 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 11:55:31 ???
acknowledgement: ack-nj
rawauthor: R. P. Brent
rawtitle: Unrestricted Algorithms for Elementary and Special Functions
entry:
@InProceedings{Brent:1980:UAE,
  author =       "R. P. Brent",
  title =        "Unrestricted Algorithms for Elementary and Special
                 Functions",
  crossref =     "Lavington:1980:IPP",
  pages =        "613--619",
  year =         "1980",
  bibdate =      "Thu Sep 01 11:55:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Brown:1980:EPB
author: W. S. Brown and S. I. Feldman
title: Environment Parameters and Basic Functions for Floating-Point Computation
journal: j-TOMS
volume: 6
number: 4
pages: 510--523
month: dec
monthnumber: 12
year: 1980
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355921.355924
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Sep 1 10:15:05 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 10:15:05 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: environment parameters, floating-point arithmetic, software portability
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. S. Brown and S. I. Feldman
rawtitle: Environment Parameters and Basic Functions for Floating-Point Computation
entry:
@Article{Brown:1980:EPB,
  author =       "W. S. Brown and S. I. Feldman",
  title =        "Environment Parameters and Basic Functions for
                 Floating-Point Computation",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "510--523",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355924",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 1 10:15:05 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 =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "environment parameters, floating-point arithmetic,
                 software portability",
}


bibtype: techreport
filename: fparith.bib
label: Brown:1980:SRM
author: W. S. Brown
title: A Simple But Realistic Model of Floating-Point Computation
type: Computer Science Technical Report
number: 83
institution: Bell Laboratories
address: Murray Hill, NJ, 07974, USA
pages: 510--523
month: may
monthnumber: 5
year: 1980
bibdate: Wed Oct 13 06:30:12 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 06:30:12 ???
note: Revised November 1980.
remark: See cite [pp. 1.9--1.10]Coonen:1984:CPS for negative comments about the model in this report.
acknowledgement: ack-nhfb
rawauthor: W. S. Brown
rawnote: Revised November 1980.
rawtitle: A Simple But Realistic Model of Floating-Point Computation
entry:
@TechReport{Brown:1980:SRM,
  author =       "W. S. Brown",
  title =        "A Simple But Realistic Model of Floating-Point
                 Computation",
  type =         "Computer Science Technical Report",
  number =       "83",
  institution =  "Bell Laboratories",
  address =      "Murray Hill, NJ, 07974, USA",
  month =        may,
  year =         "1980",
  bibdate =      "Wed Oct 13 06:30:12 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised November 1980.",
  acknowledgement = ack-nhfb,
  remark =       "See \cite[pp. 1.9--1.10]{Coonen:1984:CPS} for negative
                 comments about the model in this report.",
}


bibtype: article
filename: fparith.bib
label: Burmeister:1980:OIE
author: W. Burmeister
journal: j-COMPUTING
volume: 25
number: 3
pages: 283--295
year: 1980
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65F30 (15A57)
MRnumber: 82e:65044
bibdate: Tue Jan 2 17:40:54 MST 2001
bibtimestamp: 2001.01.02 17:40:54 MST
fjournal: Computing: Archiv fur informatik und numerik
keywords: cone; elementwise inclusion; interval enclosing; matrix interval; optimal bounds; partial ordering
acknowledgement: ack-nhfb
affiliation: Sektion Math., Tech. University of Dresden, Dresden, East Germany
journalURL: http://link.springer.com/journal/607
rawauthor: W. Burmeister
title:
Optimal interval enclosing of certain sets of matrices, with application to monotone enclosing of square roots

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date); MathSciNet database

rawtitle:
Optimal interval enclosing of certain sets of matrices, with application to monotone enclosing of square roots

entry:
@Article{Burmeister:1980:OIE,
  author =       "W. Burmeister",
  title =        "Optimal interval enclosing of certain sets of
                 matrices, with application to monotone enclosing of
                 square roots",
  journal =      j-COMPUTING,
  volume =       "25",
  number =       "3",
  pages =        "283--295",
  year =         "1980",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65F30 (15A57)",
  MRnumber =     "82e:65044",
  bibdate =      "Tue Jan 2 17:40:54 MST 2001",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "Sektion Math., Tech. University of Dresden, Dresden,
                 East Germany",
  classification = "C4140",
  description =  "matrix algebra",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "cone; elementwise inclusion; interval enclosing;
                 matrix interval; optimal bounds; partial ordering",
}


bibtype: article
filename: fparith.bib
label: Chang:1980:CAE
author: T. Chang
title: Comments on ``An approach to eliminate roundoff errors in digital filters''
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 28
number: 2
pages: 244--244
month: apr
monthnumber: 4
year: 1980
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
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: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: T. Chang
rawtitle: Comments on {``An} approach to eliminate roundoff errors in digital filters''
entry:
@Article{Chang:1980:CAE,
  author =       "T. Chang",
  title =        "Comments on {``An} approach to eliminate roundoff
                 errors in digital filters''",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "28",
  number =       "2",
  pages =        "244--244",
  month =        apr,
  year =         "1980",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 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",
}


bibtype: inproceedings
filename: fparith.bib
label: Cheng:1980:ASC
author: S. Cheng and K. Rallapalli
title: Am9512: Single Chip Floating-Point Processor
crossref: Electro:1980:ECR
pages: 14/4/1--6
year: 1980
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: S. Cheng and K. Rallapalli
rawtitle: Am9512: Single Chip Floating-Point Processor
remark:
The Am 9512 floating-point processor is claimed on at least one Web page to be compatible with the Intel 8232, and that page claims the 8232 has IEEE floating-point, while the earlier 8231 and 8231A were some other format (see cite Intel:19xx:IAP for a brief description of the 8231A 32-bit floating-point encoding).

entry:
@InProceedings{Cheng:1980:ASC,
  author =       "S. Cheng and K. Rallapalli",
  title =        "Am9512: Single Chip Floating-Point Processor",
  crossref =     "Electro:1980:ECR",
  pages =        "14/4/1--6",
  year =         "1980",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  remark =       "The Am 9512 floating-point processor is claimed on at
                 least one Web page to be compatible with the Intel
                 8232, and that page claims the 8232 has IEEE
                 floating-point, while the earlier 8231 and 8231A were
                 some other format (see \cite{Intel:19xx:IAP} for a
                 brief description of the 8231A 32-bit floating-point
                 encoding).",
}


bibtype: phdthesis
filename: fparith.bib
label: Chow:1980:VPP
author: Catherine Yuk-Fun Chow
title: A variable precision processor module
type: Thesis (Ph.D.)
school: Department of Computer Science, University of Illinois at Urbana-Champaign
address: Urbana, IL, USA
pages: vi + 183
month: jul
monthnumber: 7
year: 1980
LCCN: QA76 .I4 no. 1032
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: UIUCDCS-R 80-1032
keywords: Floating-point arithmetic.; Parallel processing (Electronic computers)
acknowledgement: ack-nj
rawauthor: Catherine Yuk-Fun Chow
rawtitle: A variable precision processor module
entry:
@PhdThesis{Chow:1980:VPP,
  author =       "Catherine Yuk-Fun Chow",
  title =        "A variable precision processor module",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, IL, USA",
  pages =        "vi + 183",
  month =        jul,
  year =         "1980",
  LCCN =         "QA76 .I4 no. 1032",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "UIUCDCS-R 80-1032",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Floating-point arithmetic.; Parallel processing
                 (Electronic computers)",
}


bibtype: article
filename: fparith.bib
label: Cluley:1980:DCB
author: J. C. Cluley
title: Digital Circuits for Binary Arithmetic
journal: j-COMP-J
volume: 23
number: 3
pages: 269--269
month: aug
monthnumber: 8
year: 1980
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/23.3.269
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:48:08 MST 2012
bibtimestamp: 2012.12.04 14:48:08 MST
URL: http://comjnl.oxfordjournals.org/content/23/3/269.full.pdf+html
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: J. C. Cluley
rawtitle: Digital Circuits for Binary Arithmetic
bibsource:
http://comjnl.oxfordjournals.org/content/23/3.toc; https://www.math.utah.edu/pub/tex/bib/compj1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Cluley:1980:DCB,
  author =       "J. C. Cluley",
  title =        "Digital Circuits for Binary Arithmetic",
  journal =      j-COMP-J,
  volume =       "23",
  number =       "3",
  pages =        "269--269",
  month =        aug,
  year =         "1980",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/23.3.269",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:08 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/23/3.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/23/3/269.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: book
filename: fparith.bib
label: Cody:1980:SME
author: W. J. Cody and W. Waite
title: Software Manual for the Elementary Functions
publisher: pub-PH
address: pub-PH:adr
pages: x + 269
year: 1980
ISBN: 0-13-822064-6 OR 0138220646
ISBN13: 978-0-13-822064-8 OR 9780138220648
LCCN: QA331 .C635 1980
bibdate: Thu Sep 1 10:12:51 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:12:51 ???
acknowledgement: ack-nj
rawauthor: W. J. Cody and W. Waite
rawtitle: Software Manual for the Elementary Functions
entry:
@Book{Cody:1980:SME,
  author =       "W. J. Cody and W. Waite",
  title =        "Software Manual for the Elementary Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 269",
  year =         "1980",
  ISBN =         "0-13-822064-6",
  ISBN-13 =      "978-0-13-822064-8",
  LCCN =         "QA331 .C635 1980",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Coonen:1980:IGP
author: Jerome T. Coonen
title: An Implementation Guide to a Proposed Standard for Floating-Point Arithmetic
journal: j-COMPUTER
volume: 13
number: 1
pages: 68--79
month: jan
monthnumber: 1
year: 1980
CODEN: CPTRB4
DOI: https://doi.org/10.1109/MC.1980.1653344
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Sun May 02 09:17:48 1999
bibtimestamp: 1999.05.02 09:17:48 ???
note: See errata in cite Coonen:1981:EIG. See cite IEEE:1985:AIS,IEEE:1985:ASI.
fjournal: Computer
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: Jerome T. Coonen
rawnote: See errata in \cite{Coonen:1981:EIG}. See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.
rawtitle: An Implementation Guide to a Proposed Standard for Floating-Point Arithmetic
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/computer1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Coonen:1980:IGP,
  author =       "Jerome T. Coonen",
  title =        "An Implementation Guide to a Proposed Standard for
                 Floating-Point Arithmetic",
  journal =      j-COMPUTER,
  volume =       "13",
  number =       "1",
  pages =        "68--79",
  month =        jan,
  year =         "1980",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/MC.1980.1653344",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sun May 02 09:17:48 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See errata in \cite{Coonen:1981:EIG}. See
                 \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nj,
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: article
filename: fparith.bib
label: Dao:1980:CNA
author: T. T. Dao and M. Davio and C. Gossart
title: Complex Number Arithmetic with Odd-Valued Logic
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 7
pages: 604--611
month: jul
monthnumber: 7
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675631
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 19:15:27 MDT 2011
bibtimestamp: 2011.07.10 19:15:27 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675631
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. T. Dao and M. Davio and C. Gossart
rawtitle: Complex Number Arithmetic with Odd-Valued Logic
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib

entry:
@Article{Dao:1980:CNA,
  author =       "T. T. Dao and M. Davio and C. Gossart",
  title =        "Complex Number Arithmetic with Odd-Valued Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "7",
  pages =        "604--611",
  month =        jul,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675631",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675631",
  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: DeVaal:1980:SZI
author: C. De Vaal and R. Nouta
title: On the suppression of zero-input parasitic oscillations in floating point wave digital filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 27
number: 2
pages: 144--145
month: feb
monthnumber: 2
year: 1980
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: C. {De Vaal} and R. Nouta
rawtitle: On the suppression of zero-input parasitic oscillations in floating point wave digital filters
entry:
@Article{DeVaal:1980:SZI,
  author =       "C. {De Vaal} and R. Nouta",
  title =        "On the suppression of zero-input parasitic
                 oscillations in floating point wave digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "27",
  number =       "2",
  pages =        "144--145",
  month =        feb,
  year =         "1980",
  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 =      "Fettweis [1] has given a condition which guarantees,
                 if satisfied, the absence of zero-input parasitic
                 oscillations in wave digital filters. In this paper a
                 method is given which can be used to implement this
                 condition in the case of floating point \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Etzel:1980:RRN
author: M. Etzel and W. Jenkins
title: Redundant residue number systems for error detection and correction in digital filters
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 28
number: 5
pages: 538--545
month: oct
monthnumber: 10
year: 1980
CODEN: IETABA
DOI: https://doi.org/10.1109/TC.1979.1675263
ISSN: 0096-3518 OR 00963518
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26148
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: M. Etzel and W. Jenkins
rawtitle: Redundant residue number systems for error detection and correction in digital filters
entry:
@Article{Etzel:1980:RRN,
  author =       "M. Etzel and W. Jenkins",
  title =        "Redundant residue number systems for error detection
                 and correction in digital filters",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "28",
  number =       "5",
  pages =        "538--545",
  month =        oct,
  year =         "1980",
  CODEN =        "IETABA",
  DOI =          "https://doi.org/10.1109/TC.1979.1675263",
  ISSN =         "0096-3518",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26148",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  keywords =     "residue arithmetic; residue number system",
  summary =      "In spite of rapid advances during the last few years
                 in the design and realization of digital filters, very
                 little attention has been given to the problems of
                 error detection and correction in digital filters. This
                 paper describes how redundant \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Farrell:1980:PFP
author: L. Farrell
title: 8232: a Peripheral for Floating-Point Arithmetic
crossref: IEEE:1980:PMA
pages: 13--18
year: 1980
bibdate: Wed Sep 07 22:25:18 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:25:18 ???
acknowledgement: ack-nj
rawauthor: L. Farrell
rawtitle: 8232: a Peripheral for Floating-Point Arithmetic
entry:
@InProceedings{Farrell:1980:PFP,
  author =       "L. Farrell",
  title =        "8232: a Peripheral for Floating-Point Arithmetic",
  crossref =     "IEEE:1980:PMA",
  pages =        "13--18",
  year =         "1980",
  bibdate =      "Wed Sep 07 22:25:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: unpublished
filename: fparith.bib
label: Fraley:1980:PSB
author: R. A. Fraley and J. S. Walther
title: A Proposed Standard for Binary Floating-Point Arithmetic, Alternative 3, Draft 1
pages: 13--18
day: 4
month: jan
monthnumber: 1
year: 1980
bibdate: Thu Nov 25 10:19:54 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.25 10:19:54 ???
note: Cited in cite Payne:1980:VFPb.
acknowledgement: ack-nhfb
rawauthor: R. A. Fraley and J. S. Walther
rawnote: Cited in \cite{Payne:1980:VFPb}.
rawtitle: A Proposed Standard for Binary Floating-Point Arithmetic, Alternative 3, Draft 1
entry:
@Unpublished{Fraley:1980:PSB,
  author =       "R. A. Fraley and J. S. Walther",
  title =        "A Proposed Standard for Binary Floating-Point
                 Arithmetic, Alternative 3, Draft 1",
  day =          "4",
  month =        jan,
  year =         "1980",
  bibdate =      "Thu Nov 25 10:19:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in \cite{Payne:1980:VFPb}.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Fraley:1980:STO
author: R. A. Fraley and J. S. Walther
title: Safe Treatment of Overflow and Underflow Conditions
crossref: Electro:1980:ECR
pages: 18/2/1--5
year: 1980
bibdate: Wed Sep 07 21:38:30 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 21:38:30 ???
acknowledgement: ack-nj
rawauthor: R. A. Fraley and J. S. Walther
rawtitle: Safe Treatment of Overflow and Underflow Conditions
entry:
@InProceedings{Fraley:1980:STO,
  author =       "R. A. Fraley and J. S. Walther",
  title =        "Safe Treatment of Overflow and Underflow Conditions",
  crossref =     "Electro:1980:ECR",
  pages =        "18/2/1--5",
  year =         "1980",
  bibdate =      "Wed Sep 07 21:38:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Gajski:1980:PC
author: D. D. Gajski
title: Parallel Compressors
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 5
pages: 393--398
month: may
monthnumber: 5
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675589
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 10:56:18 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:56:18 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. D. Gajski
rawtitle: Parallel Compressors
entry:
@Article{Gajski:1980:PC,
  author =       "D. D. Gajski",
  title =        "Parallel Compressors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "5",
  pages =        "393--398",
  month =        may,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675589",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 10:56:18 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: Gargantini:1980:PSR
author: Irene Gargantini
title: Parallel Square-Root Iterations for Multiple Roots
journal: j-COMPUT-MATH-APPL
volume: 6
number: 3
pages: 279--288
year: 1980
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:19 MST 2017
bibtimestamp: 2017.03.01 18:51:19 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122180900358
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-jr
journalURL: http://www.sciencedirect.com/science/journal/08981221/
rawauthor: Irene Gargantini
rawtitle: Parallel Square-Root Iterations for Multiple Roots
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Gargantini:1980:PSR,
  author =       "Irene Gargantini",
  title =        "Parallel Square-Root Iterations for Multiple Roots",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "3",
  pages =        "279--288",
  month =        "????",
  year =         "1980",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122180900358",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}


bibtype: article
filename: fparith.bib
label: Ginsberg:1980:MFE
author: Myron Ginsberg
title: Monitoring floating-point error propagation in scientific computation
journal: j-COMPUT-MATH-APPL
volume: 6
number: 1
pages: 23--43
year: 1980
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65G10 (65-04)
MRnumber: 82a:65031
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Myron Ginsberg
rawtitle: Monitoring floating-point error propagation in scientific computation
entry:
@Article{Ginsberg:1980:MFE,
  author =       "Myron Ginsberg",
  title =        "Monitoring floating-point error propagation in
                 scientific computation",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "1",
  pages =        "23--43",
  year =         "1980",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65G10 (65-04)",
  MRnumber =     "82a:65031",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxnote =       "Special Issue",
}


bibtype: article
filename: fparith.bib
label: Ginsberg:1980:MFP
author: Myron Ginsberg
title: Monitoring Floating-Point Error Propagation in Scientific Computation
journal: j-COMPUT-MATH-APPL
volume: 6
number: 1
pages: 23--43
year: 1980
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65G10 (65-04)
MRnumber: 82a:65031
bibdate: Wed Mar 1 18:51:18 MST 2017
bibtimestamp: 2017.03.01 18:51:18 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122180900577
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-jr
journalURL: http://www.sciencedirect.com/science/journal/08981221/
rawauthor: Myron Ginsberg
rawtitle: Monitoring Floating-Point Error Propagation in Scientific Computation
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Ginsberg:1980:MFP,
  author =       "Myron Ginsberg",
  title =        "Monitoring Floating-Point Error Propagation in
                 Scientific Computation",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "1",
  pages =        "23--43",
  month =        "????",
  year =         "1980",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65G10 (65-04)",
  MRnumber =     "82a:65031",
  bibdate =      "Wed Mar 1 18:51:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122180900577",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
  xxnote =       "Special Issue",
}


bibtype: article
filename: fparith.bib
label: Goodwin:1980:PNU
author: D. T. Goodwin
title: Partial Non-Underflow and Non-Overflow of an Arithmetic Stack
journal: j-COMP-J
volume: 23
number: 2
pages: 153--160
month: may
monthnumber: 5
year: 1980
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/23.2.153
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
MRclass: 68B20
MRnumber: 81i:68039
bibdate: Tue Dec 4 14:48:08 MST 2012
bibtimestamp: 2012.12.04 14:48:08 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C6150J (Operating systems)
corpsource: Department of Computer Sci., University of Keele, Newcastle-under-Lyme, UK
journalURL: http://comjnl.oxfordjournals.org/
reviewer: K. S. Fu
treatment: P Practical
rawauthor: D. T. Goodwin
rawtitle: Partial Non-Underflow and Non-Overflow of an Arithmetic Stack
bibsource:
Compendex database; http://comjnl.oxfordjournals.org/content/23/2.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/; https://www.math.utah.edu/pub/tex/bib/compj1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/23/2/153.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/153.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/154.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/155.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/156.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/157.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/158.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/159.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/160.tif

keywords:
arithmetic stack; computer programming; high level language compile time; overflow; stack; storage allocation; underflow

entry:
@Article{Goodwin:1980:PNU,
  author =       "D. T. Goodwin",
  title =        "Partial Non-Underflow and Non-Overflow of an
                 Arithmetic Stack",
  journal =      j-COMP-J,
  volume =       "23",
  number =       "2",
  pages =        "153--160",
  month =        may,
  year =         "1980",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/23.2.153",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "68B20",
  MRnumber =     "81i:68039",
  bibdate =      "Tue Dec 4 14:48:08 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/23/2.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/23/2/153.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/153.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/154.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/155.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/156.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/157.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/158.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/159.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/160.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150J (Operating systems)",
  classification = "723",
  corpsource =   "Department of Computer Sci., University of Keele,
                 Newcastle-under-Lyme, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic stack; computer programming; high level
                 language compile time; overflow; stack; storage
                 allocation; underflow",
  reviewer =     "K. S. Fu",
  treatment =    "P Practical",
}


bibtype: book
filename: fparith.bib
label: Gosling:1980:DAU
author: John B. Gosling
title: Design of Arithmetic Units for Digital Computers
publisher: pub-MAC
address: pub-MAC:adr
pages: x + 139
year: 1980
ISBN: 0-387-91171-5, 0-333-26397-9, 0-333-26398-7 OR 0387911715, 0333263979, 0333263987
LCCN: QA76.6.G668, TK7888.3 .G64 1980
bibdate: Wed Sep 07 20:43:22 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 20:43:22 ???
acknowledgement: ack-nj
rawauthor: John B. Gosling
rawtitle: Design of Arithmetic Units for Digital Computers
ISBN13:
978-0-387-91171-7, 978-0-333-26397-6, 978-0-333-26398-3 OR 9780387911717, 9780333263976, 9780333263983

entry:
@Book{Gosling:1980:DAU,
  author =       "John B. Gosling",
  title =        "Design of Arithmetic Units for Digital Computers",
  publisher =    pub-MAC,
  address =      pub-MAC:adr,
  pages =        "x + 139",
  year =         "1980",
  ISBN =         "0-387-91171-5, 0-333-26397-9, 0-333-26398-7",
  ISBN-13 =      "978-0-387-91171-7, 978-0-333-26397-6,
                 978-0-333-26398-3",
  LCCN =         "QA76.6.G668, TK7888.3 .G64 1980",
  bibdate =      "Wed Sep 07 20:43:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Grappel:1980:IZP
author: R. Grappel and J. Hemenway
title: Increase Z8000 power with floating-point routines
journal: j-EDN
volume: 25
number: 8
pages: 179--185
month: apr
monthnumber: 4
year: 1980
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:15:06 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 10:15:06 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: R. Grappel and J. Hemenway
rawtitle: Increase {Z8000} power with floating-point routines
entry:
@Article{Grappel:1980:IZP,
  author =       "R. Grappel and J. Hemenway",
  title =        "Increase {Z8000} power with floating-point routines",
  journal =      j-EDN,
  volume =       "25",
  number =       "8",
  pages =        "179--185",
  month =        apr,
  year =         "1980",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: book
filename: fparith.bib
label: Gregory:1980:ECW
author: Robert Todd Gregory
title: Error-Free Computation: Why it is Needed and Methods for Doing it
publisher: pub-R-E-KRIEGER
address: pub-R-E-KRIEGER:adr
pages: vi + 152
year: 1980
ISBN: 0-89874-240-4 OR 0898742404
ISBN13: 978-0-89874-240-4 OR 9780898742404
LCCN: QA297.5 .G73
MRclass: 65G05
MRnumber: MR586772 (83f:65061)
bibdate: Sat Sep 03 10:09:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.03 10:09:50 ???
keywords: Approximation theory --- Data processing; Floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Robert Todd Gregory
rawtitle: Error-Free Computation: Why it is Needed and Methods for Doing it
TOC:
1: Mathematics vs. Numerical Mathematics 2: Ill-Conditioned Problems vs. Numerically Unstable Algorithms 3: A Scaling Problem 4: ?? 5: ?? Index

rawTOC:
1: Mathematics vs. Numerical Mathematics \\ 2: Ill-Conditioned Problems vs. Numerically Unstable Algorithms \\ 3: A Scaling Problem \\ 4: ?? \\ 5: ?? \\ Index

entry:
@Book{Gregory:1980:ECW,
  author =       "Robert Todd Gregory",
  title =        "Error-Free Computation: Why it is Needed and Methods
                 for Doing it",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "vi + 152",
  year =         "1980",
  ISBN =         "0-89874-240-4",
  ISBN-13 =      "978-0-89874-240-4",
  LCCN =         "QA297.5 .G73",
  MRclass =      "65G05",
  MRnumber =     "MR586772 (83f:65061)",
  bibdate =      "Sat Sep 03 10:09:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation theory --- Data processing;
                 Floating-point arithmetic",
  tableofcontents = "1: Mathematics vs. Numerical Mathematics \\
                 2: Ill-Conditioned Problems vs. Numerically Unstable
                 Algorithms \\
                 3: A Scaling Problem \\
                 4: ?? \\
                 5: ?? \\
                 Index",
}


bibtype: article
filename: fparith.bib
label: Gruner:1980:IUC
author: K. Gruner
title: Implementation of Universal Computer Arithmetic with Optimal Accuracy
journal: j-COMPUTING
volume: 24
number: 2--3
pages: 181--193
year: 1980
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G99 (68A05)
MRnumber: 83c:65118
bibdate: Tue Jan 2 17:40:54 MST 2001
bibtimestamp: 2001.01.02 17:40:54 MST
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nhfb
affiliation: University of Karlsruhe, Karlsruhe, West Germany
journalURL: http://link.springer.com/journal/607
journalabr: Computing (Vienna/New York)
rawauthor: K. Gr{\"u}ner
rawtitle: Implementation of Universal Computer Arithmetic with Optimal Accuracy
bibsource:
Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date); MathSciNet database

keywords:
computer arithmetic; computer programming; fast algorithms; intervals; mapping properties; matrices; numerical computations; universal computer arithmetic; vectors; word length

entry:
@Article{Gruner:1980:IUC,
  author =       "K. Gr{\"u}ner",
  title =        "Implementation of Universal Computer Arithmetic with
                 Optimal Accuracy",
  journal =      j-COMPUTING,
  volume =       "24",
  number =       "2--3",
  pages =        "181--193",
  year =         "1980",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G99 (68A05)",
  MRnumber =     "83c:65118",
  bibdate =      "Tue Jan 2 17:40:54 MST 2001",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "University of Karlsruhe, Karlsruhe, West Germany",
  classification = "C4240",
  description =  "computational complexity",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer arithmetic; computer programming; fast
                 algorithms; intervals; mapping properties; matrices;
                 numerical computations; universal computer arithmetic;
                 vectors; word length",
}


bibtype: techreport
filename: fparith.bib
label: Hamacher:1980:DCV
author: V. Carl Hamacher
title: Design of a CPU for variable precision, decimal arithmetic
type: Technical Report
number: ABC
institution: Department of Electrical Engineering, University of Toronto
address: Toronto, ON, Canada
pages: 181--193
year: 1980
bibdate: Sun Dec 30 15:37:50 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.30 15:37:50 ???
keywords: decimal arithmetic
acknowledgement: ack-nhfb
rawauthor: V. Carl Hamacher
rawtitle: Design of a {CPU} for variable precision, decimal arithmetic
entry:
@TechReport{Hamacher:1980:DCV,
  author =       "V. Carl Hamacher",
  title =        "Design of a {CPU} for variable precision, decimal
                 arithmetic",
  type =         "Technical Report",
  number =       "ABC",
  institution =  "Department of Electrical Engineering, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  month =        "????",
  year =         "1980",
  bibdate =      "Sun Dec 30 15:37:50 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic",
}


bibtype: article
filename: fparith.bib
label: Havender:1980:DBF
author: J. W. Havender
title: Decimal-to-binary floating point number conversion mechanism
journal: j-IBM-TDB
volume: 23
number: 2
pages: 706--708
month: jul
monthnumber: 7
year: 1980
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:16:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:10 ???
fjournal: IBM Technical Disclosure Bulletin
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: J. W. Havender
rawtitle: Decimal-to-binary floating point number conversion mechanism
abstract:
Floating point numbers may be converted from decimal to binary using a high speed natural logarithm and exponential function calculation mechanism and a fixed point divide/multiply unit.par The problem solved is to convert numbers expressed in a radix 10 floating point form to numbers expressed in a radix 2 floating point form.

rawabstract:
Floating point numbers may be converted from decimal to binary using a high speed natural logarithm and exponential function calculation mechanism and a fixed point divide/multiply unit.\par The problem solved is to convert numbers expressed in a radix 10 floating point form to numbers expressed in a radix 2 floating point form.

entry:
@Article{Havender:1980:DBF,
  author =       "J. W. Havender",
  title =        "Decimal-to-binary floating point number conversion
                 mechanism",
  journal =      j-IBM-TDB,
  volume =       "23",
  number =       "2",
  pages =        "706--708",
  month =        jul,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point numbers may be converted from decimal
                 to binary using a high speed natural logarithm and
                 exponential function calculation mechanism and a fixed
                 point divide/multiply unit.\par

                 The problem solved is to convert numbers expressed in a
                 radix 10 floating point form to numbers expressed in a
                 radix 2 floating point form.",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Havender:1980:DBN
author: J. W. Havender
title: Decimal-to-binary Number Conversion
journal: j-IBM-TDB
volume: 23
number: 3
pages: 1126--1127
month: aug
monthnumber: 8
year: 1980
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:16:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:10 ???
fjournal: IBM Technical Disclosure Bulletin
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: J. W. Havender
rawtitle: Decimal-to-binary Number Conversion
entry:
@Article{Havender:1980:DBN,
  author =       "J. W. Havender",
  title =        "Decimal-to-binary Number Conversion",
  journal =      j-IBM-TDB,
  volume =       "23",
  number =       "3",
  pages =        "1126--1127",
  month =        aug,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Haviland:1980:CAP
author: G. L. Haviland and A. A. Tuszynski
title: A CORDIC Arithmetic Processor Chip
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 2
pages: 68--79
month: feb
monthnumber: 2
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675529
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 08 00:47:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 00:47:17 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. L. Haviland and A. A. Tuszynski
rawtitle: A {CORDIC} Arithmetic Processor Chip
entry:
@Article{Haviland:1980:CAP,
  author =       "G. L. Haviland and A. A. Tuszynski",
  title =        "A {CORDIC} Arithmetic Processor Chip",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "2",
  pages =        "68--79",
  month =        feb,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675529",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 00:47:17 1994",
  bibsource =    "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: Head:1980:MM
author: A. K. Head
title: Multiplication modulo $n$
journal: j-BIT
volume: 20
number: 1
pages: 115--116
month: mar
monthnumber: 3
year: 1980
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01933594
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 68-04 (65G10)
MRnumber: 81g:68001
MRreviewer: K. Kilberth
bibdate: Wed Jan 4 18:52:16 MST 2006
bibtimestamp: 2006.01.04 18:52:16 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=1&spage=115
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: A. K. Head
rawtitle: Multiplication modulo $n$
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Head:1980:MM,
  author =       "A. K. Head",
  title =        "Multiplication modulo $n$",
  journal =      j-BIT,
  volume =       "20",
  number =       "1",
  pages =        "115--116",
  month =        mar,
  year =         "1980",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933594",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68-04 (65G10)",
  MRnumber =     "81g:68001",
  MRreviewer =   "K. Kilberth",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&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=20&issue=1&spage=115",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: fparith.bib
label: Hehner:1980:CNR
author: E. C. R. Hehner and R. N. S. Horspool
journal: j-SIAM-J-COMPUT
volume: 9
number: 1
pages: 217--217
year: 1980
CODEN: SMJCAT
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
MRclass: 68C05 (10A30)
MRnumber: 81f:68044
bibdate: Mon Nov 29 10:59:12 MST 2010
bibtimestamp: 2010.11.29 10:59:12 MST
note: See cite Hehner:1979:NRR.
fjournal: SIAM Journal on Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
rawauthor: E. C. R. Hehner and R. N. S. Horspool
rawnote: See \cite{Hehner:1979:NRR}.
title:
Corrigendum: ``A new representation of the rational numbers for fast easy arithmetic'' [SIAM J. Comput. bf 8 (1979), no. 2, 124--134, MR 80h:68027]

bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/9/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
Corrigendum: {``A new representation of the rational numbers for fast easy arithmetic'' [SIAM J. Comput. {\bf 8} (1979), no. 2, 124--134, MR 80h:68027]}

entry:
@Article{Hehner:1980:CNR,
  author =       "E. C. R. Hehner and R. N. S. Horspool",
  title =        "Corrigendum: {``A new representation of the rational
                 numbers for fast easy arithmetic'' [SIAM J. Comput.
                 {\bf 8} (1979), no. 2, 124--134, MR 80h:68027]}",
  journal =      j-SIAM-J-COMPUT,
  volume =       "9",
  number =       "1",
  pages =        "217--217",
  month =        "????",
  year =         "1980",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68C05 (10A30)",
  MRnumber =     "81f:68044",
  bibdate =      "Mon Nov 29 10:59:12 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/9/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Hehner:1979:NRR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}


bibtype: article
filename: fparith.bib
label: Henrich:1980:FPA
author: C. J. Henrich
title: Floating-point arithmetic: can it be trusted?
journal: j-MINI-MICRO-SYSTEMS
volume: 13
number: 11
pages: 143--151
month: nov
monthnumber: 11
year: 1980
CODEN: XWJXEH
ISSN: 1000-1220 OR 10001220
bibdate: Wed Sep 14 19:14:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 19:14:42 ???
fjournal: Mini-Micro Systems
acknowledgement: ack-nj
rawauthor: C. J. Henrich
rawtitle: Floating-point arithmetic: can it be trusted?
entry:
@Article{Henrich:1980:FPA,
  author =       "C. J. Henrich",
  title =        "Floating-point arithmetic: can it be trusted?",
  journal =      j-MINI-MICRO-SYSTEMS,
  volume =       "13",
  number =       "11",
  pages =        "143--151",
  month =        nov,
  year =         "1980",
  CODEN =        "XWJXEH",
  ISSN =         "1000-1220",
  bibdate =      "Wed Sep 14 19:14:42 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 =     "Mini-Micro Systems",
}


bibtype: inproceedings
filename: fparith.bib
label: Henrici:1980:MPR
author: Peter Henrici
booktitle: Interval mathematics, 1980 (Freiburg, 1980)
title: A model for the propagation of rounding error in floating arithmetic
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: 49--73
year: 1980
DOI: https://doi.org/10.1016/B978-0-12-518850-0.50009-3
ISBN: 0-12-518850-1 OR 0125188501
ISBN13: 978-0-12-518850-0 OR 9780125188500
MRclass: 65G05
MRnumber: 651358
bibdate: Mon Jan 28 07:08:10 2019
bibtimestamp: 2019.01.28 07:08:10 ???
URL: http://www.sciencedirect.com/science/article/pii/B9780125188500500093
acknowledgement: ack-nhfb
authordates: Peter Karl Henrici (13 September 1923--13 March 1987)
rawauthor: Peter Henrici
rawbooktitle: Interval mathematics, 1980 ({Freiburg}, 1980)
rawtitle: A model for the propagation of rounding error in floating arithmetic
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The subject of propagation of rounding error, while of undisputed importance in numerical analysis, is notorious for the difficulties that it presents when it is to be taught in the classroom in such a manner that the student is neither insulted by lack of mathematical content nor bored by lack of transparence and clarity. On examination of some classical approaches, it appears that the effect of tedium is often achieved by the attempt of being absolutely rigorous. Absolute rigor in error analysis is a triviality. Perhaps, what is required in error analysis is not so much rigor but rather an understanding why some algorithms work and others do not. This chapter presents a model for the propagation of rounding error in floating arithmetic that aims at such an understanding. To bring to light the essential consequences of floating arithmetic, the model makes certain idealizing or simplifying assumptions that are not always satisfied on real-life computers. The model nevertheless furnishes realistic descriptions of the numerical performance of a large class of algorithms that can be described in terms of operations on real numbers.

rawabstract:
The subject of propagation of rounding error, while of undisputed importance in numerical analysis, is notorious for the difficulties that it presents when it is to be taught in the classroom in such a manner that the student is neither insulted by lack of mathematical content nor bored by lack of transparence and clarity. On examination of some classical approaches, it appears that the effect of tedium is often achieved by the attempt of being absolutely rigorous. Absolute rigor in error analysis is a triviality. Perhaps, what is required in error analysis is not so much rigor but rather an understanding why some algorithms work and others do not. This chapter presents a model for the propagation of rounding error in floating arithmetic that aims at such an understanding. To bring to light the essential consequences of floating arithmetic, the model makes certain idealizing or simplifying assumptions that are not always satisfied on real-life computers. The model nevertheless furnishes realistic descriptions of the numerical performance of a large class of algorithms that can be described in terms of operations on real numbers.

entry:
@InProceedings{Henrici:1980:MPR,
  author =       "Peter Henrici",
  booktitle =    "Interval mathematics, 1980 ({Freiburg}, 1980)",
  title =        "A model for the propagation of rounding error in
                 floating arithmetic",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "49--73",
  year =         "1980",
  DOI =          "https://doi.org/10.1016/B978-0-12-518850-0.50009-3",
  ISBN =         "0-12-518850-1",
  ISBN-13 =      "978-0-12-518850-0",
  MRclass =      "65G05",
  MRnumber =     "651358",
  bibdate =      "Mon Jan 28 07:08:10 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B9780125188500500093",
  abstract =     "The subject of propagation of rounding error, while of
                 undisputed importance in numerical analysis, is
                 notorious for the difficulties that it presents when it
                 is to be taught in the classroom in such a manner that
                 the student is neither insulted by lack of mathematical
                 content nor bored by lack of transparence and clarity.
                 On examination of some classical approaches, it appears
                 that the effect of tedium is often achieved by the
                 attempt of being absolutely rigorous. Absolute rigor in
                 error analysis is a triviality. Perhaps, what is
                 required in error analysis is not so much rigor but
                 rather an understanding why some algorithms work and
                 others do not. This chapter presents a model for the
                 propagation of rounding error in floating arithmetic
                 that aims at such an understanding. To bring to light
                 the essential consequences of floating arithmetic, the
                 model makes certain idealizing or simplifying
                 assumptions that are not always satisfied on real-life
                 computers. The model nevertheless furnishes realistic
                 descriptions of the numerical performance of a large
                 class of algorithms that can be described in terms of
                 operations on real numbers.",
  acknowledgement = ack-nhfb,
  author-dates = "Peter Karl Henrici (13 September 1923--13 March
                 1987)",
}


bibtype: phdthesis
filename: fparith.bib
label: Holm:1980:FAP
author: John Erick Holm
title: Floating-point arithmetic and program correctness proofs
type: Thesis (Ph.D.)
school: Cornell University
address: Ithaca, NY, USA
pages: vii + 133
month: aug
monthnumber: 8
year: 1980
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.
acknowledgement: ack-nhfb
rawauthor: John Erick Holm
rawtitle: Floating-point arithmetic and program correctness proofs
entry:
@PhdThesis{Holm:1980:FAP,
  author =       "John Erick Holm",
  title =        "Floating-point arithmetic and program correctness
                 proofs",
  type =         "Thesis ({Ph.D.})",
  school =       "Cornell University",
  address =      "Ithaca, NY, USA",
  pages =        "vii + 133",
  month =        aug,
  year =         "1980",
  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.",
}


bibtype: article
filename: fparith.bib
label: Horna:1980:FAC
author: O. A. Horna
title: Fast algorithms for the computation of binary logarithms
journal: COMSAT Technical Review
volume: 10
number: 1
pages: 91--101
month: Spring
year: 1980
bibdate: Thu Sep 1 10:16:09 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:09 ???
acknowledgement: ack-nj
rawauthor: O. A. Horna
rawtitle: Fast algorithms for the computation of binary logarithms
entry:
@Article{Horna:1980:FAC,
  author =       "O. A. Horna",
  title =        "Fast algorithms for the computation of binary
                 logarithms",
  journal =      "COMSAT Technical Review",
  volume =       "10",
  number =       "1",
  pages =        "91--101",
  month =        "Spring",
  year =         "1980",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Hough:1980:APS
author: D. Hough
title: Applications of a Proposed Standard for Floating-Point Arithmetic
crossref: Electro:1980:ECR
pages: 18/3/1--6
year: 1980
bibdate: Wed Sep 07 21:39:26 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 21:39:26 ???
acknowledgement: ack-nj
rawauthor: D. Hough
rawtitle: Applications of a Proposed Standard for Floating-Point Arithmetic
entry:
@InProceedings{Hough:1980:APS,
  author =       "D. Hough",
  title =        "Applications of a Proposed Standard for Floating-Point
                 Arithmetic",
  crossref =     "Electro:1980:ECR",
  pages =        "18/3/1--6",
  year =         "1980",
  bibdate =      "Wed Sep 07 21:39:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: fparith.bib
label: Hull:1980:PPI
author: Thomas E. Hull and Christian H. Reinsch and John R. Rice
title: Principles, Preferences and Ideals for Computer Arithmetic
type: Technical report
number: TR-339
institution: inst-CS-PURDUE
address: inst-CS-PURDUE:adr
pages: 13
day: 1
month: jun
monthnumber: 6
year: 1980
bibdate: Sun Dec 30 13:46:29 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.30 13:46:29 ???
URL: http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-339.pdf
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
authordates: Christian H. Reinsch (?? ?? 1932--8 October 2022)
rawauthor: Thomas E. Hull and Christian H. Reinsch and John R. Rice
rawtitle: Principles, Preferences and Ideals for Computer Arithmetic
abstract:
This paper presents principles and preferences for the implementation of computer arithmetic and ideals for the arithmetic facilities in future programming languages. The implementation principles and preferences are for the current approaches to the design of arithmetic units. The ideals are for the long term development of programming languages, with the hope that arithmetic units will be built to support the requirements of programming languages.

rawabstract:
This paper presents principles and preferences for the implementation of computer arithmetic and ideals for the arithmetic facilities in future programming languages. The implementation principles and preferences are for the current approaches to the design of arithmetic units. The ideals are for the long term development of programming languages, with the hope that arithmetic units will be built to support the requirements of programming languages.

entry:
@TechReport{Hull:1980:PPI,
  author =       "Thomas E. Hull and Christian H. Reinsch and John R.
                 Rice",
  title =        "Principles, Preferences and Ideals for Computer
                 Arithmetic",
  type =         "Technical report",
  number =       "TR-339",
  institution =  inst-CS-PURDUE,
  address =      inst-CS-PURDUE:adr,
  pages =        "13",
  day =          "1",
  month =        jun,
  year =         "1980",
  bibdate =      "Sun Dec 30 13:46:29 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-339.pdf",
  abstract =     "This paper presents principles and preferences for the
                 implementation of computer arithmetic and ideals for
                 the arithmetic facilities in future programming
                 languages. The implementation principles and
                 preferences are for the current approaches to the
                 design of arithmetic units. The ideals are for the long
                 term development of programming languages, with the
                 hope that arithmetic units will be built to support the
                 requirements of programming languages.",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Jenkins:1980:CRN
author: W. K. Jenkins
title: Complex residue number arithmetic for high-speed signal processing
journal: j-ELECT-LETTERS
volume: 16
number: 17
pages: 660--661
day: 14
month: aug
monthnumber: 8
year: 1980
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19800468
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
MRclass: 94A05
MRnumber: MR583226 (81h:94003)
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4244229
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: W. K. Jenkins
rawtitle: Complex residue number arithmetic for high-speed signal processing
entry:
@Article{Jenkins:1980:CRN,
  author =       "W. K. Jenkins",
  title =        "Complex residue number arithmetic for high-speed
                 signal processing",
  journal =      j-ELECT-LETTERS,
  volume =       "16",
  number =       "17",
  pages =        "660--661",
  day =          "14",
  month =        aug,
  year =         "1980",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  MRclass =      "94A05",
  MRnumber =     "MR583226 (81h:94003)",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4244229",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Complex residue number arithmetic is developed for
                 high-speed processing of complex waveforms. An
                 important feature of complex residue arithmetic is that
                 complex multiplication can be implemented by a real
                 index calculus, thereby providing a highly \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Johannes:1980:DSE
author: J. D. Johannes and C. Dennis Pegden and F. E. Petry
title: Decimal Shifting for an Exact Floating Point Representation
journal: j-COMPUT-ELECTR-ENG
volume: 7
number: 3
pages: 149--155
month: sep
monthnumber: 9
year: 1980
CODEN: CPEEBQ
ISSN: 0045-7906 (print), 1879-0755 (electronic) OR 00457906 (print), 18790755 (electronic)
ISSNL: 0045-7906 OR 00457906
bibdate: Fri Nov 28 11:42:59 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:42:59 ???
fjournal: Computers and Electrical Engineering
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: J. D. Johannes and C. Dennis Pegden and F. E. Petry
rawtitle: Decimal Shifting for an Exact Floating Point Representation
entry:
@Article{Johannes:1980:DSE,
  author =       "J. D. Johannes and C. Dennis Pegden and F. E. Petry",
  title =        "Decimal Shifting for an Exact Floating Point
                 Representation",
  journal =      j-COMPUT-ELECTR-ENG,
  volume =       "7",
  number =       "3",
  pages =        "149--155",
  month =        sep,
  year =         "1980",
  CODEN =        "CPEEBQ",
  ISSN =         "0045-7906 (print), 1879-0755 (electronic)",
  ISSN-L =       "0045-7906",
  bibdate =      "Fri Nov 28 11:42:59 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Electrical Engineering",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Johnson:1980:DQS
author: E. L. Johnson
title: A Digital Quarter Square Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 3
pages: 258--261
month: mar
monthnumber: 3
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675558
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 19:15:24 MDT 2011
bibtimestamp: 2011.07.10 19:15:24 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675558
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. L. Johnson
rawtitle: A Digital Quarter Square Multiplier
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib

entry:
@Article{Johnson:1980:DQS,
  author =       "E. L. Johnson",
  title =        "A Digital Quarter Square Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "3",
  pages =        "258--261",
  month =        mar,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675558",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675558",
  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: Jullien:1980:IMM
author: G. A. Jullien
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 10
pages: 899--905
month: oct
monthnumber: 10
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675473
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 19:15:29 MDT 2011
bibtimestamp: 2011.07.10 19:15:29 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675473
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. A. Jullien
title:
Implementation of Multiplication, Modulo a Prime Number, with Applications to Number Theoretic Transforms

rawtitle:
Implementation of Multiplication, Modulo a Prime Number, with Applications to Number Theoretic Transforms

entry:
@Article{Jullien:1980:IMM,
  author =       "G. A. Jullien",
  title =        "Implementation of Multiplication, Modulo a Prime
                 Number, with Applications to Number Theoretic
                 Transforms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "10",
  pages =        "899--905",
  month =        oct,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675473",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675473",
  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: Kahan:1980:HCE
author: William M. Kahan
title: Handheld Calculator Evaluates Integrals
journal: j-HEWLETT-PACKARD-J
volume: 31
number: 8
pages: 23--32
month: aug
monthnumber: 8
year: 1980
CODEN: HPJOAX
ISSN: 0018-1153 OR 00181153
MRclass: 65-04 (65D30)
MRnumber: MR590837 (82d:65001)
MRreviewer: S. Dubuc
bibdate: Tue Mar 25 14:12:15 MST 1997
bibtimestamp: 1997.03.25 14:12:15 MST
note: Lecture notes for Math 128.
URL: http://www.cs.berkeley.edu/~wkahan/Math128/INTGTkey.pdf
fjournal: Hewlett--Packard Journal
acknowledgement: ack-nhfb
classcodes: C4160 (Numerical integration and differentiation); C5230 (Digital arithmetic methods)
corpsource: Hewlett--Packard Co., Palo Alto, CA, USA
reviewer: S. Dubuc
treatment: G General Review; P Practical
rawauthor: William M. Kahan
rawnote: Lecture notes for Math 128.
rawtitle: Handheld Calculator Evaluates Integrals
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/hpj.bib

keywords:
34C; digital arithmetic; handheld calculator; HP; integrals; integration; numerical integration; numerical methods

entry:
@Article{Kahan:1980:HCE,
  author =       "William M. Kahan",
  title =        "Handheld Calculator Evaluates Integrals",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "31",
  number =       "8",
  pages =        "23--32",
  month =        aug,
  year =         "1980",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  MRclass =      "65-04 (65D30)",
  MRnumber =     "MR590837 (82d:65001)",
  MRreviewer =   "S. Dubuc",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hpj.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/INTGTkey.pdf",
  acknowledgement = ack-nhfb,
  classcodes =   "C4160 (Numerical integration and differentiation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Hewlett--Packard Co., Palo Alto, CA, USA",
  fjournal =     "Hewlett--Packard Journal",
  keywords =     "34C; digital arithmetic; handheld calculator; HP;
                 integrals; integration; numerical integration;
                 numerical methods",
  reviewer =     "S. Dubuc",
  treatment =    "G General Review; P Practical",
}


bibtype: unpublished
filename: fparith.bib
label: Kahan:1980:SPI
author: W. Kahan
title: Software $ sqrt x $ for the Proposed IEEE Floating-Point Standard
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
pages: 23--32
day: 25
month: aug
monthnumber: 8
year: 1980
bibdate: Mon Apr 25 18:24:02 2005
bibtimestamp: 2005.04.25 18:24:02 ???
note: Manuscript
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Manuscript
rawtitle: Software $ \sqrt x $ for the Proposed {IEEE} Floating-Point Standard
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Unpublished{Kahan:1980:SPI,
  author =       "W. Kahan",
  title =        "Software $ \sqrt x $ for the Proposed {IEEE}
                 Floating-Point Standard",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "25",
  month =        aug,
  year =         "1980",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kleinsteiber:1980:IHM
author: James R. Kleinsteiber
title: IBM 4341 hardware/microcode trade-off decisions
crossref: Johnson:1980:MPA
pages: 190--192
year: 1980
bibdate: Thu Aug 07 18:22:42 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 18:22:42 ???
keywords: decimal arithmetic
acknowledgement: ack-nhfb
rawauthor: James R. Kleinsteiber
rawtitle: {IBM} 4341 hardware/microcode trade-off decisions
abstract:
The design of IBM's 4341 Processor, as with other processors, involved many cost/performance tradeoffs. The designer is continually under pressure to increase processor speed without increasing cost or to decrease processor cost without decreasing performance. This paper will examine some of the engineering decisions that were made in the attempt to make the 4341 a high-performing yet low cost processor. These decisions include searching for, or developing, algorithms that make the best use of hardware properties, such as data path width, arithmetic/logical operations and special functions. Functions were sought such that a small amount of added hardware would go a long way towards improving system performance. Hardware designers, microcoders and performance analysis people worked together to implement instructions, functions and algorithms with the proper mixture of hardware functions and microcode in order to build a viable processor. Some specific functions will be covered to examine a few of the decisions. The TEST UNDER MASK performance problem will be discussed with its resulting implementation decision. The method of using EXCLUSIVE OR to clear storage and the resulting algorithm design will be shown. Other topics to be discussed include multiple hardware functions and the resulting effect on floating point, fixed point and decimal multiply; the divide function and its effect on floating point and fixed point divide; and the effect of an 8-byte data path for decimal arithmetic.

rawabstract:
The design of IBM's 4341 Processor, as with other processors, involved many cost/performance tradeoffs. The designer is continually under pressure to increase processor speed without increasing cost or to decrease processor cost without decreasing performance. This paper will examine some of the engineering decisions that were made in the attempt to make the 4341 a high-performing yet low cost processor. These decisions include searching for, or developing, algorithms that make the best use of hardware properties, such as data path width, arithmetic/logical operations and special functions. Functions were sought such that a small amount of added hardware would go a long way towards improving system performance. Hardware designers, microcoders and performance analysis people worked together to implement instructions, functions and algorithms with the proper mixture of hardware functions and microcode in order to build a viable processor. Some specific functions will be covered to examine a few of the decisions. The TEST UNDER MASK performance problem will be discussed with its resulting implementation decision. The method of using EXCLUSIVE OR to clear storage and the resulting algorithm design will be shown. Other topics to be discussed include multiple hardware functions and the resulting effect on floating point, fixed point and decimal multiply; the divide function and its effect on floating point and fixed point divide; and the effect of an 8-byte data path for decimal arithmetic.

entry:
@InProceedings{Kleinsteiber:1980:IHM,
  author =       "James R. Kleinsteiber",
  title =        "{IBM} 4341 hardware/microcode trade-off decisions",
  crossref =     "Johnson:1980:MPA",
  pages =        "190--192",
  year =         "1980",
  bibdate =      "Thu Aug 07 18:22:42 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The design of IBM's 4341 Processor, as with other
                 processors, involved many cost/performance tradeoffs.
                 The designer is continually under pressure to increase
                 processor speed without increasing cost or to decrease
                 processor cost without decreasing performance. This
                 paper will examine some of the engineering decisions
                 that were made in the attempt to make the 4341 a
                 high-performing yet low cost processor. These decisions
                 include searching for, or developing, algorithms that
                 make the best use of hardware properties, such as data
                 path width, arithmetic/logical operations and special
                 functions. Functions were sought such that a small
                 amount of added hardware would go a long way towards
                 improving system performance. Hardware designers,
                 microcoders and performance analysis people worked
                 together to implement instructions, functions and
                 algorithms with the proper mixture of hardware
                 functions and microcode in order to build a viable
                 processor. Some specific functions will be covered to
                 examine a few of the decisions. The TEST UNDER MASK
                 performance problem will be discussed with its
                 resulting implementation decision. The method of using
                 EXCLUSIVE OR to clear storage and the resulting
                 algorithm design will be shown. Other topics to be
                 discussed include multiple hardware functions and the
                 resulting effect on floating point, fixed point and
                 decimal multiply; the divide function and its effect on
                 floating point and fixed point divide; and the effect
                 of an 8-byte data path for decimal arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Kulisch:1980:AOI
author: U. W. Kulisch and W. L. Miranker
title: Arithmetic Operations in Interval Spaces
crossref: Alefeld:1980:FNC
pages: 51--67
year: 1980
bibdate: Tue Oct 23 08:17:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.23 08:17:48 ???
keywords: interval arithmetic
acknowledgement: ack-nhfb
rawauthor: U. W. Kulisch and W. L. Miranker
rawtitle: Arithmetic Operations in Interval Spaces
entry:
@InProceedings{Kulisch:1980:AOI,
  author =       "U. W. Kulisch and W. L. Miranker",
  title =        "Arithmetic Operations in Interval Spaces",
  crossref =     "Alefeld:1980:FNC",
  pages =        "51--67",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic",
}


bibtype: article
filename: fparith.bib
label: Ladner:1980:PPC
author: Richard E. Ladner and Michael J. Fischer
title: Parallel Prefix Computation
journal: j-J-ACM
volume: 27
number: 4
pages: 831--838
month: oct
monthnumber: 10
year: 1980
CODEN: JACOAH
DOI: https://doi.org/10.1145/322217.322232
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Wed Oct 26 22:55:08 1994
bibtimestamp: 1994.10.26 22:55:08 ???
fjournal: Journal of the Association for Computing Machinery
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: Richard E. Ladner and Michael J. Fischer
rawtitle: Parallel Prefix Computation
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Par.Arch.Indep.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib

abstract:
The prefix problem is to compute all the products $ x_1 * x_2 * cdots * x_k $ for $ 1 leq k leq n $, where $*$ is an associative operation. A recursive construction is used to obtain a product circuit for solving the prefix problem which has depth exactly $ lceil log n rceil $ and size bounded by $ 4 n $ An application yields fast, small Boolean circuits to simulate finite-state transducers. By simulating a sequential adder, a Boolean circuit which has depth $ 2 lceil log _2 n rceil + 2 $ and size bounded by $ 14 n $ is obtained for $n$-bit binary addition. The size can be decreased significantly by permitting the depth to increase by an additive constant.

rawabstract:
The prefix problem is to compute all the products $ x_1 * x_2 * \cdots * x_k $ for $ 1 \leq k \leq n $, where $*$ is an associative operation. A recursive construction is used to obtain a product circuit for solving the prefix problem which has depth exactly $ \lceil \log n \rceil $ and size bounded by $ 4 n $ An application yields fast, small Boolean circuits to simulate finite-state transducers. By simulating a sequential adder, a Boolean circuit which has depth $ 2 \lceil \log_2 n \rceil + 2 $ and size bounded by $ 14 n $ is obtained for $n$-bit binary addition. The size can be decreased significantly by permitting the depth to increase by an additive constant.

entry:
@Article{Ladner:1980:PPC,
  author =       "Richard E. Ladner and Michael J. Fischer",
  title =        "Parallel Prefix Computation",
  journal =      j-J-ACM,
  volume =       "27",
  number =       "4",
  pages =        "831--838",
  month =        oct,
  year =         "1980",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/322217.322232",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Oct 26 22:55:08 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Par.Arch.Indep.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "The prefix problem is to compute all the products $
                 x_1 * x_2 * \cdots * x_k $ for $ 1 \leq k \leq n $,
                 where $*$ is an associative operation. A recursive
                 construction is used to obtain a product circuit for
                 solving the prefix problem which has depth exactly $
                 \lceil \log n \rceil $ and size bounded by $ 4 n $ An
                 application yields fast, small Boolean circuits to
                 simulate finite-state transducers. By simulating a
                 sequential adder, a Boolean circuit which has depth $ 2
                 \lceil \log_2 n \rceil + 2 $ and size bounded by $ 14 n
                 $ is obtained for $n$-bit binary addition. The size can
                 be decreased significantly by permitting the depth to
                 increase by an additive constant.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}


bibtype: article
filename: fparith.bib
label: Lemaire:1980:INR
author: C. A. Lemaire and J. C. Svercek
title: Improved Non-restoring Division
journal: j-IBM-TDB
volume: 23
number: 3
pages: 1149--1151
month: aug
monthnumber: 8
year: 1980
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: C. A. Lemaire and J. C. Svercek
rawtitle: Improved Non-restoring Division
entry:
@Article{Lemaire:1980:INR,
  author =       "C. A. Lemaire and J. C. Svercek",
  title =        "Improved Non-restoring Division",
  journal =      j-IBM-TDB,
  volume =       "23",
  number =       "3",
  pages =        "1149--1151",
  month =        aug,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: book
filename: fparith.bib
label: Levy:1980:CPA
author: Henry M. Levy and Richard H. Eckhouse, Jr.
title: Computer Programming and Architecture--the VAX-11
publisher: pub-DP
address: pub-DP:adr
pages: xxi + 407
year: 1980
ISBN: 0-932376-07-X OR 093237607X
ISBN13: 978-0-932376-07-7 OR 9780932376077
LCCN: QA76.8 .V37 L48 1980
bibdate: Wed Dec 15 10:38:14 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1993.12.15 10:38:14 ???
acknowledgement: ack-nhfb
rawauthor: Henry M. Levy and Richard H. {Eckhouse, Jr.}
rawtitle: Computer Programming and Architecture--the {VAX-11}
entry:
@Book{Levy:1980:CPA,
  author =       "Henry M. Levy and Richard H. {Eckhouse, Jr.}",
  title =        "Computer Programming and Architecture--the {VAX-11}",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  pages =        "xxi + 407",
  year =         "1980",
  ISBN =         "0-932376-07-X",
  ISBN-13 =      "978-0-932376-07-7",
  LCCN =         "QA76.8 .V37 L48 1980",
  bibdate =      "Wed Dec 15 10:38:14 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Macke:1980:DMF
author: Edward T. Macke
title: Design of a modular floating point arithmetic unit
type: Thesis (M.S.)
school: Washington University, Department of Electrical Engineering
address: St. Louis, MO, USA
pages: ix + 174
year: 1980
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.; Microprocessors --- Design and construction.
acknowledgement: ack-nhfb
rawauthor: Edward T. Macke
rawtitle: Design of a modular floating point arithmetic unit
entry:
@MastersThesis{Macke:1980:DMF,
  author =       "Edward T. Macke",
  title =        "Design of a modular floating point arithmetic unit",
  type =         "Thesis ({M.S.})",
  school =       "Washington University, Department of Electrical
                 Engineering",
  address =      "St. Louis, MO, USA",
  pages =        "ix + 174",
  year =         "1980",
  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.; Microprocessors --- Design
                 and construction.",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1980:FFP
author: D. W. Matula
title: Foundations of Finite Precision Rational Arithmetic
crossref: Alefeld:1980:FNC
pages: 85--111
year: 1980
bibdate: Tue Oct 23 08:17:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.23 08:17:48 ???
keywords: interval arithmetic; rational arithmetic
acknowledgement: ack-nhfb
rawauthor: D. W. Matula
rawtitle: Foundations of Finite Precision Rational Arithmetic
entry:
@InProceedings{Matula:1980:FFP,
  author =       "D. W. Matula",
  title =        "Foundations of Finite Precision Rational Arithmetic",
  crossref =     "Alefeld:1980:FNC",
  pages =        "85--111",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rational arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: McMinn:1980:IND
author: C. McMinn
title: The Intel 8087: a Numeric Data Processor
crossref: Electro:1980:ECR
pages: 14/5/1--8
year: 1980
bibdate: Mon Sep 12 08:30:36 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 08:30:36 ???
acknowledgement: ack-nj
rawauthor: C. McMinn
rawtitle: The {Intel 8087}: a Numeric Data Processor
entry:
@InProceedings{McMinn:1980:IND,
  author =       "C. McMinn",
  title =        "The {Intel 8087}: a Numeric Data Processor",
  crossref =     "Electro:1980:ECR",
  pages =        "14/5/1--8",
  year =         "1980",
  bibdate =      "Mon Sep 12 08:30:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: book
filename: fparith.bib
label: Mead:1980:IVS
author: Carver Mead and Lynn Conway
title: Introduction to VLSI systems
publisher: pub-AW
address: pub-AW:adr
pages: xvi + 396
year: 1980
ISBN: 0-201-04358-0 OR 0201043580
ISBN13: 978-0-201-04358-7 OR 9780201043587
LCCN: TK7874 .M371
bibdate: Mon Sep 16 16:25:00 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:25:00 ???
acknowledgement: ack-nhfb
rawauthor: Carver Mead and Lynn Conway
rawtitle: Introduction to {VLSI} systems
entry:
@Book{Mead:1980:IVS,
  author =       "Carver Mead and Lynn Conway",
  title =        "Introduction to {VLSI} systems",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xvi + 396",
  year =         "1980",
  ISBN =         "0-201-04358-0",
  ISBN-13 =      "978-0-201-04358-7",
  LCCN =         "TK7874 .M371",
  bibdate =      "Mon Sep 16 16:25:00 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Meinardus:1980:OPN
author: Gunter Meinardus and G. D. Taylor
title: Optimal Partitioning of Newton's Method for Calculating Roots
journal: j-MATH-COMPUT
volume: 35
number: 152
pages: 1221--1230
month: oct
monthnumber: 10
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65H05 (41A30)
MRnumber: 81j:65069
MRreviewer: Derek W. Arthur
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4130 (Interpolation and function approximation)
corpsource: Fachbereich Math., University of Siegen, Siegen, West Germany
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: G{\"u}nter Meinardus and G. D. Taylor
rawtitle: Optimal Partitioning of {Newton}'s Method for Calculating Roots
keywords:
cube root; domain interval; function approximation; iterative methods; method; Newton; optimal partitioning; reciprocal square root; square root; subinterval

entry:
@Article{Meinardus:1980:OPN,
  author =       "G{\"u}nter Meinardus and G. D. Taylor",
  title =        "Optimal Partitioning of {Newton}'s Method for
                 Calculating Roots",
  journal =      j-MATH-COMPUT,
  volume =       "35",
  number =       "152",
  pages =        "1221--1230",
  month =        oct,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65H05 (41A30)",
  MRnumber =     "81j:65069",
  MRreviewer =   "Derek W. Arthur",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Fachbereich Math., University of Siegen, Siegen, West
                 Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "cube root; domain interval; function approximation;
                 iterative methods; method; Newton; optimal
                 partitioning; reciprocal square root; square root;
                 subinterval",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1980:SIN
author: N. Metropolis
title: Summation of imprecise numbers
journal: j-COMPUT-MATH-APPL
volume: 6
number: 3
pages: 297--299
year: 1980
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(80)90037-1
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65U05
MRnumber: MR604094 (82d:65092)
bibdate: Sat Feb 8 10:29:40 2020
bibtimestamp: 2020.02.08 10:29:40 ???
fjournal: Computers & Mathematics with Applications. An International Journal
ZMnumber: 0458.65029
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: N. Metropolis
rawtitle: Summation of imprecise numbers
abstract:
An algorithm is presented for computer summation of imprecise numbers that may have quite disparate magnitudes and variances. Each number is represented by its expected value and variance. Exact numbers form a subset and are treated in a consistent manner. Cancellation effects are minimized.

rawabstract:
An algorithm is presented for computer summation of imprecise numbers that may have quite disparate magnitudes and variances. Each number is represented by its expected value and variance. Exact numbers form a subset and are treated in a consistent manner. Cancellation effects are minimized.

entry:
@Article{Metropolis:1980:SIN,
  author =       "N. Metropolis",
  title =        "Summation of imprecise numbers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "3",
  pages =        "297--299",
  year =         "1980",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(80)90037-1",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65U05",
  MRnumber =     "MR604094 (82d:65092)",
  bibdate =      "Sat Feb 8 10:29:40 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0458.65029",
  abstract =     "An algorithm is presented for computer summation of
                 imprecise numbers that may have quite disparate
                 magnitudes and variances. Each number is represented by
                 its expected value and variance. Exact numbers form a
                 subset and are treated in a consistent manner.
                 Cancellation effects are minimized.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers \& Mathematics with Applications. An
                 International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Moore:1980:MIA
author: R. E. Moore
title: Microprogrammed interval arithmetic
journal: j-SIGNUM
volume: 15
number: 2
pages: 30--30
month: jun
monthnumber: 6
year: 1980
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:08 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:08 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: R. E. Moore
rawtitle: Microprogrammed interval arithmetic
entry:
@Article{Moore:1980:MIA,
  author =       "R. E. Moore",
  title =        "Microprogrammed interval arithmetic",
  journal =      j-SIGNUM,
  volume =       "15",
  number =       "2",
  pages =        "30--30",
  month =        jun,
  year =         "1980",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:08 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: inproceedings
filename: fparith.bib
label: Nave:1980:NDP
author: R. Nave and J. Palmer
title: A numeric data processor
crossref: IEEE:1980:IIS
pages: 108--109
year: 1980
bibdate: Wed Sep 07 22:22:14 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:22:14 ???
acknowledgement: ack-nj
rawauthor: R. Nave and J. Palmer
rawtitle: A numeric data processor
entry:
@InProceedings{Nave:1980:NDP,
  author =       "R. Nave and J. Palmer",
  title =        "A numeric data processor",
  crossref =     "IEEE:1980:IIS",
  pages =        "108--109",
  year =         "1980",
  bibdate =      "Wed Sep 07 22:22:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: North:1980:BRS
author: J. D. North
journal: j-J-HIST-ASTRON
volume: 11
number: 2
pages: 138--140
month: jun
monthnumber: 6
year: 1980
CODEN: JHSAA2
DOI: https://doi.org/10.1177/002182868001100210
ISSN: 0021-8286 (print), 1753-8556 (electronic) OR 00218286 (print), 17538556 (electronic)
ISSNL: 0021-8286 OR 00218286
bibdate: Mon Sep 29 17:17:57 MDT 2014
bibtimestamp: 2014.09.29 17:17:57 MDT
fjournal: Journal for the History of Astronomy
acknowledgement: ack-nhfb
journalURL: https://journals.sagepub.com/home/JHA
rawauthor: J. D. North
title:
Book Review: a Sixteenth Century Polymath, booktitle Wilhelm Schickard, 1592--1635: Astronom, Geograph, Orientalist, Erfinder der Rechenmaschine

bibsource:
http://jha.sagepub.com/content/11/2.toc; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jhistastron.bib

rawtitle:
Book Review: a {Sixteenth Century} Polymath, {{\booktitle{Wilhelm Schickard, 1592--1635: Astronom, Geograph, Orientalist, Erfinder der Rechenmaschine}}}

entry:
@Article{North:1980:BRS,
  author =       "J. D. North",
  title =        "Book Review: a {Sixteenth Century} Polymath,
                 {{\booktitle{Wilhelm Schickard, 1592--1635: Astronom,
                 Geograph, Orientalist, Erfinder der Rechenmaschine}}}",
  journal =      j-J-HIST-ASTRON,
  volume =       "11",
  number =       "2",
  pages =        "138--140",
  month =        jun,
  year =         "1980",
  CODEN =        "JHSAA2",
  DOI =          "https://doi.org/10.1177/002182868001100210",
  ISSN =         "0021-8286 (print), 1753-8556 (electronic)",
  ISSN-L =       "0021-8286",
  bibdate =      "Mon Sep 29 17:17:57 MDT 2014",
  bibsource =    "http://jha.sagepub.com/content/11/2.toc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jhistastron.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal for the History of Astronomy",
  journal-URL =  "https://journals.sagepub.com/home/JHA",
}


bibtype: inproceedings
filename: fparith.bib
label: Oberaigner:1980:AMG
author: W. Oberaigner
title: Algorithms for Multiplication with Given Precision
crossref: Alefeld:1980:FNC
pages: 121--129
year: 1980
bibdate: Tue Oct 23 08:17:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.23 08:17:48 ???
keywords: interval arithmetic
acknowledgement: ack-nhfb
rawauthor: W. Oberaigner
rawtitle: Algorithms for Multiplication with Given Precision
entry:
@InProceedings{Oberaigner:1980:AMG,
  author =       "W. Oberaigner",
  title =        "Algorithms for Multiplication with Given Precision",
  crossref =     "Alefeld:1980:FNC",
  pages =        "121--129",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Palmer:1980:IND
author: J. Palmer
title: The Intel 8087 Numeric Data Processor
crossref: Anonymous:1980:CPA
pages: 174--181
year: 1980
bibdate: Mon Sep 12 08:30:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 08:30:40 ???
acknowledgement: ack-nhfb
rawauthor: J. Palmer
rawtitle: The {Intel} 8087 Numeric Data Processor
entry:
@InProceedings{Palmer:1980:IND,
  author =       "J. Palmer",
  title =        "The {Intel} 8087 Numeric Data Processor",
  crossref =     "Anonymous:1980:CPA",
  pages =        "174--181",
  year =         "1980",
  bibdate =      "Mon Sep 12 08:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Palmer:1980:LIN
author: J. Palmer
title: An LSI Implementation of a New System for Floating-Point Arithmetic
crossref: Electro:1980:ECR
pages: 18/4/1--8
year: 1980
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: J. Palmer
rawtitle: An {LSI} Implementation of a New System for Floating-Point Arithmetic
entry:
@InProceedings{Palmer:1980:LIN,
  author =       "J. Palmer",
  title =        "An {LSI} Implementation of a New System for
                 Floating-Point Arithmetic",
  crossref =     "Electro:1980:ECR",
  pages =        "18/4/1--8",
  year =         "1980",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: misc
filename: fparith.bib
label: Palmer:1980:UND
author: John F. Palmer and Bruce W. Ravenel and Rafi Nave
title: US4338675: Numeric data processor
pages: 18/4/1--8
day: 13
month: feb
monthnumber: 2
year: 1980
bibdate: Sat Nov 09 10:23:07 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 10:23:07 ???
note: Published July 6, 1982. This patent was reissued on July 2, 1991 as patent USRE33629.
acknowledgement: ack-nhfb
howpublished: U.S. Patent
rawauthor: John F. Palmer and Bruce W. Ravenel and Rafi Nave
rawnote: Published July 6, 1982. This patent was reissued on July 2, 1991 as patent USRE33629.
rawtitle: {US4338675}: Numeric data processor
abstract:
A floating point, integrated, arithmetic circuit is organized around a file format having a floating point numeric domain exceeding that of any single or double precision floating point numbers, long or short integer words or BCD data upon which it must operate. As a result the circuit has a greater reliability, range and precision than ever previously achieved without entailing additional circuit complexity. Reliability is further enhanced by a systematic three bit rounding field, and by including means for detecting every error or exception condition with an optional expected response provided thereto by hardware. As a result of such organization, an unexpected increase of capacity is achieved wherein transcendental functions can be computed totally in hardware, and whereby mixed mode arithmetic can be implemented without difficulty. The numeric processor also includes a programmable shifter capable of arbitrary numbers of bit and byte shifts in a single clock cycle, as well as an arithmetic unit capable of implementing multiplication, division, modulo reduction and square roots directly in hardware.

rawabstract:
A floating point, integrated, arithmetic circuit is organized around a file format having a floating point numeric domain exceeding that of any single or double precision floating point numbers, long or short integer words or BCD data upon which it must operate. As a result the circuit has a greater reliability, range and precision than ever previously achieved without entailing additional circuit complexity. Reliability is further enhanced by a systematic three bit rounding field, and by including means for detecting every error or exception condition with an optional expected response provided thereto by hardware. As a result of such organization, an unexpected increase of capacity is achieved wherein transcendental functions can be computed totally in hardware, and whereby mixed mode arithmetic can be implemented without difficulty. The numeric processor also includes a programmable shifter capable of arbitrary numbers of bit and byte shifts in a single clock cycle, as well as an arithmetic unit capable of implementing multiplication, division, modulo reduction and square roots directly in hardware.

entry:
@Misc{Palmer:1980:UND,
  author =       "John F. Palmer and Bruce W. Ravenel and Rafi Nave",
  title =        "{US4338675}: Numeric data processor",
  howpublished = "U.S. Patent",
  day =          "13",
  month =        feb,
  year =         "1980",
  bibdate =      "Sat Nov 09 10:23:07 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published July 6, 1982. This patent was reissued on
                 July 2, 1991 as patent USRE33629.",
  abstract =     "A floating point, integrated, arithmetic circuit is
                 organized around a file format having a floating point
                 numeric domain exceeding that of any single or double
                 precision floating point numbers, long or short integer
                 words or BCD data upon which it must operate. As a
                 result the circuit has a greater reliability, range and
                 precision than ever previously achieved without
                 entailing additional circuit complexity. Reliability is
                 further enhanced by a systematic three bit rounding
                 field, and by including means for detecting every error
                 or exception condition with an optional expected
                 response provided thereto by hardware. As a result of
                 such organization, an unexpected increase of capacity
                 is achieved wherein transcendental functions can be
                 computed totally in hardware, and whereby mixed mode
                 arithmetic can be implemented without difficulty. The
                 numeric processor also includes a programmable shifter
                 capable of arbitrary numbers of bit and byte shifts in
                 a single clock cycle, as well as an arithmetic unit
                 capable of implementing multiplication, division,
                 modulo reduction and square roots directly in
                 hardware.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Payne:1980:VFPa
author: M. Payne and D. Bhandarkar
title: VAX Floating Point: a Solid Foundation for Numerical Computation
crossref: Electro:1980:ECR
pages: 18/1/1--12
year: 1980
bibdate: Wed Sep 07 21:37:14 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 21:37:14 ???
acknowledgement: ack-nj
rawauthor: M. Payne and D. Bhandarkar
rawtitle: {VAX} Floating Point: a Solid Foundation for Numerical Computation
entry:
@InProceedings{Payne:1980:VFPa,
  author =       "M. Payne and D. Bhandarkar",
  title =        "{VAX} Floating Point: a Solid Foundation for Numerical
                 Computation",
  crossref =     "Electro:1980:ECR",
  pages =        "18/1/1--12",
  year =         "1980",
  bibdate =      "Wed Sep 07 21:37:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Payne:1980:VFPb
author: Mary Payne and Dileep Bhandarkar
title: VAX floating point: a solid foundation for numerical computation
journal: j-COMP-ARCH-NEWS
volume: 8
number: 4
pages: 22--33
month: jun
monthnumber: 6
year: 1980
CODEN: CANED2
DOI: https://doi.org/10.1145/641845.641849
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Sat Jun 24 12:02:21 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.06.24 12:02:21 ???
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J89
rawauthor: Mary Payne and Dileep Bhandarkar
rawtitle: {VAX} floating point: a solid foundation for numerical computation
entry:
@Article{Payne:1980:VFPb,
  author =       "Mary Payne and Dileep Bhandarkar",
  title =        "{VAX} floating point: a solid foundation for numerical
                 computation",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "8",
  number =       "4",
  pages =        "22--33",
  month =        jun,
  year =         "1980",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/641845.641849",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Sat Jun 24 12:02:21 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


bibtype: article
filename: fparith.bib
label: Pedersen:1980:HBM
author: P. W. Pedersen
title: Hvordan beregner man kvadratroden? toenglish How do you calculate the square root? endtoenglish
journal: Elektronik (Denmark)
number: 4
pages: 18--21
month: apr
monthnumber: 4
year: 1980
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
acknowledgement: ack-nj
rawauthor: P. W. Pedersen
rawtitle: Hvordan beregner man kvadratroden? \toenglish {How do you calculate the square root?} \endtoenglish
entry:
@Article{Pedersen:1980:HBM,
  author =       "P. W. Pedersen",
  title =        "Hvordan beregner man kvadratroden? \toenglish {How do
                 you calculate the square root?} \endtoenglish",
  journal =      "Elektronik (Denmark)",
  volume =       "??",
  number =       "4",
  pages =        "18--21",
  month =        apr,
  year =         "1980",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Purtilo:1980:IAP
author: Jim Purtilo
title: On implementing arbitrary precision arithmetic in NIL: an exercise in data abstraction
journal: j-SIGSAM
volume: 14
number: 1
pages: 14--18
month: feb
monthnumber: 2
year: 1980
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Wed Oct 5 08:31:56 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.10.05 08:31:56 MDT
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
rawauthor: Jim Purtilo
rawtitle: On implementing arbitrary precision arithmetic in {NIL}: an exercise in data abstraction
entry:
@Article{Purtilo:1980:IAP,
  author =       "Jim Purtilo",
  title =        "On implementing arbitrary precision arithmetic in
                 {NIL}: an exercise in data abstraction",
  journal =      j-SIGSAM,
  volume =       "14",
  number =       "1",
  pages =        "14--18",
  month =        feb,
  year =         "1980",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Oct 5 08:31:56 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  issue =        "??",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: article
filename: fparith.bib
label: Rallapalli:1980:CMF
author: K. Rallapalli and J. Kroeger
title: Chips make fast math a snap for microprocessors
journal: j-ELECTRONICS
volume: 53
number: 10
pages: 153--157
month: apr
monthnumber: 4
year: 1980
ISSN: 0883-4989 OR 08834989
bibdate: Wed Sep 07 22:27:11 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:27:11 ???
fjournal: Electronics
acknowledgement: ack-nj
journalURL: https://www.mdpi.com/journal/electronics
rawauthor: K. Rallapalli and J. Kroeger
rawtitle: Chips make fast math a snap for microprocessors
entry:
@Article{Rallapalli:1980:CMF,
  author =       "K. Rallapalli and J. Kroeger",
  title =        "Chips make fast math a snap for microprocessors",
  journal =      j-ELECTRONICS,
  volume =       "53",
  number =       "10",
  pages =        "153--157",
  month =        apr,
  year =         "1980",
  ISSN =         "0883-4989",
  bibdate =      "Wed Sep 07 22:27:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}


bibtype: article
filename: fparith.bib
label: Reid:1980:CDP
author: John Reid
title: Complex double precision in association with Fortran 77
journal: j-SIGNUM
volume: 15
number: 1
pages: 16--17
month: mar
monthnumber: 3
year: 1980
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:08 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:08 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages)
corpsource: Computer Sci. and Systems Div., AERE Harwell, UK
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical
rawauthor: John Reid
rawtitle: Complex double precision in association with {Fortran 77}
keywords:
compilers; complex double precision arithmetic; digital arithmetic; FORTRAN; FORTRAN 77; portability

entry:
@Article{Reid:1980:CDP,
  author =       "John Reid",
  title =        "Complex double precision in association with {Fortran
                 77}",
  journal =      j-SIGNUM,
  volume =       "15",
  number =       "1",
  pages =        "16--17",
  month =        mar,
  year =         "1980",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:08 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages)",
  corpsource =   "Computer Sci. and Systems Div., AERE Harwell, UK",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "compilers; complex double precision arithmetic;
                 digital arithmetic; FORTRAN; FORTRAN 77; portability",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Reid:1980:FMF
author: J. K. Reid
title: Functions for manipulating floating-point numbers
journal: j-SIGPLAN
volume: 15
number: 6
pages: 68--76
month: jun
monthnumber: 6
year: 1980
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sat Apr 25 11:46:37 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.25 11:46:37 MDT
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
corpsource: Computer Sci. and Systems Div., AERE, Harwell, Didcot, UK
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
treatment: T Theoretical or Mathematical
rawauthor: J. K. Reid
rawtitle: Functions for manipulating floating-point numbers
keywords:
complete computer programs; digital arithmetic; floating point numbers; function manipulation; portability; software portability

entry:
@Article{Reid:1980:FMF,
  author =       "J. K. Reid",
  title =        "Functions for manipulating floating-point numbers",
  journal =      j-SIGPLAN,
  volume =       "15",
  number =       "6",
  pages =        "68--76",
  month =        jun,
  year =         "1980",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat Apr 25 11:46:37 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Computer Sci. and Systems Div., AERE, Harwell, Didcot,
                 UK",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "complete computer programs; digital arithmetic;
                 floating point numbers; function manipulation;
                 portability; software portability",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Rink:1980:CPS
author: R. Rink
title: Correction to ``Performance of state regulator systems with floating-point computation''
journal: j-IEEE-TRANS-AUTOMAT-CONTR
volume: 25
number: 3
pages: 612--612
month: jun
monthnumber: 6
year: 1980
CODEN: IETAA9
ISSN: 0018-9286 (print), 1558-2523 (electronic) OR 00189286 (print), 15582523 (electronic)
ISSNL: 0018-9286 OR 00189286
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
note: See cite Rink:1979:PSR.
fjournal: IEEE Transactions on Automatic Control
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
rawauthor: R. Rink
rawnote: See \cite{Rink:1979:PSR}.
rawtitle: Correction to {``Performance of state regulator systems with floating-point computation''}
entry:
@Article{Rink:1980:CPS,
  author =       "R. Rink",
  title =        "Correction to {``Performance of state regulator
                 systems with floating-point computation''}",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "25",
  number =       "3",
  pages =        "612--612",
  month =        jun,
  year =         "1980",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Rink:1979:PSR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
}


bibtype: phdthesis
filename: fparith.bib
label: Rump:1980:KFM
author: Siegfried M. Rump
title: Kleine Fehlerschranken bei Matrixproblemen. (German) [Small error bounds for matrix problems]
type: Ph.D. Thesis
school: Institut fur Angewandte Mathematik der Universitat Karlsruhe
address: Karlsruhe, Germany
pages: vi + 131 + 49
year: 1980
bibdate: Fri Jan 06 07:57:41 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.06 07:57:41 ???
URL: http://www.ti3.tuhh.de/rump/Research/topics.php#PhD
keywords: accurate dot products; accurate floating-point summation; long accumulator
language: German
acknowledgement: ack-nhfb
rawauthor: Siegfried M. Rump
rawtitle: {Kleine Fehlerschranken bei Matrixproblemen}. ({German}) [Small error bounds for matrix problems]
entry:
@PhdThesis{Rump:1980:KFM,
  author =       "Siegfried M. Rump",
  title =        "{Kleine Fehlerschranken bei Matrixproblemen}.
                 ({German}) [Small error bounds for matrix problems]",
  type =         "{Ph.D.} Thesis",
  school =       "Institut f{\"u}r Angewandte Mathematik der
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "vi + 131 + 49",
  year =         "1980",
  bibdate =      "Fri Jan 06 07:57:41 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ti3.tuhh.de/rump/Research/topics.php#PhD",
  acknowledgement = ack-nhfb,
  keywords =     "accurate dot products; accurate floating-point
                 summation; long accumulator",
  language =     "German",
}


bibtype: inproceedings
filename: fparith.bib
label: Scherer:1980:SNR
author: R. Scherer and K. Zeller
title: Shorthand Notation for Rounding Errors
crossref: Alefeld:1980:FNC
pages: 165--168
year: 1980
bibdate: Tue Oct 23 08:17:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.23 08:17:48 ???
keywords: interval arithmetic; rounding error
acknowledgement: ack-nhfb
rawauthor: R. Scherer and K. Zeller
rawtitle: Shorthand Notation for Rounding Errors
entry:
@InProceedings{Scherer:1980:SNR,
  author =       "R. Scherer and K. Zeller",
  title =        "Shorthand Notation for Rounding Errors",
  crossref =     "Alefeld:1980:FNC",
  pages =        "165--168",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rounding error",
}


bibtype: manual
filename: fparith.bib
label: SOITA:1980:AIE
title: Applesoft II: extended floating-point BASIC: quick reference guide
organization: Southwestern Ohio Instructional Television Association
address: Oxford, OH, USA
pages: 165--168
year: 1980
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: 1 pamphlet
series: SOITA #2008
keywords: Apple II (Computer) --- Programming; BASIC (Computer program language)
acknowledgement: ack-nhfb
key: SOITA
rawnote: 1 pamphlet
rawtitle: {Applesoft II}: extended floating-point {BASIC}: quick reference guide
entry:
@Manual{SOITA:1980:AIE,
  key =          "SOITA",
  title =        "{Applesoft II}: extended floating-point {BASIC}: quick
                 reference guide",
  organization = "Southwestern Ohio Instructional Television
                 Association",
  address =      "Oxford, OH, USA",
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "1 pamphlet",
  series =       "SOITA \#2008",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (Computer) --- Programming; BASIC (Computer
                 program language)",
}


bibtype: article
filename: fparith.bib
label: Speiser:1980:RCZ
author: A. P. Speiser
title: The Relay Calculator Z4
journal: j-ANN-HIST-COMPUT
volume: 2
number: 3
pages: 242--245
month: jul
monthnumber: 7
year: 1980
CODEN: AHCOE5
DOI: https://doi.org/10.1109/MAHC.1980.10026
ISSN: 0164-1239 OR 01641239
ISSNL: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:17 MST 2002
bibtimestamp: 2002.11.01 15:29:17 MST
fjournal: Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
rawauthor: A. P. Speiser
rawtitle: The Relay Calculator {Z4}
bibsource:
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://dlib.computer.org/an/books/an1980/pdf/a3242.pdf; http://www.computer.org/annals/an1980/a3242abs.htm

entry:
@Article{Speiser:1980:RCZ,
  author =       "A. P. Speiser",
  title =        "The Relay Calculator {Z4}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "2",
  number =       "3",
  pages =        "242--245",
  month =        jul # "\slash " # sep,
  year =         "1980",
  CODEN =        "AHCOE5",
  DOI =          "https://doi.org/10.1109/MAHC.1980.10026",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:17 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1980/pdf/a3242.pdf;
                 http://www.computer.org/annals/an1980/a3242abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}


bibtype: article
filename: fparith.bib
label: Stevenson:1980:RPI
author: David Stevenson
title: A report on the proposed IEEE Floating Point Standard (IEEE task p754)
journal: j-COMP-ARCH-NEWS
volume: 8
number: 5
pages: 11--12
month: aug
monthnumber: 8
year: 1980
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Wed Nov 24 10:59:34 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 10:59:34 ???
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J89
rawauthor: David Stevenson
rawtitle: A report on the proposed {IEEE Floating Point Standard (IEEE task p754)}
entry:
@Article{Stevenson:1980:RPI,
  author =       "David Stevenson",
  title =        "A report on the proposed {IEEE Floating Point Standard
                 (IEEE task p754)}",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "8",
  number =       "5",
  pages =        "11--12",
  month =        aug,
  year =         "1980",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Wed Nov 24 10:59:34 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


bibtype: book
filename: fparith.bib
label: Stone:1980: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
edition: Second
pages: 673
year: 1980
ISBN: 0-574-21225-6 OR 0574212256
ISBN13: 978-0-574-21225-2 OR 9780574212252
LCCN: QA76.9.A73 I57 1980
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: The SRA computer science series
subject: Computer architecture
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:1980: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",
  edition =      "Second",
  pages =        "673",
  year =         "1980",
  ISBN =         "0-574-21225-6",
  ISBN-13 =      "978-0-574-21225-2",
  LCCN =         "QA76.9.A73 I57 1980",
  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",
  price =        "US\$16.95 (est.)",
  series =       "The SRA computer science series",
  acknowledgement = ack-nhfb,
  subject =      "Computer architecture",
}


bibtype: inproceedings
filename: fparith.bib
label: Stone:1980:TFP
author: H. S. Stone
title: Towards a Floating-Point Standard
crossref: Electro:1980:ECR
pages: 18/0/1--5
year: 1980
bibdate: Wed Sep 07 21:33:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 21:33:52 ???
acknowledgement: ack-nj
rawauthor: H. S. Stone
rawtitle: Towards a Floating-Point Standard
entry:
@InProceedings{Stone:1980:TFP,
  author =       "H. S. Stone",
  title =        "Towards a Floating-Point Standard",
  crossref =     "Electro:1980:ECR",
  pages =        "18/0/1--5",
  year =         "1980",
  bibdate =      "Wed Sep 07 21:33:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Stummel:1980:REA
author: F. Stummel
title: Rounding Error Analysis of Elementary Numerical Algorithms
crossref: Alefeld:1980:FNC
pages: 169--195
year: 1980
bibdate: Tue Aug 28 06:19:13 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.28 06:19:13 ???
keywords: interval arithmetic; rounding error
acknowledgement: ack-nhfb
rawauthor: F. Stummel
rawtitle: Rounding Error Analysis of Elementary Numerical Algorithms
entry:
@InProceedings{Stummel:1980:REA,
  author =       "F. Stummel",
  title =        "Rounding Error Analysis of Elementary Numerical
                 Algorithms",
  crossref =     "Alefeld:1980:FNC",
  pages =        "169--195",
  year =         "1980",
  bibdate =      "Tue Aug 28 06:19:13 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rounding error",
}


bibtype: article
filename: fparith.bib
label: Swartzlander:1980:AUH
author: E. E. Swartzlander, Jr. and B. K. Gilbert
title: Arithmetic for Ultra-High-Speed Tomography
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 5
pages: 341--353
month: may
monthnumber: 5
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675584
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 19:15:25 MDT 2011
bibtimestamp: 2011.07.10 19:15:25 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675584
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 B. K. Gilbert
rawtitle: Arithmetic for Ultra-High-Speed Tomography
entry:
@Article{Swartzlander:1980:AUH,
  author =       "E. E. {Swartzlander, Jr.} and B. K. Gilbert",
  title =        "Arithmetic for Ultra-High-Speed Tomography",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "5",
  pages =        "341--353",
  month =        may,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675584",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675584",
  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: Swartzlander:1980:CA
editor: Earl E. Swartzlander, Jr.
title: Computer Arithmetic
publisher: pub-DOWDEN
address: pub-DOWDEN:adr
pages: xiii + 378
year: 1980
ISBN: 0-87933-350-2 OR 0879333502
ISBN13: 978-0-87933-350-8 OR 9780879333508
LCCN: QA76.6 .C633
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
series: Benchmark papers in electrical engineering and computer science; 21
keywords: Computer arithmetic.; Electronic digital computers --- Programming.; Floating-point arithmetic.
acknowledgement: ack-nj
raweditor: Earl E. {Swartzlander, Jr.}
rawtitle: Computer Arithmetic
entry:
@Book{Swartzlander:1980:CA,
  editor =       "Earl E. {Swartzlander, Jr.}",
  title =        "Computer Arithmetic",
  publisher =    pub-DOWDEN,
  address =      pub-DOWDEN:adr,
  pages =        "xiii + 378",
  year =         "1980",
  ISBN =         "0-87933-350-2",
  ISBN-13 =      "978-0-87933-350-8",
  LCCN =         "QA76.6 .C633",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Benchmark papers in electrical engineering and
                 computer science; 21",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Computer arithmetic.; Electronic digital computers ---
                 Programming.; Floating-point arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Swartzlander:1980:MA
author: E. E. Swartzlander, Jr.
title: Merged Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 10
pages: 946--950
month: oct
monthnumber: 10
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675482
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 19:31:28 MDT 2011
bibtimestamp: 2011.07.10 19:31:28 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675482
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.}
rawtitle: Merged Arithmetic
entry:
@Article{Swartzlander:1980:MA,
  author =       "E. E. {Swartzlander, Jr.}",
  title =        "Merged Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "10",
  pages =        "946--950",
  month =        oct,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675482",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:31:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675482",
  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: Thornton:1980:CP
author: James E. Thornton
title: The CDC 6600 Project
journal: j-ANN-HIST-COMPUT
volume: 2
number: 4
pages: 338--348
month: oct
monthnumber: 10
year: 1980
CODEN: AHCOE5
DOI: https://doi.org/10.1109/MAHC.1980.10044
ISSN: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:17 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.01 15:29:17 MST
fjournal: Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
rawauthor: James E. Thornton
rawtitle: The {CDC 6600} Project
URL:
http://dlib.computer.org/an/books/an1980/pdf/a4338.pdf; http://www.computer.org/annals/an1980/a4338abs.htm

abstract:
This article is an account of the development of the Control Data 6600 computer first developed in 1964. Of historical interest is the design team approach adopted by Control Data in which a small staff of engineers was isolated from the main operations of the company. Some review is made of the design process as well as the unique features of the machine. The article also includes some comments in retrospect about the results of certain of the initial design objectives.

rawabstract:
This article is an account of the development of the Control Data 6600 computer first developed in 1964. Of historical interest is the design team approach adopted by Control Data in which a small staff of engineers was isolated from the main operations of the company. Some review is made of the design process as well as the unique features of the machine. The article also includes some comments in retrospect about the results of certain of the initial design objectives.

entry:
@Article{Thornton:1980:CP,
  author =       "James E. Thornton",
  title =        "The {CDC 6600} Project",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "2",
  number =       "4",
  pages =        "338--348",
  month =        oct # "\slash " # dec,
  year =         "1980",
  CODEN =        "AHCOE5",
  DOI =          "https://doi.org/10.1109/MAHC.1980.10044",
  ISSN =         "0164-1239",
  bibdate =      "Fri Nov 1 15:29:17 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1980/pdf/a4338.pdf;
                 http://www.computer.org/annals/an1980/a4338abs.htm",
  abstract =     "This article is an account of the development of the
                 Control Data 6600 computer first developed in 1964. Of
                 historical interest is the design team approach adopted
                 by Control Data in which a small staff of engineers was
                 isolated from the main operations of the company. Some
                 review is made of the design process as well as the
                 unique features of the machine. The article also
                 includes some comments in retrospect about the results
                 of certain of the initial design objectives.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}


bibtype: mastersthesis
filename: fparith.bib
label: Ting:1980:MCU
author: I-chyng Ting
title: A microprocessor-based controller using floating-point arithmetic
type: Thesis (M.S.)
school: Auburn University
address: Auburn, AL, USA
pages: ix + 167
year: 1980
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.; Microprocessors.
acknowledgement: ack-nhfb
rawauthor: I-chyng Ting
rawtitle: A microprocessor-based controller using floating-point arithmetic
entry:
@MastersThesis{Ting:1980:MCU,
  author =       "I-chyng Ting",
  title =        "A microprocessor-based controller using floating-point
                 arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Auburn University",
  address =      "Auburn, AL, USA",
  pages =        "ix + 167",
  year =         "1980",
  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.; Microprocessors.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Tucker:1980:IAD
author: Richard Wesley Tucker
title: Implementation of arithmetic for the data flow machine processing unit
type: Thesis (B.S.)
school: Massachusetts Institute of Technology. Dept. of Electrical and Engineering and Computer Science
address: Cambridge, MA, USA
pages: i + 58
year: 1980
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 Jack B. Dennis.
keywords: Floating-point arithmetic.; Microprocessors --- Programming.; Val (Computer program language).
acknowledgement: ack-nhfb
rawauthor: Richard Wesley Tucker
rawnote: Supervised by Jack B. Dennis.
rawtitle: Implementation of arithmetic for the data flow machine processing unit
entry:
@MastersThesis{Tucker:1980:IAD,
  author =       "Richard Wesley Tucker",
  title =        "Implementation of arithmetic for the data flow machine
                 processing unit",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical and Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "i + 58",
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Jack B. Dennis.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors ---
                 Programming.; Val (Computer program language).",
}


bibtype: inproceedings
filename: fparith.bib
label: Ulrich:1980:IMS
author: Ch. Ulrich
title: Iterative Methods in the Spaces of Rounded Computations
crossref: Alefeld:1980:FNC
pages: 197--209
year: 1980
bibdate: Tue Oct 23 08:17:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.23 08:17:48 ???
keywords: interval arithmetic; rounding error
acknowledgement: ack-nhfb
rawauthor: Ch. Ulrich
rawtitle: Iterative Methods in the Spaces of Rounded Computations
entry:
@InProceedings{Ulrich:1980:IMS,
  author =       "Ch. Ulrich",
  title =        "Iterative Methods in the Spaces of Rounded
                 Computations",
  crossref =     "Alefeld:1980:FNC",
  pages =        "197--209",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rounding error",
}


bibtype: inproceedings
filename: fparith.bib
label: Undheim:1980:CFP
author: T. Undheim
title: Combinatorial Floating Point Processor as an Integral Part of the Computer
crossref: Electro:1980:ECR
pages: 14/1/1--6
year: 1980
bibdate: Wed Sep 7 22:31:27 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:31:27 ???
acknowledgement: ack-nj
rawauthor: T. Undheim
rawtitle: Combinatorial Floating Point Processor as an Integral Part of the Computer
entry:
@InProceedings{Undheim:1980:CFP,
  author =       "T. Undheim",
  title =        "Combinatorial Floating Point Processor as an Integral
                 Part of the Computer",
  crossref =     "Electro:1980:ECR",
  pages =        "14/1/1--6",
  year =         "1980",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Verma:1980:MPF
author: S. B. Verma and Maithili Sharan
title: Multiple Precision Floating-point Computation in FORTRAN
journal: j-SPE
volume: 10
number: 3
pages: 163--173
month: mar
monthnumber: 3
year: 1980
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Thu Sep 8 08:20:53 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:20:53 ???
fjournal: Software---Practice and Experience
acknowledgement: ack-nj
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: S. B. Verma and Maithili Sharan
rawtitle: Multiple Precision Floating-point Computation in {FORTRAN}
entry:
@Article{Verma:1980:MPF,
  author =       "S. B. Verma and Maithili Sharan",
  title =        "Multiple Precision Floating-point Computation in
                 {FORTRAN}",
  journal =      j-SPE,
  volume =       "10",
  number =       "3",
  pages =        "163--173",
  month =        mar,
  year =         "1980",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Thu Sep 8 08:20:53 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}


bibtype: techreport
filename: fparith.bib
label: Virkkunen:1980:UAF
author: V.-E. Juhani Virkkunen
title: A unified approach to floating-point rounding with applications to multiple-precision summation
type: Diss. Helsingfors
institution: Department of Computer Science, University of Helsinki
address: Helsinki, Finland
pages: 66
year: 1980
ISBN: 951-45-1948-5 OR 9514519485
ISBN13: 978-951-45-1948-2 OR 9789514519482
bibdate: Thu May 09 08:25:02 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:25:02 ???
acknowledgement: ack-nhfb
rawauthor: V.-E. Juhani Virkkunen
rawtitle: A unified approach to floating-point rounding with applications to multiple-precision summation
entry:
@TechReport{Virkkunen:1980:UAF,
  author =       "V.-E. Juhani Virkkunen",
  title =        "A unified approach to floating-point rounding with
                 applications to multiple-precision summation",
  type =         "{Diss. Helsingfors}",
  institution =  "Department of Computer Science, University of
                 Helsinki",
  address =      "Helsinki, Finland",
  pages =        "66",
  year =         "1980",
  ISBN =         "951-45-1948-5",
  ISBN-13 =      "978-951-45-1948-2",
  bibdate =      "Thu May 09 08:25:02 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: vonGudenberg:1980:EAR
author: J. Wolff von Gudenberg
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1980
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 ???
acknowledgement: ack-nj
rawauthor: J. Wolff {von Gudenberg}
title:
Einbettung allgemeiner Rechnerarithmetik in Pascal mittels eines Operatorkonzepts und Implementierung der Standardfunktionen mit optimaler Genauigkeit toenglish Embedding a General Computer Arithmetic in Pascal by Means of an Operator Concept and the Implementation of Elementary Functions with Optimal Accuracy endtoenglish 

rawtitle:
{Einbettung allgemeiner Rechnerarithmetik in Pascal mittels eines Operatorkonzepts und Implementierung der Standardfunktionen mit optimaler Genauigkeit} \toenglish {Embedding a General Computer Arithmetic in Pascal by Means of an Operator Concept and the Implementation of Elementary Functions with Optimal Accuracy} \endtoenglish

entry:
@PhdThesis{vonGudenberg:1980:EAR,
  author =       "J. Wolff {von Gudenberg}",
  title =        "{Einbettung allgemeiner Rechnerarithmetik in Pascal
                 mittels eines Operatorkonzepts und Implementierung der
                 Standardfunktionen mit optimaler Genauigkeit}
                 \toenglish {Embedding a General Computer Arithmetic in
                 Pascal by Means of an Operator Concept and the
                 Implementation of Elementary Functions with Optimal
                 Accuracy} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1980",
  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,
}


bibtype: article
filename: fparith.bib
label: Waldecker:1980:NSR
author: D. E. Waldecker
title: Nonrestoring Square Root with Simplified Answer Generation
journal: j-IBM-TDB
volume: 22
number: 11
pages: 4807--4808
month: apr
monthnumber: 4
year: 1980
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:15:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:41 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: D. E. Waldecker
rawtitle: Nonrestoring Square Root with Simplified Answer Generation
entry:
@Article{Waldecker:1980:NSR,
  author =       "D. E. Waldecker",
  title =        "Nonrestoring Square Root with Simplified Answer
                 Generation",
  journal =      j-IBM-TDB,
  volume =       "22",
  number =       "11",
  pages =        "4807--4808",
  month =        apr,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: fparith.bib
label: Waser:1980:EGP
author: S. Waser
journal: j-ELECTRONIK
volume: 29
number: 9
pages: 50--54
month: apr
monthnumber: 4
year: 1980
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
bibdate: Fri Sep 16 16:30:40 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: S. Waser
title:
Entwicklung von Gleitkomma-Prozessoren toenglish Development of Floating-Point Processors endtoenglish 

rawtitle:
{Entwicklung von Gleitkomma-Prozessoren} \toenglish {Development of Floating-Point Processors} \endtoenglish

entry:
@Article{Waser:1980:EGP,
  author =       "S. Waser",
  title =        "{Entwicklung von Gleitkomma-Prozessoren} \toenglish
                 {Development of Floating-Point Processors}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "29",
  number =       "9",
  pages =        "50--54",
  month =        apr,
  year =         "1980",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}


bibtype: mastersthesis
filename: fparith.bib
label: Watkins:1980:MFU
author: Timothy Ervin Watkins
title: A microprogrammed FFT utilizing floating point hardware
type: Thesis (M.S.)
school: UCLA
address: Los Angeles, CA, USA
pages: v + 56
year: 1980
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.; Fourier transformations --- Computer programs.; Microprogramming.
acknowledgement: ack-nhfb
rawauthor: Timothy Ervin Watkins
rawtitle: A microprogrammed {FFT} utilizing floating point hardware
entry:
@MastersThesis{Watkins:1980:MFU,
  author =       "Timothy Ervin Watkins",
  title =        "A microprogrammed {FFT} utilizing floating point
                 hardware",
  type =         "Thesis ({M.S.})",
  school =       "UCLA",
  address =      "Los Angeles, CA, USA",
  pages =        "v + 56",
  year =         "1980",
  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.; Fourier transformations
                 --- Computer programs.; Microprogramming.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Wong:1980:IOF
author: Clement Sau-Fai Wong
title: Input / output and floating-point arithmetic package
type: Thesis (M.S.)
school: University of Tennessee, Knoxville
address: Knoxville, TN, USA
pages: vi + 61
year: 1980
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: Clement Sau-Fai Wong
rawtitle: Input\slash output and floating-point arithmetic package
keywords:
Computer input-output equipment.; Electronic digital computers --- Programming.; Floating-point arithmetic.; Microcomputers.

entry:
@MastersThesis{Wong:1980:IOF,
  author =       "Clement Sau-Fai Wong",
  title =        "Input\slash output and floating-point arithmetic
                 package",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vi + 61",
  year =         "1980",
  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 input-output equipment.; Electronic digital
                 computers --- Programming.; Floating-point arithmetic.;
                 Microcomputers.",
}


bibtype: inproceedings
filename: fparith.bib
label: Yohe:1980:FPE
author: J. M. Yohe
title: Floating point exception handling for interval arithmetic
crossref: Nickel:1980:IMP
pages: 547--554
year: 1980
MRclass: 65G10
MRnumber: 83c:65115
bibdate: Fri Dec 08 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
acknowledgement: ack-nhfb
rawauthor: J. M. Yohe
rawtitle: Floating point exception handling for interval arithmetic
entry:
@InProceedings{Yohe:1980:FPE,
  author =       "J. M. Yohe",
  title =        "Floating point exception handling for interval
                 arithmetic",
  crossref =     "Nickel:1980:IMP",
  pages =        "547--554",
  year =         "1980",
  MRclass =      "65G10",
  MRnumber =     "83c:65115",
  bibdate =      "Fri Dec 08 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Yohe:1980:PSI
author: J. M. Yohe
title: Portable Software for Interval Arithmetic
crossref: Alefeld:1980:FNC
pages: 211--229
year: 1980
bibdate: Tue Oct 23 08:17:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.23 08:17:48 ???
keywords: interval arithmetic; multiple precision arithmetic
acknowledgement: ack-nhfb
rawauthor: J. M. Yohe
rawtitle: Portable Software for Interval Arithmetic
abstract:
A portable multiple precision interval arithmetic package for FORTRAN has been developed by substituting the multiple precision arithmetic package of Richard P. Brent for the underlying arithmetic in the author's earlier single precision interval arithmetic package. This package, like the earlier version, offers a complete range of operations and functions for interval calculations.par In this paper, we outline the design philosophy of the earlier package and show how this design facilitated the incorporation of the Brent package. We discuss several desirable host system features and possible adaptations of the interval package, and explain how the design of the package would allow it to serve in differing environments with only relatively minor changes.par Since the package may be of direct use to many individuals, we also discuss its installation on other host systems and its use via the AUGMENT precompiler for Fortran.

rawabstract:
A portable multiple precision interval arithmetic package for FORTRAN has been developed by substituting the multiple precision arithmetic package of Richard P. Brent for the underlying arithmetic in the author's earlier single precision interval arithmetic package. This package, like the earlier version, offers a complete range of operations and functions for interval calculations.\par In this paper, we outline the design philosophy of the earlier package and show how this design facilitated the incorporation of the Brent package. We discuss several desirable host system features and possible adaptations of the interval package, and explain how the design of the package would allow it to serve in differing environments with only relatively minor changes.\par Since the package may be of direct use to many individuals, we also discuss its installation on other host systems and its use via the AUGMENT precompiler for Fortran.

entry:
@InProceedings{Yohe:1980:PSI,
  author =       "J. M. Yohe",
  title =        "Portable Software for Interval Arithmetic",
  crossref =     "Alefeld:1980:FNC",
  pages =        "211--229",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A portable multiple precision interval arithmetic
                 package for FORTRAN has been developed by substituting
                 the multiple precision arithmetic package of Richard P.
                 Brent for the underlying arithmetic in the author's
                 earlier single precision interval arithmetic package.
                 This package, like the earlier version, offers a
                 complete range of operations and functions for interval
                 calculations.\par

                 In this paper, we outline the design philosophy of the
                 earlier package and show how this design facilitated
                 the incorporation of the Brent package. We discuss
                 several desirable host system features and possible
                 adaptations of the interval package, and explain how
                 the design of the package would allow it to serve in
                 differing environments with only relatively minor
                 changes.\par

                 Since the package may be of direct use to many
                 individuals, we also discuss its installation on other
                 host systems and its use via the AUGMENT precompiler
                 for Fortran.",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; multiple precision arithmetic",
}


bibtype: article
filename: fparith.bib
label: Zeman:1980:HSM
author: J. Zeman and H. T. Nagle, Jr.
title: A High-Speed Microprogrammable Digital Signal Processor Employing Distributed Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-29
number: 2
pages: 134--144
month: feb
monthnumber: 2
year: 1980
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1980.1675537
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 19:15:24 MDT 2011
bibtimestamp: 2011.07.10 19:15:24 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675537
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. Zeman and H. T. {Nagle, Jr.}
rawtitle: A High-Speed Microprogrammable Digital Signal Processor Employing Distributed Arithmetic
entry:
@Article{Zeman:1980:HSM,
  author =       "J. Zeman and H. T. {Nagle, Jr.}",
  title =        "A High-Speed Microprogrammable Digital Signal
                 Processor Employing Distributed Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "2",
  pages =        "134--144",
  month =        feb,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675537",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675537",
  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: Agrawal:1981:NAM
author: D. P. Agrawal and R. C. Joshi
title: Negabinary Addition and Multiplication Using Binary Circuits
crossref: IEEE:1981:PSC
pages: 270--273
year: 1981
bibdate: Thu Nov 15 11:37:51 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 11:37:51 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Agrawal_Joshi.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: D. P. Agrawal and R. C. Joshi
rawtitle: Negabinary Addition and Multiplication Using Binary Circuits
abstract:
This paper deals with design techniques that allow adoption of off-the-shelf binary arithmetic circuits to perform multi-operand addition and multiplication of negabinary numbers. The multiple operands could be easily added with augmented binary adders connected in the form of a tree. The same hardware could be used to perform multiplication. But, from an LSI implementation viewpoint, the use of cellular array structures is explored and necessary challenges to design a combined binary/negabinary multiplier unit, are also outlined.

rawabstract:
This paper deals with design techniques that allow adoption of off-the-shelf binary arithmetic circuits to perform multi-operand addition and multiplication of negabinary numbers. The multiple operands could be easily added with augmented binary adders connected in the form of a tree. The same hardware could be used to perform multiplication. But, from an LSI implementation viewpoint, the use of cellular array structures is explored and necessary challenges to design a combined binary/negabinary multiplier unit, are also outlined.

entry:
@InProceedings{Agrawal:1981:NAM,
  author =       "D. P. Agrawal and R. C. Joshi",
  title =        "Negabinary Addition and Multiplication Using Binary
                 Circuits",
  crossref =     "IEEE:1981:PSC",
  pages =        "270--273",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Agrawal_Joshi.pdf",
  abstract =     "This paper deals with design techniques that allow
                 adoption of off-the-shelf binary arithmetic circuits to
                 perform multi-operand addition and multiplication of
                 negabinary numbers. The multiple operands could be
                 easily added with augmented binary adders connected in
                 the form of a tree. The same hardware could be used to
                 perform multiplication. But, from an LSI implementation
                 viewpoint, the use of cellular array structures is
                 explored and necessary challenges to design a combined
                 binary/negabinary multiplier unit, are also outlined.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Andrews:1981:EFM
author: M. Andrews and D. Jaeger and S. F. McCormick and G. D. Taylor
title: Evaluation of Functions on Microcomputers: $ exp (x) $
journal: j-COMPUT-MATH-APPL
volume: 7
number: 6
pages: 503--508
year: 1981
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Thu Sep 15 18:40:45 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 18:40:45 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: M. Andrews and D. Jaeger and S. F. McCormick and G. D. Taylor
rawtitle: Evaluation of Functions on Microcomputers: $ \exp (x) $
entry:
@Article{Andrews:1981:EFM,
  author =       "M. Andrews and D. Jaeger and S. F. McCormick and G. D.
                 Taylor",
  title =        "Evaluation of Functions on Microcomputers: $ \exp (x)
                 $",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "7",
  number =       "6",
  pages =        "503--508",
  year =         "1981",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:40:45 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 =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}


bibtype: mastersthesis
filename: fparith.bib
label: Arnold:1981:PFP
author: Jeffrey M. Arnold
title: PSI, a floating point processor for the NU Computer
type: Thesis (B.S.)
school: Massachusetts Institute of Technology. Dept. of Electrical and Engineering and Computer Science
address: Cambridge, MA, USA
pages: 42
year: 1981
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 Stephen A. Ward.
acknowledgement: ack-nhfb
rawauthor: Jeffrey M. Arnold
rawnote: Supervised by Stephen A. Ward.
rawtitle: {PSI}, a floating point processor for the {NU} Computer
keywords:
Computer architecture.; Floating-point arithmetic.; Intel 8086 (Microprocessor); Microprocessors --- Design and construction.

entry:
@MastersThesis{Arnold:1981:PFP,
  author =       "Jeffrey M. Arnold",
  title =        "{PSI}, a floating point processor for the {NU}
                 Computer",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical and Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "42",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Stephen A. Ward.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Floating-point arithmetic.;
                 Intel 8086 (Microprocessor); Microprocessors --- Design
                 and construction.",
}


bibtype: inproceedings
filename: fparith.bib
label: Arora:1981:CSR
author: R. K. Arora and Saroj Kaushik
title: Conversion Scheme in Residue Code
crossref: IEEE:1981:PSC
pages: 152--156
year: 1981
bibdate: Thu Nov 15 11:37:51 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 11:37:51 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Arora_Kaushik.pdf
keywords: ARITH-5; residue number system
acknowledgement: ack-nhfb
rawauthor: R. K. Arora and Saroj Kaushik
rawtitle: Conversion Scheme in Residue Code
abstract:
In this paper, an implementation scheme involving decoders and residue adders has been suggested to convert input data in fixed radix representation to residue representation. A method dealing with the reverse process is also demonstrated. A comparison has been made with the methods known hitherto.

rawabstract:
In this paper, an implementation scheme involving decoders and residue adders has been suggested to convert input data in fixed radix representation to residue representation. A method dealing with the reverse process is also demonstrated. A comparison has been made with the methods known hitherto.

entry:
@InProceedings{Arora:1981:CSR,
  author =       "R. K. Arora and Saroj Kaushik",
  title =        "Conversion Scheme in Residue Code",
  crossref =     "IEEE:1981:PSC",
  pages =        "152--156",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Arora_Kaushik.pdf",
  abstract =     "In this paper, an implementation scheme involving
                 decoders and residue adders has been suggested to
                 convert input data in fixed radix representation to
                 residue representation. A method dealing with the
                 reverse process is also demonstrated. A comparison has
                 been made with the methods known hitherto.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; residue number system",
}


bibtype: inproceedings
filename: fparith.bib
label: Atkins:1981:FIS
author: D. E. Atkins and K. S. Trivedi
title: The Fifth IEEE Symposium on Computer Arithmetic: Foreword
crossref: IEEE:1981:PSC
pages: iv--iv
year: 1981
bibdate: Thu Nov 15 11:37:51 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 11:37:51 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Trivedi_Atkins.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: D. E. Atkins and K. S. Trivedi
rawtitle: The {Fifth IEEE Symposium on Computer Arithmetic}: Foreword
entry:
@InProceedings{Atkins:1981:FIS,
  author =       "D. E. Atkins and K. S. Trivedi",
  title =        "The {Fifth IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "IEEE:1981:PSC",
  pages =        "iv--iv",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Trivedi_Atkins.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Avizienis:1981:LCR
author: Algirdas Avizienis
title: Low-Cost Residue and Inverse Residue Error-Detecting Codes for Signed-Digit Arithmetic
crossref: IEEE:1981:PSC
pages: 165--168
year: 1981
bibdate: Thu Nov 15 11:37:51 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 11:37:51 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Avizienis.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Algirdas Avi{\v{z}}ienis
rawtitle: Low-Cost Residue and Inverse Residue Error-Detecting Codes for Signed-Digit Arithmetic
abstract:
Low-cost residue and inverse residue codes for error detection in signed-digit arithmetic are defined in this paper. Checking algorithms are presented for both digit-serial and parallel computation of the residues. Residue digit operations are defined for two-operand addition, multi-operand addition, multiplication, conversion, and reconversion algorithms. All algorithms employ the same Arithmetic Building Element ``ABE'' that has been previously developed for signed-digit arithmetic.

rawabstract:
Low-cost residue and inverse residue codes for error detection in signed-digit arithmetic are defined in this paper. Checking algorithms are presented for both digit-serial and parallel computation of the residues. Residue digit operations are defined for two-operand addition, multi-operand addition, multiplication, conversion, and reconversion algorithms. All algorithms employ the same Arithmetic Building Element ``ABE'' that has been previously developed for signed-digit arithmetic.

entry:
@InProceedings{Avizienis:1981:LCR,
  author =       "Algirdas Avi{\v{z}}ienis",
  title =        "Low-Cost Residue and Inverse Residue Error-Detecting
                 Codes for Signed-Digit Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "165--168",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Avizienis.pdf",
  abstract =     "Low-cost residue and inverse residue codes for error
                 detection in signed-digit arithmetic are defined in
                 this paper. Checking algorithms are presented for both
                 digit-serial and parallel computation of the residues.
                 Residue digit operations are defined for two-operand
                 addition, multi-operand addition, multiplication,
                 conversion, and reconversion algorithms. All algorithms
                 employ the same Arithmetic Building Element ``ABE''
                 that has been previously developed for signed-digit
                 arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Banerji:1981:HSD
author: Dilip K. Banerji and To-Yat Cheung and V. Ganesan
title: A High-Speed Division Method in Residue Arithmetic
crossref: IEEE:1981:PSC
pages: 158--164
year: 1981
bibdate: Wed Nov 14 17:53:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:53:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Banerji_Cheung_Ganesan.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Dilip K. Banerji and To-Yat Cheung and V. Ganesan
rawtitle: A High-Speed Division Method in Residue Arithmetic
abstract:
This paper is concerned with the operation of division in residue number systems. Residue codes are introduced and the basic residue arithmetic operations are defined. Previous results on residue division are outlined. A well-known integer division algorithm is used and adapted for residue division. A new method is proposed for choosing an approximate divisor, approximate dividends, and the partial quotients. The proposed method yields correct quotients faster than the existing methods and is general in its application i.e., it is not restricted by the choice of moduli as long as they are relatively prime.

rawabstract:
This paper is concerned with the operation of division in residue number systems. Residue codes are introduced and the basic residue arithmetic operations are defined. Previous results on residue division are outlined. A well-known integer division algorithm is used and adapted for residue division. A new method is proposed for choosing an approximate divisor, approximate dividends, and the partial quotients. The proposed method yields correct quotients faster than the existing methods and is general in its application i.e., it is not restricted by the choice of moduli as long as they are relatively prime.

entry:
@InProceedings{Banerji:1981:HSD,
  author =       "Dilip K. Banerji and To-Yat Cheung and V. Ganesan",
  title =        "A High-Speed Division Method in Residue Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "158--164",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Banerji_Cheung_Ganesan.pdf",
  abstract =     "This paper is concerned with the operation of division
                 in residue number systems. Residue codes are introduced
                 and the basic residue arithmetic operations are
                 defined. Previous results on residue division are
                 outlined. A well-known integer division algorithm is
                 used and adapted for residue division. A new method is
                 proposed for choosing an approximate divisor,
                 approximate dividends, and the partial quotients. The
                 proposed method yields correct quotients faster than
                 the existing methods and is general in its application
                 i.e., it is not restricted by the choice of moduli as
                 long as they are relatively prime.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Barlow:1981:DAA
author: Jesse Barlow
title: On the Distribution af Accumulated Roundoff Error in Floating Point Arithmetic
crossref: IEEE:1981:PSC
pages: 100--105
year: 1981
bibdate: Wed Nov 14 17:53:26 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:53:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Barlow.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Jesse Barlow
rawtitle: On the Distribution af Accumulated Roundoff Error in Floating Point Arithmetic
abstract:
This paper discusses longstanding problems in the probabilistic error analysis of numerical algorithms when they are performed in floating point arithmetic.par Local roundoff error in floating point addition is characterized and its mean and variance are approximated. We apply these results to finding distributions for the roundoff error accumulated in sums and long inner products.par We state theorems which resolve questions left open in Bustoz et al. [5] and Hamming [11]. These theorems are proven in [3].

rawabstract:
This paper discusses longstanding problems in the probabilistic error analysis of numerical algorithms when they are performed in floating point arithmetic.\par Local roundoff error in floating point addition is characterized and its mean and variance are approximated. We apply these results to finding distributions for the roundoff error accumulated in sums and long inner products.\par We state theorems which resolve questions left open in Bustoz et al. [5] and Hamming [11]. These theorems are proven in [3].

entry:
@InProceedings{Barlow:1981:DAA,
  author =       "Jesse Barlow",
  title =        "On the Distribution af Accumulated Roundoff Error in
                 Floating Point Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "100--105",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Barlow.pdf",
  abstract =     "This paper discusses longstanding problems in the
                 probabilistic error analysis of numerical algorithms
                 when they are performed in floating point
                 arithmetic.\par

                 Local roundoff error in floating point addition is
                 characterized and its mean and variance are
                 approximated. We apply these results to finding
                 distributions for the roundoff error accumulated in
                 sums and long inner products.\par

                 We state theorems which resolve questions left open in
                 Bustoz et al. [5] and Hamming [11]. These theorems are
                 proven in [3].",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: phdthesis
filename: fparith.bib
label: Barlow:1981:PEA
author: Jesse Louis Barlow
title: Probabilistic error analysis of floating point and CRD arithmetics
type: Ph.D. (Electrical Engineering and Computer Science)
school: Northwestern University
address: Evanston, IL, USA
year: 1981
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: Jesse Louis Barlow
rawtitle: Probabilistic error analysis of floating point and {CRD} arithmetics
entry:
@PhdThesis{Barlow:1981:PEA,
  author =       "Jesse Louis Barlow",
  title =        "Probabilistic error analysis of floating point and
                 {CRD} arithmetics",
  type =         "{Ph.D.} (Electrical Engineering and Computer
                 Science)",
  school =       "Northwestern University",
  address =      "Evanston, IL, USA",
  pages =        "????",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Bashe:1981:AIE
author: C. J. Bashe and W. Buchholz and G. V. Hawkins and J. J. Ingram and N. Rochester
title: The Architecture of IBM's Early Computers
journal: j-IBM-JRD
volume: 25
number: 5
pages: 363--375
month: sep
monthnumber: 9
year: 1981
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Mon Jan 24 21:36:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.01.24 21:36:17 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: C. J. Bashe and W. Buchholz and G. V. Hawkins and J. J. Ingram and N. Rochester
rawtitle: The Architecture of {IBM}'s Early Computers
entry:
@Article{Bashe:1981:AIE,
  author =       "C. J. Bashe and W. Buchholz and G. V. Hawkins and J.
                 J. Ingram and N. Rochester",
  title =        "The Architecture of {IBM}'s Early Computers",
  journal =      j-IBM-JRD,
  volume =       "25",
  number =       "5",
  pages =        "363--375",
  month =        sep,
  year =         "1981",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Jan 24 21:36:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: mastersthesis
filename: fparith.bib
label: Benjamin:1981:FPF
author: Bruce P. Benjamin
title: Fixed point to floating point converter
type: Master of Science, Plan II
school: University of California, Berkeley. Dept. of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: 60
year: 1981
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: Bruce P. Benjamin
rawtitle: Fixed point to floating point converter
entry:
@MastersThesis{Benjamin:1981:FPF,
  author =       "Bruce P. Benjamin",
  title =        "Fixed point to floating point converter",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "60",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bhuyan:1981:MAP
author: L. Bhuyan and D. P. Agrawal
title: Multiple Addition and Parallel Counter in Generalized Binary and Negabinary Systems
crossref: IEEE:1981:PSC
pages: 264--269
year: 1981
bibdate: Thu Nov 15 11:37:51 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 11:37:51 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Bhuyan_Agrawal.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: L. Bhuyan and D. P. Agrawal
rawtitle: Multiple Addition and Parallel Counter in Generalized Binary and Negabinary Systems
abstract:
This paper explores the possibility of utilizing counters for reducing the partial products generated from multiplication of two numbers represented in a generalized binary system. Algorithm for multi operand addition of Koren's generalized number system are worked out. A carry look-ahead adder is developed and hardware aspects of possible counters for this class of binary number system are discussed. Negabinary counters are also introduced in line with those proposed for binary multiplication by Stenzel et al.

rawabstract:
This paper explores the possibility of utilizing counters for reducing the partial products generated from multiplication of two numbers represented in a generalized binary system. Algorithm for multi operand addition of Koren's generalized number system are worked out. A carry look-ahead adder is developed and hardware aspects of possible counters for this class of binary number system are discussed. Negabinary counters are also introduced in line with those proposed for binary multiplication by Stenzel et al.

entry:
@InProceedings{Bhuyan:1981:MAP,
  author =       "L. Bhuyan and D. P. Agrawal",
  title =        "Multiple Addition and Parallel Counter in Generalized
                 Binary and Negabinary Systems",
  crossref =     "IEEE:1981:PSC",
  pages =        "264--269",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Bhuyan_Agrawal.pdf",
  abstract =     "This paper explores the possibility of utilizing
                 counters for reducing the partial products generated
                 from multiplication of two numbers represented in a
                 generalized binary system. Algorithm for multi operand
                 addition of Koren's generalized number system are
                 worked out. A carry look-ahead adder is developed and
                 hardware aspects of possible counters for this class of
                 binary number system are discussed. Negabinary counters
                 are also introduced in line with those proposed for
                 binary multiplication by Stenzel et al.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Bice:1981:AAS
author: P. K. Bice
title: Algorithm adds square root to micro's arithmetic capability
journal: j-ELECTRONIC-DESIGN
volume: 29
number: 11
pages: 146
month: may
monthnumber: 5
year: 1981
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:15:42 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 10:15:42 ???
fjournal: Electronic Design
acknowledgement: ack-nj
rawauthor: P. K. Bice
rawtitle: Algorithm adds square root to micro's arithmetic capability
entry:
@Article{Bice:1981:AAS,
  author =       "P. K. Bice",
  title =        "Algorithm adds square root to micro's arithmetic
                 capability",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "29",
  number =       "11",
  pages =        "146",
  month =        may,
  year =         "1981",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:15:42 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 =     "Electronic Design",
}


bibtype: article
filename: fparith.bib
label: Blikle:1981:CTI
author: Andrzej Blikle
title: The Clean Termination of Iterative Programs
journal: j-ACTA-INFO
volume: 16
number: 2
pages: 199--217
month: oct
monthnumber: 10
year: 1981
CODEN: AINFA2
ISSN: 0001-5903 (print), 1432-0525 (electronic) OR 00015903 (print), 14320525 (electronic)
ISSNL: 0001-5903 OR 00015903
MRclass: 68B10
MRnumber: 83c:68015
bibdate: Sat Nov 9 08:26:18 MST 2002
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Acta Informatica
acknowledgement: ack-nhfb
journalURL: http://www.springerlink.com/content/0001-5903
reviewer: M. F. Aribaud
rawauthor: Andrzej Blikle
rawtitle: The Clean Termination of Iterative Programs
bibsource:
ACM Computing Archive CD-ROM database (1991); ftp://ftp.ira.uka.de/pub/bibliography/Misc/HBP/ACTAI.bib; ftp://ftp.ira.uka.de/pub/bibliography/Misc/leavens.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database

subject:
D. Software; D.2 SOFTWARE ENGINEERING; D. Software; D.2 SOFTWARE ENGINEERING; F. Theory of Computation; F.3 LOGICS AND MEANINGS OF PROGRAMS

entry:
@Article{Blikle:1981:CTI,
  author =       "Andrzej Blikle",
  title =        "The Clean Termination of Iterative Programs",
  journal =      j-ACTA-INFO,
  volume =       "16",
  number =       "2",
  pages =        "199--217",
  month =        oct,
  year =         "1981",
  CODEN =        "AINFA2",
  ISSN =         "0001-5903 (print), 1432-0525 (electronic)",
  ISSN-L =       "0001-5903",
  MRclass =      "68B10",
  MRnumber =     "83c:68015",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 ftp://ftp.ira.uka.de/pub/bibliography/Misc/HBP/ACTAI.bib;
                 ftp://ftp.ira.uka.de/pub/bibliography/Misc/leavens.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  catcode =      "D.2; D.2.4; F.3",
  content =      "Most correctness proofs assume that elementary
                 instructions represent total functions. In fact this is
                 not always the case: for instance, in dealing with real
                 numbers, Brown's model of floating point computation
                 [1], a model which has been accepted by the designers
                 of ADA, uses interval analysis. If the interval of x
                 overlaps the interval of y, the Boolean value of x r y
                 is not well defined.\par

                 In this paper the author studies the clean termination
                 (i.e., without abortion) of iterative programs, not
                 supposing that the test functions are total. The
                 relational approach to computing, which the author has
                 largely worked out (cf. Sanderson [2] for an account
                 from the starting point) is very well suited for that
                 design. A general theorem links the ``global
                 correctness'' of a program with a ``well-founded''
                 breakdown of the program relation. Next the author
                 gives new validation rules, in which a Z b depart from
                 the usual meaning. Last (but not least) one finds an
                 exhaustive study of the integer square root in a
                 realistic arithmetic.\par

                 Due to the great significance of the matter, we must
                 call attention to this paper. \par

                 M. F. Aribaud, Paris, France \par

                 REFERENCES \par

                 [1] BROWN, W. S. A simple but realistic model of
                 floating-point computation, ACM Trans. Math. Softw. 7
                 (1981), 445 480. \par

                 [2] SANDERSON, J. G. A relational theory of computing,
                 Lecture Notes in Computer \ldots{}",
  CRclass =      "D.2.4 Program Verification; D.2.4 Program
                 Verification; D.2.4 Correctness proofs; F.3.1
                 Specifying and Verifying and Reasoning about Programs",
  CRnumber =     "39409",
  descriptor =   "Software, SOFTWARE ENGINEERING, Program Verification;
                 Software, SOFTWARE ENGINEERING, Program Verification,
                 Correctness proofs; Theory of Computation, LOGICS AND
                 MEANINGS OF PROGRAMS, Specifying and Verifying and
                 Reasoning about Programs",
  fjournal =     "Acta Informatica",
  genterm =      "LANGUAGES; RELIABILITY; THEORY; VERIFICATION",
  journal-URL =  "http://www.springerlink.com/content/0001-5903",
  reviewer =     "M. F. Aribaud",
  subject =      "D. Software; D.2 SOFTWARE ENGINEERING; D. Software;
                 D.2 SOFTWARE ENGINEERING; F. Theory of Computation; F.3
                 LOGICS AND MEANINGS OF PROGRAMS",
}


bibtype: techreport
filename: fparith.bib
label: Brent:1981:MUG
author: Richard P. Brent
title: MP User's Guide
number: TR-CS-81-08
institution: Department of Computer Science, Australian National University
address: Canberra, ACT, Australia
edition: Fourth
pages: 73
month: jun
monthnumber: 6
year: 1981
bibdate: Fri Nov 28 15:59:05 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 15:59:05 ???
acknowledgement: ack-mfc
rawauthor: Richard P. Brent
rawtitle: {MP} User's Guide
abstract:
MP is a multiple-precision floating-point arithmetic package. It is almost completely machine-independent, and should run on any machine with an ANSI Standard Fortran (ANS X3.9-1966) compiler, sufficient memory, and a wordlength (for integer arithmetic) of at least 16 bits. A precompiler (Augment) which facilitates the use of the MP package is available.

rawabstract:
MP is a multiple-precision floating-point arithmetic package. It is almost completely machine-independent, and should run on any machine with an ANSI Standard Fortran (ANS X3.9-1966) compiler, sufficient memory, and a wordlength (for integer arithmetic) of at least 16 bits. A precompiler (Augment) which facilitates the use of the MP package is available.

entry:
@TechReport{Brent:1981:MUG,
  author =       "Richard P. Brent",
  title =        "{MP} User's Guide",
  number =       "TR-CS-81-08",
  institution =  "Department of Computer Science, Australian National
                 University",
  address =      "Canberra, ACT, Australia",
  edition =      "Fourth",
  pages =        "73",
  month =        jun,
  year =         "1981",
  bibdate =      "Fri Nov 28 15:59:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "MP is a multiple-precision floating-point arithmetic
                 package. It is almost completely machine-independent,
                 and should run on any machine with an ANSI Standard
                 Fortran (ANS X3.9-1966) compiler, sufficient memory,
                 and a wordlength (for integer arithmetic) of at least
                 16 bits. A precompiler (Augment) which facilitates the
                 use of the MP package is available.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


