# bibtab

bibtype: article
filename: fparith.bib
label: Brown:1981:SRM
author: W. S. Brown
title: A Simple but Realistic Model of Floating-Point Computation
journal: j-TOMS
volume: 7
number: 4
pages: 445--480
month: dec
monthnumber: 12
year: 1981
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355972.355975
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Aug 29 23:03:20 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.29 23:03:20 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. S. Brown
rawtitle: A Simple but Realistic Model of Floating-Point Computation
keywords:
computer arithmetic, environment parameters, error analysis, Euclidean norm, floating-point arithmetic, software portability

entry:
@Article{Brown:1981:SRM,
  author =       "W. S. Brown",
  title =        "A Simple but Realistic Model of Floating-Point
                 Computation",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "445--480",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355975",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computer arithmetic, environment parameters, error
                 analysis, Euclidean norm, floating-point arithmetic,
                 software portability",
}


bibtype: mastersthesis
filename: fparith.bib
label: Cariker:1981:RFM
author: Earnest Allan Cariker
title: A rapid-approximation floating-point mathematics package for the INTEL 8080 microprocessor
type: Computing Science Thesis (M.S.)
school: Texas A&M University
address: College Station, TX, USA
pages: viii + 152
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: Earnest Allan Cariker
rawtitle: A rapid-approximation floating-point mathematics package for the {INTEL} 8080 microprocessor
keywords:
Mathematical analysis.; Microprocessors.; Programming (Electronic computers); Programming languages (Electronic computers)

entry:
@MastersThesis{Cariker:1981:RFM,
  author =       "Earnest Allan Cariker",
  title =        "A rapid-approximation floating-point mathematics
                 package for the {INTEL} 8080 microprocessor",
  type =         "Computing Science Thesis ({M.S.})",
  school =       "Texas A\&M University",
  address =      "College Station, TX, USA",
  pages =        "viii + 152",
  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,
  keywords =     "Mathematical analysis.; Microprocessors.; Programming
                 (Electronic computers); Programming languages
                 (Electronic computers)",
}


bibtype: mastersthesis
filename: fparith.bib
label: Cary:1981:BFP
author: David A. Cary
title: The Berkeley floating point project
type: Master of Science, Plan II
school: University of California, Berkeley. Dept. of Electrical and Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: 107
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
remark: Noted as posthumous in cite Aspinwall:1985:RVM.
acknowledgement: ack-nhfb
rawauthor: David A. Cary
rawtitle: The {Berkeley} floating point project
entry:
@MastersThesis{Cary:1981:BFP,
  author =       "David A. Cary",
  title =        "The {Berkeley} floating point project",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical and Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "107",
  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,
  remark =       "Noted as posthumous in \cite{Aspinwall:1985:RVM}.",
}


bibtype: article
filename: fparith.bib
label: Ceruzzi:1981:ECK
author: Paul E. Ceruzzi
title: The Early Computers of Konrad Zuse, 1935 to 1945
journal: j-ANN-HIST-COMPUT
volume: 3
number: 3
pages: 241--262
month: jul
monthnumber: 7
year: 1981
CODEN: AHCOE5
ISSN: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:18 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.01 15:29:18 MST
fjournal: Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
rawauthor: Paul E. Ceruzzi
rawtitle: The Early Computers of {Konrad Zuse}, 1935 to 1945
URL:
http://dlib.computer.org/an/books/an1981/pdf/a3241.pdf; http://www.computer.org/annals/an1981/a3241abs.htm

entry:
@Article{Ceruzzi:1981:ECK,
  author =       "Paul E. Ceruzzi",
  title =        "The Early Computers of {Konrad Zuse}, 1935 to 1945",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "3",
  number =       "3",
  pages =        "241--262",
  month =        jul # "\slash " # sep,
  year =         "1981",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  bibdate =      "Fri Nov 1 15:29:18 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1981/pdf/a3241.pdf;
                 http://www.computer.org/annals/an1981/a3241abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}


bibtype: manual
filename: fparith.bib
label: Cheng:1981:AAF
author: Steven Cheng
title: Am9511A / Am9512 floating point processor manual
organization: Advanced Micro Devices
address: Sunnyvale, CA, USA
pages: 55
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
keywords: Computer arithmetic and logic units.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Steven Cheng
rawtitle: {Am9511A\slash Am9512} floating point processor manual
entry:
@Manual{Cheng:1981:AAF,
  author =       "Steven Cheng",
  title =        "{Am9511A\slash Am9512} floating point processor
                 manual",
  organization = "Advanced Micro Devices",
  address =      "Sunnyvale, CA, USA",
  pages =        "55",
  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,
  keywords =     "Computer arithmetic and logic units.; Floating-point
                 arithmetic.",
}


bibtype: inproceedings
filename: fparith.bib
label: Chow:1981:PDA
author: P. Chow and Z. G. Vranesic and J. L. Yen
title: A Pipelined Distributed Arithmetic PFFT Processor
crossref: IEEE:1981:PSC
pages: 198--206
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_Chow_Vranesic_Yen.pdf
keywords: ARITH-5; Prime Factor Fourier Transform (PFFT)
acknowledgement: ack-nhfb
rawauthor: P. Chow and Z. G. Vranesic and J. L. Yen
rawtitle: A Pipelined Distributed Arithmetic {PFFT} Processor
abstract:
Previous experience i,n implementing the Prime Factor Fourier Transform showed that it was much more difficult to do than the FFT because of its complicated structure. In most FFT implementations the ``butterfly'' structure is the basic arithmetic unit implemented. It is much simpler than the equivalent PFFT unit.par This paper describes a different architecture for implementing PFFT machines using distributed arithmetic and ROM's to perform the computations. It is found to be much simpler and more modular than a design which uses multipliers and adders. The implementation of a PFFT processor with a throughput of 104 kHz for complex data points is described.

rawabstract:
Previous experience i,n implementing the Prime Factor Fourier Transform showed that it was much more difficult to do than the FFT because of its complicated structure. In most FFT implementations the ``butterfly'' structure is the basic arithmetic unit implemented. It is much simpler than the equivalent PFFT unit.\par This paper describes a different architecture for implementing PFFT machines using distributed arithmetic and ROM's to perform the computations. It is found to be much simpler and more modular than a design which uses multipliers and adders. The implementation of a PFFT processor with a throughput of 104 kHz for complex data points is described.

entry:
@InProceedings{Chow:1981:PDA,
  author =       "P. Chow and Z. G. Vranesic and J. L. Yen",
  title =        "A Pipelined Distributed Arithmetic {PFFT} Processor",
  crossref =     "IEEE:1981:PSC",
  pages =        "198--206",
  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_Chow_Vranesic_Yen.pdf",
  abstract =     "Previous experience i,n implementing the Prime Factor
                 Fourier Transform showed that it was much more
                 difficult to do than the FFT because of its complicated
                 structure. In most FFT implementations the
                 ``butterfly'' structure is the basic arithmetic unit
                 implemented. It is much simpler than the equivalent
                 PFFT unit.\par

                 This paper describes a different architecture for
                 implementing PFFT machines using distributed arithmetic
                 and ROM's to perform the computations. It is found to
                 be much simpler and more modular than a design which
                 uses multipliers and adders. The implementation of a
                 PFFT processor with a throughput of 104 kHz for complex
                 data points is described.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; Prime Factor Fourier Transform (PFFT)",
}


bibtype: article
filename: fparith.bib
label: Chroust:1981:MAD
author: G. Chroust
title: Method of Adding Decimal Numbers by Means of Binary Arithmetic
journal: j-IBM-TDB
volume: 23
number: 10
pages: 4525--4526
month: mar
monthnumber: 3
year: 1981
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:16:11 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 10:16:11 ???
fjournal: IBM Technical Disclosure Bulletin
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: G. Chroust
rawtitle: Method of Adding Decimal Numbers by Means of Binary Arithmetic
entry:
@Article{Chroust:1981:MAD,
  author =       "G. Chroust",
  title =        "Method of Adding Decimal Numbers by Means of Binary
                 Arithmetic",
  journal =      j-IBM-TDB,
  volume =       "23",
  number =       "10",
  pages =        "4525--4526",
  month =        mar,
  year =         "1981",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:11 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: inproceedings
filename: fparith.bib
label: Ciminiera:1981:AAF
author: L. Ciminiera and A. Serra
title: Arithmetic Array for Fast Inner Product Evaluation
crossref: IEEE:1981:PSC
pages: 207--214
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_Ciminiera_Serra.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: L. Ciminiera and A. Serra
rawtitle: Arithmetic Array for Fast Inner Product Evaluation
abstract:
The paper presents a new fast arithmetic array, suitable for VLSI implementation, which computes the inner product of two vectors. The operands and the result are expressed using the 2's complement notation, which is the most general and flexible one. Cells performing the $ 2 times 2 $ bit full multiplication are used for obtaining a reduction of the operation time.par A particular pipelining scheme, with different degrees of latching, is used in order to implement parallel computations with a moderate cost increase. Graphs showing the characteristics and the advantage domain of the proposed array are presented. An IC implementation of the proposed array could have a speed from 5 to 10 times greater than the multiplier-accumulator circuits currently available.

rawabstract:
The paper presents a new fast arithmetic array, suitable for VLSI implementation, which computes the inner product of two vectors. The operands and the result are expressed using the 2's complement notation, which is the most general and flexible one. Cells performing the $ 2 \times 2 $ bit full multiplication are used for obtaining a reduction of the operation time.\par A particular pipelining scheme, with different degrees of latching, is used in order to implement parallel computations with a moderate cost increase. Graphs showing the characteristics and the advantage domain of the proposed array are presented. An IC implementation of the proposed array could have a speed from 5 to 10 times greater than the multiplier-accumulator circuits currently available.

entry:
@InProceedings{Ciminiera:1981:AAF,
  author =       "L. Ciminiera and A. Serra",
  title =        "Arithmetic Array for Fast Inner Product Evaluation",
  crossref =     "IEEE:1981:PSC",
  pages =        "207--214",
  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_Ciminiera_Serra.pdf",
  abstract =     "The paper presents a new fast arithmetic array,
                 suitable for VLSI implementation, which computes the
                 inner product of two vectors. The operands and the
                 result are expressed using the 2's complement notation,
                 which is the most general and flexible one. Cells
                 performing the $ 2 \times 2 $ bit full multiplication
                 are used for obtaining a reduction of the operation
                 time.\par

                 A particular pipelining scheme, with different degrees
                 of latching, is used in order to implement parallel
                 computations with a moderate cost increase. Graphs
                 showing the characteristics and the advantage domain of
                 the proposed array are presented. An IC implementation
                 of the proposed array could have a speed from 5 to 10
                 times greater than the multiplier-accumulator circuits
                 currently available.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Ciminiera:1981:FAM
author: L. Ciminiera and A. Serra and A. Valenzano
title: Fast and Accurate Matrix Triangularization Using an Iterative Structure
crossref: IEEE:1981:PSC
pages: 215--221
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_Ciminiera_Serra_Valenzano.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: L. Ciminiera and A. Serra and A. Valenzano
rawtitle: {Fast and Accurate Matrix Triangularization Using an Iterative Structure}
abstract:
The paper presents a new iterative array, which performs the triangularization of a dense matrix, using the Givens rotation algorithm. Two slightly different arrays are presented: the first one performs the factorization of a single matrix; the second one performs the recursive triangularization. The implementation of the cell in the array is based on the on-line arithmetic, which allows us to obtain high performances. Furthermore, the cell implementation requires only three types of arithmetic units (multiplication / addition, square root, division) and shift registers for data buffering and for generating the timing signals.

rawabstract:
The paper presents a new iterative array, which performs the triangularization of a dense matrix, using the Givens rotation algorithm. Two slightly different arrays are presented: the first one performs the factorization of a single matrix; the second one performs the recursive triangularization. The implementation of the cell in the array is based on the on-line arithmetic, which allows us to obtain high performances. Furthermore, the cell implementation requires only three types of arithmetic units (multiplication\slash addition, square root, division) and shift registers for data buffering and for generating the timing signals.

entry:
@InProceedings{Ciminiera:1981:FAM,
  author =       "L. Ciminiera and A. Serra and A. Valenzano",
  title =        "{Fast and Accurate Matrix Triangularization Using an
                 Iterative Structure}",
  crossref =     "IEEE:1981:PSC",
  pages =        "215--221",
  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_Ciminiera_Serra_Valenzano.pdf",
  abstract =     "The paper presents a new iterative array, which
                 performs the triangularization of a dense matrix, using
                 the Givens rotation algorithm. Two slightly different
                 arrays are presented: the first one performs the
                 factorization of a single matrix; the second one
                 performs the recursive triangularization. The
                 implementation of the cell in the array is based on the
                 on-line arithmetic, which allows us to obtain high
                 performances. Furthermore, the cell implementation
                 requires only three types of arithmetic units
                 (multiplication\slash addition, square root, division)
                 and shift registers for data buffering and for
                 generating the timing signals.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Cody:1981:APF
author: William J. Cody, Jr.
title: Analysis of Proposals for the Floating-Point Standard
journal: j-COMPUTER
volume: 14
number: 3
pages: 63--68
month: mar
monthnumber: 3
year: 1981
CODEN: CPTRB4
DOI: https://doi.org/10.1109/C-M.1981.220379
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Sat Sep 24 09:21:33 1994
bibtimestamp: 1994.09.24 09:21:33 ???
note: See cite IEEE:1985:AIS,IEEE:1985:ASI.
fjournal: Computer
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: William J. {Cody, Jr.}
rawnote: See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.
rawtitle: Analysis of Proposals for the Floating-Point Standard
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/computer1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

entry:
@Article{Cody:1981:APF,
  author =       "William J. {Cody, Jr.}",
  title =        "Analysis of Proposals for the Floating-Point
                 Standard",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "63--68",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220379",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sat Sep 24 09:21:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: inproceedings
filename: fparith.bib
label: Cohen:1981:CAU
author: M. Cohen and V. C. Hamacher and T. E. Hull
title: CADAC: An Arithmetic Unit for Clean Decimal Arithmetic and Controlled Precision
crossref: IEEE:1981:PSC
pages: 106--112
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_Cohen_Hamacher_Bull.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: M. Cohen and V. C. Hamacher and T. E. Hull
rawtitle: {CADAC}: An Arithmetic Unit for Clean Decimal Arithmetic and Controlled Precision
abstract:
This paper describes the design of an arithmetic unit called CADAC (Clean Arithmetic with Decimal base And Controlled Precision). A brief indication of programming language specifications for carrying out ``ideal'' floating-point arithmetic is given. These specifications include detailed requirements for precision control and exception handling at the level of a programming language such as Fortran. CADAC is an arithmetic unit which performs the four floating-point operations add / subtract / multiply / divide on decimal base numbers in accordance with the language requirements. A three-level pipeline is used to overlap 2-digit-at-a-time (``double digit'') serial processing of the partial products / remainders. Although the logic design is relatively complex, the performance is efficient and the advantages gained by implementing programmer-controlled precision directly in the hardware are significant.

rawabstract:
This paper describes the design of an arithmetic unit called CADAC (Clean Arithmetic with Decimal base And Controlled Precision). A brief indication of programming language specifications for carrying out ``ideal'' floating-point arithmetic is given. These specifications include detailed requirements for precision control and exception handling at the level of a programming language such as Fortran. CADAC is an arithmetic unit which performs the four floating-point operations add\slash subtract \slash multiply\slash divide on decimal base numbers in accordance with the language requirements. A three-level pipeline is used to overlap 2-digit-at-a-time (``double digit'') serial processing of the partial products\slash remainders. Although the logic design is relatively complex, the performance is efficient and the advantages gained by implementing programmer-controlled precision directly in the hardware are significant.

entry:
@InProceedings{Cohen:1981:CAU,
  author =       "M. Cohen and V. C. Hamacher and T. E. Hull",
  title =        "{CADAC}: An Arithmetic Unit for Clean Decimal
                 Arithmetic and Controlled Precision",
  crossref =     "IEEE:1981:PSC",
  pages =        "106--112",
  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_Cohen_Hamacher_Bull.pdf",
  abstract =     "This paper describes the design of an arithmetic unit
                 called CADAC (Clean Arithmetic with Decimal base And
                 Controlled Precision). A brief indication of
                 programming language specifications for carrying out
                 ``ideal'' floating-point arithmetic is given. These
                 specifications include detailed requirements for
                 precision control and exception handling at the level
                 of a programming language such as Fortran. CADAC is an
                 arithmetic unit which performs the four floating-point
                 operations add\slash subtract \slash multiply\slash
                 divide on decimal base numbers in accordance with the
                 language requirements. A three-level pipeline is used
                 to overlap 2-digit-at-a-time (``double digit'') serial
                 processing of the partial products\slash remainders.
                 Although the logic design is relatively complex, the
                 performance is efficient and the advantages gained by
                 implementing programmer-controlled precision directly
                 in the hardware are significant.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Coonen:1981:EIG
author: Jerome T. Coonen
title: Errata: An Implementation Guide to a Proposed Standard for Floating Point Arithmetic
journal: j-COMPUTER
volume: 14
number: 3
pages: 62--62
month: mar
monthnumber: 3
year: 1981
CODEN: CPTRB4
DOI: https://doi.org/10.1109/C-M.1981.220378
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Wed Sep 14 21:15:55 1994
bibtimestamp: 1994.09.14 21:15:55 ???
note: See cite Coonen:1980:IGP,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 \cite{Coonen:1980:IGP,IEEE:1985:AIS,IEEE:1985:ASI}.
rawtitle: Errata: {An Implementation Guide to a Proposed Standard for Floating Point Arithmetic}
bibsource:
https://www.math.utah.edu/pub/tex/bib/computer1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Coonen:1981:EIG,
  author =       "Jerome T. Coonen",
  title =        "Errata: {An Implementation Guide to a Proposed
                 Standard for Floating Point Arithmetic}",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "62--62",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220378",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed Sep 14 21:15:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Coonen:1980:IGP,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: Coonen:1981:UDN
author: Jerome T. Coonen
title: Underflow and the Denormalized Numbers
journal: j-COMPUTER
volume: 14
number: 3
pages: 75--87
month: mar
monthnumber: 3
year: 1981
CODEN: CPTRB4
DOI: https://doi.org/10.1109/C-M.1981.220382
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Fri Sep 2 23:38:17 1994
bibtimestamp: 1994.09.02 23:38:17 ???
note: 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 \cite{IEEE:1985:AIS,IEEE:1985:ASI}.
rawtitle: Underflow and the Denormalized Numbers
bibsource:
https://www.math.utah.edu/pub/tex/bib/computer1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Coonen:1981:UDN,
  author =       "Jerome T. Coonen",
  title =        "Underflow and the Denormalized Numbers",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "75--87",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220382",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Sep 2 23:38:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "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: mastersthesis
filename: fparith.bib
label: Curley:1981:PPN
author: A. Curley
title: PNCL: a Prototype Numerical Computation Language
type: M.Sc. thesis
school: Department of Computer Science, University of Toronto
address: Toronto, ON, Canada
pages: 75--87
year: 1981
bibdate: Sun Dec 30 15:41:22 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.30 15:41:22 ???
acknowledgement: ack-nhfb
rawauthor: A. Curley
rawtitle: {PNCL}: a Prototype Numerical Computation Language
entry:
@MastersThesis{Curley:1981:PPN,
  author =       "A. Curley",
  title =        "{PNCL}: a Prototype Numerical Computation Language",
  type =         "{M.Sc.} thesis",
  school =       "Department of Computer Science, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  year =         "1981",
  bibdate =      "Sun Dec 30 15:41:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Davis:1981:EFA
author: Diane F. Davis
title: Elementary Functions on an Array Processor
crossref: IEEE:1981:PSC
pages: 170--178
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_Davis.pdf
keywords: ARITH-5; Floating-Point Systems FPS-164
acknowledgement: ack-nhfb
rawauthor: Diane F. Davis
rawtitle: Elementary Functions on an Array Processor
abstract:
The algorithms used for elementary functions on the FPS-164 array processor are described. In each case, the choice of the algorithm depends on the parallel hardware, the capability of the instruction word, and the precision desired. For some, the choice depends on the version, either scalar or vector. Algorithms for the divide, square root, cosine / sine, exponential, and logarithm are discussed. Those for arctangent, tangent, arc-cosine / sine, cosh, sinh, and tanh are summarized.

rawabstract:
The algorithms used for elementary functions on the FPS-164 array processor are described. In each case, the choice of the algorithm depends on the parallel hardware, the capability of the instruction word, and the precision desired. For some, the choice depends on the version, either scalar or vector. Algorithms for the divide, square root, cosine\slash sine, exponential, and logarithm are discussed. Those for arctangent, tangent, arc-cosine\slash sine, cosh, sinh, and tanh are summarized.

entry:
@InProceedings{Davis:1981:EFA,
  author =       "Diane F. Davis",
  title =        "Elementary Functions on an Array Processor",
  crossref =     "IEEE:1981:PSC",
  pages =        "170--178",
  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_Davis.pdf",
  abstract =     "The algorithms used for elementary functions on the
                 FPS-164 array processor are described. In each case,
                 the choice of the algorithm depends on the parallel
                 hardware, the capability of the instruction word, and
                 the precision desired. For some, the choice depends on
                 the version, either scalar or vector. Algorithms for
                 the divide, square root, cosine\slash sine,
                 exponential, and logarithm are discussed. Those for
                 arctangent, tangent, arc-cosine\slash sine, cosh, sinh,
                 and tanh are summarized.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; Floating-Point Systems FPS-164",
}


bibtype: manual
filename: fparith.bib
label: DECESD:1981:VIS
author: Digital Equipment Corporation.Educational Services Dept
title: VAX-11 instruction set
organization: Digital Equipment Corporation
address: Maynard, MA, USA
edition: Revised
pages: various
year: 1981
bibdate: Sun May 02 09:19:03 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.05.02 09:19:03 ???
keywords: VAX-11 (Computer) --- Programming.
acknowledgement: ack-nhfb
rawauthor: {Digital Equipment Corporation.Educational Services Dept}
rawtitle: {VAX-11} instruction set
remark:
In container. Student guide --- Programming examples --- Character string instructions --- Instruction formats and addressing modes --- Variable bit field instructions --- Stack and address instructions --- Integer, logical and branch instructions --- Floating point instructions --- Decimal string instructions --Procedure and subroutine instructions --- Special instructions --- Module tests --- Evaluation sheets --- Selected tables.

entry:
@Manual{DECESD:1981:VIS,
  author =       "{Digital Equipment Corporation.Educational Services
                 Dept}",
  title =        "{VAX-11} instruction set",
  organization = "Digital Equipment Corporation",
  address =      "Maynard, MA, USA",
  edition =      "Revised",
  pages =        "various",
  year =         "1981",
  bibdate =      "Sun May 02 09:19:03 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "VAX-11 (Computer) --- Programming.",
  remark =       "In container. Student guide --- Programming examples
                 --- Character string instructions --- Instruction
                 formats and addressing modes --- Variable bit field
                 instructions --- Stack and address instructions ---
                 Integer, logical and branch instructions --- Floating
                 point instructions --- Decimal string instructions
                 --Procedure and subroutine instructions --- Special
                 instructions --- Module tests --- Evaluation sheets ---
                 Selected tables.",
}


bibtype: inproceedings
filename: fparith.bib
label: Demmel:1981:EUS
author: James Demmel
title: Effects of Underflow on Solving Linear Systems
crossref: IEEE:1981:PSC
pages: 113--119
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_Demmel.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: James Demmel
rawtitle: Effects of Underflow on Solving Linear Systems
abstract:
Software to solve systems of linear equations by Gaussian elimination has in the past ignored the effects of underflow. But when underflows are replaced by zeroes, this software can give spurious though plausible results much worse than would be blamed on roundoff. When underflow is gradual, as in the proposed IEEE standard for floating point arithmetic, the same software gives provably more reliable results. To achieve the same reliability without gradual underflow, but with underflows set to zero, complicated tests must be inserted into the software.

rawabstract:
Software to solve systems of linear equations by Gaussian elimination has in the past ignored the effects of underflow. But when underflows are replaced by zeroes, this software can give spurious though plausible results much worse than would be blamed on roundoff. When underflow is gradual, as in the proposed IEEE standard for floating point arithmetic, the same software gives provably more reliable results. To achieve the same reliability without gradual underflow, but with underflows set to zero, complicated tests must be inserted into the software.

entry:
@InProceedings{Demmel:1981:EUS,
  author =       "James Demmel",
  title =        "Effects of Underflow on Solving Linear Systems",
  crossref =     "IEEE:1981:PSC",
  pages =        "113--119",
  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_Demmel.pdf",
  abstract =     "Software to solve systems of linear equations by
                 Gaussian elimination has in the past ignored the
                 effects of underflow. But when underflows are replaced
                 by zeroes, this software can give spurious though
                 plausible results much worse than would be blamed on
                 roundoff. When underflow is gradual, as in the proposed
                 IEEE standard for floating point arithmetic, the same
                 software gives provably more reliable results. To
                 achieve the same reliability without gradual underflow,
                 but with underflows set to zero, complicated tests must
                 be inserted into the software.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Efe:1981:MOA
author: Kemal Efe
title: Multi-Operand Addition with Conditional Sum Logic
crossref: IEEE:1981:PSC
pages: 251--255
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_Efe.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Kemal Efe
rawtitle: Multi-Operand Addition with Conditional Sum Logic
abstract:
Column-wise addition schemes involve counting the number of 1's in a column and representing this number in binary weighted form. In Conditional Sum Logic (CSL), partial results are first generated for every column, then one of these results is selected depending on the incoming carry value. A compact scheme for counting the number of 1's and generating partial results for all possible distributions of incoming carries is introduced. Application of such counters to CSL yields a high speed in multi-operand addition.

rawabstract:
Column-wise addition schemes involve counting the number of 1's in a column and representing this number in binary weighted form. In Conditional Sum Logic (CSL), partial results are first generated for every column, then one of these results is selected depending on the incoming carry value. A compact scheme for counting the number of 1's and generating partial results for all possible distributions of incoming carries is introduced. Application of such counters to CSL yields a high speed in multi-operand addition.

entry:
@InProceedings{Efe:1981:MOA,
  author =       "Kemal Efe",
  title =        "Multi-Operand Addition with Conditional Sum Logic",
  crossref =     "IEEE:1981:PSC",
  pages =        "251--255",
  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_Efe.pdf",
  abstract =     "Column-wise addition schemes involve counting the
                 number of 1's in a column and representing this number
                 in binary weighted form. In Conditional Sum Logic
                 (CSL), partial results are first generated for every
                 column, then one of these results is selected depending
                 on the incoming carry value. A compact scheme for
                 counting the number of 1's and generating partial
                 results for all possible distributions of incoming
                 carries is introduced. Application of such counters to
                 CSL yields a high speed in multi-operand addition.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: techreport
filename: fparith.bib
label: Eide:1981:FPA
author: Vigleik Eide
title: Floating-point arithmetic on a micro-computer
type: Hovedoppgave i informatikk (cand. real)
institution: Universitetet i Oslo
address: Oslo, Norway
pages: 71
year: 1981
bibdate: Thu May 09 08:12:55 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:12:55 ???
acknowledgement: ack-nhfb
rawauthor: Vigleik Eide
rawtitle: Floating-point arithmetic on a micro-computer
entry:
@TechReport{Eide:1981:FPA,
  author =       "Vigleik Eide",
  title =        "Floating-point arithmetic on a micro-computer",
  type =         "Hovedoppgave i informatikk (cand. real)",
  institution =  "Universitetet i Oslo",
  address =      "Oslo, Norway",
  pages =        "71",
  year =         "1981",
  bibdate =      "Thu May 09 08:12:55 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Farmwald:1981:DHP
author: P. M. Farmwald
title: On the Design of High Performance Digital Arithmetic Units
type: Thesis (Ph.D.)
school: Stanford University
address: Stanford, CA, USA
month: aug
monthnumber: 8
year: 1981
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: P. M. Farmwald
rawtitle: On the Design of High Performance Digital Arithmetic Units
entry:
@PhdThesis{Farmwald:1981:DHP,
  author =       "P. M. Farmwald",
  title =        "On the Design of High Performance Digital Arithmetic
                 Units",
  type =         "Thesis ({Ph.D.})",
  school =       "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  month =        aug,
  year =         "1981",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Farmwald:1981:HBE
author: P. Michael Farmwald
title: High bandwidth evaluation of certain elementary functions
crossref: IEEE:1981:PSC
pages: 139--142
year: 1981
bibdate: Mon May 20 05:27:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.20 05:27:32 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Farmwald.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: P. Michael Farmwald
rawtitle: High bandwidth evaluation of certain elementary functions
abstract:
Among the requirements currently being imposed on high-performance digital computers to an increasing extent are the high-bandwidth computations of elementary functions, which are relatively time-consuming procedures when conducted in software. In this paper, we elaborate on a technique for computing piecewise quadratic approximations to many elementary functions. This method permits the effective use of large RAMs or ROMs and parallel multipliers for rapidly generating single-precision floating-point function values (e.g., 30-45 bits of fraction, with current RAM and ROM technology). The technique, based on the use of Taylor series, may be readily pipelined. Its use for calculating values for floating-point reciprocal, square root, sine, cosine, arctangent, logarithm, exponential and error functions is discussed.

rawabstract:
Among the requirements currently being imposed on high-performance digital computers to an increasing extent are the high-bandwidth computations of elementary functions, which are relatively time-consuming procedures when conducted in software. In this paper, we elaborate on a technique for computing piecewise quadratic approximations to many elementary functions. This method permits the effective use of large RAMs or ROMs and parallel multipliers for rapidly generating single-precision floating-point function values (e.g., 30-45 bits of fraction, with current RAM and ROM technology). The technique, based on the use of Taylor series, may be readily pipelined. Its use for calculating values for floating-point reciprocal, square root, sine, cosine, arctangent, logarithm, exponential and error functions is discussed.

entry:
@InProceedings{Farmwald:1981:HBE,
  author =       "P. Michael Farmwald",
  title =        "High bandwidth evaluation of certain elementary
                 functions",
  crossref =     "IEEE:1981:PSC",
  pages =        "139--142",
  year =         "1981",
  bibdate =      "Mon May 20 05:27:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Farmwald.pdf",
  abstract =     "Among the requirements currently being imposed on
                 high-performance digital computers to an increasing
                 extent are the high-bandwidth computations of
                 elementary functions, which are relatively
                 time-consuming procedures when conducted in software.
                 In this paper, we elaborate on a technique for
                 computing piecewise quadratic approximations to many
                 elementary functions. This method permits the effective
                 use of large RAMs or ROMs and parallel multipliers for
                 rapidly generating single-precision floating-point
                 function values (e.g., 30-45 bits of fraction, with
                 current RAM and ROM technology). The technique, based
                 on the use of Taylor series, may be readily pipelined.
                 Its use for calculating values for floating-point
                 reciprocal, square root, sine, cosine, arctangent,
                 logarithm, exponential and error functions is
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Fredette:1981:RES
author: G. Fredette
title: 68000 routine extracts square roots
journal: j-EDN
volume: 26
number: 16
pages: 185--194
month: aug
monthnumber: 8
year: 1981
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
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: EDN
acknowledgement: ack-nj
rawauthor: G. Fredette
rawtitle: 68000 routine extracts square roots
entry:
@Article{Fredette:1981:RES,
  author =       "G. Fredette",
  title =        "68000 routine extracts square roots",
  journal =      j-EDN,
  volume =       "26",
  number =       "16",
  pages =        "185--194",
  month =        aug,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  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 =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Ganesan:1981:GSC
author: K. Ganesan and A. Augustine
title: 8086 generates sines and cosines
journal: j-EDN
volume: 26
number: 6
pages: 186--188
month: mar
monthnumber: 3
year: 1981
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
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: EDN
acknowledgement: ack-nj
rawauthor: K. Ganesan and A. Augustine
rawtitle: 8086 generates sines and cosines
entry:
@Article{Ganesan:1981:GSC,
  author =       "K. Ganesan and A. Augustine",
  title =        "8086 generates sines and cosines",
  journal =      j-EDN,
  volume =       "26",
  number =       "6",
  pages =        "186--188",
  month =        mar,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  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 =     "EDN",
}


bibtype: book
filename: fparith.bib
label: Glaser:1981:HBO
author: Anton Glaser
title: History of Binary and Other Nondecimal Numeration
publisher: Tomash
address: Los Angeles, CA, USA
edition: Revised
pages: xiii + 218
year: 1981
ISBN: 0-938228-00-5 OR 0938228005
ISBN13: 978-0-938228-00-4 OR 9780938228004
LCCN: QA141.2 .G55 1981
bibdate: Fri Mar 17 08:12:27 MDT 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2023.03.17 08:12:27 MDT
note: See also original edition cite Glaser:1971:HBO.
acknowledgement: ack-nhfb
authordates: 1924--
rawauthor: Anton Glaser
rawnote: See also original edition \cite{Glaser:1971:HBO}.
rawtitle: History of Binary and Other Nondecimal Numeration
remark:
Based on the author's thesis (Ph.D.--Temple University), presented under the title: History of modern numeration systems.

subject:
Numeration; History; 31.14 number theory; 15.00 history: general; Numeration; Dualsystem; Geschichte; Talstelsels; History; Numeration; Histoire; Dualsystem; Geschichte.

entry:
@Book{Glaser:1981:HBO,
  author =       "Anton Glaser",
  title =        "History of Binary and Other Nondecimal Numeration",
  publisher =    "Tomash",
  address =      "Los Angeles, CA, USA",
  edition =      "Revised",
  pages =        "xiii + 218",
  year =         "1981",
  ISBN =         "0-938228-00-5",
  ISBN-13 =      "978-0-938228-00-4",
  LCCN =         "QA141.2 .G55 1981",
  bibdate =      "Fri Mar 17 08:12:27 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "See also original edition \cite{Glaser:1971:HBO}.",
  acknowledgement = ack-nhfb,
  author-dates = "1924--",
  remark =       "Based on the author's thesis (Ph.D.--Temple
                 University), presented under the title: History of
                 modern numeration systems.",
  subject =      "Numeration; History; 31.14 number theory; 15.00
                 history: general; Numeration; Dualsystem; Geschichte;
                 Talstelsels; History; Num{\'e}ration; Histoire;
                 Dualsystem; Geschichte.",
}


bibtype: book
filename: fparith.bib
label: Gorin:1981:IDA
author: Ralph E. Gorin
title: Introduction to DECSYSTEM-20 Assembly Language Programming
publisher: pub-DP
address: pub-DP:adr
pages: xxx + 545
year: 1981
ISBN: 0-932376-12-6 OR 0932376126
ISBN13: 978-0-932376-12-1 OR 9780932376121
LCCN: QA76.8.D17 .G67
bibdate: Tue Dec 14 22:54:14 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1993.12.14 22:54:14 ???
acknowledgement: ack-nhfb
rawauthor: Ralph E. Gorin
rawtitle: Introduction to {DECSYSTEM}-20 Assembly Language Programming
entry:
@Book{Gorin:1981:IDA,
  author =       "Ralph E. Gorin",
  title =        "Introduction to {DECSYSTEM}-20 Assembly Language
                 Programming",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  pages =        "xxx + 545",
  year =         "1981",
  ISBN =         "0-932376-12-6",
  ISBN-13 =      "978-0-932376-12-1",
  LCCN =         "QA76.8.D17 .G67",
  bibdate =      "Tue Dec 14 22:54:14 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$40.00",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Gorji-Sinaki:1981:DDS
author: A. Gorji-Sinaki and M. D. Ercegovac
title: Design of a Digit-Slice On-Line Arithmetic Unit
crossref: IEEE:1981:PSC
pages: 72--80
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_GorjiSinaki_Ercegovac.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: A. Gorji-Sinaki and M. D. Ercegovac
rawtitle: Design of a Digit-Slice On-Line Arithmetic Unit
abstract:
A gate level design of a digit-slice on-line arithmetic unit is presented. This unit is designed as a set of basic modules Processing Elements (PE), each of which operates on a single digit of the operands and the results. It is capable of executing four basic operations of addition / subtraction, multiplication and division in an on-line manner. The results are generated during the digit-serial input of the operands, beginning always with the most significant digit. A general (with respect to radix) analysis of the cost and speed of the proposed unit is also given.

rawabstract:
A gate level design of a digit-slice on-line arithmetic unit is presented. This unit is designed as a set of basic modules Processing Elements (PE), each of which operates on a single digit of the operands and the results. It is capable of executing four basic operations of addition\slash subtraction, multiplication and division in an on-line manner. The results are generated during the digit-serial input of the operands, beginning always with the most significant digit. A general (with respect to radix) analysis of the cost and speed of the proposed unit is also given.

entry:
@InProceedings{Gorji-Sinaki:1981:DDS,
  author =       "A. Gorji-Sinaki and M. D. Ercegovac",
  title =        "Design of a Digit-Slice On-Line Arithmetic Unit",
  crossref =     "IEEE:1981:PSC",
  pages =        "72--80",
  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_GorjiSinaki_Ercegovac.pdf",
  abstract =     "A gate level design of a digit-slice on-line
                 arithmetic unit is presented. This unit is designed as
                 a set of basic modules Processing Elements (PE), each
                 of which operates on a single digit of the operands and
                 the results. It is capable of executing four basic
                 operations of addition\slash subtraction,
                 multiplication and division in an on-line manner. The
                 results are generated during the digit-serial input of
                 the operands, beginning always with the most
                 significant digit. A general (with respect to radix)
                 analysis of the cost and speed of the proposed unit is
                 also given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Gosling:1981:CSH
author: J. B. Gosling and J. H. P. Zurawski and D. B. G. Edwards
title: A Chip-Set for a High-Speed Low-cost Floating-Point Unit
crossref: IEEE:1981:PSC
pages: 50--55
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_Gosling_Zurawski_Edwards.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: J. B. Gosling and J. H. P. Zurawski and D. B. G. Edwards
rawtitle: A Chip-Set for a High-Speed Low-cost Floating-Point Unit
abstract:
Although the advent of microprocessors has put considerable computing power in the hands of large numbers of users, there is still an important group who have yet to benefit fully from large scale integration., As a step in the direction of rectifying this situation, a highly flexible chip set is being designed, with a view to reducing the cost of a powerful floating point processor by a factor of about 4. Processing speed will be up to twice that of an equivalent unit built from MSI devices, before allowance is made for savings on wiring delays. It will be possible to construct a unit satisfying all published standards, proposed and existing (de facto), as well as permitting a number of extensions not specifically in these standards. At a cost between 100 and 150 ICs, and with a floating-point add time of around 120ns, the proposed unit is cost-effective compared to currently available coprocessors.

rawabstract:
Although the advent of microprocessors has put considerable computing power in the hands of large numbers of users, there is still an important group who have yet to benefit fully from large scale integration., As a step in the direction of rectifying this situation, a highly flexible chip set is being designed, with a view to reducing the cost of a powerful floating point processor by a factor of about 4. Processing speed will be up to twice that of an equivalent unit built from MSI devices, before allowance is made for savings on wiring delays. It will be possible to construct a unit satisfying all published standards, proposed and existing (de facto), as well as permitting a number of extensions not specifically in these standards. At a cost between 100 and 150 ICs, and with a floating-point add time of around 120ns, the proposed unit is cost-effective compared to currently available coprocessors.

entry:
@InProceedings{Gosling:1981:CSH,
  author =       "J. B. Gosling and J. H. P. Zurawski and D. B. G.
                 Edwards",
  title =        "A Chip-Set for a High-Speed Low-cost Floating-Point
                 Unit",
  crossref =     "IEEE:1981:PSC",
  pages =        "50--55",
  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_Gosling_Zurawski_Edwards.pdf",
  abstract =     "Although the advent of microprocessors has put
                 considerable computing power in the hands of large
                 numbers of users, there is still an important group who
                 have yet to benefit fully from large scale
                 integration., As a step in the direction of rectifying
                 this situation, a highly flexible chip set is being
                 designed, with a view to reducing the cost of a
                 powerful floating point processor by a factor of about
                 4. Processing speed will be up to twice that of an
                 equivalent unit built from MSI devices, before
                 allowance is made for savings on wiring delays. It will
                 be possible to construct a unit satisfying all
                 published standards, proposed and existing (de facto),
                 as well as permitting a number of extensions not
                 specifically in these standards. At a cost between 100
                 and 150 ICs, and with a floating-point add time of
                 around 120ns, the proposed unit is cost-effective
                 compared to currently available coprocessors.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Grappel:1981:RDB
author: R. D. Grappel
title: 68000 routine divides 32-bit numbers
journal: j-EDN
volume: 26
number: 5
pages: 161--162
month: mar
monthnumber: 3
year: 1981
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
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: EDN
acknowledgement: ack-nj
rawauthor: R. D. Grappel
rawtitle: 68000 routine divides 32-bit numbers
entry:
@Article{Grappel:1981:RDB,
  author =       "R. D. Grappel",
  title =        "68000 routine divides 32-bit numbers",
  journal =      j-EDN,
  volume =       "26",
  number =       "5",
  pages =        "161--162",
  month =        mar,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  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 =     "EDN",
}


bibtype: inproceedings
filename: fparith.bib
label: Gregory:1981:RAR
author: R. T. Gregory
title: Residue Arithmetic with Rational Operands
crossref: IEEE:1981:PSC
pages: 144--145
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_Gregory.pdf
keywords: ARITH-5; residue number system
acknowledgement: ack-nhfb
rawauthor: R. T. Gregory
rawtitle: Residue Arithmetic with Rational Operands
abstract:
A method is described for doing residue arithmetic when the operands are rational numbers. A rational operand $ a / b $ is mapped onto the integer $ a b^-1|_p $ and the arithmetic is performed in $ mathrm GF(p) $. A method is given for taking an integer result and finding its rational equivalent (the one which corresponds to the correct rational result).

rawabstract:
A method is described for doing residue arithmetic when the operands are rational numbers. A rational operand $ a / b $ is mapped onto the integer $ a b^{-1}|_p $ and the arithmetic is performed in $ \mathrm {GF}(p) $. A method is given for taking an integer result and finding its rational equivalent (the one which corresponds to the correct rational result).

entry:
@InProceedings{Gregory:1981:RAR,
  author =       "R. T. Gregory",
  title =        "Residue Arithmetic with Rational Operands",
  crossref =     "IEEE:1981:PSC",
  pages =        "144--145",
  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_Gregory.pdf",
  abstract =     "A method is described for doing residue arithmetic
                 when the operands are rational numbers. A rational
                 operand $ a / b $ is mapped onto the integer $ a
                 b^{-1}|_p $ and the arithmetic is performed in $
                 \mathrm {GF}(p) $. A method is given for taking an
                 integer result and finding its rational equivalent (the
                 one which corresponds to the correct rational
                 result).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; residue number system",
}


bibtype: article
filename: fparith.bib
label: Griffiths:1981:BDC
author: L. K. Griffiths
title: Binary-to-Decimal Conversion
journal: j-IBM-TDB
volume: 24
number: 1A
pages: 237--238
month: jun
monthnumber: 6
year: 1981
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Fri Nov 28 17:04:53 2003
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:04:53 ???
fjournal: IBM Technical Disclosure Bulletin
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: L. K. Griffiths
rawtitle: Binary-to-Decimal Conversion
abstract:
Binary to decimal conversion can be achieved by multiplying $ 1 / 10 $ as $ 51 / 512 times 256 / 255 $ and using the fact that $ 256 / 255 = 1 + 1 / 256 + 1 / 256^2 + cdots $, i.e., $ 256 / 255 = 257 - 256 $ rounded up.par This method can be performed efficiently on short word computers with only adding and shifting operations, i.e., first multiplying by $ 51 / 512 $ and then correcting by multiplying by $ 256 / 255 $.

rawabstract:
Binary to decimal conversion can be achieved by multiplying $ 1 / 10 $ as $ 51 / 512 \times 256 / 255 $ and using the fact that $ 256 / 255 = 1 + 1 / 256 + 1 / 256^2 + \cdots $, i.e., $ 256 / 255 = 257 - 256 $ rounded up.\par This method can be performed efficiently on short word computers with only adding and shifting operations, i.e., first multiplying by $ 51 / 512 $ and then correcting by multiplying by $ 256 / 255 $.

entry:
@Article{Griffiths:1981:BDC,
  author =       "L. K. Griffiths",
  title =        "Binary-to-Decimal Conversion",
  journal =      j-IBM-TDB,
  volume =       "24",
  number =       "1A",
  pages =        "237--238",
  month =        jun,
  year =         "1981",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 28 17:04:53 2003",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Binary to decimal conversion can be achieved by
                 multiplying $ 1 / 10 $ as $ 51 / 512 \times 256 / 255 $
                 and using the fact that $ 256 / 255 = 1 + 1 / 256 + 1 /
                 256^2 + \cdots $, i.e., $ 256 / 255 = 257 - 256 $
                 rounded up.\par

                 This method can be performed efficiently on short word
                 computers with only adding and shifting operations,
                 i.e., first multiplying by $ 51 / 512 $ and then
                 correcting by multiplying by $ 256 / 255 $.",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Grote:1981:CIS
author: H. Grote
title: Code improves on a square-root routine
journal: j-EDN
volume: 26
number: 11
pages: 198--200
month: may
monthnumber: 5
year: 1981
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
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: EDN
acknowledgement: ack-nj
rawauthor: H. Grote
rawtitle: Code improves on a square-root routine
entry:
@Article{Grote:1981:CIS,
  author =       "H. Grote",
  title =        "Code improves on a square-root routine",
  journal =      j-EDN,
  volume =       "26",
  number =       "11",
  pages =        "198--200",
  month =        may,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  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 =     "EDN",
}


bibtype: mastersthesis
filename: fparith.bib
label: Hazlerig:1981:CES
author: Steven Jackson Hazlerig
title: Comparison and evaluation of several floating-point schemes for the Motorola 68000 microprocessor
type: Thesis (M.S.)
school: Massachusetts Institute of Technology. Dept. of Electrical and Engineering and Computer Science
address: Cambridge, MA, USA
pages: 103
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 Richard E. Zippel.
keywords: Floating-point arithmetic.; Microprocessors --- Programming.; Microprogramming.
acknowledgement: ack-mfc
rawauthor: Steven Jackson Hazlerig
rawnote: Supervised by Richard E. Zippel.
rawtitle: Comparison and evaluation of several floating-point schemes for the {Motorola} 68000 microprocessor
entry:
@MastersThesis{Hazlerig:1981:CES,
  author =       "Steven Jackson Hazlerig",
  title =        "Comparison and evaluation of several floating-point
                 schemes for the {Motorola} 68000 microprocessor",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical and Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "103",
  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 Richard E. Zippel.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors ---
                 Programming.; Microprogramming.",
}


bibtype: techreport
filename: fparith.bib
label: Hendra:1981:FPS
author: R. G. Hendra
title: A floating point software package for use on LSI-11 computers at SLAC
type: Technical note
number: SLAC TN 81-3
institution: SLAC
address: Stanford, CA, USA
pages: 8
month: jun
monthnumber: 6
year: 1981
bibdate: Fri May 25 05:50:26 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.05.25 05:50:26 ???
URL: http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0046833
acknowledgement: ack-nhfb
rawauthor: R. G. Hendra
rawtitle: A floating point software package for use on {LSI-11} computers at {SLAC}
entry:
@TechReport{Hendra:1981:FPS,
  author =       "R. G. Hendra",
  title =        "A floating point software package for use on {LSI-11}
                 computers at {SLAC}",
  type =         "Technical note",
  number =       "SLAC TN 81-3",
  institution =  "SLAC",
  address =      "Stanford, CA, USA",
  pages =        "8",
  month =        jun,
  year =         "1981",
  bibdate =      "Fri May 25 05:50:26 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0046833",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Hough:1981:API
author: David Hough
title: Applications of the Proposed IEEE-754 Standard for Floating Point Arithmetic
journal: j-COMPUTER
volume: 14
number: 3
pages: 70--74
month: mar
monthnumber: 3
year: 1981
CODEN: CPTRB4
DOI: https://doi.org/10.1109/C-M.1981.220381
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Fri Sep 2 23:38:14 1994
bibtimestamp: 1994.09.02 23:38:14 ???
note: See cite IEEE:1985:AIS,IEEE:1985:ASI.
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: David Hough
rawnote: See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.
rawtitle: Applications of the Proposed {IEEE-754} Standard for Floating Point Arithmetic
bibsource:
https://www.math.utah.edu/pub/tex/bib/computer1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Hough:1981:API,
  author =       "David Hough",
  title =        "Applications of the Proposed {IEEE-754} Standard for
                 Floating Point Arithmetic",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "70--74",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220381",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Sep 2 23:38:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: article
filename: fparith.bib
label: Huang:1981:IFD
author: Chao Huang and D. Peterson and H. Rauch and J. Teague and D. Fraser
title: Implementation of a fast digital processor using the residue number system
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 28
number: 1
pages: 32--38
month: jan
monthnumber: 1
year: 1981
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19800468
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
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=23509
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Chao Huang and D. Peterson and H. Rauch and J. Teague and D. Fraser
rawtitle: Implementation of a fast digital processor using the residue number system
entry:
@Article{Huang:1981:IFD,
  author =       "Chao Huang and D. Peterson and H. Rauch and J. Teague
                 and D. Fraser",
  title =        "Implementation of a fast digital processor using the
                 residue number system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "28",
  number =       "1",
  pages =        "32--38",
  month =        jan,
  year =         "1981",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  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=23509",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper contains a description of a special purpose
                 digital processor which has been implemented using
                 residue arithmetic. The processor does two-dimensional
                 pulse matching by convolving a two-dimensional
                 five-by-five filter with the Incoming data \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Hwang:1981:CFF
author: Shu-Hwa Hwang
title: Computation in a finite field using rational operands
type: Thesis (M.S.)
school: University of Tennessee, Knoxville
address: Knoxville, TN, USA
pages: v + 80
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
keywords: Algorithms.; Floating-point arithmetic.; Modular arithmetic.; Programming (Electronic computers)
acknowledgement: ack-nhfb
rawauthor: Shu-Hwa Hwang
rawtitle: Computation in a finite field using rational operands
entry:
@MastersThesis{Hwang:1981:CFF,
  author =       "Shu-Hwa Hwang",
  title =        "Computation in a finite field using rational
                 operands",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "v + 80",
  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,
  keywords =     "Algorithms.; Floating-point arithmetic.; Modular
                 arithmetic.; Programming (Electronic computers)",
}


bibtype: inproceedings
filename: fparith.bib
label: Hwang:1981:PAV
author: Kai Hwang and Yen-Heng Cheng
title: Partitioned Algorithms and VLSI Structures for Large-Scale Matrix Computations
crossref: IEEE:1981:PSC
pages: 222--232
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_Hwang_Cheng.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Kai Hwang and Yen-Heng Cheng
rawtitle: Partitioned Algorithms and {VLSI} Structures for Large-Scale Matrix Computations
abstract:
VLSI modular arithmetic structures and new partitioned matrix algorithms are developed in this paper to perform hardware matrix computations in solving large-scale linear system of equations. Gaussian elimination and inversion of triangular matrices are shown systematically partitionable. All the partitioned algorithms being developed can achieve linear computation time $ O(n) $, where $n$ is the order of the linear system. The partitioned matrix computations are feasible for modular VLSI implementation with constrained I/O terminals. Performance analysis and design tradeoffs of the partitioned VLSI arithmetic structures are also provided.

rawabstract:
VLSI modular arithmetic structures and new partitioned matrix algorithms are developed in this paper to perform hardware matrix computations in solving large-scale linear system of equations. Gaussian elimination and inversion of triangular matrices are shown systematically partitionable. All the partitioned algorithms being developed can achieve linear computation time $ O(n) $, where $n$ is the order of the linear system. The partitioned matrix computations are feasible for modular VLSI implementation with constrained I/O terminals. Performance analysis and design tradeoffs of the partitioned VLSI arithmetic structures are also provided.

entry:
@InProceedings{Hwang:1981:PAV,
  author =       "Kai Hwang and Yen-Heng Cheng",
  title =        "Partitioned Algorithms and {VLSI} Structures for
                 Large-Scale Matrix Computations",
  crossref =     "IEEE:1981:PSC",
  pages =        "222--232",
  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_Hwang_Cheng.pdf",
  abstract =     "VLSI modular arithmetic structures and new partitioned
                 matrix algorithms are developed in this paper to
                 perform hardware matrix computations in solving
                 large-scale linear system of equations. Gaussian
                 elimination and inversion of triangular matrices are
                 shown systematically partitionable. All the partitioned
                 algorithms being developed can achieve linear
                 computation time $ O(n) $, where $n$ is the order of
                 the linear system. The partitioned matrix computations
                 are feasible for modular VLSI implementation with
                 constrained I/O terminals. Performance analysis and
                 design tradeoffs of the partitioned VLSI arithmetic
                 structures are also provided.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Irwin:1981:RAP
author: Mary Jane Irwin and Dwight R. Smith
title: A Rational Arithmetic Processor
crossref: IEEE:1981:PSC
pages: 241--245
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_Irwin_Smith.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Mary Jane Irwin and Dwight R. Smith
rawtitle: A Rational Arithmetic Processor
abstract:
An arithmetic processor based upon a rational representation scheme is examined. The key feature of this rational processor is its ability to efficiently reduce a result ratio to its irreducible form (the greatest common divisor of the numerator and denominator is unity). The reduction algorithm presented generates the reduced ratio in parallel with the evaluation of the ratio's greatest common divisor. Hardware designs for the reduction algorithm and the basic arithmetic operations are given.

rawabstract:
An arithmetic processor based upon a rational representation scheme is examined. The key feature of this rational processor is its ability to efficiently reduce a result ratio to its irreducible form (the greatest common divisor of the numerator and denominator is unity). The reduction algorithm presented generates the reduced ratio in parallel with the evaluation of the ratio's greatest common divisor. Hardware designs for the reduction algorithm and the basic arithmetic operations are given.

entry:
@InProceedings{Irwin:1981:RAP,
  author =       "Mary Jane Irwin and Dwight R. Smith",
  title =        "A Rational Arithmetic Processor",
  crossref =     "IEEE:1981:PSC",
  pages =        "241--245",
  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_Irwin_Smith.pdf",
  abstract =     "An arithmetic processor based upon a rational
                 representation scheme is examined. The key feature of
                 this rational processor is its ability to efficiently
                 reduce a result ratio to its irreducible form (the
                 greatest common divisor of the numerator and
                 denominator is unity). The reduction algorithm
                 presented generates the reduced ratio in parallel with
                 the evaluation of the ratio's greatest common divisor.
                 Hardware designs for the reduction algorithm and the
                 basic arithmetic operations are given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Jenkins:1981:CSP
author: W. K. Jenkins and M. H. Etzel
title: Correction to ``Special properties of complement codes for redundant residue number systems''
journal: j-PROC-IEEE
volume: 69
number: 8
pages: 1086--1086
month: aug
monthnumber: 8
year: 1981
CODEN: IEEPAD
DOI: https://doi.org/10.1049/el:19800468
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
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
note: See cite Jenkins:1981:SPC.
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31304
fjournal: Proceedings of the IEEE
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: W. K. Jenkins and M. H. Etzel
rawnote: See \cite{Jenkins:1981:SPC}.
rawtitle: Correction to {``Special} properties of complement codes for redundant residue number systems''
entry:
@Article{Jenkins:1981:CSP,
  author =       "W. K. Jenkins and M. H. Etzel",
  title =        "Correction to {``Special} properties of complement
                 codes for redundant residue number systems''",
  journal =      j-PROC-IEEE,
  volume =       "69",
  number =       "8",
  pages =        "1086--1086",
  month =        aug,
  year =         "1981",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Jenkins:1981:SPC}.",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31304",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  keywords =     "residue arithmetic; residue number system",
}


bibtype: article
filename: fparith.bib
label: Jenkins:1981:SPC
author: W. K. Jenkins and M. H. Etzel
title: Special properties of complement codes for redundant residue number systems
journal: j-PROC-IEEE
volume: 69
number: 1
pages: 132--133
month: jan
monthnumber: 1
year: 1981
CODEN: IEEPAD
DOI: https://doi.org/10.1049/el:19800468
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
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
note: See correction cite Jenkins:1981:CSP.
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31297
fjournal: Proceedings of the IEEE
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: W. K. Jenkins and M. H. Etzel
rawnote: See correction \cite{Jenkins:1981:CSP}.
rawtitle: Special properties of complement codes for redundant residue number systems
entry:
@Article{Jenkins:1981:SPC,
  author =       "W. K. Jenkins and M. H. Etzel",
  title =        "Special properties of complement codes for redundant
                 residue number systems",
  journal =      j-PROC-IEEE,
  volume =       "69",
  number =       "1",
  pages =        "132--133",
  month =        jan,
  year =         "1981",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Jenkins:1981:CSP}.",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31297",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Redundant residue number systems are of interest
                 because they have properties that are useful for error
                 control and failure recovery in digital processors.
                 This letter shows how complement coding interferes with
                 error detection in redundant residue \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1981:WDW
author: W. Kahan
title: Why Do We Need a Floating-Point Arithmetic Standard?
type: Technical Report
institution: inst-BERKELEY
address: inst-BERKELEY:adr
pages: 41
day: 12
month: feb
monthnumber: 2
year: 1981
bibdate: Fri Apr 7 12:22:17 GMT 1995
bibtimestamp: 1995.04.07 12:22:17 GMT
remark: Available in a retypeset version cite Kahan:2001:WDW.
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Why Do We Need a Floating-Point Arithmetic 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-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

entry:
@TechReport{Kahan:1981:WDW,
  author =       "W. Kahan",
  title =        "Why Do We Need a Floating-Point Arithmetic Standard?",
  type =         "Technical Report",
  institution =  inst-BERKELEY,
  address =      inst-BERKELEY:adr,
  pages =        "41",
  day =          "12",
  month =        feb,
  year =         "1981",
  bibdate =      "Fri Apr 7 12:22:17 GMT 1995",
  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-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",
  acknowledgement = ack-nhfb,
  remark =       "Available in a retypeset version
                 \cite{Kahan:2001:WDW}.",
}


bibtype: article
filename: fparith.bib
label: Karplus:1981:ASI
author: W. J. Karplus and D. Cohen
title: Architectural and Software Issues in the Design of Peripheral Array Processors
journal: j-COMPUTER
pages: ??--??
month: sep
monthnumber: 9
year: 1981
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Fri Nov 09 19:01:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:01:34 ???
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: W. J. Karplus and D. Cohen
rawtitle: Architectural and Software Issues in the Design of Peripheral Array Processors
entry:
@Article{Karplus:1981:ASI,
  author =       "W. J. Karplus and D. Cohen",
  title =        "Architectural and Software Issues in the Design of
                 Peripheral Array Processors",
  journal =      j-COMPUTER,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        sep,
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Nov 09 19:01:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: inproceedings
filename: fparith.bib
label: Kaushik:1981:SDS
author: Saroj Kaushik and R. K. Arora
title: Sign Detection in the Symmetric Residue Number System
crossref: IEEE:1981:PSC
pages: 146--150
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_Kaushik_Arora.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Saroj Kaushik and R. K. Arora
rawtitle: Sign Detection in the Symmetric Residue Number System
abstract:
This paper is concerned with the algebraic sign detection of a number in the Symmetric Residue Number System. A new approach has been suggested which completely avoids the time consuming process of the Symmetric Mixed Radix Conversion (SMRC). An algorithm based on the above approach implementable in parallel for sign detection is also presented. The hardware representation of the above algorithm is shown. The time and hardware complexity required for the process have also been computed.

rawabstract:
This paper is concerned with the algebraic sign detection of a number in the Symmetric Residue Number System. A new approach has been suggested which completely avoids the time consuming process of the Symmetric Mixed Radix Conversion (SMRC). An algorithm based on the above approach implementable in parallel for sign detection is also presented. The hardware representation of the above algorithm is shown. The time and hardware complexity required for the process have also been computed.

entry:
@InProceedings{Kaushik:1981:SDS,
  author =       "Saroj Kaushik and R. K. Arora",
  title =        "Sign Detection in the Symmetric Residue Number
                 System",
  crossref =     "IEEE:1981:PSC",
  pages =        "146--150",
  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_Kaushik_Arora.pdf",
  abstract =     "This paper is concerned with the algebraic sign
                 detection of a number in the Symmetric Residue Number
                 System. A new approach has been suggested which
                 completely avoids the time consuming process of the
                 Symmetric Mixed Radix Conversion (SMRC). An algorithm
                 based on the above approach implementable in parallel
                 for sign detection is also presented. The hardware
                 representation of the above algorithm is shown. The
                 time and hardware complexity required for the process
                 have also been computed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Kielbasinski:1981:IRL
author: Andrzej Kielbasinski
title: Iterative refinement for linear systems in variable-precision arithmetic
journal: j-BIT
volume: 21
number: 1
pages: 97--103
month: mar
monthnumber: 3
year: 1981
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01934074
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65G05
MRnumber: 83a:65042
bibdate: Wed Jan 4 18:52:17 MST 2006
bibtimestamp: 2006.01.04 18:52:17 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=1&spage=97
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; variable-precision arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Andrzej Kie{\l}basi{\'n}ski
rawtitle: Iterative refinement for linear systems in variable-precision arithmetic
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Kielbasinski:1981:IRL,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "Iterative refinement for linear systems in
                 variable-precision arithmetic",
  journal =      j-BIT,
  volume =       "21",
  number =       "1",
  pages =        "97--103",
  month =        mar,
  year =         "1981",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01934074",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "83a:65042",
  bibdate =      "Wed Jan 4 18:52:17 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&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=21&issue=1&spage=97",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; variable-precision
                 arithmetic",
}


bibtype: book
filename: fparith.bib
label: Knuth:1981:SA
author: Donald E. Knuth
title: Seminumerical Algorithms
volume: 2
publisher: pub-AW
address: pub-AW:adr
edition: Second
pages: xi + 624
year: 1981
ISBN: 0-201-03822-6 OR 0201038226
ISBN13: 978-0-201-03822-4 OR 9780201038224
LCCN: QA76.6 .K64
bibdate: Wed Dec 15 15:47:38 1993
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1993.12.15 15:47:38 ???
series: The Art of Computer Programming
acknowledgement: ack-nj
rawauthor: Donald E. Knuth
rawtitle: Semi\-nu\-mer\-i\-cal Algorithms
entry:
@Book{Knuth:1981:SA,
  author =       "Donald E. Knuth",
  title =        "Semi\-nu\-mer\-i\-cal Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xi + 624",
  year =         "1981",
  ISBN =         "0-201-03822-6",
  ISBN-13 =      "978-0-201-03822-4",
  LCCN =         "QA76.6 .K64",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Kobayashi:1981:FMO
author: Hideaki Kobayashi
title: A Fast Multi-Operand Multiplication Scheme
crossref: IEEE:1981:PSC
pages: 246--250
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_Kobayashi.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Hideaki Kobayashi
rawtitle: A Fast Multi-Operand Multiplication Scheme
abstract:
Recent developments in integrated circuit technology have made efficient schemes for computer arithmetic possible. This paper discusses a generation-summation scheme for fast multi-operand multiplication. Synthesis of three-operand multipliers utilizing a single type of standard LSI device is also discussed.

rawabstract:
Recent developments in integrated circuit technology have made efficient schemes for computer arithmetic possible. This paper discusses a generation-summation scheme for fast multi-operand multiplication. Synthesis of three-operand multipliers utilizing a single type of standard LSI device is also discussed.

entry:
@InProceedings{Kobayashi:1981:FMO,
  author =       "Hideaki Kobayashi",
  title =        "A Fast Multi-Operand Multiplication Scheme",
  crossref =     "IEEE:1981:PSC",
  pages =        "246--250",
  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_Kobayashi.pdf",
  abstract =     "Recent developments in integrated circuit technology
                 have made efficient schemes for computer arithmetic
                 possible. This paper discusses a generation-summation
                 scheme for fast multi-operand multiplication. Synthesis
                 of three-operand multipliers utilizing a single type of
                 standard LSI device is also discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: book
filename: fparith.bib
label: Kogge:1981:APC
author: Peter M. Kogge
title: The Architecture of Pipelined Computers
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: xii + 334
year: 1981
ISBN: 0-07-035237-2 OR 0070352372
ISBN13: 978-0-07-035237-7 OR 9780070352377
LCCN: QA76.5 .K587
bibdate: Wed Dec 15 10:37:46 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1993.12.15 10:37:46 ???
acknowledgement: ack-nhfb
rawauthor: Peter M. Kogge
rawtitle: The Architecture of Pipelined Computers
entry:
@Book{Kogge:1981:APC,
  author =       "Peter M. Kogge",
  title =        "The Architecture of Pipelined Computers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xii + 334",
  year =         "1981",
  ISBN =         "0-07-035237-2",
  ISBN-13 =      "978-0-07-035237-7",
  LCCN =         "QA76.5 .K587",
  bibdate =      "Wed Dec 15 10:37:46 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Koren:1981:CPN
author: I. Koren and Y. Maliniak
title: On Classes of Positive, Negative, and Imaginary Radix Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: 30
number: 5
pages: 212--317
month: may
monthnumber: 5
year: 1981
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1981.1675788
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Aug 22 09:00:57 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 09:00:57 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: I. Koren and Y. Maliniak
rawtitle: On Classes of Positive, Negative, and Imaginary Radix Number Systems
abstract:
A unified approach to a broad class of finite number representation systems is proposed. This class contains aDl positive and negative radix systems and other well-known number systems. In addition, it can be extended to include imaginary radix number systems. The proposed approach enables us to develop a single set of algorithms for arithmetic operations.

rawabstract:
A unified approach to a broad class of finite number representation systems is proposed. This class contains aDl positive and negative radix systems and other well-known number systems. In addition, it can be extended to include imaginary radix number systems. The proposed approach enables us to develop a single set of algorithms for arithmetic operations.

entry:
@Article{Koren:1981:CPN,
  author =       "I. Koren and Y. Maliniak",
  title =        "On Classes of Positive, Negative, and Imaginary Radix
                 Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "30",
  number =       "5",
  pages =        "212--317",
  month =        may,
  year =         "1981",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1981.1675788",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Aug 22 09:00:57 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A unified approach to a broad class of finite number
                 representation systems is proposed. This class contains
                 aDl positive and negative radix systems and other
                 well-known number systems. In addition, it can be
                 extended to include imaginary radix number systems. The
                 proposed approach enables us to develop a single set of
                 algorithms for arithmetic operations.",
  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: Kornerup:1981:IRA
author: Peter Kornerup and David W. Matula
title: An Integrated Rational Arithmetic Unit
crossref: IEEE:1981:PSC
pages: 233--240
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_Kornerup_Matula.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Peter Kornerup and David W. Matula
rawtitle: An Integrated Rational Arithmetic Unit
abstract:
Based on the classical Euclidian Algorithm, we develop the foundations of an arithmetic unit performing Add, Subtract, Multiply and Divide on rational operands. The unit uses one unified algorithm for all operations, including rounding. A binary implementation, based on techniques known from the SRT division, is described. Finally, a hardware implementation using ripple-free, carry-save addition is analyzed, and adapted to a floating-slash representation of the rational operands.

rawabstract:
Based on the classical Euclidian Algorithm, we develop the foundations of an arithmetic unit performing Add, Subtract, Multiply and Divide on rational operands. The unit uses one unified algorithm for all operations, including rounding. A binary implementation, based on techniques known from the SRT division, is described. Finally, a hardware implementation using ripple-free, carry-save addition is analyzed, and adapted to a floating-slash representation of the rational operands.

entry:
@InProceedings{Kornerup:1981:IRA,
  author =       "Peter Kornerup and David W. Matula",
  title =        "An Integrated Rational Arithmetic Unit",
  crossref =     "IEEE:1981:PSC",
  pages =        "233--240",
  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_Kornerup_Matula.pdf",
  abstract =     "Based on the classical Euclidian Algorithm, we develop
                 the foundations of an arithmetic unit performing Add,
                 Subtract, Multiply and Divide on rational operands. The
                 unit uses one unified algorithm for all operations,
                 including rounding. A binary implementation, based on
                 techniques known from the SRT division, is described.
                 Finally, a hardware implementation using ripple-free,
                 carry-save addition is analyzed, and adapted to a
                 floating-slash representation of the rational
                 operands.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: book
filename: fparith.bib
label: Kulisch:1981:CAT
author: Ulrich W. Kulisch and Willard L. Miranker
title: Computer arithmetic in theory and practice
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xiii + 249
year: 1981
ISBN: 0-12-428650-X OR 012428650X
ISBN13: 978-0-12-428650-4 OR 9780124286504
LCCN: QA162 .K84
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: Computer science and applied mathematics
acknowledgement: ack-nhfb
rawauthor: Ulrich W. Kulisch and Willard L. Miranker
rawtitle: Computer arithmetic in theory and practice
keywords:
Algebra, Abstract.; Computer arithmetic.; Floating-point arithmetic.; Interval analysis (Mathematics)

remark:
See cite [pp. 1.10--1.11]Coonen:1984:CPS for negative comments about the floating-point model in this book, and the impracticality of implementing it in early-1980s technology. Coonen comments: ``their scheme is em sufficient to perform reliable computation, aided by devious algorithms; there is no evidence that their scheme is em necessary. nor that the deviousness of their algorithms is unavoidable.''

entry:
@Book{Kulisch:1981:CAT,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "Computer arithmetic in theory and practice",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiii + 249",
  year =         "1981",
  ISBN =         "0-12-428650-X",
  ISBN-13 =      "978-0-12-428650-4",
  LCCN =         "QA162 .K84",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Computer science and applied mathematics",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra, Abstract.; Computer arithmetic.;
                 Floating-point arithmetic.; Interval analysis
                 (Mathematics)",
  remark =       "See \cite[pp. 1.10--1.11]{Coonen:1984:CPS} for
                 negative comments about the floating-point model in
                 this book, and the impracticality of implementing it in
                 early-1980s technology. Coonen comments: ``their scheme
                 is {\em sufficient\/} to perform reliable computation,
                 aided by devious algorithms; there is no evidence that
                 their scheme is {\em necessary}. nor that the
                 deviousness of their algorithms is unavoidable.''",
}


bibtype: article
filename: fparith.bib
label: Kunz:1981:QZ
author: W. Kunz
title: Quadratwurzel mit dem $ mu $P Z80 toenglish Square Roots with the Z80 Microprocessor endtoenglish
journal: j-ELECTRONIK
volume: 7
pages: 109--110
year: 1981
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: W. Kunz
rawtitle:
{Quadratwurzel mit dem $ \mu $P Z80} \toenglish {Square Roots with the Z80 Microprocessor} \endtoenglish

entry:
@Article{Kunz:1981:QZ,
  author =       "W. Kunz",
  title =        "{Quadratwurzel mit dem $ \mu $P Z80} \toenglish
                 {Square Roots with the Z80 Microprocessor}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "7",
  pages =        "109--110",
  year =         "1981",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  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,
  fjournal =     "Elektronik",
}


bibtype: inproceedings
filename: fparith.bib
label: Ligomenides:1981:CRF
author: P. Ligomenides and R. Newcomb
title: Complement Representations in the Fibonacci Computer
crossref: IEEE:1981:PSC
pages: 6--9
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_Ligomenides_Newcomb.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: P. Ligomenides and R. Newcomb
rawtitle: Complement Representations in the {Fibonacci} Computer
abstract:
Two complement representations and a sign-magnitude one are introduced which allow for handling negative numbers using only binary coefficients in Fibonacci base expansions. These are developed for practical implementation in Fibonacci computers.

rawabstract:
Two complement representations and a sign-magnitude one are introduced which allow for handling negative numbers using only binary coefficients in Fibonacci base expansions. These are developed for practical implementation in Fibonacci computers.

entry:
@InProceedings{Ligomenides:1981:CRF,
  author =       "P. Ligomenides and R. Newcomb",
  title =        "Complement Representations in the {Fibonacci}
                 Computer",
  crossref =     "IEEE:1981:PSC",
  pages =        "6--9",
  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_Ligomenides_Newcomb.pdf",
  abstract =     "Two complement representations and a sign-magnitude
                 one are introduced which allow for handling negative
                 numbers using only binary coefficients in Fibonacci
                 base expansions. These are developed for practical
                 implementation in Fibonacci computers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Ling:1981:HSB
author: Huey Ling
title: High-speed binary adder
journal: j-IBM-JRD
volume: 25
number: 2/3
pages: 156--166
month: may
monthnumber: 5
year: 1981
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Tue Mar 25 14:26:59 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.03.25 14:26:59 MST
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
classcodes: C5120 (Logic and switching circuits)
corpsource: IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
treatment: N New Development
rawauthor: Huey Ling
rawtitle: High-speed binary adder
keywords:
adders; fewer logic levels; high; neighbouring bit; new carry propagation; new scheme; pairs; reduced component count; speed binary adder; uniform fanin loading; uniform fanout loading

entry:
@Article{Ling:1981:HSB,
  author =       "Huey Ling",
  title =        "High-speed binary adder",
  journal =      j-IBM-JRD,
  volume =       "25",
  number =       "2/3",
  pages =        "156--166",
  month =        may # "\slash " # jun,
  year =         "1981",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C5120 (Logic and switching circuits)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "adders; fewer logic levels; high; neighbouring bit;
                 new carry propagation; new scheme; pairs; reduced
                 component count; speed binary adder; uniform fanin
                 loading; uniform fanout loading",
  treatment =    "N New Development",
}


bibtype: article
filename: fparith.bib
label: Linnainmaa:1981:CEU
author: Seppo Linnainmaa
title: Combatting the effects of underflow and overflow in determining real roots of polynomials
journal: j-SIGNUM
volume: 16
number: 2
pages: 11--16
month: jun
monthnumber: 6
year: 1981
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:09 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:09 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J690
rawauthor: Seppo Linnainmaa
rawtitle: Combatting the effects of underflow and overflow in determining real roots of polynomials
entry:
@Article{Linnainmaa:1981:CEU,
  author =       "Seppo Linnainmaa",
  title =        "Combatting the effects of underflow and overflow in
                 determining real roots of polynomials",
  journal =      j-SIGNUM,
  volume =       "16",
  number =       "2",
  pages =        "11--16",
  month =        jun,
  year =         "1981",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:09 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 =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}


bibtype: article
filename: fparith.bib
label: Linnainmaa:1981:SDP
author: Seppo Linnainmaa
title: Software for Doubled-Precision Floating-Point Computations
journal: j-TOMS
volume: 7
number: 3
pages: 272--283
month: sep
monthnumber: 9
year: 1981
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355958.355960
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 68B99 (65G99 68C05)
MRnumber: 82h:68041
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 ???
URL: http://doi.acm.org/10.1145/355958.355960
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Seppo Linnainmaa
rawtitle: Software for Doubled-Precision Floating-Point Computations
keywords:
accurate floating-point summation; exact multiplication; floating-point arithmetic; rounding errors; software portability

entry:
@Article{Linnainmaa:1981:SDP,
  author =       "Seppo Linnainmaa",
  title =        "Software for Doubled-Precision Floating-Point
                 Computations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "272--283",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355960",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68B99 (65G99 68C05)",
  MRnumber =     "82h:68041",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/355958.355960",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation; exact
                 multiplication; floating-point arithmetic; rounding
                 errors; software portability",
}


bibtype: article
filename: fparith.bib
label: Louie:1981:APS
author: T. Louie
title: Array Processors: a Selected Bibliography
journal: j-COMPUTER
pages: ??--??
month: sep
monthnumber: 9
year: 1981
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Fri Nov 09 19:04:04 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:04:04 ???
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: T. Louie
rawtitle: Array Processors: a Selected Bibliography
entry:
@Article{Louie:1981:APS,
  author =       "T. Louie",
  title =        "Array Processors: a Selected Bibliography",
  journal =      j-COMPUTER,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        sep,
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Nov 09 19:04:04 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: inproceedings
filename: fparith.bib
label: Markov:1981:IAA
author: Svetoslav Markov
title: On an Interval Arithmetic and Its Applications
crossref: IEEE:1981:PSC
pages: 274--278
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_Markov.pdf
keywords: ARITH-5; interval arithmetic
acknowledgement: ack-nhfb
rawauthor: Svetoslav Markov
rawtitle: On an Interval Arithmetic and Its Applications
abstract:
It is our point of view that familiar interval arithmetic defined by $ A*B = a * b : a in A, b in B $, $ * in +, -, times , : $ is inefficient in certain respects. For instance, it is not in a position to produce exact representations of sets of the form $ f(x, y, ldots , z) : x in X. y in Y, ldots , z in Z $ even for simple functions $f$ of one variable. We make use of another interval arithmetic which is very convenient for computer computations and for construction of interval algorithms. As an example we consider a method for the construction of interval expressions for sets of the form $ f(x) : x in [x_1, x_2] $, where $f$ is an elementary function.

rawabstract:
It is our point of view that familiar interval arithmetic defined by $ A*B = \{ a * b : a \in A, b \in B \} $, $ * \in \{ +, -, \times, : \} $ is inefficient in certain respects. For instance, it is not in a position to produce exact representations of sets of the form $ \{ f(x, y, \ldots {}, z) : x \in X. y \in Y, \ldots {}, z \in Z \} $ even for simple functions $f$ of one variable. We make use of another interval arithmetic which is very convenient for computer computations and for construction of interval algorithms. As an example we consider a method for the construction of interval expressions for sets of the form $ \{ f(x) : x \in [x_1, x_2] \} $, where $f$ is an elementary function.

entry:
@InProceedings{Markov:1981:IAA,
  author =       "Svetoslav Markov",
  title =        "On an Interval Arithmetic and Its Applications",
  crossref =     "IEEE:1981:PSC",
  pages =        "274--278",
  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_Markov.pdf",
  abstract =     "It is our point of view that familiar interval
                 arithmetic defined by $ A*B = \{ a * b : a \in A, b \in
                 B \} $, $ * \in \{ +, -, \times, : \} $ is inefficient
                 in certain respects. For instance, it is not in a
                 position to produce exact representations of sets of
                 the form $ \{ f(x, y, \ldots {}, z) : x \in X. y \in Y,
                 \ldots {}, z \in Z \} $ even for simple functions $f$
                 of one variable. We make use of another interval
                 arithmetic which is very convenient for computer
                 computations and for construction of interval
                 algorithms. As an example we consider a method for the
                 construction of interval expressions for sets of the
                 form $ \{ f(x) : x \in [x_1, x_2] \} $, where $f$ is an
                 elementary function.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; interval arithmetic",
}


bibtype: article
filename: fparith.bib
label: Maron:1981:IAP
author: N. Maron and T. A. Brengle
title: Integrating an Array Processor into a Scientific Computing System
journal: j-COMPUTER
volume: 14
number: 9
pages: 41--44
month: sep
monthnumber: 9
year: 1981
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Wed Nov 14 19:04:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Parallel/Multi.bib
bibtimestamp: 2007.11.14 19:04:40 ???
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
key: Maron & Brengle
rawauthor: N. Maron and T. A. Brengle
rawtitle: Integrating an Array Processor into a Scientific Computing System
entry:
@Article{Maron:1981:IAP,
  author =       "N. Maron and T. A. Brengle",
  key =          "Maron \& Brengle",
  title =        "Integrating an Array Processor into a Scientific
                 Computing System",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "9",
  pages =        "41--44",
  month =        sep,
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Parallel/Multi.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: article
filename: fparith.bib
label: Matsui:1981:OUF
author: S. Matsui and M. Iri
title: An overflow / underflow-free floating-point representation of numbers
journal: j-J-INF-PROCESS
volume: 4
number: 3
pages: 123--133
year: 1981
CODEN: JIPRDE
ISSN: 0387-6101 OR 03876101
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Journal of Information Processing
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
reviewer: A. C. R. Newbery; Newbery, A. C. R
rawauthor: S. Matsui and M. Iri
rawtitle: An overflow\slash underflow-free floating-point representation of numbers
entry:
@Article{Matsui:1981:OUF,
  author =       "S. Matsui and M. Iri",
  title =        "An overflow\slash underflow-free floating-point
                 representation of numbers",
  journal =      j-J-INF-PROCESS,
  volume =       "4",
  number =       "3",
  pages =        "123--133",
  year =         "1981",
  CODEN =        "JIPRDE",
  ISSN =         "0387-6101",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0",
  content =      "The authors propose a floating-point number
                 representation whereby the allocation of digits between
                 exponent and mantissa would vary with the size of the
                 number. In extreme cases in which the entire word is
                 not long enough to contain the exponent, they move to a
                 different ``level'' and work with exponents of
                 exponents. They have implemented the scheme in
                 software, and they claim that a hardware implementation
                 is possible without loss of efficiency. Their examples
                 include Graeffe's method, which seems to survive better
                 in their environment than in a conventional
                 floating-point environment, and Racah symbols, which
                 are functions of factorials.\par

                 The examples are not totally convincing.
                 Polynomial-factoring is not a computational bottleneck.
                 The Racah symbols would indeed cause trouble if
                 computed in a direct manner in conventional floating
                 point; however, the use of a log-gamma function would
                 largely eliminate the problem.\par

                 By using certain bit-configurations to denote
                 ``nonnumbers'' the authors make good their claim of
                 overflow-free arithmetic. The system clearly has the
                 merit of convenience. In the absence of a formal error
                 analysis it is not yet clear what price has to be paid
                 for the convenience. \par

                 A. C. R. Newbery, Lexington.",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  CRnumber =     "40691",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  fjournal =     "Journal of Information Processing",
  genterm =      "DESIGN; PERFORMANCE",
  reviewer =     "A. C. R. Newbery; Newbery, A. C. R",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: fparith.bib
label: Miller:1981:RGU
author: W. Miller
title: A Remark on Gradual Underflow
journal: j-COMPUTING
volume: 27
number: 3
pages: 217--225
year: 1981
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Oct 12 16:33:42 MDT 1999
bibtimestamp: 1999.10.12 16:33:42 MDT
fjournal: Computing: Archiv fur informatik und numerik
keywords: computer arithmetic; computer metatheory; floating-point arithmetic; IEEE 754 arithmetic
acknowledgement: ack-nj
affiliation: Univ of Ariz, Tucson, USA
journalURL: http://link.springer.com/journal/607
journalabr: Computing (Vienna/New York)
rawauthor: W. Miller
rawtitle: A Remark on Gradual Underflow
bibsource:
Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Miller:1981:RGU,
  author =       "W. Miller",
  title =        "A Remark on Gradual Underflow",
  journal =      j-COMPUTING,
  volume =       "27",
  number =       "3",
  pages =        "217--225",
  year =         "1981",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Univ of Ariz, Tucson, USA",
  classification = "723",
  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 metatheory;
                 floating-point arithmetic; IEEE 754 arithmetic",
}


bibtype: article
filename: fparith.bib
label: Mitra:1981:CRA
author: D. Mitra and V. Lawrence
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 28
number: 9
pages: 894--905
month: sep
monthnumber: 9
year: 1981
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 11:25:03 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:03 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: D. Mitra and V. Lawrence
title:
Controlled rounding arithmetics, for second-order direct-form digital filters, that eliminate all self-sustained oscillations

rawtitle:
Controlled rounding arithmetics, for second-order direct-form digital filters, that eliminate all self-sustained oscillations

entry:
@Article{Mitra:1981:CRA,
  author =       "D. Mitra and V. Lawrence",
  title =        "Controlled rounding arithmetics, for second-order
                 direct-form digital filters, that eliminate all
                 self-sustained oscillations",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "28",
  number =       "9",
  pages =        "894--905",
  month =        sep,
  year =         "1981",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Quantization often allows a recursive second-order
                 filter to oscillate even when the underlying linear
                 model is absolutely stable and there is no external
                 signal present to excite the filter. One of the
                 significant innovative ideas recently \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Munson:1981:FPR
author: David C. Munson, Jr. and Bede Liu
title: Floating point roundoff error in the prime factor FFT
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 29
number: 4
pages: 877--882
month: aug
monthnumber: 8
year: 1981
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
MRclass: 65R10 (94A05)
MRnumber: 82f:65132
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 Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: David C. {Munson, Jr.} and Bede Liu
rawtitle: Floating point roundoff error in the prime factor {FFT}
abstract:
The prime factor fast Fourier transform (PF FFT), developed by Kolba and Parks, makes use of recent computational complexity results by Winograd to compute the DFT with a fewer number of multiplications than that required by the FFT. Patterson and McClellan have derived an expression for the mean squared error (MSE) in the PF FFT, assuming finite precision fixed point arithmetic. In this paper, we derive an expression for the MSE in the PF FFT, assuming floating point arithmetic. This expression is quite complicated, so an upper bound on the MSE is also derived which is easier to compute. Simulation results are presented comparing the error in the PF FFT with both the derived bound and the error observed in a radix-2 FFT.

rawabstract:
The prime factor fast Fourier transform (PF FFT), developed by Kolba and Parks, makes use of recent computational complexity results by Winograd to compute the DFT with a fewer number of multiplications than that required by the FFT. Patterson and McClellan have derived an expression for the mean squared error (MSE) in the PF FFT, assuming finite precision fixed point arithmetic. In this paper, we derive an expression for the MSE in the PF FFT, assuming floating point arithmetic. This expression is quite complicated, so an upper bound on the MSE is also derived which is easier to compute. Simulation results are presented comparing the error in the PF FFT with both the derived bound and the error observed in a radix-2 FFT.

entry:
@Article{Munson:1981:FPR,
  author =       "David C. {Munson, Jr.} and Bede Liu",
  title =        "Floating point roundoff error in the prime factor
                 {FFT}",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "29",
  number =       "4",
  pages =        "877--882",
  month =        aug,
  year =         "1981",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  MRclass =      "65R10 (94A05)",
  MRnumber =     "82f:65132",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The prime factor fast Fourier transform (PF FFT),
                 developed by Kolba and Parks, makes use of recent
                 computational complexity results by Winograd to compute
                 the DFT with a fewer number of multiplications than
                 that required by the FFT. Patterson and McClellan have
                 derived an expression for the mean squared error (MSE)
                 in the PF FFT, assuming finite precision fixed point
                 arithmetic. In this paper, we derive an expression for
                 the MSE in the PF FFT, assuming floating point
                 arithmetic. This expression is quite complicated, so an
                 upper bound on the MSE is also derived which is easier
                 to compute. Simulation results are presented comparing
                 the error in the PF FFT with both the derived bound and
                 the error observed in a radix-2 FFT.",
  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: Nguyen:1981:SAD
author: Diem Dinh Nguyen
crossref: IEEE:1981:PSC
pages: 42--49
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_Nguyen.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Diem Dinh Nguyen
title:
A Systematic Approach to the Design of Structures for Addition and Subtraction --- Case of Radix $ r = m^k $

abstract:
The results of Robertson concerning a systematic approach to the design of Adder / Subtracter structures of radix $ r = 2^k $, $ k geq I $ are generalised to cover all structures of radix $ r = m^k $, $ k geq I $ and $ m geq 2 $. The use of quasibinary representations help reduce the number of types of fundamental structures required. In addition to the types encountered in the earlier case, only one new type of fundamental structure called Radix-$m$ Carry Generator is needed. Examples in the particular case of Decimal Adder / Subtracter structures are used to illustrate the results.

rawabstract:
The results of Robertson concerning a systematic approach to the design of Adder\slash Subtracter structures of radix $ r = 2^k $, $ k \geq I $ are generalised to cover all structures of radix $ r = m^k $, $ k \geq I $ and $ m \geq 2 $. The use of quasibinary representations help reduce the number of types of fundamental structures required. In addition to the types encountered in the earlier case, only one new type of fundamental structure called Radix-$m$ Carry Generator is needed. Examples in the particular case of Decimal Adder\slash Subtracter structures are used to illustrate the results.

rawtitle:
A Systematic Approach to the Design of Structures for Addition and Subtraction --- Case of Radix $ r = m^k $

entry:
@InProceedings{Nguyen:1981:SAD,
  author =       "Diem Dinh Nguyen",
  title =        "A Systematic Approach to the Design of Structures for
                 Addition and Subtraction --- Case of Radix $ r = m^k
                 $",
  crossref =     "IEEE:1981:PSC",
  pages =        "42--49",
  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_Nguyen.pdf",
  abstract =     "The results of Robertson concerning a systematic
                 approach to the design of Adder\slash Subtracter
                 structures of radix $ r = 2^k $, $ k \geq I $ are
                 generalised to cover all structures of radix $ r = m^k
                 $, $ k \geq I $ and $ m \geq 2 $. The use of
                 quasibinary representations help reduce the number of
                 types of fundamental structures required. In addition
                 to the types encountered in the earlier case, only one
                 new type of fundamental structure called Radix-$m$
                 Carry Generator is needed. Examples in the particular
                 case of Decimal Adder\slash Subtracter structures are
                 used to illustrate the results.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Ong:1981:TQC
author: S. Ong and D. E. Atkins
title: Towards Quantitative Comparison of Computer Number Systems
crossref: IEEE:1981:PSC
pages: 21--33
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_Ong_Atkins.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: S. Ong and D. E. Atkins
rawtitle: Towards Quantitative Comparison of Computer Number Systems
abstract:
This paper describes an evolving Arithmetic Design System (ADS) to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology. In computer arithmetic we are concerned with establishing a correspondence between abstract quantities (numbers) and some physical representation (symbols), and with simulating the operations on these symbols. The ADS is intended to help study the cost and performance of alternate simulations. A finite number system is a triple consisting of a symbol set (elements are called ``digit-vectors''), an interpretation set, a mapping between these two sets, and a set of operators (digit-vector algorithms) defined on its symbol set. A set of these digit vector algorithms are proposed for conducting arithmetic design. A number system matrix defines the digit vector algorithm for numerous number systems and a method for computing time and space complexity of compositions of these algorithms is proposed. An example of how the system could be used to compare addition, with and without overflow detection, for three number systems is given.

rawabstract:
This paper describes an evolving Arithmetic Design System (ADS) to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology. In computer arithmetic we are concerned with establishing a correspondence between abstract quantities (numbers) and some physical representation (symbols), and with simulating the operations on these symbols. The ADS is intended to help study the cost and performance of alternate simulations. A finite number system is a triple consisting of a symbol set (elements are called ``digit-vectors''), an interpretation set, a mapping between these two sets, and a set of operators (digit-vector algorithms) defined on its symbol set. A set of these digit vector algorithms are proposed for conducting arithmetic design. A number system matrix defines the digit vector algorithm for numerous number systems and a method for computing time and space complexity of compositions of these algorithms is proposed. An example of how the system could be used to compare addition, with and without overflow detection, for three number systems is given.

entry:
@InProceedings{Ong:1981:TQC,
  author =       "S. Ong and D. E. Atkins",
  title =        "Towards Quantitative Comparison of Computer Number
                 Systems",
  crossref =     "IEEE:1981:PSC",
  pages =        "21--33",
  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_Ong_Atkins.pdf",
  abstract =     "This paper describes an evolving Arithmetic Design
                 System (ADS) to support the quantitative evaluation of
                 alternate number systems with respect to a given
                 application and realization technology. In computer
                 arithmetic we are concerned with establishing a
                 correspondence between abstract quantities (numbers)
                 and some physical representation (symbols), and with
                 simulating the operations on these symbols. The ADS is
                 intended to help study the cost and performance of
                 alternate simulations. A finite number system is a
                 triple consisting of a symbol set (elements are called
                 ``digit-vectors''), an interpretation set, a mapping
                 between these two sets, and a set of operators
                 (digit-vector algorithms) defined on its symbol set. A
                 set of these digit vector algorithms are proposed for
                 conducting arithmetic design. A number system matrix
                 defines the digit vector algorithm for numerous number
                 systems and a method for computing time and space
                 complexity of compositions of these algorithms is
                 proposed. An example of how the system could be used to
                 compare addition, with and without overflow detection,
                 for three number systems is given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Owens:1981:CAD
author: Robert Michael Owens
title: Compound Algorithms for Digit On-Line Arithmetic
crossref: IEEE:1981:PSC
pages: 64--71
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_Owens.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Robert Michael Owens
rawtitle: Compound Algorithms for Digit On-Line Arithmetic
abstract:
This paper describes a systematic method which has been. successfully used to create several digit online algorithms. Basically, the method entails converting in a systematic way a known continued sums / products algorithm and combining the converted form of the continued sums / product algorithm with a generalized digitization algorithm. Not only does the method seem to have wide applicability in the creation of digit online algorithms for many elementary functions but the algorithms which have resulted from this method themselves have several desirable properties.

rawabstract:
This paper describes a systematic method which has been. successfully used to create several digit online algorithms. Basically, the method entails converting in a systematic way a known continued sums\slash products algorithm and combining the converted form of the continued sums\slash product algorithm with a generalized digitization algorithm. Not only does the method seem to have wide applicability in the creation of digit online algorithms for many elementary functions but the algorithms which have resulted from this method themselves have several desirable properties.

entry:
@InProceedings{Owens:1981:CAD,
  author =       "Robert Michael Owens",
  title =        "Compound Algorithms for Digit On-Line Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "64--71",
  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_Owens.pdf",
  abstract =     "This paper describes a systematic method which has
                 been. successfully used to create several digit online
                 algorithms. Basically, the method entails converting in
                 a systematic way a known continued sums\slash products
                 algorithm and combining the converted form of the
                 continued sums\slash product algorithm with a
                 generalized digitization algorithm. Not only does the
                 method seem to have wide applicability in the creation
                 of digit online algorithms for many elementary
                 functions but the algorithms which have resulted from
                 this method themselves have several desirable
                 properties.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Padegs:1981:SB
author: A. Padegs
title: System / 360 and Beyond
journal: j-IBM-JRD
volume: 25
number: 5
pages: 377--390
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: Sat Jan 29 17:56:34 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.01.29 17:56:34 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: A. Padegs
rawtitle: {System\slash 360} and Beyond
entry:
@Article{Padegs:1981:SB,
  author =       "A. Padegs",
  title =        "{System\slash 360} and Beyond",
  journal =      j-IBM-JRD,
  volume =       "25",
  number =       "5",
  pages =        "377--390",
  month =        sep,
  year =         "1981",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Sat Jan 29 17:56:34 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: article
filename: fparith.bib
label: Pan:1981:BCA
author: V. Pan
title: The bit-complexity of arithmetic algorithms
journal: j-J-ALG
volume: 2
number: 2
pages: 144--163
month: jun
monthnumber: 6
year: 1981
CODEN: JOALDV
DOI: https://doi.org/10.1016/0196-6774(81)90016-X
ISSN: 0196-6774 (print), 1090-2678 (electronic) OR 01966774 (print), 10902678 (electronic)
ISSNL: 0196-6774 OR 01966774
bibdate: Tue Dec 11 09:13:49 MST 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jalg.bib
bibtimestamp: 2012.12.11 09:13:49 MST
URL: http://www.sciencedirect.com/science/article/pii/019667748190016X
fjournal: Journal of Algorithms
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01966774
rawauthor: V. Pan
rawtitle: The bit-complexity of arithmetic algorithms
entry:
@Article{Pan:1981:BCA,
  author =       "V. Pan",
  title =        "The bit-complexity of arithmetic algorithms",
  journal =      j-J-ALG,
  volume =       "2",
  number =       "2",
  pages =        "144--163",
  month =        jun,
  year =         "1981",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1016/0196-6774(81)90016-X",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:13:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/019667748190016X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}


bibtype: inproceedings
filename: fparith.bib
label: Papachristou:1981:APA
author: C. A. Papachristou
title: Algorithms for Parallel Addition and Parallel Polynomial Evaluation
crossref: IEEE:1981:PSC
pages: 256--263
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_Papachristou.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: C. A. Papachristou
rawtitle: Algorithms for Parallel Addition and Parallel Polynomial Evaluation
abstract:
This paper presents two related algorithms for implementing parallel $n$-bit binary addition and evaluating $n$-th degree polynomials, respectively. The approach taken makes use of an iterative construction, the computation tree. The algorithms are particularly effective for moderate values of $n$ and are in accord with well-known asymptotic bounds. In the case of $n$-bit addition, the implementations constitute lookahead tree circuits of $r$-input standard logic elements. Extensions to modular tree structures for lookahead adders are also considered. In the case of parallel polynomial evaluation, the operations of ordinary addition and multiplication are assumed with the capability to employ $r$ arguments simultaneously.

rawabstract:
This paper presents two related algorithms for implementing parallel $n$-bit binary addition and evaluating $n$-th degree polynomials, respectively. The approach taken makes use of an iterative construction, the computation tree. The algorithms are particularly effective for moderate values of $n$ and are in accord with well-known asymptotic bounds. In the case of $n$-bit addition, the implementations constitute lookahead tree circuits of $r$-input standard logic elements. Extensions to modular tree structures for lookahead adders are also considered. In the case of parallel polynomial evaluation, the operations of ordinary addition and multiplication are assumed with the capability to employ $r$ arguments simultaneously.

entry:
@InProceedings{Papachristou:1981:APA,
  author =       "C. A. Papachristou",
  title =        "Algorithms for Parallel Addition and Parallel
                 Polynomial Evaluation",
  crossref =     "IEEE:1981:PSC",
  pages =        "256--263",
  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_Papachristou.pdf",
  abstract =     "This paper presents two related algorithms for
                 implementing parallel $n$-bit binary addition and
                 evaluating $n$-th degree polynomials, respectively. The
                 approach taken makes use of an iterative construction,
                 the computation tree. The algorithms are particularly
                 effective for moderate values of $n$ and are in accord
                 with well-known asymptotic bounds. In the case of
                 $n$-bit addition, the implementations constitute
                 lookahead tree circuits of $r$-input standard logic
                 elements. Extensions to modular tree structures for
                 lookahead adders are also considered. In the case of
                 parallel polynomial evaluation, the operations of
                 ordinary addition and multiplication are assumed with
                 the capability to employ $r$ arguments
                 simultaneously.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Peng:1981:AES
author: Hong Peng
title: Algorithms for extracting square roots and cube roots
crossref: IEEE:1981:PSC
pages: 121--126
year: 1981
bibdate: Thu Sep 01 11:37:17 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 11:37:17 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf
keywords: ARITH-5
acknowledgement: ack-nj
rawauthor: Hong Peng
rawtitle: Algorithms for extracting square roots and cube roots
abstract:
This paper describes a kind of algorithms for fast extracting square roots and cube roots, their mathematical proofs, their revised algorithm formulae, and hardware implementation of the square root algorithm. These algorithms may be of no significance for large scale computer with fast division. But I am sure that it is effective and economical to apply these algorithms to the circuit designs of some mini- and microcomputers with general multiplication and division, such as nonrestoring division.

rawabstract:
This paper describes a kind of algorithms for fast extracting square roots and cube roots, their mathematical proofs, their revised algorithm formulae, and hardware implementation of the square root algorithm. These algorithms may be of no significance for large scale computer with fast division. But I am sure that it is effective and economical to apply these algorithms to the circuit designs of some mini- and microcomputers with general multiplication and division, such as nonrestoring division.

entry:
@InProceedings{Peng:1981:AES,
  author =       "Hong Peng",
  title =        "Algorithms for extracting square roots and cube
                 roots",
  crossref =     "IEEE:1981:PSC",
  pages =        "121--126",
  year =         "1981",
  bibdate =      "Thu Sep 01 11:37:17 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/arith5/papers/ARITH5_Peng.pdf",
  abstract =     "This paper describes a kind of algorithms for fast
                 extracting square roots and cube roots, their
                 mathematical proofs, their revised algorithm formulae,
                 and hardware implementation of the square root
                 algorithm. These algorithms may be of no significance
                 for large scale computer with fast division. But I am
                 sure that it is effective and economical to apply these
                 algorithms to the circuit designs of some mini- and
                 microcomputers with general multiplication and
                 division, such as nonrestoring division.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Peters:1981:EFB
author: James V. Peters
title: An Equivalent Form of Benford's Law
journal: j-FIB-QUART
volume: 19
number: 1
pages: 74--75
month: feb
monthnumber: 2
year: 1981
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:59:53 MDT 2011
bibtimestamp: 2011.10.20 17:59:53 MDT
URL: http://www.fq.math.ca/Scanned/19-1/peters.pdf
fjournal: The Fibonacci Quarterly
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: James V. Peters
rawtitle: An Equivalent Form of {Benford's Law}
bibsource:
http://www.fq.math.ca/19-1.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Peters:1981:EFB,
  author =       "James V. Peters",
  title =        "An Equivalent Form of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "1",
  pages =        "74--75",
  month =        feb,
  year =         "1981",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:53 MDT 2011",
  bibsource =    "http://www.fq.math.ca/19-1.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: inproceedings
filename: fparith.bib
label: Raghavendra:1981:SLA
author: C. S. Raghavendra and M. D. Ercegovac
title: A Simulator for On-Line Arithmetic
crossref: IEEE:1981:PSC
pages: 92--98
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_Raghavendra_Ercegovac.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: C. S. Raghavendra and M. D. Ercegovac
rawtitle: A Simulator for On-Line Arithmetic
abstract:
On-line arithmetic is a special class of serial arithmetic where algorithms produce results with the most significant digit first during the serial input of the operands. Speedup of computations can be achieved by overlapping or pipelining successive operations with small delays. This paper describes the design and implementation of a simulator for on-line arithmetic algorithms. The simulator was designed primarily to serve aspar (1) an experimental tool for synthesis of on-line algorithms;par (2) a performance evaluation tool of on-line arithmetic;par (3) an on-line calculator in solving some problems involving linear and non-linear recurrences.par The simulator evaluates arithmetic expressions given in a highly functional form. Presently, the set of operations supported include addition, subtraction, multiplication, division, and square root. Several examples are presented in this paper to illustrate the usage of the simulator. The simulator package is implemented in 'C' language on a VAX 11/780 system.

rawabstract:
On-line arithmetic is a special class of serial arithmetic where algorithms produce results with the most significant digit first during the serial input of the operands. Speedup of computations can be achieved by overlapping or pipelining successive operations with small delays. This paper describes the design and implementation of a simulator for on-line arithmetic algorithms. The simulator was designed primarily to serve as\par (1) an experimental tool for synthesis of on-line algorithms;\par (2) a performance evaluation tool of on-line arithmetic;\par (3) an on-line calculator in solving some problems involving linear and non-linear recurrences.\par The simulator evaluates arithmetic expressions given in a highly functional form. Presently, the set of operations supported include addition, subtraction, multiplication, division, and square root. Several examples are presented in this paper to illustrate the usage of the simulator. The simulator package is implemented in 'C' language on a VAX 11/780 system.

entry:
@InProceedings{Raghavendra:1981:SLA,
  author =       "C. S. Raghavendra and M. D. Ercegovac",
  title =        "A Simulator for On-Line Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "92--98",
  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_Raghavendra_Ercegovac.pdf",
  abstract =     "On-line arithmetic is a special class of serial
                 arithmetic where algorithms produce results with the
                 most significant digit first during the serial input of
                 the operands. Speedup of computations can be achieved
                 by overlapping or pipelining successive operations with
                 small delays. This paper describes the design and
                 implementation of a simulator for on-line arithmetic
                 algorithms. The simulator was designed primarily to
                 serve as\par

                 (1) an experimental tool for synthesis of on-line
                 algorithms;\par

                 (2) a performance evaluation tool of on-line
                 arithmetic;\par

                 (3) an on-line calculator in solving some problems
                 involving linear and non-linear recurrences.\par

                 The simulator evaluates arithmetic expressions given in
                 a highly functional form. Presently, the set of
                 operations supported include addition, subtraction,
                 multiplication, division, and square root. Several
                 examples are presented in this paper to illustrate the
                 usage of the simulator. The simulator package is
                 implemented in 'C' language on a VAX 11/780 system.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1981:AFF
author: T. R. N. Rao
title: Arithmetic of Finite Fields
crossref: IEEE:1981:PSC
pages: 2--5
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_Rao.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: T. R. N. Rao
rawtitle: Arithmetic of Finite Fields
abstract:
The arithmetic operations in finite fields and their implementation are important to the construction of error detecting and correcting codes. The addition, multiplication and division in the field $ mathrm GF(2^m) $ are implemented as polynomial operations using binary logic of flip-flops and EXOR's. For fields of nonbinary characteristic, modular arithmetic (with modulus $p$, a prime) becomes important. This paper focuses on problems relating to the arithmetic of $ mathrm GF(p) $, and some recent results and new ideas on this topic are presented here.

rawabstract:
The arithmetic operations in finite fields and their implementation are important to the construction of error detecting and correcting codes. The addition, multiplication and division in the field $ \mathrm {GF}(2^m) $ are implemented as polynomial operations using binary logic of flip-flops and EXOR's. For fields of nonbinary characteristic, modular arithmetic (with modulus $p$, a prime) becomes important. This paper focuses on problems relating to the arithmetic of $ \mathrm {GF}(p) $, and some recent results and new ideas on this topic are presented here.

entry:
@InProceedings{Rao:1981:AFF,
  author =       "T. R. N. Rao",
  title =        "Arithmetic of Finite Fields",
  crossref =     "IEEE:1981:PSC",
  pages =        "2--5",
  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_Rao.pdf",
  abstract =     "The arithmetic operations in finite fields and their
                 implementation are important to the construction of
                 error detecting and correcting codes. The addition,
                 multiplication and division in the field $ \mathrm
                 {GF}(2^m) $ are implemented as polynomial operations
                 using binary logic of flip-flops and EXOR's. For fields
                 of nonbinary characteristic, modular arithmetic (with
                 modulus $p$, a prime) becomes important. This paper
                 focuses on problems relating to the arithmetic of $
                 \mathrm {GF}(p) $, and some recent results and new
                 ideas on this topic are presented here.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1981:CHC
author: T. M. Rao and R. T. Gregory
title: The Conversion of Hensel Codes to Rational Numbers
crossref: IEEE:1981:PSC
pages: 10--14
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_Rao_Gregory.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: T. M. Rao and R. T. Gregory
rawtitle: The Conversion of {Hensel} Codes to Rational Numbers
abstract:
In a finite-segment p-adic number system one of the difficult problems is concerned with converting Hensel codes back into rational numbers. An algorithm for this conversion is proposed which is based on a sophisticated table look-up procedure.

rawabstract:
In a finite-segment p-adic number system one of the difficult problems is concerned with converting Hensel codes back into rational numbers. An algorithm for this conversion is proposed which is based on a sophisticated table look-up procedure.

entry:
@InProceedings{Rao:1981:CHC,
  author =       "T. M. Rao and R. T. Gregory",
  title =        "The Conversion of {Hensel} Codes to Rational Numbers",
  crossref =     "IEEE:1981:PSC",
  pages =        "10--14",
  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_Rao_Gregory.pdf",
  abstract =     "In a finite-segment p-adic number system one of the
                 difficult problems is concerned with converting Hensel
                 codes back into rational numbers. An algorithm for this
                 conversion is proposed which is based on a
                 sophisticated table look-up procedure.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Redinbo:1981:SRN
author: G. Redinbo and W. Hunnebeck
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '81
title: On the simulation of residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 339--342
year: 1981
DOI: https://doi.org/10.1049/el:19800468
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: G. Redinbo and W. Hunnebeck
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '81}
rawtitle: On the simulation of residue number systems
entry:
@InProceedings{Redinbo:1981:SRN,
  author =       "G. Redinbo and W. Hunnebeck",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '81}",
  title =        "On the simulation of residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "339--342",
  year =         "1981",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19800468",
  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 =      "It is sometimes difficult to simulate on general
                 purpose computers the performance of digital systems
                 that use residue number systems. This paper
                 demonstrates a new technique that makes effective use
                 of a Fast Fourier Transform (FFT) to simulate the
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Robertson:1981:SAD
author: J. E. Robertson
title: A Systematic Approach to the Design of Structures for Arithmetic
crossref: IEEE:1981:PSC
pages: 35--41
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_Robertson.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: J. E. Robertson
rawtitle: A Systematic Approach to the Design of Structures for Arithmetic
abstract:
A design tool for the decomposition of binary digital structures for addition and subtraction has been developed. A simplified theory reduces a complex structure to a collection of basic structures of one type, namely, a full adder. The simplified theory is applicable to the design of parallel counters and array multipliers. A general theory is used for decomposition to three types of basic structures, whose complexity is usually on the order of a half-adder. The general theory is applicable to redundant array multipliers and signed-digit adders.

rawabstract:
A design tool for the decomposition of binary digital structures for addition and subtraction has been developed. A simplified theory reduces a complex structure to a collection of basic structures of one type, namely, a full adder. The simplified theory is applicable to the design of parallel counters and array multipliers. A general theory is used for decomposition to three types of basic structures, whose complexity is usually on the order of a half-adder. The general theory is applicable to redundant array multipliers and signed-digit adders.

entry:
@InProceedings{Robertson:1981:SAD,
  author =       "J. E. Robertson",
  title =        "A Systematic Approach to the Design of Structures for
                 Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "35--41",
  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_Robertson.pdf",
  abstract =     "A design tool for the decomposition of binary digital
                 structures for addition and subtraction has been
                 developed. A simplified theory reduces a complex
                 structure to a collection of basic structures of one
                 type, namely, a full adder. The simplified theory is
                 applicable to the design of parallel counters and array
                 multipliers. A general theory is used for decomposition
                 to three types of basic structures, whose complexity is
                 usually on the order of a half-adder. The general
                 theory is applicable to redundant array multipliers and
                 signed-digit adders.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Rodrigues:1981:HEM
author: M. R. D. Rodrigues and J. H. P. Zurawski and J. B. Gosling
title: Hardware evaluation of mathematical functions
journal: j-IEE-PROC-E
volume: 128
number: 4
pages: 155--164
month: jul
monthnumber: 7
year: 1981
CODEN: IPETD3
ISSN: 0143-7062 OR 01437062
bibdate: Thu Sep 1 10:15:39 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:39 ???
fjournal: IEE proceedings, E: Computers and digital techniques
acknowledgement: ack-nj
rawauthor: M. R. D. Rodrigues and J. H. P. Zurawski and J. B. Gosling
rawtitle: Hardware evaluation of mathematical functions
entry:
@Article{Rodrigues:1981:HEM,
  author =       "M. R. D. Rodrigues and J. H. P. Zurawski and J. B.
                 Gosling",
  title =        "Hardware evaluation of mathematical functions",
  journal =      j-IEE-PROC-E,
  volume =       "128",
  number =       "4",
  pages =        "155--164",
  month =        jul,
  year =         "1981",
  CODEN =        "IPETD3",
  ISSN =         "0143-7062",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEE proceedings, E: Computers and digital techniques",
}


bibtype: inproceedings
filename: fparith.bib
label: Rutenbar:1981:CSV
author: R. A. Rutenbar and Y. E. Park
title: Case Study of a VLSI Design Project: a Simple Inner Product Machine
crossref: IEEE:1981:PSC
pages: 184--189
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_Rutenbar_Park.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: R. A. Rutenbar and Y. E. Park
rawtitle: Case Study of a {VLSI} Design Project: a Simple Inner Product Machine
abstract:
We present a case study of the application of recently evolved structured VLSI design methodologies to the design and implementation of a simple VLSI quasi-serial inner product machine.

rawabstract:
We present a case study of the application of recently evolved structured VLSI design methodologies to the design and implementation of a simple VLSI quasi-serial inner product machine.

entry:
@InProceedings{Rutenbar:1981:CSV,
  author =       "R. A. Rutenbar and Y. E. Park",
  title =        "Case Study of a {VLSI} Design Project: a Simple Inner
                 Product Machine",
  crossref =     "IEEE:1981:PSC",
  pages =        "184--189",
  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_Rutenbar_Park.pdf",
  abstract =     "We present a case study of the application of recently
                 evolved structured VLSI design methodologies to the
                 design and implementation of a simple VLSI quasi-serial
                 inner product machine.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Schonfelder:1981:ECP
author: J. L. Schonfelder and M. Razaz
title: Error control with polynomial approximations
journal: j-IMA-J-NUMER-ANAL
volume: 1
number: 1
pages: 105--114
year: 1981
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65D15
MRnumber: 83d:65043, 607250
bibdate: Sat Dec 23 17:06:35 MST 2000
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: J. L. Schonfelder and M. Razaz
rawtitle: Error control with polynomial approximations
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; MathSciNet database

entry:
@Article{Schonfelder:1981:ECP,
  author =       "J. L. Schonfelder and M. Razaz",
  title =        "Error control with polynomial approximations",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "1",
  number =       "1",
  pages =        "105--114",
  year =         "1981",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65D15",
  MRnumber =     "83d:65043, 607250",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}


bibtype: techreport
filename: fparith.bib
label: Schryer:1981:TCF
author: N. L. Schryer
title: A Test of a Computer's Floating-Point Arithmetic Unit
number: Computer Science Technical Report 89
institution: AT&T Bell Laboratories
pages: 66
month: feb
monthnumber: 2
year: 1981
bibdate: Fri Nov 30 11:20:24 2001
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.11.30 11:20:24 ???
URL: http://plan9.bell-labs.com/cm/cs/cstr/89.ps.gz; http://www.bell-labs.com/topic/swdist/
keywords: floating-point testing
acknowledgement: ack-nj
rawauthor: N. L. Schryer
rawtitle: A Test of a Computer's Floating-Point Arithmetic Unit
entry:
@TechReport{Schryer:1981:TCF,
  author =       "N. L. Schryer",
  title =        "A Test of a Computer's Floating-Point Arithmetic
                 Unit",
  number =       "Computer Science Technical Report 89",
  institution =  "AT\&T Bell Laboratories",
  pages =        "66",
  month =        feb,
  year =         "1981",
  bibdate =      "Fri Nov 30 11:20:24 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://plan9.bell-labs.com/cm/cs/cstr/89.ps.gz;
                 http://www.bell-labs.com/topic/swdist/",
  acknowledgement = ack-nj,
  keywords =     "floating-point testing",
}


bibtype: article
filename: fparith.bib
label: Schwarz:1981:EYC
author: H. R. Schwarz
title: The Early Years of Computing in Switzerland
journal: j-ANN-HIST-COMPUT
volume: 3
number: 2
pages: 121--132
month: apr
monthnumber: 4
year: 1981
CODEN: AHCOE5
ISSN: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.01 15:29:18 MST
fjournal: Annals of the History of Computing
subject: K. Computing Milieux; K.2 HISTORY OF COMPUTING
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
reviewer: D. Ross
rawauthor: H. R. Schwarz
rawtitle: The Early Years of Computing in {Switzerland}
URL:
http://dlib.computer.org/an/books/an1981/pdf/a2121.pdf; http://www.computer.org/annals/an1981/a2121abs.htm

entry:
@Article{Schwarz:1981:EYC,
  author =       "H. R. Schwarz",
  title =        "The Early Years of Computing in {Switzerland}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "3",
  number =       "2",
  pages =        "121--132",
  month =        apr # "\slash " # jun,
  year =         "1981",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  bibdate =      "Fri Nov 1 15:29:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1981/pdf/a2121.pdf;
                 http://www.computer.org/annals/an1981/a2121abs.htm",
  acknowledgement = ack-nhfb,
  catcode =      "K; K.2; K.2; K.2",
  content =      "Schwartz describes two early computers used at the
                 Swiss Federal Institute of Technology (whose German
                 acronym is ETH) during the 1950s. Despite the more
                 general title, he does not mention any non-ETH
                 computers in this article. According to Schwartz, the
                 first programmable computer in Switzerland was the Z4
                 developed by Konrad Zuse in Germany during World War II
                 and installed at the ETH in 1950. Except for the ERMETH
                 (also at the ETH), he does not mention any subsequent
                 Swiss installations during the period, leaving a weak
                 implication that there were none.\par

                 The Z4 was an electromechanical machine with a total
                 data memory of 64 32-bit words and no program memory.
                 Programs were executed while being read from punched
                 tape. Conditional test instructions permitted
                 instructions on the tape to be skipped; other control
                 instructions caused an alternate tape reader to begin
                 processing a program (a form of subroutine-call). The
                 arithmetic unit could perform true floating-point
                 operations. This arithmetic unit contained built-in
                 functions for computing squares, reciprocals, and
                 square roots. (Ten years later, mere integer division
                 was still optional at an extra cost on the IBM 1401.)
                 There were special representations for infinity and
                 ``undefined'' so that operations such as division by
                 zero could continue without interruption but with a
                 meaningful result.",
  CRclass =      "K.2.7 ERMETH; K.2 Hardware; K.2 Software",
  CRnumber =     "39473",
  descriptor =   "Computing Milieux, HISTORY OF COMPUTING; Computing
                 Milieux, HISTORY OF COMPUTING, ERMETH; Computing
                 Milieux, HISTORY OF COMPUTING, Hardware; Computing
                 Milieux, HISTORY OF COMPUTING, Software",
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
  reviewer =     "D. Ross",
  subject =      "K. Computing Milieux; K.2 HISTORY OF COMPUTING",
}


bibtype: article
filename: fparith.bib
label: Smith:1981:ERA
author: J. M. Smith and F. W. J. Olver and D. W. Lozier
title: Extended-Range Arithmetic and Normalized Legendre Polynomials
journal: j-TOMS
volume: 7
number: 1
pages: 93--105
month: mar
monthnumber: 3
year: 1981
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355934.355940
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65G05)
MRnumber: 83a:65017
bibdate: Mon Aug 29 22:02:12 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.29 22:02:12 ???
URL: http://doi.acm.org/10.1145/355934.355940
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: angular momentum; extended-range arithmetic; Legendre polynomials; overflow; underflow
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: J. M. Smith and F. W. J. Olver and D. W. Lozier
rawtitle: Extended-Range Arithmetic and Normalized {Legendre} Polynomials
entry:
@Article{Smith:1981:ERA,
  author =       "J. M. Smith and F. W. J. Olver and D. W. Lozier",
  title =        "Extended-Range Arithmetic and Normalized {Legendre}
                 Polynomials",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "93--105",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355940",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65G05)",
  MRnumber =     "83a:65017",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/355934.355940",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "angular momentum; extended-range arithmetic; Legendre
                 polynomials; overflow; underflow",
}


bibtype: book
filename: fparith.bib
label: Spaniol:1981:CAL
author: Otto Spaniol
title: Computer Arithmetic: Logic and Design
publisher: pub-WILEY
address: pub-WILEY:adr
pages: 280
year: 1981
ISBN: 0-471-27926-9 OR 0471279269
ISBN13: 978-0-471-27926-6 OR 9780471279266
LCCN: QA76.6 .S6613, TK7888.3.S7
bibdate: Thu Sep 01 22:26:58 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 22:26:58 ???
note: English translation of cite Spaniol:1976:AR.
acknowledgement: ack-nhfb
rawauthor: Otto Spaniol
rawnote: English translation of \cite{Spaniol:1976:AR}.
rawtitle: Computer Arithmetic: Logic and Design
entry:
@Book{Spaniol:1981:CAL,
  author =       "Otto Spaniol",
  title =        "Computer Arithmetic: Logic and Design",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "280",
  year =         "1981",
  ISBN =         "0-471-27926-9",
  ISBN-13 =      "978-0-471-27926-6",
  LCCN =         "QA76.6 .S6613, TK7888.3.S7",
  bibdate =      "Thu Sep 01 22:26:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation of \cite{Spaniol:1976:AR}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Stevenson:1981:ITP
author: David Stevenson
title: IEEE Task 754: a Proposed Standard for Binary Floating-Point Arithmetic: Draft 8.0
journal: j-COMPUTER
volume: 14
number: 3
pages: 51--62
month: mar
monthnumber: 3
year: 1981
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Thu Sep 1 10:14:17 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:17 ???
fjournal: Computer
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: David Stevenson
rawtitle: {IEEE Task 754}: a Proposed Standard for Binary Floating-Point Arithmetic: Draft 8.0
annote:
Offered here for public comment, this proposed standard facilitates transportation of numerically oriented programs and encourages development of high-quality numerical software.

entry:
@Article{Stevenson:1981:ITP,
  author =       "David Stevenson",
  title =        "{IEEE Task 754}: a Proposed Standard for Binary
                 Floating-Point Arithmetic: Draft 8.0",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "51--62",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Sep 1 10:14:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  annote =       "Offered here for public comment, this proposed
                 standard facilitates transportation of numerically
                 oriented programs and encourages development of
                 high-quality numerical software.",
  country =      "USA",
  date =         "30/10/88",
  descriptors =  "Standardization; computer arithmetic; IEEE 754;
                 floating point; computation structure; numerical
                 software",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: article
filename: fparith.bib
label: Stevenson:1981:PSBa
author: David Stevenson
title: A Proposed Standard for Binary Floating-Point Arithmetic
journal: j-COMPUTER
volume: 14
number: 3
pages: 51--62
month: mar
monthnumber: 3
year: 1981
CODEN: CPTRB4
DOI: https://doi.org/10.1109/C-M.1981.220377
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Sun May 2 09:21:54 1999
bibtimestamp: 1999.05.02 09:21:54 ???
note: See cite IEEE:1985:AIS,IEEE:1985:ASI.
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: David Stevenson
rawnote: See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.
rawtitle: A Proposed Standard for Binary Floating-Point Arithmetic
bibsource:
Distributed/QLD.bib; Distributed/QLD/1981.bib; https://www.math.utah.edu/pub/tex/bib/computer1980.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

annote:
Offered here for public comment, this proposed standard facilitates transportation of numerically oriented programs and encourages development of high-quality numerical software.

entry:
@Article{Stevenson:1981:PSBa,
  author =       "David Stevenson",
  title =        "A Proposed Standard for Binary Floating-Point
                 Arithmetic",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "51--62",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220377",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sun May 2 09:21:54 1999",
  bibsource =    "Distributed/QLD.bib; Distributed/QLD/1981.bib;
                 https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  annote =       "Offered here for public comment, this proposed
                 standard facilitates transportation of numerically
                 oriented programs and encourages development of
                 high-quality numerical software.",
  country =      "USA",
  date =         "30/10/88",
  descriptors =  "Standardization; computer arithmetic; IEEE 754;
                 floating point; computation structure; numerical
                 software",
  enum =         "2967",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  location =     "PKI-OG: Li-Ord.Le; RWTH-AC-DFV: Bibl.",
  references =   "0",
  revision =     "21/04/91",
}


bibtype: book
filename: fparith.bib
label: Stevenson:1981:PSBb
author: David Stevenson
title: A proposed standard for binary floating-point arithmetic: draft 8.0 of IEEE Task P754
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 36
year: 1981
bibdate: Sun May 02 09:22:07 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.05.02 09:22:07 ???
note: See cite IEEE:1985:AIS,IEEE:1985:ASI.
keywords: Compiling (Electronic computers).; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: David Stevenson
rawnote: See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.
rawtitle: A proposed standard for binary floating-point arithmetic: draft 8.0 of {IEEE} Task {P754}
remark:
Reprinted from: Computer, v. 14, no. 3 (Mar. 1981): 51--87. Includes articles by W.J. Cody, David Hough, and Jerome T. Coonen.

entry:
@Book{Stevenson:1981:PSBb,
  author =       "David Stevenson",
  title =        "A proposed standard for binary floating-point
                 arithmetic: draft 8.0 of {IEEE} Task {P754}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "36",
  year =         "1981",
  bibdate =      "Sun May 02 09:22:07 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nhfb,
  keywords =     "Compiling (Electronic computers).; Floating-point
                 arithmetic.",
  remark =       "Reprinted from: Computer, v. 14, no. 3 (Mar. 1981):
                 51--87. Includes articles by W.J. Cody, David Hough,
                 and Jerome T. Coonen.",
}


bibtype: inproceedings
filename: fparith.bib
label: Stummel:1981:PAM
author: F. Stummel
title: Optimal error estimates for Gaussian elimination in floating-point arithmetic
crossref: GAMM:1981:PAM
journal: j-Z-ANGE-MATH-MECH
volume: 62
number: 5
pages: T355--T357
year: 1981
CODEN: ZAMMAX
ISSN: 0044-2267 (print), 1521-4001 (electronic) OR 00442267 (print), 15214001 (electronic)
ISSNL: 0044-2267 OR 00442267
MRclass: 65G05 (65F10)
MRnumber: 84j:65039
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: Zeitschrift fur Angewandte Mathematik und Mechanik
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001
rawauthor: F. Stummel
rawtitle: Optimal error estimates for {Gaussian} elimination in floating-point arithmetic
entry:
@InProceedings{Stummel:1981:PAM,
  author =       "F. Stummel",
  title =        "Optimal error estimates for {Gaussian} elimination in
                 floating-point arithmetic",
  crossref =     "GAMM:1981:PAM",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "62",
  number =       "5",
  pages =        "T355--T357",
  year =         "1981",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  MRclass =      "65G05 (65F10)",
  MRnumber =     "84j:65039",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
}


bibtype: inproceedings
filename: fparith.bib
label: Tan:1981:ADC
author: C.-I. Tan and B. C. McInnis
booktitle: 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes
title: Adaptive digital control implemented using residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 808--812
year: 1981
DOI: https://doi.org/10.1109/CDC.1981.269326
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: C.-I. Tan and B. C. McInnis
rawbooktitle: 20th {IEEE} Conference on Decision and Control including the Symposium on Adaptive Processes
rawtitle: Adaptive digital control implemented using residue number systems
entry:
@InProceedings{Tan:1981:ADC,
  author =       "C.-I. Tan and B. C. McInnis",
  booktitle =    "20th {IEEE} Conference on Decision and Control
                 including the Symposium on Adaptive Processes",
  title =        "Adaptive digital control implemented using residue
                 number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "808--812",
  year =         "1981",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/CDC.1981.269326",
  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 =      "The application of residue number systems for the
                 implementation of adaptive digital controllers is
                 presented. Division operations are avoided through the
                 use of iteration to solve for the value of the control.
                 Decoding computations are simplified \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Taylor:1981:CHD
author: George S. Taylor
title: Compatible hardware for division and square root
crossref: IEEE:1981:PSC
pages: 127--134
year: 1981
bibdate: Mon Sep 16 16:30:51 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:30:51 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf
keywords: ARITH-5; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: George S. Taylor
rawtitle: Compatible hardware for division and square root
abstract:
Hardware for radix four division and radix two square root is shared in a processor designed to implement the proposed IEEE floating-point standard. The division hardware looks ahead to find the next quotient digit in parallel with the next partial remainder. An 8-bit ALU estimates the next remainder's leading bits. The quotient digit look-up table is addressed with a truncation of the estimate rather than a truncation of the full partial remainder. The estimation ALU and the look-up table are asymmetric for positive and negative remainders. This asymmetry reduces the width of the ALU and the number of minterms in the logic equations for the look-up table. The square root algorithm obtains the correctly rounded result in about two division times using small extensions to the division hardware.

rawabstract:
Hardware for radix four division and radix two square root is shared in a processor designed to implement the proposed IEEE floating-point standard. The division hardware looks ahead to find the next quotient digit in parallel with the next partial remainder. An 8-bit ALU estimates the next remainder's leading bits. The quotient digit look-up table is addressed with a truncation of the estimate rather than a truncation of the full partial remainder. The estimation ALU and the look-up table are asymmetric for positive and negative remainders. This asymmetry reduces the width of the ALU and the number of minterms in the logic equations for the look-up table. The square root algorithm obtains the correctly rounded result in about two division times using small extensions to the division hardware.

entry:
@InProceedings{Taylor:1981:CHD,
  author =       "George S. Taylor",
  title =        "Compatible hardware for division and square root",
  crossref =     "IEEE:1981:PSC",
  pages =        "127--134",
  year =         "1981",
  bibdate =      "Mon Sep 16 16:30:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf",
  abstract =     "Hardware for radix four division and radix two square
                 root is shared in a processor designed to implement the
                 proposed IEEE floating-point standard. The division
                 hardware looks ahead to find the next quotient digit in
                 parallel with the next partial remainder. An 8-bit ALU
                 estimates the next remainder's leading bits. The
                 quotient digit look-up table is addressed with a
                 truncation of the estimate rather than a truncation of
                 the full partial remainder. The estimation ALU and the
                 look-up table are asymmetric for positive and negative
                 remainders. This asymmetry reduces the width of the ALU
                 and the number of minterms in the logic equations for
                 the look-up table. The square root algorithm obtains
                 the correctly rounded result in about two division
                 times using small extensions to the division
                 hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; correct rounding; floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Taylor:1981:FPR
author: Fred J. Taylor and Chao H. Huang
title: A floating-point residue arithmetic unit
journal: j-J-FRANKLIN-INST
volume: 311
number: 1
pages: 33--53
month: jan
monthnumber: 1
year: 1981
CODEN: JFINAB
ISSN: 0016-0032 (print), 1879-2693 (electronic) OR 00160032 (print), 18792693 (electronic)
ISSNL: 0016-0032 OR 00160032
MRclass: 94A11 (68A05)
MRnumber: 82a:94013
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Journal of The Franklin Institute
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00160032
reviewer: B. Hazeltine; Hazeltine, B
rawauthor: Fred J. Taylor and Chao H. Huang
rawtitle: A floating-point residue arithmetic unit
subject:
B. Hardware; B.2 ARITHMETIC AND LOGIC STRUCTURES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Taylor:1981:FPR,
  author =       "Fred J. Taylor and Chao H. Huang",
  title =        "A floating-point residue arithmetic unit",
  journal =      j-J-FRANKLIN-INST,
  volume =       "311",
  number =       "1",
  pages =        "33--53",
  month =        jan,
  year =         "1981",
  CODEN =        "JFINAB",
  ISSN =         "0016-0032 (print), 1879-2693 (electronic)",
  ISSN-L =       "0016-0032",
  MRclass =      "94A11 (68A05)",
  MRnumber =     "82a:94013",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "B.2; G.1.0",
  content =      "This paper describes the logical design of a floating
                 point arithmetic unit using a hybrid residue number
                 system. Mantissas of numbers are operated in a residue
                 system while the exponents are in binary. Some basic
                 operations, such as scaling and underflow/overflow
                 detection, are described, and circuit implementation
                 using ROMs indicated. ``For example, let m(z)` be a
                 2N-bit work in integer form and H_0 and H_1 represent
                 the two following hypotheses. If m(z`) e H_1, then
                 m(z`) W 1-2- 2^2N = 2^2N 1. If m(z)` e H_0, then m(z)`
                 < 1-2- 2^2N = 2^2N 1. The hypothesis testing is
                 accomplished by comparing each of the mixed-radix
                 digits of m(z)` to that of 2^2N 1 through L independent
                 binary comparators.'' Circuits for multiplication,
                 addition, and subtraction are derived. The procedures
                 seem reasonable and the proofs rigorous. Table look up
                 cycle times and memory requirements for different
                 implementation of the arithmetic units are estimated.
                 These are comparable with corresponding times and
                 memory needs for PDP/11. Use in algorithms such as FFT
                 is argued for.\par

                 The exposition is somewhat difficult. As with many
                 logical designs one is not sure whether the approach
                 given is optimum (for any sense of the word
                 ``optimum''). In the absence of a working system one
                 can not be sure",
  CRclass =      "B.2.1 Design Styles; G.1.0 General; G.1.0 Computer
                 arithmetic",
  CRnumber =     "39211",
  descriptor =   "Hardware, ARITHMETIC AND LOGIC STRUCTURES, Design
                 Styles; Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic",
  fjournal =     "Journal of {The Franklin Institute}",
  genterm =      "DESIGN",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00160032",
  reviewer =     "B. Hazeltine; Hazeltine, B",
  subject =      "B. Hardware; B.2 ARITHMETIC AND LOGIC STRUCTURES; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: inproceedings
filename: fparith.bib
label: Taylor:1981:VHP
author: George S. Taylor and David A. Patterson
title: VAX Hardware for the Proposed IEEE Floating-Point Standard
crossref: IEEE:1981:PSC
pages: 190--196
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_Taylor_Patterson.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: George S. Taylor and David A. Patterson
rawtitle: {VAX} Hardware for the Proposed {IEEE} Floating-Point Standard
abstract:
The proposed IEEE floating-point standard has been implemented in a substitute floating-point accelerator for the VAX-11/760. We explain how features of the proposed standard influenced the design of the new processor. By comparing it with the original VAX accelerator, we illustrate the differences between hardware for the proposed standard and hardware for a more traditional floating-point architecture.

rawabstract:
The proposed IEEE floating-point standard has been implemented in a substitute floating-point accelerator for the VAX-11/760. We explain how features of the proposed standard influenced the design of the new processor. By comparing it with the original VAX accelerator, we illustrate the differences between hardware for the proposed standard and hardware for a more traditional floating-point architecture.

entry:
@InProceedings{Taylor:1981:VHP,
  author =       "George S. Taylor and David A. Patterson",
  title =        "{VAX} Hardware for the Proposed {IEEE} Floating-Point
                 Standard",
  crossref =     "IEEE:1981:PSC",
  pages =        "190--196",
  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_Taylor_Patterson.pdf",
  abstract =     "The proposed IEEE floating-point standard has been
                 implemented in a substitute floating-point accelerator
                 for the VAX-11/760. We explain how features of the
                 proposed standard influenced the design of the new
                 processor. By comparing it with the original VAX
                 accelerator, we illustrate the differences between
                 hardware for the proposed standard and hardware for a
                 more traditional floating-point architecture.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Todericiu:1981:AOBb
author: Doru Todericiu
journal: j-REV-HIST-SCI
volume: 34
number: 3--4
pages: 374--374
month: juillet--octobre
year: 1981
CODEN: RHSAAM
DOI: https://doi.org/10.2307/23632469
ISSN: 0151-4105 (print), 1969-6582 (electronic) OR 01514105 (print), 19696582 (electronic)
ISSNL: 0048-7996 OR 00487996
bibdate: Tue Jun 16 11:06:47 MDT 2015
bibtimestamp: 2015.06.16 11:06:47 MDT
URL: http://www.jstor.org/stable/23632469
fjournal: Revue d'Histoire des Sciences
language: French
acknowledgement: ack-nhfb
ajournal: Rev. hist. sci.
journalURL: http://www.jstor.org/journals/00487996.html; http://www.persee.fr/collection/rhs
rawauthor: Doru Todericiu
title:
Analyses d'ouvrages: booktitle Whilhelm Schickard (1592--1635), Astronom, Geograph, Orientalist, Erfinder der Rechenmaschine par Friedrich Seck

bibsource:
http://www.jstor.org/stable/i23631674; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/revhistsci.bib

rawtitle:
Analyses d'ouvrages: {{\booktitle{Whilhelm Schickard (1592--1635), Astronom, Geograph, Orientalist, Erfinder der Rechenmaschine}} par Friedrich Seck}

entry:
@Article{Todericiu:1981:AOBb,
  author =       "Doru Todericiu",
  title =        "Analyses d'ouvrages: {{\booktitle{Whilhelm Schickard
                 (1592--1635), Astronom, Geograph, Orientalist, Erfinder
                 der Rechenmaschine}} par Friedrich Seck}",
  journal =      j-REV-HIST-SCI,
  volume =       "34",
  number =       "3--4",
  pages =        "374--374",
  month =        "juillet--octobre",
  year =         "1981",
  CODEN =        "RHSAAM",
  DOI =          "https://doi.org/10.2307/23632469",
  ISSN =         "0151-4105 (print), 1969-6582 (electronic)",
  ISSN-L =       "0048-7996",
  bibdate =      "Tue Jun 16 11:06:47 MDT 2015",
  bibsource =    "http://www.jstor.org/stable/i23631674;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/revhistsci.bib",
  URL =          "http://www.jstor.org/stable/23632469",
  acknowledgement = ack-nhfb,
  ajournal =     "Rev. hist. sci.",
  fjournal =     "Revue d'Histoire des Sciences",
  journal-URL =  "http://www.jstor.org/journals/00487996.html;
                 http://www.persee.fr/collection/rhs",
  language =     "French",
}


bibtype: book
filename: fparith.bib
label: Tyner:1981:GDP
author: Paul Tyner
title: iAPX 432 General Data Processor Architecture Reference Manual
publisher: pub-INTEL
address: pub-INTEL:adr
pages: various
year: 1981
LCCN: TK7895.M5 T85 1981
bibdate: Fri Dec 08 13:03:20 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:03:20 ???
acknowledgement: ack-nhfb
rawauthor: Paul Tyner
rawtitle: {iAPX} 432 General Data Processor Architecture Reference Manual
entry:
@Book{Tyner:1981:GDP,
  author =       "Paul Tyner",
  title =        "{iAPX} 432 General Data Processor Architecture
                 Reference Manual",
  publisher =    pub-INTEL,
  address =      pub-INTEL:adr,
  pages =        "various",
  year =         "1981",
  LCCN =         "TK7895.M5 T85 1981",
  bibdate =      "Fri Dec 08 13:03:20 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}


bibtype: manual
filename: fparith.bib
label: vonGudenberg:1981:GAP
author: J. Wolff von Gudenberg
organization: Institute for Applied Mathematics, University of Karlsruhe
address: Karlsruhe, West Germany
year: 1981
bibdate: Wed Oct 13 22:27:27 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 22:27:27 ???
language: German
acknowledgement: ack-nhfb
rawauthor: J. Wolff von Gudenberg
title:
Gesamte Arithmetik des Pascal-SC Rechners. Benutzerhandbuch. (German) [Complete Arithmetic of the Pascal-SC Computer: User Handbook]

rawtitle:
{Gesamte Arithmetik des Pascal-SC Rechners. Benutzerhandbuch}. ({German}) [{Complete} Arithmetic of the {Pascal-SC} Computer: User Handbook]

entry:
@Manual{vonGudenberg:1981:GAP,
  author =       "J. Wolff von Gudenberg",
  title =        "{Gesamte Arithmetik des Pascal-SC Rechners.
                 Benutzerhandbuch}. ({German}) [{Complete} Arithmetic of
                 the {Pascal-SC} Computer: User Handbook]",
  organization = "Institute for Applied Mathematics, University of
                 Karlsruhe",
  address =      "Karlsruhe, West Germany",
  pages =        "????",
  year =         "1981",
  bibdate =      "Wed Oct 13 22:27:27 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: inproceedings
filename: fparith.bib
label: Walker:1981:EMA
author: Gregory Walker
title: Extension of the MC68000 Architecture to Include Standard Floating-Point Arithmetic
crossref: IEEE:1981:PSC
pages: 179--182
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_Walker.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Gregory Walker
rawtitle: Extension of the {MC68000} Architecture to Include Standard Floating-Point Arithmetic
abstract:
The synthetic aspect of designing a computer architecture is particularly evident when the design is highly constrained from two independent directions. Floating-point extensions of the MC68000 architecture incorporate the IEEE Proposed Floating-point Standard into the existing MC68000 architecture.

rawabstract:
The synthetic aspect of designing a computer architecture is particularly evident when the design is highly constrained from two independent directions. Floating-point extensions of the MC68000 architecture incorporate the IEEE Proposed Floating-point Standard into the existing MC68000 architecture.

entry:
@InProceedings{Walker:1981:EMA,
  author =       "Gregory Walker",
  title =        "Extension of the {MC68000} Architecture to Include
                 Standard Floating-Point Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "179--182",
  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_Walker.pdf",
  abstract =     "The synthetic aspect of designing a computer
                 architecture is particularly evident when the design is
                 highly constrained from two independent directions.
                 Floating-point extensions of the MC68000 architecture
                 incorporate the IEEE Proposed Floating-point Standard
                 into the existing MC68000 architecture.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Washington:1981:BLF
author: Lawrence C. Washington
title: Benford's Law for Fibonacci and Lucas Numbers
journal: j-FIB-QUART
volume: 19
number: 2
pages: 175--176
month: apr
monthnumber: 4
year: 1981
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:59:55 MDT 2011
bibtimestamp: 2011.10.20 17:59:55 MDT
URL: http://www.fq.math.ca/Scanned/19-2/washington.pdf
fjournal: The Fibonacci Quarterly
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Lawrence C. Washington
rawtitle: {Benford's Law} for {Fibonacci} and {Lucas} Numbers
bibsource:
http://www.fq.math.ca/19-2.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Washington:1981:BLF,
  author =       "Lawrence C. Washington",
  title =        "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "2",
  pages =        "175--176",
  month =        apr,
  year =         "1981",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:55 MDT 2011",
  bibsource =    "http://www.fq.math.ca/19-2.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: techreport
filename: fparith.bib
label: Watanuki:1981:FOAa
author: Osaaki Watanuki
institution: Computer Science Dept. Research Laboratory
address: Los Angeles, CA, USA
pages: xvi + 149
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
keywords: Differential equations, Partial.; Floating-point arithmetic.
remark: Consists of the author's thesis (Ph.D.)--UCLA, 1981. Bibliography: p. 146-149.
acknowledgement: ack-nhfb
rawauthor: Osaaki Watanuki
title:
Floating-point on-line arithmetic for highly concurrent digit-serial computation: application to mesh problems

series:
UCLA-ENG; 8107 ReRport [sic] / UCLA Computer Science Department; no. CSD 810529 Report (University of California, Los Angeles. Computer Science Dept.); no. CSD-810529

rawtitle:
Floating-point on-line arithmetic for highly concurrent digit-serial computation: application to mesh problems

entry:
@TechReport{Watanuki:1981:FOAa,
  author =       "Osaaki Watanuki",
  title =        "Floating-point on-line arithmetic for highly
                 concurrent digit-serial computation: application to
                 mesh problems",
  institution =  "Computer Science Dept. Research Laboratory",
  address =      "Los Angeles, CA, USA",
  pages =        "xvi + 149",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "UCLA-ENG; 8107 ReRport [sic] / UCLA Computer Science
                 Department; no. CSD 810529 Report (University of
                 California, Los Angeles. Computer Science Dept.); no.
                 CSD-810529",
  acknowledgement = ack-nhfb,
  keywords =     "Differential equations, Partial.; Floating-point
                 arithmetic.",
  remark =       "Consists of the author's thesis ({Ph.D.})--UCLA, 1981.
                 Bibliography: p. 146-149.",
}


bibtype: phdthesis
filename: fparith.bib
label: Watanuki:1981:FOAb
author: Osaaki Watanuki
type: Thesis (Ph.D.)
school: UCLA
address: Los Angeles, CA, USA
pages: xvi + 149
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
keywords: Differential equations, Partial.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Osaaki Watanuki
title:
Floating-point on-line arithmetic for highly concurrent digit-serial computation: application to mesh problems

entry:
@PhdThesis{Watanuki:1981:FOAb,
  author =       "Osaaki Watanuki",
  title =        "Floating-point on-line arithmetic for highly
                 concurrent digit-serial computation: application to
                 mesh problems",
  type =         "Thesis ({Ph.D.})",
  school =       "UCLA",
  address =      "Los Angeles, CA, USA",
  pages =        "xvi + 149",
  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,
  keywords =     "Differential equations, Partial.; Floating-point
                 arithmetic.",
}


bibtype: inproceedings
filename: fparith.bib
label: Watanuki:1981:FPLa
author: O. Watanuki and M. D. Ercegovac
title: Floating-point On-Line Arithmetic: Algorithms
crossref: IEEE:1981:PSC
pages: 81--86
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_Watanuki_Ercegovac_a.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: O. Watanuki and M. D. Ercegovac
rawtitle: Floating-point On-Line Arithmetic: Algorithms
abstract:
For effective application of on-line arithmetic to practical numerical problems, floating-point algorithms for on-line addition / subtraction and multiplication have been implemented by introducing the notion of quasi-normalization. Those proposed are normalized fixed-precision FLPOL (floating-point on-line) algorithms.

rawabstract:
For effective application of on-line arithmetic to practical numerical problems, floating-point algorithms for on-line addition\slash subtraction and multiplication have been implemented by introducing the notion of quasi-normalization. Those proposed are normalized fixed-precision FLPOL (floating-point on-line) algorithms.

entry:
@InProceedings{Watanuki:1981:FPLa,
  author =       "O. Watanuki and M. D. Ercegovac",
  title =        "Floating-point On-Line Arithmetic: Algorithms",
  crossref =     "IEEE:1981:PSC",
  pages =        "81--86",
  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_Watanuki_Ercegovac_a.pdf",
  abstract =     "For effective application of on-line arithmetic to
                 practical numerical problems, floating-point algorithms
                 for on-line addition\slash subtraction and
                 multiplication have been implemented by introducing the
                 notion of quasi-normalization. Those proposed are
                 normalized fixed-precision FLPOL (floating-point
                 on-line) algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: inproceedings
filename: fparith.bib
label: Watanuki:1981:FPLb
author: O. Watanuki and M. D. Ercegovac
title: Floating-point On-Line Arithmetic: Error Analysis
crossref: IEEE:1981:PSC
pages: 87--91
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_Watanuki_Ercegovac_b.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: O. Watanuki and M. D. Ercegovac
rawtitle: Floating-point On-Line Arithmetic: Error Analysis
abstract:
The properties of redundant number system in mantissa representation are studied and the range of the redundant mantissa is derived. From the range of the mantissa and the absolute error of on-line operations, the MRRE (maximum relative representation error) is defined and analyzed for redundant floating-point numbers.

rawabstract:
The properties of redundant number system in mantissa representation are studied and the range of the redundant mantissa is derived. From the range of the mantissa and the absolute error of on-line operations, the MRRE (maximum relative representation error) is defined and analyzed for redundant floating-point numbers.

entry:
@InProceedings{Watanuki:1981:FPLb,
  author =       "O. Watanuki and M. D. Ercegovac",
  title =        "Floating-point On-Line Arithmetic: Error Analysis",
  crossref =     "IEEE:1981:PSC",
  pages =        "87--91",
  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_Watanuki_Ercegovac_b.pdf",
  abstract =     "The properties of redundant number system in mantissa
                 representation are studied and the range of the
                 redundant mantissa is derived. From the range of the
                 mantissa and the absolute error of on-line operations,
                 the MRRE (maximum relative representation error) is
                 defined and analyzed for redundant floating-point
                 numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Wehringer:1981:FSA
author: A. Wehringer
title: Fliess komma-Arithmetik toenglish Floating-point Arithmetic endtoenglish
journal: Elektronikschau
volume: 5
pages: 34--36
year: 1981
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: A. Wehringer
rawtitle: {Flie{\ss}komma-Arithmetik} \toenglish {Floating-point Arithmetic} \endtoenglish
entry:
@Article{Wehringer:1981:FSA,
  author =       "A. Wehringer",
  title =        "{Flie{\ss}komma-Arithmetik} \toenglish {Floating-point
                 Arithmetic} \endtoenglish",
  journal =      "Elektronikschau",
  volume =       "5",
  pages =        "34--36",
  year =         "1981",
  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: Wehringer:1981:SBM
author: A. Wehringer
journal: Elektronikschau
volume: 10
pages: 36--37
year: 1981
bibdate: Fri Sep 16 16:30:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
acknowledgement: ack-nj
rawauthor: A. Wehringer
title:
Schnelle 16-bit-Multiplikation und Division toenglish Fast 16-bit Multiplication and Division endtoenglish 

rawtitle:
{Schnelle 16-bit-Multiplikation und Division} \toenglish {Fast 16-bit Multiplication and Division} \endtoenglish

entry:
@Article{Wehringer:1981:SBM,
  author =       "A. Wehringer",
  title =        "{Schnelle 16-bit-Multiplikation und Division}
                 \toenglish {Fast 16-bit Multiplication and Division}
                 \endtoenglish",
  journal =      "Elektronikschau",
  volume =       "10",
  pages =        "36--37",
  year =         "1981",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: manual
filename: fparith.bib
label: Weinreb:1981:LMM
author: Daniel Weinreb and David Moon
title: LISP Machine Manual
organization: MIT Artificial Intelligence Laboratory
address: Cambridge, MA, USA
edition: Third
pages: 36--37
month: mar
monthnumber: 3
year: 1981
bibdate: Wed Jan 29 17:08:51 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 17:08:51 ???
acknowledgement: ack-nhfb
rawauthor: Daniel Weinreb and David Moon
rawtitle: {LISP} Machine Manual
remark:
From cite Steele:2004:RHP: ``The number of digits printed is the `correct' number; no information present in the flonum is lost, and no extra trailing digits are printed that do not represent information in the flonum. Feeding the [printed representation] of a flonum back to the reader is always supposed to produce an equal flonum.''

entry:
@Manual{Weinreb:1981:LMM,
  author =       "Daniel Weinreb and David Moon",
  title =        "{LISP} Machine Manual",
  organization = "MIT Artificial Intelligence Laboratory",
  address =      "Cambridge, MA, USA",
  edition =      "Third",
  month =        mar,
  year =         "1981",
  bibdate =      "Wed Jan 29 17:08:51 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``The number of digits
                 printed is the `correct' number; no information present
                 in the flonum is lost, and no extra trailing digits are
                 printed that do not represent information in the
                 flonum. Feeding the [printed representation] of a
                 flonum back to the reader is always supposed to produce
                 an equal flonum.''",
}


bibtype: inproceedings
filename: fparith.bib
label: Willoner:1981:AME
author: Robert Willoner and I-Ngo Chen
title: An Algorithm for Modular Exponentiation
crossref: IEEE:1981:PSC
pages: 135--138
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_Willoner_Chen.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: Robert Willoner and I-Ngo Chen
rawtitle: An Algorithm for Modular Exponentiation
abstract:
The best known algorithm for em modular exponentiation, $ M^e bmod t $ for arbitrary $M$, $e$, and $t$ is of $ O(n^3) $ where $n$ is the number ot bits in the largest of $M$, $e$ and $t$. This paper presents an $ O(n) $ algorithm for the problem where $ M^e bmod t $ is required for many values of $M$ and $e$ with constant $t$. Some preprocessing is done on $t$, and the results are applied repeatedly to different values of $M$ and $e$. The main algorithm involves em on-line arithmetic in a em redundant number system. An immediate application is in encoding / decoding of messages in an RSA-based em public-key cryptosystem.

rawabstract:
The best known algorithm for {\em modular exponentiation}, $ M^e \bmod t $ for arbitrary $M$, $e$, and $t$ is of $ O(n^3) $ where $n$ is the number ot bits in the largest of $M$, $e$ and $t$. This paper presents an $ O(n) $ algorithm for the problem where $ M^e \bmod t $ is required for many values of $M$ and $e$ with constant $t$. Some preprocessing is done on $t$, and the results are applied repeatedly to different values of $M$ and $e$. The main algorithm involves {\em on-line} arithmetic in a {\em redundant} number system. An immediate application is in encoding\slash decoding of messages in an RSA-based {\em public-key cryptosystem}.

entry:
@InProceedings{Willoner:1981:AME,
  author =       "Robert Willoner and I-Ngo Chen",
  title =        "An Algorithm for Modular Exponentiation",
  crossref =     "IEEE:1981:PSC",
  pages =        "135--138",
  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_Willoner_Chen.pdf",
  abstract =     "The best known algorithm for {\em modular
                 exponentiation}, $ M^e \bmod t $ for arbitrary $M$,
                 $e$, and $t$ is of $ O(n^3) $ where $n$ is the number
                 ot bits in the largest of $M$, $e$ and $t$. This paper
                 presents an $ O(n) $ algorithm for the problem where $
                 M^e \bmod t $ is required for many values of $M$ and
                 $e$ with constant $t$. Some preprocessing is done on
                 $t$, and the results are applied repeatedly to
                 different values of $M$ and $e$. The main algorithm
                 involves {\em on-line} arithmetic in a {\em redundant}
                 number system. An immediate application is in
                 encoding\slash decoding of messages in an RSA-based
                 {\em public-key cryptosystem}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: fparith.bib
label: Zurawski:1981:DHS
author: J. H. P. Zurawski and J. B. Gosling
title: Design of High-Speed Digital Divider Units
journal: j-IEEE-TRANS-COMPUT
volume: C-30
number: 9
pages: 691--699
month: sep
monthnumber: 9
year: 1981
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1981.1675869
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 18:45:22 MDT 2011
bibtimestamp: 2011.07.10 18:45:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675869
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. H. P. Zurawski and J. B. Gosling
rawtitle: Design of High-Speed Digital Divider Units
entry:
@Article{Zurawski:1981:DHS,
  author =       "J. H. P. Zurawski and J. B. Gosling",
  title =        "Design of High-Speed Digital Divider Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-30",
  number =       "9",
  pages =        "691--699",
  month =        sep,
  year =         "1981",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1981.1675869",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 18:45:22 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=1675869",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: incollection
filename: fparith.bib
label: Aiken:1982:ASC
author: Howard H. Aiken and Grace M. Hopper
title: The Automatic Sequence Controlled Calculator (1946)
crossref: Randell:1982:ODC
pages: 203--222
year: 1982
bibdate: Sun Nov 03 08:36:11 2002
bibtimestamp: 2002.11.03 08:36:11 ???
acknowledgement: ack-nhfb
rawauthor: Howard H. Aiken and Grace M. Hopper
rawtitle: The Automatic Sequence Controlled Calculator (1946)
bibsource:
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@InCollection{Aiken:1982:ASC,
  author =       "Howard H. Aiken and Grace M. Hopper",
  title =        "The Automatic Sequence Controlled Calculator (1946)",
  crossref =     "Randell:1982:ODC",
  pages =        "203--222",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Andrews:1982:MMS
author: M. Andrews
title: Mathematical Microprocessor Software: a $ sqrt (x) $ Comparison
journal: j-IEEE-MICRO
volume: 2
number: 3
pages: 63--79
month: jul
monthnumber: 7
year: 1982
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1982.290970
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
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: IEEE Micro
acknowledgement: ack-nj
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: M. Andrews
rawtitle: Mathematical Microprocessor Software: a $ \sqrt (x) $ Comparison
entry:
@Article{Andrews:1982:MMS,
  author =       "M. Andrews",
  title =        "Mathematical Microprocessor Software: a $ \sqrt (x) $
                 Comparison",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "3",
  pages =        "63--79",
  month =        jul # "\slash " # sep,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.290970",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  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 =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: article
filename: fparith.bib
label: Andrews:1982:SRX
author: M. Andrews
title: Square-Root-X Comparison --- New Results Discovered --- Reply
journal: j-IEEE-MICRO
volume: 2
number: 4
pages: 5--6
month: oct
monthnumber: 10
year: 1982
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1982.291010
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Science Citation Index database (1980--2000)
bibtimestamp: 2000.12.14 06:08:58 MST
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: M. Andrews
rawtitle: Square-Root-{X} Comparison --- New Results Discovered --- Reply
entry:
@Article{Andrews:1982:SRX,
  author =       "M. Andrews",
  title =        "Square-Root-{X} Comparison --- New Results Discovered
                 --- Reply",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "4",
  pages =        "5--6",
  month =        oct # "\slash " # dec,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.291010",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1982:ARBf
author: Anonymous
journal: j-MICROPROC-MICROSYS
volume: 6
number: 9
pages: 497--498
month: nov
monthnumber: 11
year: 1982
CODEN: MIMID5
DOI: https://doi.org/10.1016/0141-9331(82)90515-4
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
bibdate: Mon Jan 14 21:50:13 MST 2013
bibtimestamp: 2013.01.14 21:50:13 MST
URL: http://www.sciencedirect.com/science/article/pii/0141933182905154
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nhfb
rawauthor: Anonymous
title:
Article Review: booktitle Ada model arithmetic: costs and benefits: Wallis, P. J. L. booktitle IEE Proc.-E Comput. Dig. Tech. Vol 129 No 2 (March 1982) pp 75--80

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

rawtitle:
Article Review: {{\booktitle{Ada model arithmetic: costs and benefits}}: Wallis, P. J. L. \booktitle{IEE Proc.-E Comput. Dig. Tech.} Vol 129 No 2 (March 1982) pp 75--80}

entry:
@Article{Anonymous:1982:ARBf,
  author =       "Anonymous",
  title =        "Article Review: {{\booktitle{Ada model arithmetic:
                 costs and benefits}}: Wallis, P. J. L. \booktitle{IEE
                 Proc.-E Comput. Dig. Tech.} Vol 129 No 2 (March 1982)
                 pp 75--80}",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "6",
  number =       "9",
  pages =        "497--498",
  month =        nov,
  year =         "1982",
  CODEN =        "MIMID5",
  DOI =          "https://doi.org/10.1016/0141-9331(82)90515-4",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Mon Jan 14 21:50:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0141933182905154",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessors and Microsystems",
}


bibtype: techreport
filename: fparith.bib
label: Anonymous:1982:MKF
author: Anonymous
type: Bericht
number: 30
institution: Regionales Rechenzentrum fur Niedersachsen bei der Universitat Hannover
address: Hannover, Germany
pages: 58
year: 1982
bibdate: Thu May 09 09:13:36 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:13:36 ???
acknowledgement: ack-nhfb
rawauthor: Anonymous
title:
Materialiensammlung zum 5. Kolloquium (mit Floating Point Systems) Neue Rechnerarchitekturen: Anwendungsgebiete und Realisierungen: Hannover, (18.Mai 1982)

rawtitle:
{Materialiensammlung zum 5. Kolloquium (mit Floating Point Systems) Neue Rechnerarchitekturen: Anwendungsgebiete und Realisierungen: Hannover, (18.Mai 1982)}

entry:
@TechReport{Anonymous:1982:MKF,
  author =       "Anonymous",
  title =        "{Materialiensammlung zum 5. Kolloquium (mit Floating
                 Point Systems) Neue Rechnerarchitekturen:
                 Anwendungsgebiete und Realisierungen: Hannover, (18.Mai
                 1982)}",
  type =         "{Bericht}",
  number =       "30",
  institution =  "Regionales Rechenzentrum f{\"u}r Niedersachsen bei der
                 Universit{\"a}t Hannover",
  address =      "Hannover, Germany",
  pages =        "58",
  year =         "1982",
  bibdate =      "Thu May 09 09:13:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Anonymous:1982:NPAa
author: Anonymous
journal: j-IEEE-SPECTRUM
volume: 19
number: 1
pages: 104--118
month: jan
monthnumber: 1
year: 1982
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1982.6366777
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Sat Jan 18 16:51:45 2020
bibtimestamp: 2020.01.18 16:51:45 ???
fjournal: IEEE Spectrum
keywords: Algorithms; Arrays; Microcomputers; Microprocessors; Process control; Speech; Standards
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Anonymous
title:
New product applications: Array processor performs 5 million floating-point operations per second, has 200-ns operation time

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib

rawtitle:
New product applications: Array processor performs 5 million floating-point operations per second, has 200-ns operation time

entry:
@Article{Anonymous:1982:NPAa,
  author =       "Anonymous",
  title =        "New product applications: Array processor performs 5
                 million floating-point operations per second, has
                 200-ns operation time",
  journal =      j-IEEE-SPECTRUM,
  volume =       "19",
  number =       "1",
  pages =        "104--118",
  month =        jan,
  year =         "1982",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1982.6366777",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 16:51:45 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Algorithms; Arrays; Microcomputers; Microprocessors;
                 Process control; Speech; Standards",
}


bibtype: mastersthesis
filename: fparith.bib
label: Arnold:1982:EPS
author: Mark Gordon Arnold
title: Extending the Precision of the Sign Logarithm Number System
type: M.S. Thesis
school: University of Wyoming
address: Laramie, WY, USA
pages: 104--118
year: 1982
bibdate: Fri Jun 24 16:06:13 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 16:06:13 ???
acknowledgement: ack-nhfb
rawauthor: Mark Gordon Arnold
rawtitle: Extending the Precision of the Sign Logarithm Number System
entry:
@MastersThesis{Arnold:1982:EPS,
  author =       "Mark Gordon Arnold",
  title =        "Extending the Precision of the Sign Logarithm Number
                 System",
  type =         "{M.S.} Thesis",
  school =       "University of Wyoming",
  address =      "Laramie, WY, USA",
  year =         "1982",
  bibdate =      "Fri Jun 24 16:06:13 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Bairstow:1982:FPP
author: R. Bairstow and J. Barlow and M. Jires and M. Waters
title: A floating point processor for Intel 8080A microprocessor systems
type: Technical report
number: RL 82-020
institution: Rutherford Appleton Lab.
address: Harwell, Oxon, UK
pages: 44
month: mar
monthnumber: 3
year: 1982
bibdate: Fri May 25 05:47:40 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.05.25 05:47:40 ???
URL: http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0050018
acknowledgement: ack-nhfb
rawauthor: R. Bairstow and J. Barlow and M. Jires and M. Waters
rawtitle: A floating point processor for {Intel 8080A} microprocessor systems
entry:
@TechReport{Bairstow:1982:FPP,
  author =       "R. Bairstow and J. Barlow and M. Jires and M. Waters",
  title =        "A floating point processor for {Intel 8080A}
                 microprocessor systems",
  type =         "Technical report",
  number =       "RL 82-020",
  institution =  "Rutherford Appleton Lab.",
  address =      "Harwell, Oxon, UK",
  pages =        "44",
  month =        mar,
  year =         "1982",
  bibdate =      "Fri May 25 05:47:40 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0050018",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Baraniecki:1982:QEL
author: A. Baraniecki and G. Jullien
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '82
title: Quantization error and limit cycles analysis in residue number system coded recursive filters
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 52--55
year: 1982
DOI: https://doi.org/10.1049/el:19820632
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: A. Baraniecki and G. Jullien
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '82}
rawtitle: Quantization error and limit cycles analysis in residue number system coded recursive filters
entry:
@InProceedings{Baraniecki:1982:QEL,
  author =       "A. Baraniecki and G. Jullien",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '82}",
  title =        "Quantization error and limit cycles analysis in
                 residue number system coded recursive filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "52--55",
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19820632",
  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 =      "The paper discusses the Residue Number System (RNS)
                 implementation of second order recursive digital filter
                 sections. The RNS offers the advantage of using integer
                 based arithmetic operations and a simple hardware
                 realization involving arrays of \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Barnes:1982:RNI
author: C. Barnes and T. Miyawaki
title: Roundoff Noise Invariants in Normal Digital Filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 29
number: 4
pages: 251--256
month: apr
monthnumber: 4
year: 1982
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
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 Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: C. Barnes and T. Miyawaki
rawtitle: Roundoff Noise Invariants in Normal Digital Filters
entry:
@Article{Barnes:1982:RNI,
  author =       "C. Barnes and T. Miyawaki",
  title =        "Roundoff Noise Invariants in Normal Digital Filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "29",
  number =       "4",
  pages =        "251--256",
  month =        apr,
  year =         "1982",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  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 Circuits and Systems",
  summary =      "The unit noise gains for optimal and parallel normal
                 realizations of digital filters can be expressed in
                 terms of a set of noise gain parameters that are simply
                 related to the pole locations and pole residues. These
                 noise gain parameters are shown \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Bernhard:1982:CCS
author: R. Bernhard
journal: j-IEEE-SPECTRUM
volume: 19
number: 7
pages: 26--31
month: jul
monthnumber: 7
year: 1982
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1982.6366940
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Sat Jan 18 16:51:45 2020
bibtimestamp: 2020.01.18 16:51:45 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: R. Bernhard
title:
Computers: Computing at the speed limit: Computers 1000 times faster than today's supercomputers would benefit vital scientific applications

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib; https://www.math.utah.edu/pub/tex/bib/super.bib

keywords:
Computational modeling; Computer architecture; computer industry; Computers; Educational institutions; engineering applications; floating-point operations per second; flops; Program processors; scientific applications; Solid modeling; special purpose computers; very large-scale integration; VLSI

rawtitle:
Computers: Computing at the speed limit: Computers 1000 times faster than today's supercomputers would benefit vital scientific applications

entry:
@Article{Bernhard:1982:CCS,
  author =       "R. Bernhard",
  title =        "Computers: Computing at the speed limit: Computers
                 1000 times faster than today's supercomputers would
                 benefit vital scientific applications",
  journal =      j-IEEE-SPECTRUM,
  volume =       "19",
  number =       "7",
  pages =        "26--31",
  month =        jul,
  year =         "1982",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1982.6366940",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 16:51:45 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Computational modeling; Computer architecture;
                 computer industry; Computers; Educational institutions;
                 engineering applications; floating-point operations per
                 second; flops; Program processors; scientific
                 applications; Solid modeling; special purpose
                 computers; very large-scale integration; VLSI",
}


bibtype: article
filename: fparith.bib
label: Bernhard:1982:GSP
author: R. Bernhard
title: Giants in small packages [array processors]
journal: j-IEEE-SPECTRUM
volume: 19
number: 2
pages: 39--44
month: feb
monthnumber: 2
year: 1982
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1982.6366796
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Sat Jan 18 16:51:45 2020
bibtimestamp: 2020.01.18 16:51:45 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: R. Bernhard
rawtitle: Giants in small packages [array processors]
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib

keywords:
architecture; array processor; Arrays; arrays of numbers; computer; computer architecture; digital arithmetic; digital computers; Hardware; matrices; Microcomputers; Pipelines; Program processors; repetitive arithmetic operations; Vectors; vectors

entry:
@Article{Bernhard:1982:GSP,
  author =       "R. Bernhard",
  title =        "Giants in small packages [array processors]",
  journal =      j-IEEE-SPECTRUM,
  volume =       "19",
  number =       "2",
  pages =        "39--44",
  month =        feb,
  year =         "1982",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1982.6366796",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 16:51:45 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "architecture; array processor; Arrays; arrays of
                 numbers; computer; computer architecture; digital
                 arithmetic; digital computers; Hardware; matrices;
                 Microcomputers; Pipelines; Program processors;
                 repetitive arithmetic operations; Vectors; vectors",
}


bibtype: article
filename: fparith.bib
label: Bohannan:1982:MAP
author: J. W. Bohannan and D. J. Bradley and D. A. Kummer and J. A. Saenz
title: Multiplication Algorithm for Packed BCD Numbers
journal: j-IBM-TDB
volume: 25
number: 4
pages: 2225
month: sep
monthnumber: 9
year: 1982
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:16:11 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 10:16:11 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: J. W. Bohannan and D. J. Bradley and D. A. Kummer and J. A. Saenz
rawtitle: Multiplication Algorithm for Packed {BCD} Numbers
entry:
@Article{Bohannan:1982:MAP,
  author =       "J. W. Bohannan and D. J. Bradley and D. A. Kummer and
                 J. A. Saenz",
  title =        "Multiplication Algorithm for Packed {BCD} Numbers",
  journal =      j-IBM-TDB,
  volume =       "25",
  number =       "4",
  pages =        "2225",
  month =        sep,
  year =         "1982",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:11 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: Bohlender:1982:ROA
author: G. Bohlender and K. Gruner and J. Wolff von Gudenberg
title: Realisierung einer optimalen Arithmetik toenglish Realization of Optimal Arithmetic endtoenglish
journal: j-ELEK-RECHENANLAGEN
volume: 24
number: 2
pages: 68--72
month: apr
monthnumber: 4
year: 1982
CODEN: ELRAA4
ISSN: 0013-5720 OR 00135720
bibdate: Sat Feb 10 12:41:07 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.10 12:41:07 ???
fjournal: Elektronische Rechenanlagen
acknowledgement: ack-nj
rawauthor: G. Bohlender and K. Gr{\"u}ner and J. Wolff {von Gudenberg}
rawtitle:
{Realisierung einer optimalen Arithmetik} \toenglish {Realization of Optimal Arithmetic} \endtoenglish

entry:
@Article{Bohlender:1982:ROA,
  author =       "G. Bohlender and K. Gr{\"u}ner and J. Wolff {von
                 Gudenberg}",
  title =        "{Realisierung einer optimalen Arithmetik} \toenglish
                 {Realization of Optimal Arithmetic} \endtoenglish",
  journal =      j-ELEK-RECHENANLAGEN,
  volume =       "24",
  number =       "2",
  pages =        "68--72",
  month =        apr,
  year =         "1982",
  CODEN =        "ELRAA4",
  ISSN =         "0013-5720",
  bibdate =      "Sat Feb 10 12:41:07 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronische Rechenanlagen",
}


bibtype: article
filename: fparith.bib
label: Brent:1982:RLP
author: R. P. Brent and H. T. Kung
title: A regular layout for parallel adders
journal: j-IEEE-TRANS-COMPUT
volume: C-31
pages: 260--264
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1675982
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Sep 16 16:06:24 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:06:24 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. P. Brent and H. T. Kung
rawtitle: A regular layout for parallel adders
entry:
@Article{Brent:1982:RLP,
  author =       "R. P. Brent and H. T. Kung",
  title =        "A regular layout for parallel adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "??",
  pages =        "260--264",
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675982",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Sep 16 16:06:24 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Brooks:1982:OCL
author: R. A. Brooks and R. P. Gabriel and G. L. Steele Jr.
title: An optimizing compiler for lexically scoped LISP
journal: j-SIGPLAN
volume: 17
number: 6
pages: 261--275
month: jun
monthnumber: 6
year: 1982
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: MIT, Cambridge, MA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
treatment: P Practical
rawauthor: R. A. Brooks and R. P. Gabriel and G. L. {Steele Jr.}
rawtitle: An optimizing compiler for lexically scoped {LISP}
keywords:
BLISS-11; complex numbers; floating-point; FORTRAN; lexically scoped LISP; LISP; list manipulation; multiprocessing supercomputer; optimizing compiler; PASCAL; PQCC compiler; program compilers; S-1 PASCAL; stable-driven; symbolic processing; TNBIND technique; vectors

entry:
@Article{Brooks:1982:OCL,
  author =       "R. A. Brooks and R. P. Gabriel and G. L. {Steele
                 Jr.}",
  title =        "An optimizing compiler for lexically scoped {LISP}",
  journal =      j-SIGPLAN,
  volume =       "17",
  number =       "6",
  pages =        "261--275",
  month =        jun,
  year =         "1982",
  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 = "C6140D (High level languages); C6150C (Compilers,
                 interpreters and other processors)",
  conflocation = "Boston, MA, USA; 23--25 June 1982",
  conftitle =    "Proceedings of the SIGPLAN '82 Symposium on Compiler
                 Construction",
  corpsource =   "MIT, Cambridge, MA, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "BLISS-11; complex numbers; floating-point; FORTRAN;
                 lexically scoped LISP; LISP; list manipulation;
                 multiprocessing supercomputer; optimizing compiler;
                 PASCAL; PQCC compiler; program compilers; S-1 PASCAL;
                 stable-driven; symbolic processing; TNBIND technique;
                 vectors",
  sponsororg =   "ACM",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Burr:1982:CCR
author: S. A. Burr
title: Computing cube roots when a fast square root is available
journal: j-COMPUT-MATH-APPL
volume: 8
number: 3
pages: 181--183
year: 1982
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(82)90041-4
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:22 MST 2017
bibtimestamp: 2017.03.01 18:51:22 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122182900414
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221/
rawauthor: S. A. Burr
rawtitle: Computing cube roots when a fast square root is available
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{Burr:1982:CCR,
  author =       "S. A. Burr",
  title =        "Computing cube roots when a fast square root is
                 available",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "8",
  number =       "3",
  pages =        "181--183",
  month =        "????",
  year =         "1982",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(82)90041-4",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:22 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/0898122182900414",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}


bibtype: article
filename: fparith.bib
label: Cassola:1982:FPA
author: R. L. Cassola
title: Floating Point Algorithm Design
journal: j-COMP-DESIGN
volume: 21
number: 6
pages: 107--114
month: jun
monthnumber: 6
year: 1982
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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 ???
fjournal: Computer Design
acknowledgement: ack-nj
rawauthor: R. L. Cassola
rawtitle: Floating Point Algorithm Design
entry:
@Article{Cassola:1982:FPA,
  author =       "R. L. Cassola",
  title =        "Floating Point Algorithm Design",
  journal =      j-COMP-DESIGN,
  volume =       "21",
  number =       "6",
  pages =        "107--114",
  month =        jun,
  year =         "1982",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  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,
  fjournal =     "Computer Design",
}


bibtype: article
filename: fparith.bib
label: Cassola:1982:FPM
author: R. L. Cassola
title: A Floating Point Module for Military Computers
journal: j-COMP-DESIGN
volume: 21
number: 2
pages: 67--76
month: feb
monthnumber: 2
year: 1982
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
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 ???
fjournal: Computer Design
acknowledgement: ack-nj
rawauthor: R. L. Cassola
rawtitle: A Floating Point Module for Military Computers
entry:
@Article{Cassola:1982:FPM,
  author =       "R. L. Cassola",
  title =        "A Floating Point Module for Military Computers",
  journal =      j-COMP-DESIGN,
  volume =       "21",
  number =       "2",
  pages =        "67--76",
  month =        feb,
  year =         "1982",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  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,
  fjournal =     "Computer Design",
}


bibtype: mastersthesis
filename: fparith.bib
label: Cavanagh:1982:DCA
author: Joseph J. F. Cavanagh
title: Digital computer arithmetic: design and implementation
type: Thesis (M.S.)
school: University of Santa Clara
address: Santa Clara, CA, USA
pages: vii + 503
year: 1982
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic and logic units.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Joseph J. F. Cavanagh
rawtitle: Digital computer arithmetic: design and implementation
entry:
@MastersThesis{Cavanagh:1982:DCA,
  author =       "Joseph J. F. Cavanagh",
  title =        "Digital computer arithmetic: design and
                 implementation",
  type =         "Thesis ({M.S.})",
  school =       "University of Santa Clara",
  address =      "Santa Clara, CA, USA",
  pages =        "vii + 503",
  year =         "1982",
  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.; Floating-point
                 arithmetic.",
}


bibtype: inproceedings
filename: fparith.bib
label: Cody:1982:BCC
author: W. J. Cody
title: Basic concepts for computational software
crossref: Messina:1982:PMM
pages: 1--23
year: 1982
DOI: https://doi.org/10.1007/3-540-11603-6_1
bibdate: Fri Sep 23 23:12:32 1994
bibtimestamp: 1994.09.23 23:12:32 ???
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawtitle: Basic concepts for computational software
entry:
@InProceedings{Cody:1982:BCC,
  author =       "W. J. Cody",
  title =        "Basic concepts for computational software",
  crossref =     "Messina:1982:PMM",
  pages =        "1--23",
  year =         "1982",
  DOI =          "https://doi.org/10.1007/3-540-11603-6_1",
  bibdate =      "Fri Sep 23 23:12:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Cody:1982:FPM
author: W. J. Cody
title: Floating-point parameters, models, and standards
crossref: Reid:1982:RBN
pages: 51--69
year: 1982
bibdate: Sat Nov 9 08:26:18 MST 2002
bibtimestamp: 2002.11.09 08:26:18 MST
keywords: languages; standardization
acknowledgement: ack-nhfb
reviewer: Hansen, E
rawauthor: W. J. Cody
rawtitle: Floating-point parameters, models, and standards
bibsource:
ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

subject:
D.3.0 Software, PROGRAMMING LANGUAGES, General, Standards G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; D. Software; D.3 PROGRAMMING LANGUAGES

entry:
@InProceedings{Cody:1982:FPM,
  author =       "W. J. Cody",
  title =        "Floating-point parameters, models, and standards",
  crossref =     "Reid:1982:RBN",
  pages =        "51--69",
  year =         "1982",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; D.3.0",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic; D.3.0
                 General; D.3.0 Standards",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic; Software, PROGRAMMING LANGUAGES,
                 General, Standards",
  genterm =      "THEORY; STANDARDIZATION",
  guideno =      "10367",
  keywords =     "languages; standardization",
  review =       "ACM CR 8402-0092",
  reviewer =     "Hansen, E",
  subject =      "D.3.0 Software, PROGRAMMING LANGUAGES, General,
                 Standards \\ G.1.0 Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic; G. Mathematics
                 of Computing; G.1 NUMERICAL ANALYSIS; D. Software; D.3
                 PROGRAMMING LANGUAGES",
}


bibtype: techreport
filename: fparith.bib
label: Cody:1982:GPI
author: W. J. Cody
title: A Generalization of the Proposed IEEE Standard for Floating-Point Arithmetic
type: Technical Report
institution: inst-ANL
address: inst-ANL:adr
pages: 20
year: 1982
bibdate: Thu Nov 17 10:40:11 1994
bibtimestamp: 1994.11.17 10:40:11 ???
note: Republished in cite Cody:1983:GPI.
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawnote: Republished in \cite{Cody:1983:GPI}.
rawtitle: A Generalization of the Proposed {IEEE} Standard for Floating-Point Arithmetic
entry:
@TechReport{Cody:1982:GPI,
  author =       "W. J. Cody",
  title =        "A Generalization of the Proposed {IEEE} Standard for
                 Floating-Point Arithmetic",
  type =         "Technical Report",
  number =       "??",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "20",
  year =         "1982",
  bibdate =      "Thu Nov 17 10:40:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Republished in \cite{Cody:1983:GPI}.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Cody:1982:ITF
author: W. J. Cody
title: Implementation and Testing of Function Software
crossref: Messina:1982:PMM
pages: 24--47
year: 1982
DOI: https://doi.org/10.1007/3-540-11603-6_1
bibdate: Sat Sep 24 01:18:12 1994
bibtimestamp: 1994.09.24 01:18:12 ???
keywords: range reduction
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawtitle: Implementation and Testing of Function Software
entry:
@InProceedings{Cody:1982:ITF,
  author =       "W. J. Cody",
  title =        "Implementation and Testing of Function Software",
  crossref =     "Messina:1982:PMM",
  pages =        "24--47",
  year =         "1982",
  DOI =          "https://doi.org/10.1007/3-540-11603-6_1",
  bibdate =      "Sat Sep 24 01:18:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "range reduction",
}


bibtype: article
filename: fparith.bib
label: Corbett:1982:EAF
author: R. P. Corbett
title: Enhanced arithmetic for Fortran
journal: j-SIGPLAN
volume: 17
number: 12
pages: 41--48
month: dec
monthnumber: 12
year: 1982
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: Department of Computer Sci., University of California, Berkeley, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
treatment: P Practical
rawauthor: R. P. Corbett
rawtitle: Enhanced arithmetic for {Fortran}
keywords:
accuracy; arithmetic; digital arithmetic; efficiency; FORTRAN; Fortran; programmers; speed; widest need evaluation

entry:
@Article{Corbett:1982:EAF,
  author =       "R. P. Corbett",
  title =        "Enhanced arithmetic for {Fortran}",
  journal =      j-SIGPLAN,
  volume =       "17",
  number =       "12",
  pages =        "41--48",
  month =        dec,
  year =         "1982",
  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 = "C6140D (High level languages)",
  corpsource =   "Department of Computer Sci., University of California,
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  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "accuracy; arithmetic; digital arithmetic; efficiency;
                 FORTRAN; Fortran; programmers; speed; widest need
                 evaluation",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Dao:1982:KCA
author: T. T. Dao
editor: IEEE
booktitle: Proceedings of the 12th International Symposium on Multiple-Valued Logic, May 1982
title: Knuth's Complex Arithmetic with Quaternary Hardware
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 94--98
month: may
monthnumber: 5
year: 1982
bibdate: Sat Aug 22 09:14:13 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 09:14:13 ???
acknowledgement: ack-nhfb
rawauthor: T. T. Dao
rawbooktitle: Proceedings of the 12th International Symposium on Multiple-Valued Logic, May 1982
raweditor: {IEEE}
rawtitle: {Knuth}'s Complex Arithmetic with Quaternary Hardware
entry:
@InProceedings{Dao:1982:KCA,
  author =       "T. T. Dao",
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 12th International Symposium on
                 Multiple-Valued Logic, May 1982",
  title =        "{Knuth}'s Complex Arithmetic with Quaternary
                 Hardware",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "94--98",
  month =        may,
  year =         "1982",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 09:14:13 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Dekker:1982:PCM
author: T. J. Dekker
editor: Paul C. Messina and Almerico Murli
booktitle: Problems and Methodologies in Mathematical Software Production
title: Program Correctness and Machine Arithmetic
volume: 142
publisher: pub-SV
address: pub-SV:adr
pages: 48--80
year: 1982
bibdate: Sat May 1 15:24:45 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.05.01 15:24:45 ???
series: ser-LNCS
acknowledgement: ack-nhfb
rawauthor: T. J. Dekker
rawbooktitle: Problems and Methodologies in Mathematical Software Production
raweditor: Paul C. Messina and Almerico Murli
rawtitle: Program Correctness and Machine Arithmetic
entry:
@InProceedings{Dekker:1982:PCM,
  author =       "T. J. Dekker",
  editor =       "Paul C. Messina and Almerico Murli",
  booktitle =    "Problems and Methodologies in Mathematical Software
                 Production",
  title =        "Program Correctness and Machine Arithmetic",
  volume =       "142",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "48--80",
  year =         "1982",
  bibdate =      "Sat May 1 15:24:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: DeSautels:1982:ALP
author: Edouard J. DeSautels
publisher: William C. Brown Co. Publ.
address: Dubuque, IA
pages: 574
year: 1982
ISBN: 0-697-08164-8 OR 0697081648
ISBN13: 978-0-697-08164-3 OR 9780697081643
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
acknowledgement: ack-nhfb
reviewer: P. Abel; Abel, P
rawauthor: Edouard J. DeSautels
title:
Assembly language programming for PDP-11 and LSI-11 computers: an introduction to computer organization

subject:
A. General Literature; A.1 INTRODUCTORY AND SURVEY; C. Computer Systems Organization; C.1 PROCESSOR ARCHITECTURES; D. Software; D.3 PROGRAMMING LANGUAGES; D. Software; D.3 PROGRAMMING LANGUAGES; D. Software; D.3 PROGRAMMING LANGUAGES

rawtitle:
Assembly language programming for {PDP-11} and {LSI-11} computers: an introduction to computer organization

entry:
@Book{DeSautels:1982:ALP,
  author =       "Edouard J. DeSautels",
  title =        "Assembly language programming for {PDP-11} and
                 {LSI-11} computers: an introduction to computer
                 organization",
  publisher =    "William C. Brown Co. Publ.",
  address =      "Dubuque, IA",
  pages =        "574",
  year =         "1982",
  ISBN =         "0-697-08164-8",
  ISBN-13 =      "978-0-697-08164-3",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$21.95",
  acknowledgement = ack-nhfb,
  catcode =      "A; C.1.1; D.3; D.3.2; D.3.2",
  content =      "The author has provided material on the Assembler
                 language for the PDP-11 or LSI-11 computers in an
                 original and comprehensive manner. Users of this
                 Assembler or even of this computer should find this
                 text especially valuable as a student text or as a
                 permanent reference. Much of the material in the
                 PDP-11, MACRO-11 Reference Manual, Processor Handbook,
                 Peripheral Handbook, and Terminals and Communications
                 Handbook is organized in this book in a readable,
                 step-by-step manner. Required is access to a PDP-11 (or
                 LSI-11) and some knowledge of programming in a
                 high-level language.\par

                 Topics include the following: \par

                 * Very accessible and detailed material on introduction
                 to computers and programming. It is unlikely that a
                 reader would require much if any prior knowledge of
                 computers.\par

                 * An early introduction to machine language to explain
                 the functioning of a computer, and then a lead-in into
                 Assembler language.\par

                 * Development of the use of registers, Assembler
                 Directives, indexing, immediate operands, arithmetic
                 for signed and unsigned data, subroutines, stacks,
                 passing parameters, input/output, floating-point
                 arithmetic, and more.\par

                 * An interesting chapter, ``Selected Topics,'' covering
                 such subjects as tables, lists, queues, trees, threaded
                 code, and reentrant co",
  CRclass =      "C.1.1 Single Data Stream Architectures; C.1.1 PDP-11;
                 D.3.2 Language Classifications; D.3.2 Language
                 Classifications; D.3.2 Macro and assembly languages;
                 D.3.2 Language Classifications; D.3.2 PDP-11 assembly
                 language",
  CRnumber =     "40452",
  descriptor =   "General Literature, INTRODUCTORY AND SURVEY; Computer
                 Systems Organization, PROCESSOR ARCHITECTURES, Single
                 Data Stream Architectures, PDP-11; Software,
                 PROGRAMMING LANGUAGES, Language Classifications;
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Macro and assembly languages;
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, PDP-11 assembly language",
  genterm =      "LANGUAGES",
  pubname =      "William C. Brown Co. Publ., Dubuque, IA",
  reviewer =     "P. Abel; Abel, P",
  subject =      "A. General Literature; A.1 INTRODUCTORY AND SURVEY; C.
                 Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; D. Software; D.3 PROGRAMMING LANGUAGES;
                 D. Software; D.3 PROGRAMMING LANGUAGES; D. Software;
                 D.3 PROGRAMMING LANGUAGES",
}


bibtype: incollection
filename: fparith.bib
label: Dreyer:1982:ACI
author: H.-J. Dreyer and A. Walther
title: The Automatic Calculator IPM (1946)
crossref: Randell:1982:ODC
pages: 155--161
year: 1982
bibdate: Sun Nov 03 08:36:11 2002
bibtimestamp: 2002.11.03 08:36:11 ???
acknowledgement: ack-nhfb
rawauthor: H.-J. Dreyer and A. Walther
rawtitle: The Automatic Calculator {IPM} (1946)
entry:
@InCollection{Dreyer:1982:ACI,
  author =       "H.-J. Dreyer and A. Walther",
  title =        "The Automatic Calculator {IPM} (1946)",
  crossref =     "Randell:1982:ODC",
  pages =        "155--161",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Epstein:1982:UAF
author: C. Epstein and W. L. Miranker and T. J. Rivlin
title: Ultra-arithmetic I: function data types
journal: j-MATH-COMP-SIM
volume: 24
number: 1
pages: 1--18
month: feb
monthnumber: 2
year: 1982
CODEN: MCSIDR
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784754
rawauthor: C. Epstein and W. L. Miranker and T. J. Rivlin
rawtitle: Ultra-arithmetic {I}: function data types
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Epstein:1982:UAF,
  author =       "C. Epstein and W. L. Miranker and T. J. Rivlin",
  title =        "Ultra-arithmetic {I}: function data types",
  journal =      j-MATH-COMP-SIM,
  volume =       "24",
  number =       "1",
  pages =        "1--18",
  month =        feb,
  year =         "1982",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1; G.1.2; G.1.2",
  CRclass =      "G.1.5 Roots of Nonlinear Equations; G.1.2
                 Approximation; G.1.2 Chebyshev approximation and
                 theory; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Mathematics and Computers in Simulation",
  genterm =      "algorithms",
  guideno =      "09324",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: fparith.bib
label: Epstein:1982:UAI
author: C. Epstein and W. L. Miranker and T. J. Rivlin
title: Ultra-arithmetic II: intervals of polynomials
journal: j-MATH-COMP-SIM
volume: 24
number: 1
pages: 19--29
month: feb
monthnumber: 2
year: 1982
CODEN: MCSIDR
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784754
rawauthor: C. Epstein and W. L. Miranker and T. J. Rivlin
rawtitle: Ultra-arithmetic {II}: intervals of polynomials
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Epstein:1982:UAI,
  author =       "C. Epstein and W. L. Miranker and T. J. Rivlin",
  title =        "Ultra-arithmetic {II}: intervals of polynomials",
  journal =      j-MATH-COMP-SIM,
  volume =       "24",
  number =       "1",
  pages =        "19--29",
  month =        feb,
  year =         "1982",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.1; G.1.0",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.1 Interpolation; G.1.1 Spline and
                 piecewise polynomial interpolation; G.1.0 General;
                 G.1.0 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Error analysis",
  fjournal =     "Mathematics and Computers in Simulation",
  genterm =      "algorithms",
  guideno =      "09325",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: fparith.bib
label: Fateman:1982:HLL
author: Richard J. Fateman
title: High-Level Language Implications of the Proposed IEEE Floating-Point Standard
journal: j-TOPLAS
volume: 4
number: 2
pages: 239--257
month: apr
monthnumber: 4
year: 1982
CODEN: ATPSDT
DOI: https://doi.org/10.1145/357162.357168
ISSN: 0164-0925 (print), 1558-4593 (electronic) OR 01640925 (print), 15584593 (electronic)
ISSNL: 0164-0925 OR 01640925
bibdate: Thu Nov 8 14:50:28 2007
bibsource: Compiler/bevan.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:28 ???
fjournal: ACM Transactions on Programming Languages and Systems
acknowledgement: ack-pb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J783
rawauthor: Richard J. Fateman
rawtitle: High-Level Language Implications of the Proposed {IEEE} Floating-Point Standard
abstract:
An IEEE Computer Society working group on floating-point arithmetic has recommended a standard for binary floating-point number formats, operations, and semantics. This paper, which has evolved in part during the deliberations of that committee, describes the significance to languages and, in particular, to FORTRAN and its variants, of various novel features of the recommended standard.

keywords:
computer arithmetic; control structures; data types and structures; error handling and recovery; floating-point arithmetic; FORTRAN; run-time environments

rawabstract:
An IEEE Computer Society working group on floating-point arithmetic has recommended a standard for binary floating-point number formats, operations, and semantics. This paper, which has evolved in part during the deliberations of that committee, describes the significance to languages and, in particular, to FORTRAN and its variants, of various novel features of the recommended standard.

entry:
@Article{Fateman:1982:HLL,
  author =       "Richard J. Fateman",
  title =        "High-Level Language Implications of the Proposed
                 {IEEE} Floating-Point Standard",
  journal =      j-TOPLAS,
  volume =       "4",
  number =       "2",
  pages =        "239--257",
  month =        apr,
  year =         "1982",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/357162.357168",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Thu Nov 8 14:50:28 2007",
  bibsource =    "Compiler/bevan.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An IEEE Computer Society working group on
                 floating-point arithmetic has recommended a standard
                 for binary floating-point number formats, operations,
                 and semantics. This paper, which has evolved in part
                 during the deliberations of that committee, describes
                 the significance to languages and, in particular, to
                 FORTRAN and its variants, of various novel features of
                 the recommended standard.",
  acknowledgement = ack-pb,
  checked =      "19940302",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
  keywords =     "computer arithmetic; control structures; data types
                 and structures; error handling and recovery;
                 floating-point arithmetic; FORTRAN; run-time
                 environments",
  source =       "Dept. Library",
}


bibtype: techreport
filename: fparith.bib
label: Feldstein:1982:EPI
author: A. Feldstein and R. Goodman
type: Technical report
institution: Department of Mathematics, Arizona State University
address: Tempe, AZ, USA
pages: 239--257
year: 1982
bibdate: Tue Oct 09 09:50:41 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.09 09:50:41 ???
acknowledgement: ack-nhfb
rawauthor: A. Feldstein and R. Goodman
title:
The evaluation of probability integrals for the loss of significance in floating point subtraction and addition

rawtitle:
The evaluation of probability integrals for the loss of significance in floating point subtraction and addition

entry:
@TechReport{Feldstein:1982:EPI,
  author =       "A. Feldstein and R. Goodman",
  title =        "The evaluation of probability integrals for the loss
                 of significance in floating point subtraction and
                 addition",
  type =         "Technical report",
  institution =  "Department of Mathematics, Arizona State University",
  address =      "Tempe, AZ, USA",
  year =         "1982",
  bibdate =      "Tue Oct 09 09:50:41 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Feldstein:1982:LSF
author: A. Feldstein and R. Goodman
title: Loss of Significance in Floating Point Subtraction and Addition
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 4
pages: 328--335
month: apr
monthnumber: 4
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1676002
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
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: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Feldstein and R. Goodman
rawtitle: Loss of Significance in Floating Point Subtraction and Addition
abstract:
We study the loss of significant $ beta $ its (base $ beta $ digits) in floating point addition or subtraction. To do this, we calculate the conditional probability of a post-arithmetic normalization shift of $m$ $ beta $ its, given an exponent difference of $k$ $ beta $ its. The study is done for various bases $ beta $, under two different assumptions---that the operands are selected at random from the logarithmic distribution or from the uniform distribution.

rawabstract:
We study the loss of significant $ \beta $ its (base $ \beta $ digits) in floating point addition or subtraction. To do this, we calculate the conditional probability of a post-arithmetic normalization shift of $m$ $ \beta $ its, given an exponent difference of $k$ $ \beta $ its. The study is done for various bases $ \beta $, under two different assumptions---that the operands are selected at random from the logarithmic distribution or from the uniform distribution.

entry:
@Article{Feldstein:1982:LSF,
  author =       "A. Feldstein and R. Goodman",
  title =        "Loss of Significance in Floating Point Subtraction and
                 Addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "4",
  pages =        "328--335",
  month =        apr,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676002",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  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",
  abstract =     "We study the loss of significant $ \beta $ its (base $
                 \beta $ digits) in floating point addition or
                 subtraction. To do this, we calculate the conditional
                 probability of a post-arithmetic normalization shift of
                 $m$ $ \beta $ its, given an exponent difference of $k$
                 $ \beta $ its. The study is done for various bases $
                 \beta $, under two different assumptions---that the
                 operands are selected at random from the logarithmic
                 distribution or from the uniform distribution.",
  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: Fulton:1982:BJB
author: T. A. Fulton and L. N. Dunkleberger
title: B.S.T.J. Briefs: a Josephson Parallel Multiplier
journal: j-BELL-SYST-TECH-J
volume: 61
number: 5
pages: 931--933
month: may
monthnumber: 5
year: 1982
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:56 MST 2010
bibtimestamp: 2010.11.09 11:15:56 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol61/bstj61-5-931.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: T. A. Fulton and L. N. Dunkleberger
rawtitle: {B.S.T.J.} Briefs: a {Josephson} Parallel Multiplier
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1982/BSTJ.1982.6105.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Fulton:1982:BJB,
  author =       "T. A. Fulton and L. N. Dunkleberger",
  title =        "{B.S.T.J.} Briefs: a {Josephson} Parallel Multiplier",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "61",
  number =       "5",
  pages =        "931--933",
  month =        may # "--" # jun,
  year =         "1982",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:56 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1982/BSTJ.1982.6105.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol61/bstj61-5-931.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: fparith.bib
label: Gerrity:1982:CRR
author: G. W. Gerrity
title: Computer Representation of Real Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 8
pages: 709--714
month: aug
monthnumber: 8
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1676076
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:14 MDT 2011
bibtimestamp: 2011.07.10 10:33:14 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676076
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. W. Gerrity
rawtitle: Computer Representation of Real Numbers
abstract:
Hwang's model for the computer representation of real numbers is extended to explicitly distinguish between the representational system used to denote real numbers and the internal encoding of the digits of the representation in the computer memory. The encoding function can then be chosen to preserve certain properties of the real number system and to optimize the computer arithmetic in a sense to be described herein. Two examples of optimal computer arithmetics are discussed.

rawabstract:
Hwang's model for the computer representation of real numbers is extended to explicitly distinguish between the representational system used to denote real numbers and the internal encoding of the digits of the representation in the computer memory. The encoding function can then be chosen to preserve certain properties of the real number system and to optimize the computer arithmetic in a sense to be described herein. Two examples of optimal computer arithmetics are discussed.

entry:
@Article{Gerrity:1982:CRR,
  author =       "G. W. Gerrity",
  title =        "Computer Representation of Real Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "8",
  pages =        "709--714",
  month =        aug,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676076",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676076",
  abstract =     "Hwang's model for the computer representation of real
                 numbers is extended to explicitly distinguish between
                 the representational system used to denote real numbers
                 and the internal encoding of the digits of the
                 representation in the computer memory. The encoding
                 function can then be chosen to preserve certain
                 properties of the real number system and to optimize
                 the computer arithmetic in a sense to be described
                 herein. Two examples of optimal computer arithmetics
                 are discussed.",
  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: Goodrich:1982:VEP
author: J. L. Goodrich
title: Very efficient 8080 program multiplies and divides
journal: j-ELECTRONICS
volume: 55
number: 4
pages: 144--145
month: feb
monthnumber: 2
year: 1982
ISSN: 0883-4989 OR 08834989
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
acknowledgement: ack-nj
journalURL: https://www.mdpi.com/journal/electronics
rawauthor: J. L. Goodrich
rawtitle: Very efficient 8080 program multiplies and divides
entry:
@Article{Goodrich:1982:VEP,
  author =       "J. L. Goodrich",
  title =        "Very efficient 8080 program multiplies and divides",
  journal =      j-ELECTRONICS,
  volume =       "55",
  number =       "4",
  pages =        "144--145",
  month =        feb,
  year =         "1982",
  ISSN =         "0883-4989",
  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",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}


bibtype: inproceedings
filename: fparith.bib
label: Gordon:1982:BFS
author: E. Gordon and C. Hastings
booktitle: Conference Record, SOUTHCON, 1982
title: Big, Fast and Simple Algorithms, Architecture and Components for High-end Minis
year: 1982
bibdate: Fri Nov 09 18:54:03 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 18:54:03 ???
note: Paper 21/3.
acknowledgement: ack-nhfb
rawauthor: E. Gordon and C. Hastings
rawbooktitle: Conference Record, {SOUTHCON, 1982}
rawnote: Paper 21/3.
rawtitle: Big, Fast and Simple Algorithms, Architecture and Components for High-end Minis
entry:
@InProceedings{Gordon:1982:BFS,
  author =       "E. Gordon and C. Hastings",
  booktitle =    "Conference Record, {SOUTHCON, 1982}",
  title =        "Big, Fast and Simple Algorithms, Architecture and
                 Components for High-end Minis",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "1982",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Nov 09 18:54:03 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Paper 21/3.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Hantler:1982:ESS
author: S. L. Hantler and A. H. Karp
title: Exponential by Sequential Squaring
journal: j-IBM-TDB
volume: 25
number: 1
pages: 171--173
month: jun
monthnumber: 6
year: 1982
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:16:09 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:09 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: S. L. Hantler and A. H. Karp
rawtitle: Exponential by Sequential Squaring
entry:
@Article{Hantler:1982:ESS,
  author =       "S. L. Hantler and A. H. Karp",
  title =        "Exponential by Sequential Squaring",
  journal =      j-IBM-TDB,
  volume =       "25",
  number =       "1",
  pages =        "171--173",
  month =        jun,
  year =         "1982",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: inproceedings
filename: fparith.bib
label: Hull:1982:PCE
author: T. E. Hull
title: Precision Control, Exception Handling and a Choice of Numerical Algorithms
crossref: Watson:1982:NAP
pages: 169--178
year: 1982
DOI: https://doi.org/10.1007/BFb0093156
bibdate: Sat Feb 8 10:29:52 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.02.08 10:29:52 ???
keywords: decimal floating-point arithmetic
remark: Proposes precision control as later provided in Numerical Turing.
acknowledgement: ack-nhfb
rawauthor: T. E. Hull
rawtitle: Precision Control, Exception Handling and a Choice of Numerical Algorithms
entry:
@InProceedings{Hull:1982:PCE,
  author =       "T. E. Hull",
  title =        "Precision Control, Exception Handling and a Choice of
                 Numerical Algorithms",
  crossref =     "Watson:1982:NAP",
  pages =        "169--178",
  year =         "1982",
  DOI =          "https://doi.org/10.1007/BFb0093156",
  bibdate =      "Sat Feb 8 10:29:52 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "Proposes precision control as later provided in
                 Numerical Turing.",
}


bibtype: inproceedings
filename: fparith.bib
label: Hull:1982:UCP
author: T. E. Hull
title: The uses of controlled precision
crossref: Reid:1982:RBN
pages: 71--82
year: 1982
bibdate: Fri Jan 04 12:57:37 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.04 12:57:37 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: T. E. Hull
rawtitle: The uses of controlled precision
entry:
@InProceedings{Hull:1982:UCP,
  author =       "T. E. Hull",
  title =        "The uses of controlled precision",
  crossref =     "Reid:1982:RBN",
  pages =        "71--82",
  year =         "1982",
  bibdate =      "Fri Jan 04 12:57:37 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  xxpages =      "71--84",
}


bibtype: article
filename: fparith.bib
label: Hwang:1982:PMA
author: Kai Hwang and Yeng-Heng Cheng
title: Partitioned Matrix Algorithms for VLSI Arithmetic Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 12
pages: 1215--1224
month: dec
monthnumber: 12
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1675945
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:17 MDT 2011
bibtimestamp: 2011.07.10 10:33:17 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675945
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 and Yeng-Heng Cheng
rawtitle: Partitioned Matrix Algorithms for {VLSI} Arithmetic Systems
entry:
@Article{Hwang:1982:PMA,
  author =       "Kai Hwang and Yeng-Heng Cheng",
  title =        "Partitioned Matrix Algorithms for {VLSI} Arithmetic
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "12",
  pages =        "1215--1224",
  month =        dec,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675945",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:17 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=1675945",
  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: Jenkins:1982:FRD
author: W. Jenkins
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '82
title: Failure resistant digital filters based on residue number system product codes
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 60--63
year: 1982
DOI: https://doi.org/10.1049/el:19820632
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: W. Jenkins
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '82}
rawtitle: Failure resistant digital filters based on residue number system product codes
entry:
@InProceedings{Jenkins:1982:FRD,
  author =       "W. Jenkins",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '82}",
  title =        "Failure resistant digital filters based on residue
                 number system product codes",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "60--63",
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19820632",
  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 =      "Residue number system product codes are proposed for
                 the design of self-checking digital filters. It is
                 shown that product codes require redundancy that is
                 similar to, but slightly less than that of systematic
                 codes for simultaneous overflow \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Jenkins:1982:RNS
author: W. K. Jenkins
title: Residue number system error checking using expanded projection
journal: j-ELECT-LETTERS
volume: 18
number: 21
pages: 927--928
day: 14
month: oct
monthnumber: 10
year: 1982
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19820632
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
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=4246948
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: Residue number system error checking using expanded projection
entry:
@Article{Jenkins:1982:RNS,
  author =       "W. K. Jenkins",
  title =        "Residue number system error checking using expanded
                 projection",
  journal =      j-ELECT-LETTERS,
  volume =       "18",
  number =       "21",
  pages =        "927--928",
  day =          "14",
  month =        oct,
  year =         "1982",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19820632",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  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=4246948",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new concept called expanded projection is presented
                 that simplifies the process of error detection and
                 location in redundant residue number codes. Expanded
                 projection simplifies the circuit complexity of the
                 error checker, resulting in a structure \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Kahan:1982:NOS
author: W. Kahan and Jerome T. Coonen
title: The Near Orthogonality of Syntax, Semantics, and Diagnostics in Numerical Programming Environments
crossref: Reid:1982:RBN
pages: 103--115
year: 1982
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
keywords: floating-point arithmetic; rounding errors
remark: This article forms the body of cite [Chapter 3]Coonen:1984:CPS.
acknowledgement: ack-nhfb
reviewer: M. Marcotty; Marcotty, M
rawauthor: W. Kahan and Jerome T. Coonen
rawtitle: The Near Orthogonality of Syntax, Semantics, and Diagnostics in Numerical Programming Environments
subject:
D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.3 LOGICS AND MEANINGS OF PROGRAMS; D. Software; D.2 SOFTWARE ENGINEERING; D. Software; D.2 SOFTWARE ENGINEERING; D. Software; D.3 PROGRAMMING LANGUAGES

entry:
@InProceedings{Kahan:1982:NOS,
  author =       "W. Kahan and Jerome T. Coonen",
  title =        "The Near Orthogonality of Syntax, Semantics, and
                 Diagnostics in Numerical Programming Environments",
  crossref =     "Reid:1982:RBN",
  pages =        "103--115",
  year =         "1982",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "D.3; G.1.0; F.3.2; D.2.5; D.2; D.3",
  content =      "Programmers of early computers had to content
                 themselves with what the machine designers offered and
                 be glad that the hardware worked at all. Later, with
                 the introduction of higher-level languages, the
                 computing environment was modified by the language
                 designers who attempted to resolve a three-cornered
                 tug-of-war among implementation efficiency, program
                 portability, and usefulness to the programmer. The
                 conflict between the first two resulted in languages
                 that reflected the least common denominator of
                 available hardware, since language designers were
                 disinclined to mention any capability not available on
                 all computers. A case in point is floating-point
                 arithmetic, where the subtleties of overflow,
                 underflow, and rounding are generally well beyond the
                 control of the programmer in a high-level language. The
                 new standard for binary floating-point arithmetic that
                 has been proposed by IEEE Computer Society's
                 Floating-Point Committee, Task P754 [1], makes an
                 attempt to escape from this situation. It represents
                 the Committee's view of the floating-point requirements
                 of the \ldots{}",
  CRclass =      "D.3.1 Formal Definitions and Theory; G.1.0 General;
                 G.1.0 Computer arithmetic; F.3.2 Semantics of
                 Programming Languages; F.3.2 Algebraic approaches to
                 semantics; D.2.5 Testing and Debugging; D.2.5
                 Diagnostics; D.2.6 Programming Environments; D.3.3
                 Language Constructs",
  CRnumber =     "8401-0021",
  descriptor =   "Software, PROGRAMMING LANGUAGES, Formal Definitions
                 and Theory; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic; Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics
                 of Programming Languages, Algebraic approaches to
                 semantics; Software, SOFTWARE ENGINEERING, Testing and
                 Debugging, Diagnostics; Software, SOFTWARE ENGINEERING,
                 Programming Environments; Software, PROGRAMMING
                 LANGUAGES, Language Constructs",
  genterm =      "LANGUAGES; STANDARDIZATION",
  keywords =     "floating-point arithmetic; rounding errors",
  remark =       "This article forms the body of \cite[Chapter
                 3]{Coonen:1984:CPS}.",
  reviewer =     "M. Marcotty; Marcotty, M",
  source =       "in the relationship between numerical computation and
                 programming languages. Proc. IFIP TC2 working
                 conference (Boulder, CO, Aug. 3--7, 1981) J. K. Reid
                 (Ed.) Elsevier North-Holland, Inc., New York, 1982",
  subject =      "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
                 of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of
                 Computation; F.3 LOGICS AND MEANINGS OF PROGRAMS; D.
                 Software; D.2 SOFTWARE ENGINEERING; D. Software; D.2
                 SOFTWARE ENGINEERING; D. Software; D.3 PROGRAMMING
                 LANGUAGES",
}


bibtype: book
filename: fparith.bib
label: Katzan:1982:IAA
author: Harry Katzan
title: Invitation to Ada and Ada reference manual (July 1980)
publisher: PBI
address: New York, NY, USA
pages: xi + 429
year: 1982
ISBN: 0-89433-132-9 OR 0894331329
ISBN13: 978-0-89433-132-9 OR 9780894331329
LCCN: QA76.73.A35 K37 1982
bibdate: Wed Oct 13 06:37:40 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.13 06:37:40 MDT
subject: Ada (computer program language)
acknowledgement: ack-nhfb
rawauthor: Harry Katzan
rawtitle: Invitation to {Ada} and {Ada} reference manual ({July 1980})
remark:
See cite [p. 1.10]Coonen:1984:CPS for negative comments about the floating-point model for Ada in this book.

entry:
@Book{Katzan:1982:IAA,
  author =       "Harry Katzan",
  title =        "Invitation to {Ada} and {Ada} reference manual ({July
                 1980})",
  publisher =    "PBI",
  address =      "New York, NY, USA",
  pages =        "xi + 429",
  year =         "1982",
  ISBN =         "0-89433-132-9",
  ISBN-13 =      "978-0-89433-132-9",
  LCCN =         "QA76.73.A35 K37 1982",
  bibdate =      "Wed Oct 13 06:37:40 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "See \cite[p. 1.10]{Coonen:1984:CPS} for negative
                 comments about the floating-point model for Ada in this
                 book.",
  subject =      "Ada (computer program language)",
}


bibtype: inproceedings
filename: fparith.bib
label: Kerkhoff:1982:LDM
author: H. G. Kerkhoff and H. A. J. Robroek
editor: IEEE
booktitle: Proceedings of the 12th International Symposium on Multiple-Valued Logic, May 1982
title: The Logic Design of Multiple-valued Logic Functions Using CCD's
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 35--44
year: 1982
bibdate: Sat Aug 22 09:16:45 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 09:16:45 ???
acknowledgement: ack-nhfb
rawauthor: H. G. Kerkhoff and H. A. J. Robroek
rawbooktitle: Proceedings of the 12th International Symposium on Multiple-Valued Logic, May 1982
raweditor: {IEEE}
rawtitle: The Logic Design of Multiple-valued Logic Functions Using {CCD}'s
entry:
@InProceedings{Kerkhoff:1982:LDM,
  author =       "H. G. Kerkhoff and H. A. J. Robroek",
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 12th International Symposium on
                 Multiple-Valued Logic, May 1982",
  title =        "The Logic Design of Multiple-valued Logic Functions
                 Using {CCD}'s",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "35--44",
  year =         "1982",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 09:16:45 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Korn:1982:EDF
author: G. A. Korn
journal: j-SIMULATION
volume: 38
number: 5
pages: 151--159
month: may
monthnumber: 5
year: 1982
CODEN: SIMUA2
ISSN: 0037-5497 (print), 1741-3133 (electronic) OR 00375497 (print), 17413133 (electronic)
ISSNL: 0037-5497 OR 00375497
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: Simulation
acknowledgement: ack-nhfb
journalURL: http://sim.sagepub.com/content/by/year
rawauthor: G. A. Korn
title:
EARLY DESIRE: a floating-point equation language simulation system for minicomputers and microcomputers

subject:
I. Computing Methodologies; I.6 SIMULATION AND MODELING; G. Mathematics of Computing; G.m MISCELLANEOUS; D. Software; D.4 OPERATING SYSTEMS

rawtitle:
{EARLY DESIRE}: a floating-point equation language simulation system for minicomputers and microcomputers

entry:
@Article{Korn:1982:EDF,
  author =       "G. A. Korn",
  title =        "{EARLY DESIRE}: a floating-point equation language
                 simulation system for minicomputers and
                 microcomputers",
  journal =      j-SIMULATION,
  volume =       "38",
  number =       "5",
  pages =        "151--159",
  month =        may,
  year =         "1982",
  CODEN =        "SIMUA2",
  ISSN =         "0037-5497 (print), 1741-3133 (electronic)",
  ISSN-L =       "0037-5497",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "I.6; G; D.4.7",
  CRclass =      "I.6.2 Simulation Languages; D.4.7 Organization and
                 Design; D.4.7 Interactive systems",
  descriptor =   "Computing Methodologies, SIMULATION AND MODELING,
                 Simulation Languages; Mathematics of Computing,
                 MISCELLANEOUS; Software, OPERATING SYSTEMS,
                 Organization and Design, Interactive systems",
  fjournal =     "Simulation",
  genterm =      "DESIGN; LANGUAGES",
  guideno =      "08785",
  journal-URL =  "http://sim.sagepub.com/content/by/year",
  subject =      "I. Computing Methodologies; I.6 SIMULATION AND
                 MODELING; G. Mathematics of Computing; G.m
                 MISCELLANEOUS; D. Software; D.4 OPERATING SYSTEMS",
}


bibtype: article
filename: fparith.bib
label: Leuprecht:1982:PAR
author: H. Leuprecht and W. Oberaigner
title: Parallel Algorithms for the Rounding-Exact Summation of Floating-Point Numbers
journal: j-COMPUTING
volume: 28
number: 2
pages: 89--104
year: 1982
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 68A05 (65G05)
MRnumber: 83c:68009
bibdate: Fri Dec 08 11:53:42 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 11:53:42 ???
fjournal: Computing: Archiv fur informatik und numerik
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: H. Leuprecht and W. Oberaigner
rawtitle: Parallel Algorithms for the Rounding-Exact Summation of Floating-Point Numbers
entry:
@Article{Leuprecht:1982:PAR,
  author =       "H. Leuprecht and W. Oberaigner",
  title =        "Parallel Algorithms for the Rounding-Exact Summation
                 of Floating-Point Numbers",
  journal =      j-COMPUTING,
  volume =       "28",
  number =       "2",
  pages =        "89--104",
  month =        "????",
  year =         "1982",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68A05 (65G05)",
  MRnumber =     "83c:68009",
  bibdate =      "Fri Dec 08 11:53:42 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: McCormick:1982:EFM
author: S. F. McCormick and G. D. Taylor and D. V. Pryor
title: Evaluation of Functions on Microcomputers: $ ln (x) $
journal: j-COMPUT-MATH-APPL
volume: 8
number: 5
pages: 389--392
year: 1982
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Thu Sep 15 18:41:01 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 18:41:01 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: S. F. McCormick and G. D. Taylor and D. V. Pryor
rawtitle: Evaluation of Functions on Microcomputers: $ \ln (x) $
entry:
@Article{McCormick:1982:EFM,
  author =       "S. F. McCormick and G. D. Taylor and D. V. Pryor",
  title =        "Evaluation of Functions on Microcomputers: $ \ln (x)
                 $",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "8",
  number =       "5",
  pages =        "389--392",
  year =         "1982",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:41:01 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: article
filename: fparith.bib
label: McPherson:1982:LSG
author: John C. McPherson and Frank E. Hamilton and Robert R. Seeber, Jr.
title: A Large-Scale, general-Purpose Electronic Digital calculator: The SSEC
journal: j-ANN-HIST-COMPUT
volume: 4
number: 4
pages: 313--326
month: oct
monthnumber: 10
year: 1982
CODEN: AHCOE5
ISSN: 0164-1239 OR 01641239
ISSNL: 0164-1239 OR 01641239
bibdate: Fri Nov 1 15:29:19 MST 2002
bibtimestamp: 2002.11.01 15:29:19 MST
fjournal: Annals of the History of Computing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650
rawauthor: John C. McPherson and Frank E. Hamilton and Robert R. {Seeber, Jr.}
rawtitle: A Large-Scale, general-Purpose Electronic Digital calculator: The {SSEC}
URL:
http://dlib.computer.org/an/books/an1982/pdf/a4313.pdf; http://www.computer.org/annals/an1982/a4313abs.htm

entry:
@Article{McPherson:1982:LSG,
  author =       "John C. McPherson and Frank E. Hamilton and Robert R.
                 {Seeber, Jr.}",
  title =        "A Large-Scale, general-Purpose Electronic Digital
                 calculator: The {SSEC}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "4",
  number =       "4",
  pages =        "313--326",
  month =        oct # "\slash " # dec,
  year =         "1982",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:19 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/an1982/pdf/a4313.pdf;
                 http://www.computer.org/annals/an1982/a4313abs.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: Monroe:1982:FFP
author: Alfred J. Monroe
title: Forth Floating Point Package
journal: j-DDJ
volume: 7
number: 9
pages: 16--??
month: sep
monthnumber: 9
year: 1982
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Alfred J. Monroe
rawtitle: {Forth} Floating Point Package
entry:
@Article{Monroe:1982:FFP,
  author =       "Alfred J. Monroe",
  title =        "{Forth} Floating Point Package",
  journal =      j-DDJ,
  volume =       "7",
  number =       "9",
  pages =        "16--??",
  month =        sep,
  year =         "1982",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Oklobdzija:1982:LSR
author: V. G. Oklobdzija and M. D. Ercegovac
title: An On-Line Square Root Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 1
pages: 70--75
month: jan
monthnumber: 1
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1675887
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:09 MDT 2011
bibtimestamp: 2011.07.10 10:33:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. G. Oklobdzija and M. D. Ercegovac
rawtitle: An On-Line Square Root Algorithm
entry:
@Article{Oklobdzija:1982:LSR,
  author =       "V. G. Oklobdzija and M. D. Ercegovac",
  title =        "An On-Line Square Root Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "1",
  pages =        "70--75",
  month =        jan,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675887",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
  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: Palmer:1982:VRN
author: J. F. Palmer
title: VLSI and the Revolution in Numeric Computation
crossref: Ruschitzka:1982:IWC
pages: 339--341
year: 1982
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. F. Palmer
rawtitle: {VLSI} and the Revolution in Numeric Computation
entry:
@InProceedings{Palmer:1982:VRN,
  author =       "J. F. Palmer",
  title =        "{VLSI} and the Revolution in Numeric Computation",
  crossref =     "Ruschitzka:1982:IWC",
  pages =        "339--341",
  year =         "1982",
  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: incollection
filename: fparith.bib
label: Phillips:1982:BC
author: E. William Phillips
title: Binary Calculation
crossref: Randell:1982:ODC
pages: 303--314
year: 1982
bibdate: Wed Oct 13 09:51:37 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 09:51:37 ???
acknowledgement: ack-nhfb
rawauthor: E. William Phillips
rawtitle: Binary Calculation
remark:
The 1936 epigraph credited to this author in cite [Chapter 7]Coonen:1984:CPS says: ``The ultimate aim is to persuade all of the civilized world to abandon the decimal numeration and to use octonal in its place; to discontinue counting in tens and to count in eights instead. However, it seems unlikely that the whole civilized world will be persuaded to complete this change during the next twelve months, having previously declined similar invitations.''

entry:
@InCollection{Phillips:1982:BC,
  author =       "E. William Phillips",
  title =        "Binary Calculation",
  crossref =     "Randell:1982:ODC",
  pages =        "303--314",
  year =         "1982",
  bibdate =      "Wed Oct 13 09:51:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "The 1936 epigraph credited to this author in
                 \cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
                 aim is to persuade all of the civilized world to
                 abandon the decimal numeration and to use octonal in
                 its place; to discontinue counting in tens and to count
                 in eights instead. However, it seems unlikely that the
                 whole civilized world will be persuaded to complete
                 this change during the next twelve months, having
                 previously declined similar invitations.''",
}


bibtype: inproceedings
filename: fparith.bib
label: Rall:1982:ACA
author: L. B. Rall
editor: Anonymous
booktitle: Proceedings of the 1982 Army Numerical Analysis and Computers Conference
title: Accurate computer arithmetic for scientific computation
volume: 82--83
publisher: US Army Research Office
address: Research Triangle Park, NC, USA
pages: 343--356
month: aug
monthnumber: 8
year: 1982
bibdate: Wed Oct 13 21:52:01 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 21:52:01 ???
note: Two volumes.
URL: http://books.google.com/books?id=pFb-QQAACAAJ
remark: The theme of the 1982 Conference was Grid Techniques for Partial Differential Equations.
acknowledgement: ack-nhfb
bookpages: xiv + 606
rawauthor: L. B. Rall
rawbooktitle: {Proceedings of the 1982 Army Numerical Analysis and Computers Conference}
raweditor: Anonymous
rawnote: Two volumes.
rawtitle: Accurate computer arithmetic for scientific computation
abstract:
The operations of accurate arithmetic can be implemented easily on a microcomputer or a computer with microprogrammable arithmetic operations. In addition, for accurate final results, a compiler is necessary which will select the appropriate operations. A language of this type (PASCAL-SC) was developed. Along with accurate real arithmetic, this compiler provides accurate complex arithmetic, real and complex interval arithmetic, and vector and matrix arithmetic over these data types. Some features of PASCAL-SC related to scientific and engineering computation are described. In most cases, the operations of accurate arithmetic are performed at the same speed as ordinary (uncontrolled) floating-point arithmetic.

keywords:
analysis (mathematics); arithmetic; computation; microcomputers; microprogramming; Pascal (programming language)

subject:
Numerical analysis; Computer programs; Congresses; Numerical Mathematics. Computer Hardware. Computers. Partial differential equations. Symposia. Numerical analysis. Grids. Computations. Methodology. Mathematical programming. Finite difference theory. Finite element analysis. Boundaries. Hydrodynamics. Gas dynamics. Interior ballistics. Autofrettage. Land mines. Blast loads. Conduction(heat transfer) Magnet coils. Water waves. Currents

rawabstract:
The operations of accurate arithmetic can be implemented easily on a microcomputer or a computer with microprogrammable arithmetic operations. In addition, for accurate final results, a compiler is necessary which will select the appropriate operations. A language of this type (PASCAL-SC) was developed. Along with accurate real arithmetic, this compiler provides accurate complex arithmetic, real and complex interval arithmetic, and vector and matrix arithmetic over these data types. Some features of PASCAL-SC related to scientific and engineering computation are described. In most cases, the operations of accurate arithmetic are performed at the same speed as ordinary (uncontrolled) floating-point arithmetic.

entry:
@InProceedings{Rall:1982:ACA,
  author =       "L. B. Rall",
  editor =       "Anonymous",
  booktitle =    "{Proceedings of the 1982 Army Numerical Analysis and
                 Computers Conference}",
  title =        "Accurate computer arithmetic for scientific
                 computation",
  volume =       "82--83",
  publisher =    "US Army Research Office",
  address =      "Research Triangle Park, NC, USA",
  bookpages =    "xiv + 606",
  pages =        "343--356",
  month =        aug,
  year =         "1982",
  bibdate =      "Wed Oct 13 21:52:01 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  URL =          "http://books.google.com/books?id=pFb-QQAACAAJ",
  abstract =     "The operations of accurate arithmetic can be
                 implemented easily on a microcomputer or a computer
                 with microprogrammable arithmetic operations. In
                 addition, for accurate final results, a compiler is
                 necessary which will select the appropriate operations.
                 A language of this type (PASCAL-SC) was developed.
                 Along with accurate real arithmetic, this compiler
                 provides accurate complex arithmetic, real and complex
                 interval arithmetic, and vector and matrix arithmetic
                 over these data types. Some features of PASCAL-SC
                 related to scientific and engineering computation are
                 described. In most cases, the operations of accurate
                 arithmetic are performed at the same speed as ordinary
                 (uncontrolled) floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "analysis (mathematics); arithmetic; computation;
                 microcomputers; microprogramming; Pascal (programming
                 language)",
  meetingname =  "Army Numerical Analysis and Computers Conference (1982
                 : Vicksburg, Miss.)",
  remark =       "The theme of the 1982 Conference was Grid Techniques
                 for Partial Differential Equations.",
  subject =      "Numerical analysis; Computer programs; Congresses;
                 Numerical Mathematics. Computer Hardware. Computers.
                 Partial differential equations. Symposia. Numerical
                 analysis. Grids. Computations. Methodology.
                 Mathematical programming. Finite difference theory.
                 Finite element analysis. Boundaries. Hydrodynamics. Gas
                 dynamics. Interior ballistics. Autofrettage. Land
                 mines. Blast loads. Conduction(heat transfer) Magnet
                 coils. Water waves. Currents",
  xxtitle =      "Accurate arithmetic for scientific computation",
  xxvolume =     "82-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Ramnarayan:1982:AER
author: R. Ramnarayan and F. Taylor
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '82
title: Analysis of errors in residue number system (RNS) based IIR digital filters
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 56--59
year: 1982
DOI: https://doi.org/10.1049/el:19820632
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: R. Ramnarayan and F. Taylor
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '82}
rawtitle: Analysis of errors in residue number system ({RNS}) based {IIR} digital filters
entry:
@InProceedings{Ramnarayan:1982:AER,
  author =       "R. Ramnarayan and F. Taylor",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '82}",
  title =        "Analysis of errors in residue number system ({RNS})
                 based {IIR} digital filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "56--59",
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19820632",
  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 =      "The problem of analyzing errors in Residue Number
                 System (RNS) based IIR Digital filters is considered in
                 this paper. There are basically three types of errors
                 in RNS based digital filters, They are coefficient
                 quantization errors(1), scaling errors \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Rix:1982:UQA
author: P. Rix
title: Universeller Quadratwurzel-Algorithmus toenglish Universal Square Root Algorithms endtoenglish
journal: j-ELECTRONIK
volume: 23
pages: 81--82
year: 1982
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: P. Rix
rawtitle:
{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus} \toenglish {Universal Square Root Algorithms} \endtoenglish

entry:
@Article{Rix:1982:UQA,
  author =       "P. Rix",
  title =        "{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus}
                 \toenglish {Universal Square Root Algorithms}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "23",
  pages =        "81--82",
  year =         "1982",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  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,
  fjournal =     "Elektronik",
}


bibtype: article
filename: fparith.bib
label: Rump:1982:CR
author: Siegfried M. Rump
title: Computer und Rechengenauigkeit toenglish Computer and Computational Precision endtoenglish
journal: j-ELEK-RECHENANLAGEN
volume: 24
number: 6
pages: 268--277
month: dec
monthnumber: 12
year: 1982
CODEN: ELRAA4
ISSN: 0013-5720 OR 00135720
bibdate: Sat Feb 10 12:41:06 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.10 12:41:06 ???
fjournal: Elektronische Rechenanlagen
acknowledgement: ack-nj
rawauthor: Siegfried M. Rump
rawtitle: {Computer und Rechengenauigkeit} \toenglish {Computer and Computational Precision} \endtoenglish
entry:
@Article{Rump:1982:CR,
  author =       "Siegfried M. Rump",
  title =        "{Computer und Rechengenauigkeit} \toenglish {Computer
                 and Computational Precision} \endtoenglish",
  journal =      j-ELEK-RECHENANLAGEN,
  volume =       "24",
  number =       "6",
  pages =        "268--277",
  month =        dec,
  year =         "1982",
  CODEN =        "ELRAA4",
  ISSN =         "0013-5720",
  bibdate =      "Sat Feb 10 12:41:06 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronische Rechenanlagen",
}


bibtype: article
filename: fparith.bib
label: Sacks-Davis:1982:ARN
author: R. Sacks-Davis
title: Applications of Redundant Number Representations to Decimal Arithmetic
journal: j-COMP-J
volume: 25
number: 4
pages: 471--477
month: nov
monthnumber: 11
year: 1982
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Mar 25 13:51:56 MST 1997
bibtimestamp: 1997.03.25 13:51:56 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C5260 (Digital signal processing)
corpsource: Department of Computer Sci., Monash University, Clayton, Vic., Australia
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: R. Sacks-Davis
rawtitle: Applications of Redundant Number Representations to Decimal Arithmetic
bibsource:
Compendex database; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/471.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/472.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/473.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/474.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/475.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/476.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/477.tif

abstract:
A decimal arithmetic unit is proposed for both integer and floating-point computations. To achieve comparable speed to a binary arithmetic unit, the decimal unit is based on a redundant number representation. With this representation no loss of compactness is made relative to binary coded decimal (BCD) form. In this paper the hardware required for the implementation of the basic operations of addition, subtraction, multiplication and division are described and the properties of floating-point arithmetic based on a redundant number representation are investigated.

keywords:
addition; binary; binary arithmetic unit; coded decimal; computers, digital; decimal floating-point arithmetic; digital arithmetic; division; floating point arithmetic; floating-point; integer; multiplication; redundant number representations; subtraction

remark:
The redundant number representation postpones the need to carry during add, subtract, multiply, and divide, delaying it until the final rounding step in a store instruction. See cite Fahmy:2003:CRF,Fahmy:2003:RDF.

rawabstract:
A decimal arithmetic unit is proposed for both integer and floating-point computations. To achieve comparable speed to a binary arithmetic unit, the decimal unit is based on a redundant number representation. With this representation no loss of compactness is made relative to binary coded decimal (BCD) form. In this paper the hardware required for the implementation of the basic operations of addition, subtraction, multiplication and division are described and the properties of floating-point arithmetic based on a redundant number representation are investigated.

entry:
@Article{Sacks-Davis:1982:ARN,
  author =       "R. Sacks-Davis",
  title =        "Applications of Redundant Number Representations to
                 Decimal Arithmetic",
  journal =      j-COMP-J,
  volume =       "25",
  number =       "4",
  pages =        "471--477",
  month =        nov,
  year =         "1982",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/471.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/472.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/473.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/474.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/475.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/476.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/477.tif",
  abstract =     "A decimal arithmetic unit is proposed for both integer
                 and floating-point computations. To achieve comparable
                 speed to a binary arithmetic unit, the decimal unit is
                 based on a redundant number representation. With this
                 representation no loss of compactness is made relative
                 to binary coded decimal (BCD) form. In this paper the
                 hardware required for the implementation of the basic
                 operations of addition, subtraction, multiplication and
                 division are described and the properties of
                 floating-point arithmetic based on a redundant number
                 representation are investigated.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5260 (Digital signal processing)",
  classification = "721; 723",
  corpsource =   "Department of Computer Sci., Monash University,
                 Clayton, Vic., Australia",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "addition; binary; binary arithmetic unit; coded
                 decimal; computers, digital; decimal floating-point
                 arithmetic; digital arithmetic; division; floating
                 point arithmetic; floating-point; integer;
                 multiplication; redundant number representations;
                 subtraction",
  remark =       "The redundant number representation postpones the need
                 to carry during add, subtract, multiply, and divide,
                 delaying it until the final rounding step in a store
                 instruction. See
                 \cite{Fahmy:2003:CRF,Fahmy:2003:RDF}.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Samsen:1982:AFP
author: G. R. Samsen
title: An Advanced Floating Point Processor to Enhance Speed of Mathematical Processing
crossref: Southcon:1982:SCR
pages: 16/1/1--3
year: 1982
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: G. R. Samsen
rawtitle: An Advanced Floating Point Processor to Enhance Speed of Mathematical Processing
entry:
@InProceedings{Samsen:1982:AFP,
  author =       "G. R. Samsen",
  title =        "An Advanced Floating Point Processor to Enhance Speed
                 of Mathematical Processing",
  crossref =     "Southcon:1982:SCR",
  pages =        "16/1/1--3",
  year =         "1982",
  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: Sasaki:1982:EGE
author: T. Sasaki and H. Murao
title: Efficient Gaussian elimination method for symbolic determinants and linear systems
journal: j-TOMS
volume: 8
number: 3
pages: 277--289
month: sep
monthnumber: 9
year: 1982
CODEN: ACMSCU
DOI: https://doi.org/10.1145/356004.356007
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 9 08:26:18 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.09 08:26:18 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
key: Symbolic_determinant; Symbolic_linear_systems; Gaussian_elimination
reviewer: R. J. Fateman; Fateman, R. J
rawauthor: T. Sasaki and H. Murao
rawtitle: Efficient {Gaussian} elimination method for symbolic determinants and linear systems
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION

entry:
@Article{Sasaki:1982:EGE,
  author =       "T. Sasaki and H. Murao",
  key =          "Symbolic_determinant; Symbolic_linear_systems;
                 Gaussian_elimination",
  title =        "Efficient {Gaussian} elimination method for symbolic
                 determinants and linear systems",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "277--289",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356007",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "F.2; G.1.3; I.1.2",
  content =      "The computation of the solution of a linear system
                 whose entries are indeterminates or polynomials is of
                 interest both for theoretic and practical reasons. The
                 similar problem of computing the determinant is
                 important because of the relationship of the
                 determinant and resultant to factorization, polynomial
                 greatest-common-divisor calculations, and computation
                 with algebraic functions. Engineering application areas
                 of this material include the analysis of electrical or
                 other networks.\par

                 These computation problems are quite distinct from
                 others which would appear to be superficially similar,
                 namely numerical linear algebra problems. The result of
                 computing a numerical determinant is a floating point
                 number with an associated error. The result of
                 computing an exact algebraic determinant is, typically,
                 a large expression whose terms may be rearranged into
                 various ``factored'' forms for savings in computation
                 time and space. This answer has no error
                 whatsoever.\par

                 Clever and efficient programs in each domain have been
                 shown to be disastrous in the other. Thus one of the
                 best algebraic techniques for determinant calculations
                 for ``sparse polynomial'' matrices is expansion by
                 minors [1]; whereas Gaussian elimination is far
                 superior \ldots{}",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; G.1.3
                 Numerical Linear Algebra; G.1.3 Linear systems (direct
                 and iterative methods); I.1.2 Algorithms; I.1.2
                 Algebraic algorithms",
  CRnumber =     "40106",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods); Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "ALGORITHMS; PERFORMANCE",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. J. Fateman; Fateman, R. J",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}


bibtype: article
filename: fparith.bib
label: Sasaki:1982:PFM
author: T. Sasaki and Y. Kanada
title: Practically Fast Multiple Precision Evaluation of LOG ($ X $)
journal: j-INFO-PROC
volume: 5
number: 4
pages: 247--250
year: 1982
bibdate: Thu Sep 8 08:20:54 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:20:54 ???
acknowledgement: ack-nj
rawauthor: T. Sasaki and Y. Kanada
rawtitle: Practically Fast Multiple Precision Evaluation of {LOG} ($ {X} $)
entry:
@Article{Sasaki:1982:PFM,
  author =       "T. Sasaki and Y. Kanada",
  title =        "Practically Fast Multiple Precision Evaluation of
                 {LOG} ($ {X} $)",
  journal =      j-INFO-PROC,
  volume =       "5",
  number =       "4",
  pages =        "247--250",
  month =        "????",
  year =         "1982",
  bibdate =      "Thu Sep 8 08:20:54 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: Schatte:1982:FPF
author: P. Schatte
title: The Frequency of Postshifts in Floating-Point Multiplication
journal: Elektronische Informationsverarbeitung und Kybernetik
volume: 18
number: 9
pages: 523--526
year: 1982
bibdate: Thu Sep 1 10:15:07 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:07 ???
acknowledgement: ack-nj
rawauthor: P. Schatte
rawtitle: The Frequency of Postshifts in Floating-Point Multiplication
entry:
@Article{Schatte:1982:FPF,
  author =       "P. Schatte",
  title =        "The Frequency of Postshifts in Floating-Point
                 Multiplication",
  journal =      "Elektronische Informationsverarbeitung und
                 Kybernetik",
  volume =       "18",
  number =       "9",
  pages =        "523--526",
  month =        "????",
  year =         "1982",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Sewell:1982:RLT
author: B. T. Sewell
title: A Rapid Lookup Table Method for Trigonometric Functions
journal: j-SPE
volume: 12
number: 10
pages: 885--887
month: oct
monthnumber: 10
year: 1982
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
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: Software---Practice and Experience
keywords: algorithms
acknowledgement: ack-nj
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: B. T. Sewell
rawtitle: A Rapid Lookup Table Method for Trigonometric Functions
subject:
G Mathematics of Computing, MISCELLANEOUS J.2 Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Chemistry

entry:
@Article{Sewell:1982:RLT,
  author =       "B. T. Sewell",
  title =        "A Rapid Lookup Table Method for Trigonometric
                 Functions",
  journal =      j-SPE,
  volume =       "12",
  number =       "10",
  pages =        "885--887",
  month =        oct,
  year =         "1982",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  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 =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "algorithms",
  subject =      "G Mathematics of Computing, MISCELLANEOUS \\ J.2
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Chemistry",
}


bibtype: incollection
filename: fparith.bib
label: Sheldon:1982:ICP
author: John W. Sheldon and Liston Tatum
title: The IBM Card-Programmed Electronic Calculator (1951)
crossref: Randell:1982:ODC
pages: 233--239
year: 1982
bibdate: Sun Nov 03 08:36:11 2002
bibtimestamp: 2002.11.03 08:36:11 ???
acknowledgement: ack-nhfb
rawauthor: John W. Sheldon and Liston Tatum
rawtitle: The {IBM} Card-Programmed Electronic Calculator (1951)
entry:
@InCollection{Sheldon:1982:ICP,
  author =       "John W. Sheldon and Liston Tatum",
  title =        "The {IBM} Card-Programmed Electronic Calculator
                 (1951)",
  crossref =     "Randell:1982:ODC",
  pages =        "233--239",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Sippel:1982:FRI
author: Timothy N. Sippel
title: Floating RISCS: implementation and analysis of floating point on RISC I
type: Electrical Engineering and Computer Sciences Master of Science Report
school: University of California, Department of Electrical Engineering and Computer Sciences
address: Berkeley, CA, USA
pages: various
year: 1982
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: Timothy N. Sippel
rawtitle: Floating {RISCS}: implementation and analysis of floating point on {RISC} {I}
entry:
@MastersThesis{Sippel:1982:FRI,
  author =       "Timothy N. Sippel",
  title =        "Floating {RISCS}: implementation and analysis of
                 floating point on {RISC} {I}",
  type =         "Electrical Engineering and Computer Sciences Master of
                 Science Report",
  school =       "University of California, Department of Electrical
                 Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "various",
  year =         "1982",
  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: Sips:1982:CPM
author: H. J. Sips
title: Comments on ``An $ O(n) $ Parallel Multiplier with Bit-Sequential Input and Output''
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 4
pages: 325--327
month: apr
monthnumber: 4
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1676000
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:11 MDT 2011
bibtimestamp: 2011.07.10 10:33:11 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676000
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. J. Sips
rawtitle: Comments on {``An $ O(n) $ Parallel Multiplier with Bit-Sequential Input and Output''}
entry:
@Article{Sips:1982:CPM,
  author =       "H. J. Sips",
  title =        "Comments on {``An $ O(n) $ Parallel Multiplier with
                 Bit-Sequential Input and Output''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "4",
  pages =        "325--327",
  month =        apr,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676000",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:11 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=1676000",
  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: Strader:1982:CBS
author: N. R. Strader and V. T. Rhyne
title: A Canonical Bit-Sequential Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 8
pages: 791--795
month: aug
monthnumber: 8
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1676085
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:14 MDT 2011
bibtimestamp: 2011.07.10 10:33:14 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676085
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. R. Strader and V. T. Rhyne
rawtitle: A Canonical Bit-Sequential Multiplier
entry:
@Article{Strader:1982:CBS,
  author =       "N. R. Strader and V. T. Rhyne",
  title =        "A Canonical Bit-Sequential Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "8",
  pages =        "791--795",
  month =        aug,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676085",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:14 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=1676085",
  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: Tan:1982:ADC
author: Chung-I Tan and B. McInnis
title: Adaptive digital control implemented using residue number systems
journal: j-IEEE-TRANS-AUTOMAT-CONTR
volume: 27
number: 2
pages: 499--502
month: apr
monthnumber: 4
year: 1982
CODEN: IETAA9
DOI: https://doi.org/10.1109/CDC.1981.269326
ISSN: 0018-9286 (print), 1558-2523 (electronic) OR 00189286 (print), 15582523 (electronic)
ISSNL: 0018-9286 OR 00189286
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
note: See comments cite Pei:1984:CAD.
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24189
fjournal: IEEE Transactions on Automatic Control
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
rawauthor: Chung-I Tan and B. McInnis
rawnote: See comments \cite{Pei:1984:CAD}.
rawtitle: Adaptive digital control implemented using residue number systems
entry:
@Article{Tan:1982:ADC,
  author =       "Chung-I Tan and B. McInnis",
  title =        "Adaptive digital control implemented using residue
                 number systems",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "27",
  number =       "2",
  pages =        "499--502",
  month =        apr,
  year =         "1982",
  CODEN =        "IETAA9",
  DOI =          "https://doi.org/10.1109/CDC.1981.269326",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Pei:1984:CAD}.",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24189",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The application of residue number systems for the
                 implementation of adaptive digital controllers is
                 presented. Division operations are avoided through the
                 use of iteration to solve for the value of the control.
                 Decoding computations are simplified \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Taylor:1982:ARM
author: F. J. Taylor and C. H. Huang
title: An Autoscale Residue Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 4
pages: 321--325
month: apr
monthnumber: 4
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1675999
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:30:01 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:30:01 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. J. Taylor and C. H. Huang
rawtitle: An Autoscale Residue Multiplier
entry:
@Article{Taylor:1982:ARM,
  author =       "F. J. Taylor and C. H. Huang",
  title =        "An Autoscale Residue Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "4",
  pages =        "321--325",
  month =        apr,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675999",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:30:01 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: Taylor:1982:VRA
author: F. J. Taylor
title: A VLSI Residue Arithmetic Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-31
number: 6
pages: 540--546
month: jun
monthnumber: 6
year: 1982
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1982.1676036
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:33:12 MDT 2011
bibtimestamp: 2011.07.10 10:33:12 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676036
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. J. Taylor
rawtitle: A {VLSI} Residue Arithmetic Multiplier
entry:
@Article{Taylor:1982:VRA,
  author =       "F. J. Taylor",
  title =        "A {VLSI} Residue Arithmetic Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "6",
  pages =        "540--546",
  month =        jun,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676036",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:12 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=1676036",
  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: Teachey:1982:SRX
author: R. D. Teachey
title: Square-Root-X Comparison --- New Results Discovered
journal: j-IEEE-MICRO
volume: 2
number: 4
pages: 5--5
month: oct
monthnumber: 10
year: 1982
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1982.290929
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Science Citation Index database (1980--2000)
bibtimestamp: 2000.12.14 06:08:58 MST
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: R. D. Teachey
rawtitle: Square-Root-{X} Comparison --- New Results Discovered
entry:
@Article{Teachey:1982:SRX,
  author =       "R. D. Teachey",
  title =        "Square-Root-{X} Comparison --- New Results
                 Discovered",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "4",
  pages =        "5--5",
  month =        oct # "\slash " # dec,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.290929",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: incollection
filename: fparith.bib
label: TorresyQuevedo:1982:EAD
author: Leonardo Torres y Quevedo
title: Essays on Automatics --- Its Definitions --- Theoretical Extent of its Applications (1914)
crossref: Randell:1982:ODC
pages: 89--107
year: 1982
bibdate: Sun Nov 03 08:36:11 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.03 08:36:11 ???
acknowledgement: ack-nhfb
rawauthor: Leonardo {Torres y Quevedo}
rawtitle: Essays on Automatics --- Its Definitions --- Theoretical Extent of its Applications (1914)
remark:
This translation and reprint contains a description of what is believed to be the first design, albeit purely theoretical, and for an electromechanical device, of floating-point arithmetic. See, however, the independent work, and first practical implementation of floating-point arithmetic of Zuse cite Zuse:1982:MAE,Zuse:1982:OCD.

entry:
@InCollection{TorresyQuevedo:1982:EAD,
  author =       "Leonardo {Torres y Quevedo}",
  title =        "Essays on Automatics --- Its Definitions ---
                 Theoretical Extent of its Applications (1914)",
  crossref =     "Randell:1982:ODC",
  pages =        "89--107",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "This translation and reprint contains a description of
                 what is believed to be the first design, albeit purely
                 theoretical, and for an electromechanical device, of
                 floating-point arithmetic. See, however, the
                 independent work, and first practical implementation of
                 floating-point arithmetic of Zuse
                 \cite{Zuse:1982:MAE,Zuse:1982:OCD}.",
}


bibtype: article
filename: fparith.bib
label: Turner:1982:DLS
author: Peter R. Turner
title: The distribution of leading significant digits
journal: j-IMA-J-NUMER-ANAL
volume: 2
number: 4
pages: 407--412
year: 1982
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65G99 (60E05)
MRnumber: 84f:65038
MRreviewer: Seppo Linnainmaa
bibdate: Sat Dec 23 17:06:35 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: Peter R. Turner
rawtitle: The distribution of leading significant digits
entry:
@Article{Turner:1982:DLS,
  author =       "Peter R. Turner",
  title =        "The distribution of leading significant digits",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "2",
  number =       "4",
  pages =        "407--412",
  year =         "1982",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G99 (60E05)",
  MRnumber =     "84f:65038",
  MRreviewer =   "Seppo Linnainmaa",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Velasevic:1982:RLC
author: Dusan M. Velasevic
title: Right-to-Left Code Generation for Arithmetic Expressions
journal: j-COMP-J
volume: 25
number: 3
pages: 316--326
month: aug
monthnumber: 8
year: 1982
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/25.3.316
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:48:13 MST 2012
bibtimestamp: 2012.12.04 14:48:13 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C6110 (Systems analysis and programming); C6120 (File organisation)
corpsource: Faculty of Electrical Engng., University of Belgrade, Belgrade, Yugoslavia
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: Dusan M. Velasevi{\'c}
rawtitle: Right-to-Left Code Generation for Arithmetic Expressions
bibsource:
Compendex database; http://comjnl.oxfordjournals.org/content/25/3.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/; 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/25/3/316.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/316.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/317.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/318.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/319.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/320.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/321.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/322.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/323.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/324.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/325.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/326.tif

keywords:
arithmetic; automatic programming; binary tree structure; code generator; codes, symbolic; data structures; expressions; FORTRAN; notation; postfix; right-to-left code generation; translation grammar; vector-generatrice

entry:
@Article{Velasevic:1982:RLC,
  author =       "Dusan M. Velasevi{\'c}",
  title =        "Right-to-Left Code Generation for Arithmetic
                 Expressions",
  journal =      j-COMP-J,
  volume =       "25",
  number =       "3",
  pages =        "316--326",
  month =        aug,
  year =         "1982",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/25.3.316",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:13 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/25/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/;
                 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/25/3/316.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/316.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/317.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/318.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/319.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/320.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/321.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/322.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/323.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/324.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/325.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/326.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C6110 (Systems analysis and programming); C6120 (File
                 organisation)",
  classification = "723",
  corpsource =   "Faculty of Electrical Engng., University of Belgrade,
                 Belgrade, Yugoslavia",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic; automatic programming; binary tree
                 structure; code generator; codes, symbolic; data
                 structures; expressions; FORTRAN; notation; postfix;
                 right-to-left code generation; translation grammar;
                 vector-generatrice",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Ware:1982:BMF
author: F. A. Ware and W. H. McAllister and J. R. Carlson and D. K. Sun and R. J. Vlach
title: 64 Bit Monolithic Floating Point Processors
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: SC-17
number: 5
pages: 898--907
month: oct
monthnumber: 10
year: 1982
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nj
rawauthor: F. A. Ware and W. H. McAllister and J. R. Carlson and D. K. Sun and R. J. Vlach
rawtitle: 64 Bit Monolithic Floating Point Processors
entry:
@Article{Ware:1982:BMF,
  author =       "F. A. Ware and W. H. McAllister and J. R. Carlson and
                 D. K. Sun and R. J. Vlach",
  title =        "64 Bit Monolithic Floating Point Processors",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "SC-17",
  number =       "5",
  pages =        "898--907",
  month =        oct,
  year =         "1982",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "Describes a set of three processor chips capable of
                 performing 32 and 64 bit floating point add/subtract,
                 multiply, and divide operations. The chips can perform
                 over one million scalar floating point operations per
                 second, and over four million vector \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Waser:1982:IAD
author: Shlomo Waser and Michael J. Flynn
title: Introduction to Arithmetic for Digital Systems Designers
publisher: pub-HRW
address: pub-HRW:adr
pages: xvii + 308
year: 1982
ISBN: 0-03-060571-7 OR 0030605717
ISBN13: 978-0-03-060571-0 OR 9780030605710
LCCN: TK7895 A65 W37 1982
bibdate: Sat Sep 03 09:25:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.03 09:25:17 ???
acknowledgement: ack-nj
rawauthor: Shlomo Waser and Michael J. Flynn
rawtitle: Introduction to Arithmetic for Digital Systems Designers
note:
Master copy output on Alphatype CRS high-resolution phototypesetter. This book went to press while the IEEE 754 Floating-Point Standard was still in development; consequently, some of the material on that system was invalidated by the final Standard (1985) cite IEEE:1985:AIS.

TOC:
Preface Acknowledgments Abbreviations and Symbols 1. Numeric Data Representation 2. Residue Numbers and the Limits of Fast Arithmetic 3. Addition and Subtraction 4. Multiplication 5. Division 6. Pipelining of Arithmetic Operations Appendix. References. Index.

rawnote:
Master copy output on Alphatype CRS high-resolution phototypesetter. This book went to press while the IEEE 754 Floating-Point Standard was still in development; consequently, some of the material on that system was invalidated by the final Standard (1985) \cite{IEEE:1985:AIS}.

rawTOC:
Preface\\ Acknowledgments\\ Abbreviations and Symbols\\ 1. Numeric Data Representation\\ 2. Residue Numbers and the Limits of Fast Arithmetic\\ 3. Addition and Subtraction\\ 4. Multiplication\\ 5. Division\\ 6. Pipelining of Arithmetic Operations\\ Appendix.\\ References.\\ Index.

entry:
@Book{Waser:1982:IAD,
  author =       "Shlomo Waser and Michael J. Flynn",
  title =        "Introduction to Arithmetic for Digital Systems
                 Designers",
  publisher =    pub-HRW,
  address =      pub-HRW:adr,
  pages =        "xvii + 308",
  year =         "1982",
  ISBN =         "0-03-060571-7",
  ISBN-13 =      "978-0-03-060571-0",
  LCCN =         "TK7895 A65 W37 1982",
  bibdate =      "Sat Sep 03 09:25:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Master copy output on Alphatype CRS high-resolution
                 phototypesetter. This book went to press while the IEEE
                 754 Floating-Point Standard was still in development;
                 consequently, some of the material on that system was
                 invalidated by the final Standard (1985)
                 \cite{IEEE:1985:AIS}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  tableofcontents = "Preface\\
                 Acknowledgments\\
                 Abbreviations and Symbols\\
                 1. Numeric Data Representation\\
                 2. Residue Numbers and the Limits of Fast Arithmetic\\
                 3. Addition and Subtraction\\
                 4. Multiplication\\
                 5. Division\\
                 6. Pipelining of Arithmetic Operations\\
                 Appendix.\\
                 References.\\
                 Index.",
}


bibtype: book
filename: fparith.bib
label: Wilkes:1982:PPE
author: M. V. (Maurice Vincent) Wilkes and David J. Wheeler and Stanley Gill
volume: 1
publisher: pub-TOMASH
address: pub-TOMASH:adr
pages: xxxi + 167
year: 1982
ISBN: 0-262-23118-2 (MIT Press 1984), 0-938228-03-X OR 0262231182 (MIT Press 1984), 093822803X
LCCN: QA76.6 .W545 1982
bibdate: Mon Feb 10 11:33:59 MST 2020
bibtimestamp: 2020.02.10 11:33:59 MST
note: With a new introduction by Martin Campbell-Kelly.
series: Charles Babbage Institute reprint series for the history of computing
acknowledgement: ack-nhfb
rawauthor: M. V. (Maurice Vincent) Wilkes and David J. Wheeler and Stanley Gill
rawnote: With a new introduction by Martin Campbell-Kelly.
title:
The Preparation of Programs for an Electronic Digital Computer: with Special Reference to the EDSAC and the Use of a Library of Subroutines

ISBN13:
978-0-262-23118-3 (MIT Press 1984), 978-0-938228-03-5 OR 9780262231183 (MIT Press 1984), 9780938228035

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
The Preparation of Programs for an Electronic Digital Computer: with Special Reference to the {EDSAC} and the Use of a Library of Subroutines

entry:
@Book{Wilkes:1982:PPE,
  author =       "M. V. (Maurice Vincent) Wilkes and David J. Wheeler
                 and Stanley Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer: with Special Reference to the {EDSAC} and the
                 Use of a Library of Subroutines",
  volume =       "1",
  publisher =    pub-TOMASH,
  address =      pub-TOMASH:adr,
  pages =        "xxxi + 167",
  year =         "1982",
  ISBN =         "0-262-23118-2 (MIT Press 1984), 0-938228-03-X",
  ISBN-13 =      "978-0-262-23118-3 (MIT Press 1984),
                 978-0-938228-03-5",
  LCCN =         "QA76.6 .W545 1982",
  bibdate =      "Mon Feb 10 11:33:59 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With a new introduction by Martin Campbell-Kelly.",
  series =       "Charles Babbage Institute reprint series for the
                 history of computing",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Wilson:1982:PC
author: Kenneth G. Wilson
title: Experiences with a floating point systems array processor
crossref: Rodrigue:1982:AC
pages: 279--314
year: 1982
MRclass: 65W05
MRnumber: 759 559
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
acknowledgement: ack-nhfb
rawauthor: Kenneth G. Wilson
rawtitle: Experiences with a floating point systems array processor
entry:
@InCollection{Wilson:1982:PC,
  author =       "Kenneth G. Wilson",
  title =        "Experiences with a floating point systems array
                 processor",
  crossref =     "Rodrigue:1982:AC",
  pages =        "279--314",
  year =         "1982",
  MRclass =      "65W05",
  MRnumber =     "759 559",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Wu:1982:DFA
author: Market Wen-Han Wu
title: Design of a fast addressable hardware floating-point arithmetic package for small computer
type: Thesis (M.S.)
school: Tufts University. Department of Engineering
address: Boston, MA, USA
pages: iii + 102
year: 1982
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.; Microcomputers --- Programming.
acknowledgement: ack-nhfb
rawauthor: Market Wen-Han Wu
rawtitle: Design of a fast addressable hardware floating-point arithmetic package for small computer
entry:
@MastersThesis{Wu:1982:DFA,
  author =       "Market Wen-Han Wu",
  title =        "Design of a fast addressable hardware floating-point
                 arithmetic package for small computer",
  type =         "Thesis ({M.S.})",
  school =       "Tufts University. Department of Engineering",
  address =      "Boston, MA, USA",
  pages =        "iii + 102",
  year =         "1982",
  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.; Microcomputers ---
                 Programming.",
}


bibtype: incollection
filename: fparith.bib
label: Zuse:1982:MAE
author: Konrad Zuse
title: Method for Automatic Execution of Calculations with the aid of Computers (1936)
crossref: Randell:1982:ODC
pages: 163--170
year: 1982
bibdate: Sun Nov 03 08:36:11 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.03 08:36:11 ???
acknowledgement: ack-nhfb
rawauthor: Konrad Zuse
rawtitle: Method for Automatic Execution of Calculations with the aid of Computers (1936)
remark:
This translation and reprint of a German patent application of 11 April 1936 briefly describes the floating-point system that was first successfully implemented in a digital computer, the Zuse Z3, in 1941.

entry:
@InCollection{Zuse:1982:MAE,
  author =       "Konrad Zuse",
  title =        "Method for Automatic Execution of Calculations with
                 the aid of Computers (1936)",
  crossref =     "Randell:1982:ODC",
  pages =        "163--170",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "This translation and reprint of a German patent
                 application of 11 April 1936 briefly describes the
                 floating-point system that was first successfully
                 implemented in a digital computer, the Zuse Z3, in
                 1941.",
}


bibtype: inproceedings
filename: fparith.bib
label: Agrawal:1983:DPV
author: Dharma P. Agrawal and Girish C. Pathak and Nikunja K. Swain and Shuwan K. Agrawal
title: On Design and Performance of VLSI Based Parallel Multiplier
crossref: IEEE:1983:PSC
pages: 17--21
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Agrawal_Pathak_Swain_Agrawal.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: Dharma P. Agrawal and Girish C. Pathak and Nikunja K. Swain and Shuwan K. Agrawal
rawtitle: On Design and Performance of {VLSI} Based Parallel Multiplier
abstract:
This paper introduces the VLSI design and layout of a $ (log ^2 n) $ time $n$-bit binary parallel multiplier for two unsigned operands. Proposed design consists of partitioning the multiplier and multiplicand bits into four groups of $ n / 4 $ bits each and then reducing the matrix of sixteen product terms using three to two parallel counters and Brent-Kung $ (log n) $ time parallel adder. Area-time performance of the present scheme has been compared with the existing schemes for parallel multipliers. Regular and recursive design of the multiplier is shown to be suitable for VLSI implementation and an improved table look up multiplier has been used to form the basis of the recursive design scheme.

rawabstract:
This paper introduces the VLSI design and layout of a $ (\log^2 n) $ time $n$-bit binary parallel multiplier for two unsigned operands. Proposed design consists of partitioning the multiplier and multiplicand bits into four groups of $ n / 4 $ bits each and then reducing the matrix of sixteen product terms using three to two parallel counters and Brent-Kung $ (\log n) $ time parallel adder. Area-time performance of the present scheme has been compared with the existing schemes for parallel multipliers. Regular and recursive design of the multiplier is shown to be suitable for VLSI implementation and an improved table look up multiplier has been used to form the basis of the recursive design scheme.

entry:
@InProceedings{Agrawal:1983:DPV,
  author =       "Dharma P. Agrawal and Girish C. Pathak and Nikunja K.
                 Swain and Shuwan K. Agrawal",
  title =        "On Design and Performance of {VLSI} Based Parallel
                 Multiplier",
  crossref =     "IEEE:1983:PSC",
  pages =        "17--21",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Agrawal_Pathak_Swain_Agrawal.pdf",
  abstract =     "This paper introduces the VLSI design and layout of a
                 $ (\log^2 n) $ time $n$-bit binary parallel multiplier
                 for two unsigned operands. Proposed design consists of
                 partitioning the multiplier and multiplicand bits into
                 four groups of $ n / 4 $ bits each and then reducing
                 the matrix of sixteen product terms using three to two
                 parallel counters and Brent-Kung $ (\log n) $ time
                 parallel adder. Area-time performance of the present
                 scheme has been compared with the existing schemes for
                 parallel multipliers. Regular and recursive design of
                 the multiplier is shown to be suitable for VLSI
                 implementation and an improved table look up multiplier
                 has been used to form the basis of the recursive design
                 scheme.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


bibtype: article
filename: fparith.bib
label: Agrawal:1983:ICA
author: D. P. Agrawal and T. R. N. Rao
title: Introduction: Computer Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-32
number: 4
pages: 329--330
month: apr
monthnumber: 4
year: 1983
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1983.1676232
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 10:01:08 MDT 2011
bibtimestamp: 2011.07.10 10:01:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232
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 and T. R. N. Rao
rawtitle: Introduction: Computer Arithmetic
entry:
@Article{Agrawal:1983:ICA,
  author =       "D. P. Agrawal and T. R. N. Rao",
  title =        "Introduction: Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "329--330",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676232",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 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=1676232",
  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: Akamine:1983:SMQ
author: Masami Akamine and Tatsuo Higuchi
title: Synthesis of minimum quantization error digital filters using floating-point arithmetic
journal: j-ELECTRON-COMMUN-JPN
volume: 66
number: 10
pages: 29--38
year: 1983
CODEN: ECOJAL
ISSN: 0424-8368 OR 04248368
MRclass: 94A12
MRnumber: 85k:94010
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: Electronics and communications in Japan
acknowledgement: ack-nhfb
rawauthor: Masami Akamine and Tatsuo Higuchi
rawtitle: Synthesis of minimum quantization error digital filters using floating-point arithmetic
entry:
@Article{Akamine:1983:SMQ,
  author =       "Masami Akamine and Tatsuo Higuchi",
  title =        "Synthesis of minimum quantization error digital
                 filters using floating-point arithmetic",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "66",
  number =       "10",
  pages =        "29--38",
  year =         "1983",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  MRclass =      "94A12",
  MRnumber =     "85k:94010",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}


bibtype: inproceedings
filename: fparith.bib
label: Annaratone:1983:MME
author: M. Annaratone and R. Stefanelli
title: A Multiplier with Multiple Error Correction Capability
crossref: IEEE:1983:PSC
pages: 44--51
year: 1983
bibdate: Tue Nov 13 15:58:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 15:58:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Annaratone_Stefanelli.pdf
keywords: ARITH-6
acknowledgement: ack-nhfb
rawauthor: M. Annaratone and R. Stefanelli
rawtitle: A Multiplier with Multiple Error Correction Capability
abstract:
This paper presents a technique for increasing the reliability of arithmetic units. An error model is then presented: this model well represents the faulty behavior of many arithmetic units. The Residue Number System and its related properties are used in order to obtain a simple architecture (called Reliability Network, R-Net). The main characteristics of the presented technique are a significant reduction in the number of gates and a limited increase of global execution times. The extensive use of combinational logic makes it possible to implement the R-Net almost completely by means of Programmable Logic Arrays (PLA's). Finally, both the intrinsic regularity of the R-Net and its simple internal interconnection scheme make this approach suitable for a practical VLSI implementation.

rawabstract:
This paper presents a technique for increasing the reliability of arithmetic units. An error model is then presented: this model well represents the faulty behavior of many arithmetic units. The Residue Number System and its related properties are used in order to obtain a simple architecture (called Reliability Network, R-Net). The main characteristics of the presented technique are a significant reduction in the number of gates and a limited increase of global execution times. The extensive use of combinational logic makes it possible to implement the R-Net almost completely by means of Programmable Logic Arrays (PLA's). Finally, both the intrinsic regularity of the R-Net and its simple internal interconnection scheme make this approach suitable for a practical VLSI implementation.

entry:
@InProceedings{Annaratone:1983:MME,
  author =       "M. Annaratone and R. Stefanelli",
  title =        "A Multiplier with Multiple Error Correction
                 Capability",
  crossref =     "IEEE:1983:PSC",
  pages =        "44--51",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Annaratone_Stefanelli.pdf",
  abstract =     "This paper presents a technique for increasing the
                 reliability of arithmetic units. An error model is then
                 presented: this model well represents the faulty
                 behavior of many arithmetic units. The Residue Number
                 System and its related properties are used in order to
                 obtain a simple architecture (called Reliability
                 Network, R-Net). The main characteristics of the
                 presented technique are a significant reduction in the
                 number of gates and a limited increase of global
                 execution times. The extensive use of combinational
                 logic makes it possible to implement the R-Net almost
                 completely by means of Programmable Logic Arrays
                 (PLA's). Finally, both the intrinsic regularity of the
                 R-Net and its simple internal interconnection scheme
                 make this approach suitable for a practical VLSI
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}


