# bibtab

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


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

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

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

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


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

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

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

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


bibtype: techreport
filename: fparith.bib
label: Kulisch:1969:AAR
author: Ulrich W. Kulisch
title: An axiomatic approach to rounded computations
type: Technical Summary Report
number: 1020
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: xi + 624
month: nov
monthnumber: 11
year: 1969
bibdate: Sat Nov 01 07:26:28 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.01 07:26:28 ???
remark: Published in cite Kulisch:1971:AAR.
acknowledgement: ack-nhfb
rawauthor: Ulrich W. Kulisch
rawtitle: An axiomatic approach to rounded computations
entry:
@TechReport{Kulisch:1969:AAR,
  author =       "Ulrich W. Kulisch",
  title =        "An axiomatic approach to rounded computations",
  type =         "Technical Summary Report",
  number =       "1020",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        nov,
  year =         "1969",
  bibdate =      "Sat Nov 01 07:26:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Published in \cite{Kulisch:1971:AAR}.",
}


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

entry:
@Article{Linhardt:1969:DDT,
  author =       "R. J. Linhardt and H. S. Miller",
  title =        "Digit-by-Digit Transcendental-Function Computation",
  journal =      j-RCA-REV,
  volume =       "30",
  number =       "2",
  pages =        "209--247",
  month =        jun,
  year =         "1969",
  CODEN =        "RCARCI",
  ISSN =         "0033-6831",
  bibdate =      "Fri Sep 16 10:31:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.worldradiohistory.com/ARCHIVE-RCA/RCA-Review/RCA-Review-1969-06.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "RCA Rev.",
  fjournal =     "RCA Review",
  journal-URL =  "https://www.worldradiohistory.com/ARCHIVE-RCA/RCA_Review_Issue_Key.htm",
}


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


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


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


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


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


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

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

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

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


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

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

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


bibtype: article
filename: fparith.bib
label: Shea:1969:NDN
author: Dale D. Shea
title: On the Number of Divisions Needed in Finding the Greatest Common Divisor
journal: j-FIB-QUART
volume: 7
number: 4
pages: 337--340
month: nov
monthnumber: 11
year: 1969
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 18:05:19 MDT 2011
bibtimestamp: 2011.10.20 18:05:19 MDT
URL: http://www.fq.math.ca/Scanned/7-4/shea.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Dale D. Shea
rawtitle: On the Number of Divisions Needed in Finding the Greatest Common Divisor
bibsource:
http://www.fq.math.ca/7-4.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Shea:1969:NDN,
  author =       "Dale D. Shea",
  title =        "On the Number of Divisions Needed in Finding the
                 Greatest Common Divisor",
  journal =      j-FIB-QUART,
  volume =       "7",
  number =       "4",
  pages =        "337--340",
  month =        nov,
  year =         "1969",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:19 MDT 2011",
  bibsource =    "http://www.fq.math.ca/7-4.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/7-4/shea.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: phdthesis
filename: fparith.bib
label: Smith:1969:EBB
author: Brian Thomas Smith
title: Error Bounds, Based Upon Gerschgorin's Theorem, for the Zeros of a Polynomial
type: Ph.D.
school: Department of Computer Science, University of Toronto
address: Toronto, ON, Canada
pages: 337--340
day: 13
month: jun
monthnumber: 6
year: 1969
bibdate: Fri Oct 31 07:28:17 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.31 07:28:17 ???
URL: https://www.proquest.com/pqdtglobal/docview/302455669
remark: See also cite Smith:1967:ZFA.
acknowledgement: ack-nhfb
rawauthor: Brian Thomas Smith
rawtitle: Error Bounds, Based Upon {Gerschgorin}'s Theorem, for the Zeros of a Polynomial
entry:
@PhdThesis{Smith:1969:EBB,
  author =       "Brian Thomas Smith",
  title =        "Error Bounds, Based Upon {Gerschgorin}'s Theorem, for
                 the Zeros of a Polynomial",
  type =         "{Ph.D.}",
  school =       "Department of Computer Science, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  day =          "13",
  month =        jun,
  year =         "1969",
  bibdate =      "Fri Oct 31 07:28:17 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.proquest.com/pqdtglobal/docview/302455669",
  acknowledgement = ack-nhfb,
  remark =       "See also \cite{Smith:1967:ZFA}.",
}


bibtype: article
filename: fparith.bib
label: Sterbenz:1969:OSA
author: P. H. Sterbenz and C. T. Fike
title: Optimal Starting Approximations for Newton's Method
journal: j-MATH-COMPUT
volume: 23
number: 106
pages: 313--318
month: apr
monthnumber: 4
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nj
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: P. H. Sterbenz and C. T. Fike
rawtitle: Optimal Starting Approximations for {Newton}'s Method
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; JSTOR database

abstract:
Various writers have dealt with the subject of optimal starting approximations for square-root calculation by Newton's method. Three optimality criteria that have been used can be shown to lead to closely related approximations. This fact makes it surprisingly easy to choose a starting approximation of some prescribed form so that the maximum relative error after any number of Newton iterations is as small as possible.

rawabstract:
Various writers have dealt with the subject of optimal starting approximations for square-root calculation by Newton's method. Three optimality criteria that have been used can be shown to lead to closely related approximations. This fact makes it surprisingly easy to choose a starting approximation of some prescribed form so that the maximum relative error after any number of Newton iterations is as small as possible.

entry:
@Article{Sterbenz:1969:OSA,
  author =       "P. H. Sterbenz and C. T. Fike",
  title =        "Optimal Starting Approximations for {Newton}'s
                 Method",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "106",
  pages =        "313--318",
  month =        apr,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  abstract =     "Various writers have dealt with the subject of optimal
                 starting approximations for square-root calculation by
                 Newton's method. Three optimality criteria that have
                 been used can be shown to lead to closely related
                 approximations. This fact makes it surprisingly easy to
                 choose a starting approximation of some prescribed form
                 so that the maximum relative error after any number of
                 Newton iterations is as small as possible.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Svoboda:1969:DAS
author: A. Svoboda
title: Decimal Adder with Signed Digit Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-18
number: 3
pages: 212--215
month: mar
monthnumber: 3
year: 1969
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1969.222633
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Jun 24 20:44:42 2005
bibtimestamp: 2005.06.24 20:44:42 ???
fjournal: IEEE Transactions on Computers
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Svoboda
rawtitle: Decimal Adder with Signed Digit Arithmetic
entry:
@Article{Svoboda:1969:DAS,
  author =       "A. Svoboda",
  title =        "Decimal Adder with Signed Digit Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "3",
  pages =        "212--215",
  month =        mar,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222633",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 20:44:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Troelstra:1969:EA
author: A. S. Troelstra
title: Elementary arithmetic
journal: j-LECT-NOTES-MATH
volume: 95
pages: 12--13
year: 1969
CODEN: LNMAA2
DOI: https://doi.org/10.1007/BFb0080646
ISBN: 3-540-04614-3 (print), 3-540-36130-8 (e-book) OR 3540046143 (print), 3540361308 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
bibdate: Thu May 8 17:39:14 MDT 2014
bibtimestamp: 2014.05.08 17:39:14 MDT
URL: http://link.springer.com/chapter/10.1007/BFb0080646
fjournal: Lecture Notes in Mathematics
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/BFb0080643
bookURL: http://www.springerlink.com/content/978-3-540-36130-5
journalURL: http://link.springer.com/bookseries/304
rawauthor: A. S. Troelstra
rawtitle: Elementary arithmetic
ISBN13:
978-3-540-04614-1 (print), 978-3-540-36130-5 (e-book) OR 9783540046141 (print), 9783540361305 (ebook)

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

entry:
@Article{Troelstra:1969:EA,
  author =       "A. S. Troelstra",
  title =        "Elementary arithmetic",
  journal =      j-LECT-NOTES-MATH,
  volume =       "95",
  pages =        "12--13",
  year =         "1969",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0080646",
  ISBN =         "3-540-04614-3 (print), 3-540-36130-8 (e-book)",
  ISBN-13 =      "978-3-540-04614-1 (print), 978-3-540-36130-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Thu May 8 17:39:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0080646",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0080643",
  book-URL =     "http://www.springerlink.com/content/978-3-540-36130-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}


bibtype: article
filename: fparith.bib
label: Turner:1969:CSI
author: L. Richard Turner
title: Comment on Some IBM Software
journal: SHARE Secretary Distribution
volume: SSD 199
number: C5279
pages: 40--43
year: 1969
bibdate: Fri Aug 20 10:23:55 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 10:23:55 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: L. Richard Turner
rawtitle: Comment on Some {IBM} Software
entry:
@Article{Turner:1969:CSI,
  author =       "L. Richard Turner",
  title =        "Comment on Some {IBM} Software",
  journal =      "{SHARE Secretary Distribution}",
  volume =       "SSD 199",
  number =       "C5279",
  pages =        "40--43",
  year =         "1969",
  bibdate =      "Fri Aug 20 10:23:55 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Turner:1969:DSC
author: L. Richard Turner
title: Difficulty in tt sin / cos Routine
journal: j-SIGNUM
volume: 4
number: 3
pages: 13--13
month: oct
monthnumber: 10
year: 1969
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Feb 15 15:23:23 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 15:23:23 ???
fjournal: ACM SIGNUM Newsletter
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: L. Richard Turner
rawtitle: Difficulty in {\tt sin\slash cos} Routine
entry:
@Article{Turner:1969:DSC,
  author =       "L. Richard Turner",
  title =        "Difficulty in {\tt sin\slash cos} Routine",
  journal =      j-SIGNUM,
  volume =       "4",
  number =       "3",
  pages =        "13--13",
  month =        oct,
  year =         "1969",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Feb 15 15:23:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: techreport
filename: fparith.bib
label: Turner:1969:IOC
author: L. R. Turner
title: Input-Output Conversion in System / 360
number: SSD 194, C5173
institution: SHARE Secretary Distribution
pages: 1--8
year: 1969
bibdate: Thu Feb 15 15:21:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 15:21:42 ???
acknowledgement: ack-nhfb
rawauthor: L. R. Turner
rawtitle: Input-Output Conversion in {System\slash 360}
entry:
@TechReport{Turner:1969:IOC,
  author =       "L. R. Turner",
  title =        "Input-Output Conversion in {System\slash 360}",
  number =       "SSD 194, C5173",
  institution =  "SHARE Secretary Distribution",
  address =      "????",
  pages =        "1--8",
  year =         "1969",
  bibdate =      "Thu Feb 15 15:21:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Usow:1969:SSC
author: Karl H. Usow
title: SIGNUM subroutine certification committee
journal: j-SIGNUM
volume: 4
number: 3
pages: 15--18
month: oct
monthnumber: 10
year: 1969
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Mon Mar 5 17:26:29 MST 2007
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.05 17:26:29 MST
fjournal: ACM SIGNUM Newsletter
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Karl H. Usow
rawtitle: {SIGNUM} subroutine certification committee
entry:
@Article{Usow:1969:SSC,
  author =       "Karl H. Usow",
  title =        "{SIGNUM} subroutine certification committee",
  journal =      j-SIGNUM,
  volume =       "4",
  number =       "3",
  pages =        "15--18",
  month =        oct,
  year =         "1969",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Mar 5 17:26:29 MST 2007",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: techreport
filename: fparith.bib
label: Veltkamp:1969:APV
author: G. W. Veltkamp
type: Technical report
number: 21
institution: RC-Informatie, Technische Hogeschool Eindhoven
address: Eindhoven, The Netherlands
pages: 15--18
year: 1969
bibdate: Tue Dec 26 14:53:03 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.26 14:53:03 ???
language: Dutch
acknowledgement: ack-nhfb
rawauthor: G. W. Veltkamp
title:
ALGOL procedures voor het rekenen in dubbele lengte. (Dutch) [ALGOL procedures for double-length arithmetic]

rawtitle:
{ALGOL} procedures voor het rekenen in dubbele lengte. ({Dutch}) [{ALGOL} procedures for double-length arithmetic]

entry:
@TechReport{Veltkamp:1969:APV,
  author =       "G. W. Veltkamp",
  title =        "{ALGOL} procedures voor het rekenen in dubbele lengte.
                 ({Dutch}) [{ALGOL} procedures for double-length
                 arithmetic]",
  type =         "Technical report",
  number =       "21",
  institution =  "RC-Informatie, Technische Hogeschool Eindhoven",
  address =      "Eindhoven, The Netherlands",
  year =         "1969",
  bibdate =      "Tue Dec 26 14:53:03 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Dutch",
}


bibtype: article
filename: fparith.bib
label: Weinstein:1969:CCR
author: C. Weinstein and A. V. Oppenheim
journal: j-PROC-IEEE
volume: 57
number: 8
pages: 1466--1466
month: aug
monthnumber: 8
year: 1969
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
note: See cite Weinstein:1969:CRN.
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: C. Weinstein and A. V. Oppenheim
rawnote: See \cite{Weinstein:1969:CRN}.
title:
Correction to ``A comparison of roundoff noise in floating point and fixed point digital filter realizations''

rawtitle:
Correction to {``A comparison of roundoff noise in floating point and fixed point digital filter realizations''}

entry:
@Article{Weinstein:1969:CCR,
  author =       "C. Weinstein and A. V. Oppenheim",
  title =        "Correction to {``A comparison of roundoff noise in
                 floating point and fixed point digital filter
                 realizations''}",
  journal =      j-PROC-IEEE,
  volume =       "57",
  number =       "8",
  pages =        "1466--1466",
  month =        aug,
  year =         "1969",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Weinstein:1969:CRN}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}


bibtype: article
filename: fparith.bib
label: Weinstein:1969:CRN
author: C. Weinstein and A. V. Oppenheim
title: A comparison of roundoff noise in floating point and fixed point digital filter realizations
journal: j-PROC-IEEE
volume: 57
number: 6
pages: 1181--1183
month: jun
monthnumber: 6
year: 1969
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
note: See correction cite Weinstein:1969:CCR.
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: C. Weinstein and A. V. Oppenheim
rawnote: See correction \cite{Weinstein:1969:CCR}.
rawtitle: A comparison of roundoff noise in floating point and fixed point digital filter realizations
entry:
@Article{Weinstein:1969:CRN,
  author =       "C. Weinstein and A. V. Oppenheim",
  title =        "A comparison of roundoff noise in floating point and
                 fixed point digital filter realizations",
  journal =      j-PROC-IEEE,
  volume =       "57",
  number =       "6",
  pages =        "1181--1183",
  month =        jun,
  year =         "1969",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Weinstein:1969:CCR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "A statistical model for roundoff noise in floating
                 point digital filters, proposed by Kaneko and Liu, is
                 tested experimentally for first- and second-order
                 digital filters. Good agreement between theory and
                 experiment is obtained. The model is used to \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Weinstein:1969:RNF
author: C. Weinstein
title: Roundoff noise in floating point fast Fourier transform computation
journal: j-IEEE-TRANS-AUDIO-ELECTROACOUST
volume: 17
number: 3
pages: 209--215
month: sep
monthnumber: 9
year: 1969
CODEN: ITADAS
ISSN: 0018-9278 (print), 1558-2582 (electronic) OR 00189278 (print), 15582582 (electronic)
ISSNL: 0018-9278 OR 00189278
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 Audio and Electroacoustics
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337
rawauthor: C. Weinstein
rawtitle: Roundoff noise in floating point fast {Fourier} transform computation
entry:
@Article{Weinstein:1969:RNF,
  author =       "C. Weinstein",
  title =        "Roundoff noise in floating point fast {Fourier}
                 transform computation",
  journal =      j-IEEE-TRANS-AUDIO-ELECTROACOUST,
  volume =       "17",
  number =       "3",
  pages =        "209--215",
  month =        sep,
  year =         "1969",
  CODEN =        "ITADAS",
  ISSN =         "0018-9278 (print), 1558-2582 (electronic)",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
  summary =      "A statistical model for roundoff errors is used to
                 predict output noise-to-signal ratio when a fast
                 Fourier transform is computed using floating point
                 arithmetic. The result, derived for the case of white
                 input signal, is that the ratio of mean-square
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Whipple:1969:CHR
author: W. L. Whipple
title: Comments on ``Higher-Radix Division Using Estimates of the Divisor and Partial Remainders''
journal: j-IEEE-TRANS-COMPUT
volume: C-18
number: 2
pages: 183--183
month: feb
monthnumber: 2
year: 1969
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1969.222623
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 16:55:18 MDT 2011
bibtimestamp: 2011.07.13 16:55:18 MDT
note: See cite Atkins:1968:HRD.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671216
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: W. L. Whipple
rawnote: See \cite{Atkins:1968:HRD}.
rawtitle: Comments on {``Higher-Radix Division Using Estimates of the Divisor and Partial Remainders''}
entry:
@Article{Whipple:1969:CHR,
  author =       "W. L. Whipple",
  title =        "Comments on {``Higher-Radix Division Using Estimates
                 of the Divisor and Partial Remainders''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "2",
  pages =        "183--183",
  month =        feb,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222623",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  note =         "See \cite{Atkins:1968:HRD}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671216",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Young:1969:SCN
author: David M. Young and Alvis E. McDonald
crossref: Morrell:1970:IPP
pages: 145--152
year: 1969
MRclass: 65.80
MRnumber: 40\#8303
bibdate: Thu Jan 18 13:48:21 1996
bibtimestamp: 1996.01.18 13:48:21 ???
remark: Cited in cite Sterbenz:1974:FPC, but given year 1968.
acknowledgement: ack-nhfb
rawauthor: David M. Young and Alvis E. McDonald
title:
On the surveillance and control of number range and accuracy in numerical computation (with discussion)

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
On the surveillance and control of number range and accuracy in numerical computation (with discussion)

entry:
@InProceedings{Young:1969:SCN,
  author =       "David M. Young and Alvis E. McDonald",
  title =        "On the surveillance and control of number range and
                 accuracy in numerical computation (with discussion)",
  crossref =     "Morrell:1970:IPP",
  pages =        "145--152",
  year =         "1969",
  MRclass =      "65.80",
  MRnumber =     "40\#8303",
  bibdate =      "Thu Jan 18 13:48:21 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}, but given year
                 1968.",
}


bibtype: article
filename: fparith.bib
label: Atkins:1970:DAU
author: D. E. Atkins
title: Design of the Arithmetic Units of ILLIAC III: Use of Redundancy and Higher Radix Methods
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 720--723
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223022
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Oct 09 19:03:30 2007
bibtimestamp: 2007.10.09 19:03:30 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Atkins.pdf
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. E. Atkins
rawtitle: Design of the Arithmetic Units of {ILLIAC III}: Use of Redundancy and Higher Radix Methods
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

abstract:
In keeping with the experimental nature of the Illinois Pattern Recognition Computer (ILLIAC III), the arithmetic units are intended to be a practical testing ground for recent theoretical work in computer arithmetic. This paper describes the use of redundant number systems and the design of a structure with which multiplication and division are executed radix 256. The heart of the unit is the stored-sign subtracter, a recently discovered member of the family of borrow-save subtracters and carry-save adders. A cascade of these subtracters, controlled by a multiplier recoder, provides multiplication. The same structure, controlled by a ``model division'' (a quotient recoder), performs division.

keywords:
arithmetic unit; computer arithmetic; division; higher radix arithmetic; ILLIAC III; multiplication; redundant number systems; signed-digit subtracter; stored-sign subtracter; stored-sign subtracter. Arithmetic unit

remark:
Despite statements elsewhere that the ILLIAC III used base 256, that is incorrect. The original manuals for the machine clearly show an IBM System/360-style base-16 encoding. This paper reveals the source of the confusion: the multiplier uses a Wallace recoding scheme, first defined for radix 4, but extended for the ILLIAC III to radix 256. Thus, multiplication is done 8 bits at a time. Division is done 4 bits at a time.

rawabstract:
In keeping with the experimental nature of the Illinois Pattern Recognition Computer (ILLIAC III), the arithmetic units are intended to be a practical testing ground for recent theoretical work in computer arithmetic. This paper describes the use of redundant number systems and the design of a structure with which multiplication and division are executed radix 256. The heart of the unit is the stored-sign subtracter, a recently discovered member of the family of borrow-save subtracters and carry-save adders. A cascade of these subtracters, controlled by a multiplier recoder, provides multiplication. The same structure, controlled by a ``model division'' (a quotient recoder), performs division.

entry:
@Article{Atkins:1970:DAU,
  author =       "D. E. Atkins",
  title =        "Design of the Arithmetic Units of {ILLIAC III}: Use of
                 Redundancy and Higher Radix Methods",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "720--723",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223022",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 09 19:03:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Atkins.pdf",
  abstract =     "In keeping with the experimental nature of the
                 Illinois Pattern Recognition Computer (ILLIAC III), the
                 arithmetic units are intended to be a practical testing
                 ground for recent theoretical work in computer
                 arithmetic. This paper describes the use of redundant
                 number systems and the design of a structure with which
                 multiplication and division are executed radix 256. The
                 heart of the unit is the stored-sign subtracter, a
                 recently discovered member of the family of borrow-save
                 subtracters and carry-save adders. A cascade of these
                 subtracters, controlled by a multiplier recoder,
                 provides multiplication. The same structure, controlled
                 by a ``model division'' (a quotient recoder), performs
                 division.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "arithmetic unit; computer arithmetic; division; higher
                 radix arithmetic; ILLIAC III; multiplication; redundant
                 number systems; signed-digit subtracter; stored-sign
                 subtracter; stored-sign subtracter. Arithmetic unit",
  remark =       "Despite statements elsewhere that the ILLIAC III used
                 base 256, that is incorrect. The original manuals for
                 the machine clearly show an IBM System/360-style
                 base-16 encoding. This paper reveals the source of the
                 confusion: the multiplier uses a Wallace recoding
                 scheme, first defined for radix 4, but extended for the
                 ILLIAC III to radix 256. Thus, multiplication is done 8
                 bits at a time. Division is done 4 bits at a time.",
}


bibtype: article
filename: fparith.bib
label: Avizienis:1970:UAB
author: Algirdas Avizienis and Chin Tung
title: A Universal Arithmetic Building Element (ABE) and Design Methods for Arithmetic Processors
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 733--745
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223023
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Avizienis.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-1
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Algirdas Avi{\v{z}}ienis and Chin Tung
rawtitle: A Universal Arithmetic Building Element ({ABE}) and Design Methods for Arithmetic Processors
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

abstract:
The advent of large-scale integration of logic circuits requires the definition of digital computer structure in terms of large functional arrays of logic of very few types. This paper describes a single-package arithmetic processor called the arithmetic building element (ABE). The ABE accepts operands in either conventional or signed-digit radix-r representation and produces signed-digit results, which the ABE can reconvert to conventional form. Radix 16 is chosen for illustrations. Arrays of ABE's may be arranged to implement unit-time parallel addition, all-combinational multiplication, and more complex functions which are presently computed by subroutines. To facilitate such arithmetic design, a graph model is developed which permits a translation of the given arithmetical algorithm into an interconnection diagram of ABE's. The design procedure is illustrated by an array for polynomial evaluation. Speed, cost, and roundoff error of the array are considered. A computer program has been written for the automatic translation of the algorithm graph to an interconnection graph, and for the evaluation of the cost and speed for a given polynomial degree and a given precision requirement.

rawabstract:
The advent of large-scale integration of logic circuits requires the definition of digital computer structure in terms of large functional arrays of logic of very few types. This paper describes a single-package arithmetic processor called the arithmetic building element (ABE). The ABE accepts operands in either conventional or signed-digit radix-r representation and produces signed-digit results, which the ABE can reconvert to conventional form. Radix 16 is chosen for illustrations. Arrays of ABE's may be arranged to implement unit-time parallel addition, all-combinational multiplication, and more complex functions which are presently computed by subroutines. To facilitate such arithmetic design, a graph model is developed which permits a translation of the given arithmetical algorithm into an interconnection diagram of ABE's. The design procedure is illustrated by an array for polynomial evaluation. Speed, cost, and roundoff error of the array are considered. A computer program has been written for the automatic translation of the algorithm graph to an interconnection graph, and for the evaluation of the cost and speed for a given polynomial degree and a given precision requirement.

entry:
@Article{Avizienis:1970:UAB,
  author =       "Algirdas Avi{\v{z}}ienis and Chin Tung",
  title =        "A Universal Arithmetic Building Element ({ABE}) and
                 Design Methods for Arithmetic Processors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "733--745",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223023",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Avizienis.pdf",
  abstract =     "The advent of large-scale integration of logic
                 circuits requires the definition of digital computer
                 structure in terms of large functional arrays of logic
                 of very few types. This paper describes a
                 single-package arithmetic processor called the
                 arithmetic building element (ABE). The ABE accepts
                 operands in either conventional or signed-digit radix-r
                 representation and produces signed-digit results, which
                 the ABE can reconvert to conventional form. Radix 16 is
                 chosen for illustrations. Arrays of ABE's may be
                 arranged to implement unit-time parallel addition,
                 all-combinational multiplication, and more complex
                 functions which are presently computed by subroutines.
                 To facilitate such arithmetic design, a graph model is
                 developed which permits a translation of the given
                 arithmetical algorithm into an interconnection diagram
                 of ABE's. The design procedure is illustrated by an
                 array for polynomial evaluation. Speed, cost, and
                 roundoff error of the array are considered. A computer
                 program has been written for the automatic translation
                 of the algorithm graph to an interconnection graph, and
                 for the evaluation of the cost and speed for a given
                 polynomial degree and a given precision requirement.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}


bibtype: article
filename: fparith.bib
label: Behringer:1970:BFI
author: F. A. Behringer
journal: j-COMPUTING
volume: 5
number: 4
pages: 333--348
year: 1970
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:51 MST 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date)
bibtimestamp: 2001.01.02 17:40:51 MST
fjournal: Computing: Archiv fur informatik und numerik
language: German
acknowledgement: ack-ec
affiliation: Tech. Hochschule, Munchen, West Germany
journalURL: http://link.springer.com/journal/607
rawauthor: F. A. Behringer
title:
Eine bedingte Form der Integral-Ungleichun von Gronwal, leichte Verallgemeinerung eins Stabilitatsatzes von Perron und uberlauffreie Skalierung von Analogrechenschaltungen. (German) [A conditional version of the integral inequality of Gronwall, a slight generalization of a stability theorem of Perron, and overflow-free scaling of analogue computer set-ups]

rawtitle:
{Eine bedingte Form der Integral-Ungleichun von Gronwal, leichte Verallgemeinerung eins Stabilit{\"a}tsatzes von Perron und {\"u}berlauffreie Skalierung von Analogrechenschaltungen}. ({German}) [{A} conditional version of the integral inequality of {Gronwall}, a slight generalization of a stability theorem of {Perron}, and overflow-free scaling of analogue computer set-ups]

entry:
@Article{Behringer:1970:BFI,
  author =       "F. A. Behringer",
  title =        "{Eine bedingte Form der Integral-Ungleichun von
                 Gronwal, leichte Verallgemeinerung eins
                 Stabilit{\"a}tsatzes von Perron und {\"u}berlauffreie
                 Skalierung von Analogrechenschaltungen}. ({German})
                 [{A} conditional version of the integral inequality of
                 {Gronwall}, a slight generalization of a stability
                 theorem of {Perron}, and overflow-free scaling of
                 analogue computer set-ups]",
  journal =      j-COMPUTING,
  volume =       "5",
  number =       "4",
  pages =        "333--348",
  year =         "1970",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-ec # " and " # ack-nhfb,
  affiliation =  "Tech. Hochschule, M{\"u}nchen, West Germany",
  classification = "C5460",
  description =  "analogue computer methods; differential equations",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Beyer:1970:GST
author: W. A. Beyer and N. Metropolis and J. R. Neergaard
title: The Generalized Serial Test Applied to Expansions of Some Irrational Square Roots in Various Bases
journal: j-MATH-COMPUT
volume: 24
number: 111
pages: 745--747
month: jul
monthnumber: 7
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.15
MRnumber: MR0273773 (42 \#8649)
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://links.jstor.org/sici?sici=0025-5718%28197007%2924%3A111%3C745%3ATGSTAT%3E2.0.CO%3B2-2
fjournal: Mathematics of Computation
ZMnumber: 0227.10044
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: W. A. Beyer and N. Metropolis and J. R. Neergaard
rawtitle: The Generalized Serial Test Applied to Expansions of Some Irrational Square Roots in Various Bases
entry:
@Article{Beyer:1970:GST,
  author =       "W. A. Beyer and N. Metropolis and J. R. Neergaard",
  title =        "The Generalized Serial Test Applied to Expansions of
                 Some Irrational Square Roots in Various Bases",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "111",
  pages =        "745--747",
  month =        jul,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.15",
  MRnumber =     "MR0273773 (42 \#8649)",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197007%2924%3A111%3C745%3ATGSTAT%3E2.0.CO%3B2-2",
  ZMnumber =     "0227.10044",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Beyer:1970:SSD
author: W. A. Beyer and N. Metropolis and J. R. Neergaard
title: Statistical Study of Digits of Some Square Roots of Integers in Various Bases
journal: j-MATH-COMPUT
volume: 24
number: 110
pages: 455--473
month: apr
monthnumber: 4
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 62.70
MRnumber: MR0272129 (42 \#7010)
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://links.jstor.org/sici?sici=0025-5718%28197004%2924%3A110%3C455%3ASSODOS%3E2.0.CO%3B2-I
fjournal: Mathematics of Computation
ZMnumber: 0208.19505
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: W. A. Beyer and N. Metropolis and J. R. Neergaard
rawtitle: Statistical Study of Digits of Some Square Roots of Integers in Various Bases
entry:
@Article{Beyer:1970:SSD,
  author =       "W. A. Beyer and N. Metropolis and J. R. Neergaard",
  title =        "Statistical Study of Digits of Some Square Roots of
                 Integers in Various Bases",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "455--473",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "62.70",
  MRnumber =     "MR0272129 (42 \#7010)",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197004%2924%3A110%3C455%3ASSODOS%3E2.0.CO%3B2-I",
  ZMnumber =     "0208.19505",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Brent:1970:ABN
author: R. Brent
title: On the Addition of Binary Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 758--759
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223027
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Brent.pdf
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. Brent
rawtitle: On the Addition of Binary Numbers
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

abstract:
An upper bound is derived for the time required to add numbers modulo $ 2^n $, using circuit elements with a limited fan-in and unit delay, and assuming that all numbers have the usual binary encoding. The upper bound is within a factor $ (1 + epsilon ) $ of Winograd's lower bound (which holds for all encodings), where $ epsilon rightarrow 0 $ as $ n rightarrow infty $, and only $ O(n log n) $ circuit elements are required.

keywords:
addition; ARITH-1; binary numbers; computational complexity; group multiplication; logic circuits; logical design

rawabstract:
An upper bound is derived for the time required to add numbers modulo $ 2^n $, using circuit elements with a limited fan-in and unit delay, and assuming that all numbers have the usual binary encoding. The upper bound is within a factor $ (1 + \epsilon) $ of Winograd's lower bound (which holds for all encodings), where $ \epsilon \rightarrow 0 $ as $ n \rightarrow \infty $, and only $ O(n \log n) $ circuit elements are required.

entry:
@Article{Brent:1970:ABN,
  author =       "R. Brent",
  title =        "On the Addition of Binary Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "758--759",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223027",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Brent.pdf",
  abstract =     "An upper bound is derived for the time required to add
                 numbers modulo $ 2^n $, using circuit elements with a
                 limited fan-in and unit delay, and assuming that all
                 numbers have the usual binary encoding. The upper bound
                 is within a factor $ (1 + \epsilon) $ of Winograd's
                 lower bound (which holds for all encodings), where $
                 \epsilon \rightarrow 0 $ as $ n \rightarrow \infty $,
                 and only $ O(n \log n) $ circuit elements are
                 required.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "addition; ARITH-1; binary numbers; computational
                 complexity; group multiplication; logic circuits;
                 logical design",
}


bibtype: techreport
filename: fparith.bib
label: deLugish:1970:CAA
author: B. G. de Lugish
title: A Class of Algorithms for Automatic Evaluation of Certain Elementary Function in a Binary Computer
type: Report
number: 399
institution: Department of Computer Science, University of Illinois
month: jun
monthnumber: 6
year: 1970
bibdate: Fri Sep 02 22:49:20 1994
bibtimestamp: 1994.09.02 22:49:20 ???
remark: Also Ph.D. dissertation same year.
acknowledgement: ack-nj
rawauthor: B. G. de Lugish
rawtitle: A Class of Algorithms for Automatic Evaluation of Certain Elementary Function in a Binary Computer
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{deLugish:1970:CAA,
  author =       "B. G. de Lugish",
  title =        "A Class of Algorithms for Automatic Evaluation of
                 Certain Elementary Function in a Binary Computer",
  type =         "Report",
  number =       "399",
  institution =  "Department of Computer Science, University of
                 Illinois",
  pages =        "??",
  month =        jun,
  year =         "1970",
  bibdate =      "Fri Sep 02 22:49:20 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  remark =       "Also Ph.D. dissertation same year.",
}


bibtype: article
filename: fparith.bib
label: Flynn:1970:DFI
author: M. J. Flynn
title: On Division by Functional Iteration
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 702--706
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223019
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
note: Reprinted in cite Swartzlander:1990:CAa.
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Flynn.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-1
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. J. Flynn
rawnote: Reprinted in \cite{Swartzlander:1990:CAa}.
rawtitle: On Division by Functional Iteration
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

abstract:
In order to avoid the time delays associated with linearly convergent division based on subtraction, other iterative schemes can be used. These are based on (1) series expansion of the reciprocal, (2) multiplicative sequence, or (3) additive sequence convergent to the quotient. These latter techniques are based on finding the root of an arbitrary function at either the quotient or reciprocal value. A Newton--Raphson iteration or root finding iteration can be used. The most useful techniques are quadratically convergent (i.e., $ mathrm error_i + 1 = O((mathrm error_i)^2) $). These techniques generally require two arithmetic operations (add or multiply) to double the precision of the quotient.

rawabstract:
In order to avoid the time delays associated with linearly convergent division based on subtraction, other iterative schemes can be used. These are based on (1) series expansion of the reciprocal, (2) multiplicative sequence, or (3) additive sequence convergent to the quotient. These latter techniques are based on finding the root of an arbitrary function at either the quotient or reciprocal value. A Newton--Raphson iteration or root finding iteration can be used. The most useful techniques are quadratically convergent (i.e., $ \mathrm {error}_{i + 1} = O((\mathrm {error}_i)^2) $). These techniques generally require two arithmetic operations (add or multiply) to double the precision of the quotient.

entry:
@Article{Flynn:1970:DFI,
  author =       "M. J. Flynn",
  title =        "On Division by Functional Iteration",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "702--706",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223019",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "Reprinted in \cite{Swartzlander:1990:CAa}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Flynn.pdf",
  abstract =     "In order to avoid the time delays associated with
                 linearly convergent division based on subtraction,
                 other iterative schemes can be used. These are based on
                 (1) series expansion of the reciprocal, (2)
                 multiplicative sequence, or (3) additive sequence
                 convergent to the quotient. These latter techniques are
                 based on finding the root of an arbitrary function at
                 either the quotient or reciprocal value. A
                 Newton--Raphson iteration or root finding iteration can
                 be used.

                 The most useful techniques are quadratically convergent
                 (i.e., $ \mathrm {error}_{i + 1} = O((\mathrm
                 {error}_i)^2) $). These techniques generally require
                 two arithmetic operations (add or multiply) to double
                 the precision of the quotient.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}


bibtype: article
filename: fparith.bib
label: Forsythe:1970:PCW
author: George E. Forsythe
title: Pitfalls in Computation, or Why a Math Book Isn't Enough
journal: j-AMER-MATH-MONTHLY
volume: 77
number: 9
pages: 931--956
month: nov
monthnumber: 11
year: 1970
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: Contributed Item
MRnumber: MR1536090
bibdate: Tue Nov 22 09:08:17 MST 2005
bibtimestamp: 2005.11.22 09:08:17 MST
fjournal: The American Mathematical Monthly
ZMnumber: 0207.15401
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: George E. Forsythe
rawtitle: Pitfalls in Computation, or Why a Math Book Isn't Enough
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database

entry:
@Article{Forsythe:1970:PCW,
  author =       "George E. Forsythe",
  title =        "Pitfalls in Computation, or Why a Math Book Isn't
                 Enough",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "77",
  number =       "9",
  pages =        "931--956",
  month =        nov,
  year =         "1970",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1536090",
  bibdate =      "Tue Nov 22 09:08:17 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  ZMnumber =     "0207.15401",
  acknowledgement = ack-nhfb,
  classmath =    "*65G50 Roundoff error 65Y20 Complexity and performance
                 of numerical algorithms",
  fjournal =     "The American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: techreport
filename: fparith.bib
label: Gardiner:1970:SDA
author: V. Gardiner and N. Metropolis
title: Significant Digit Arithmetic on a CDC 6600
type: Technical Report
number: LA--4470
institution: inst-LASL
address: inst-LASL:adr
pages: 4
day: 1
month: jan
monthnumber: 1
year: 1970
bibdate: Tue Mar 20 11:46:17 2007
bibtimestamp: 2007.03.20 11:46:17 ???
URL: http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4093265&query_id=0
acknowledgement: ack-nhfb
rawauthor: V. Gardiner and N. Metropolis
rawtitle: Significant Digit Arithmetic on a {CDC 6600}
entry:
@TechReport{Gardiner:1970:SDA,
  author =       "V. Gardiner and N. Metropolis",
  title =        "Significant Digit Arithmetic on a {CDC 6600}",
  type =         "Technical Report",
  number =       "LA--4470",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  pages =        "4",
  day =          "1",
  month =        jan,
  year =         "1970",
  bibdate =      "Tue Mar 20 11:46:17 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4093265&query_id=0",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Good:1970:CIA
author: Donald I. Good and Ralph L. London
title: Computer Interval Arithmetic: Definition and Proof of Correct Implementation
journal: j-J-ACM
volume: 17
number: 4
pages: 603--612
month: oct
monthnumber: 10
year: 1970
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Sun Nov 6 11:55:54 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.06 11:55:54 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Donald I. Good and Ralph L. London
rawtitle: Computer Interval Arithmetic: Definition and Proof of Correct Implementation
entry:
@Article{Good:1970:CIA,
  author =       "Donald I. Good and Ralph L. London",
  title =        "Computer Interval Arithmetic: Definition and Proof of
                 Correct Implementation",
  journal =      j-J-ACM,
  volume =       "17",
  number =       "4",
  pages =        "603--612",
  month =        oct,
  year =         "1970",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sun Nov 6 11:55:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}


bibtype: article
filename: fparith.bib
label: Habibi:1970:FM
author: A. Habibi and P. A. Wintz
title: Fast Multipliers
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 2
pages: 153--157
month: feb
monthnumber: 2
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.222881
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 08:01:30 MDT 2011
bibtimestamp: 2011.07.13 08:01:30 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671474
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Habibi and P. A. Wintz
rawtitle: Fast Multipliers
entry:
@Article{Habibi:1970:FM,
  author =       "A. Habibi and P. A. Wintz",
  title =        "Fast Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "2",
  pages =        "153--157",
  month =        feb,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222881",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671474",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Hall:1970:GPQ
author: E. L. Hall and D. D. Lynch and S. J. Dwyer
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 2
pages: 97--105
month: feb
monthnumber: 2
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.222874
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 08:01:30 MDT 2011
bibtimestamp: 2011.07.13 08:01:30 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671467
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. L. Hall and D. D. Lynch and S. J. Dwyer
title:
Generation of Products and Quotients Using Approximate Binary Logarithms for Digital Filtering Applications

rawtitle:
Generation of Products and Quotients Using Approximate Binary Logarithms for Digital Filtering Applications

entry:
@Article{Hall:1970:GPQ,
  author =       "E. L. Hall and D. D. Lynch and S. J. Dwyer",
  title =        "Generation of Products and Quotients Using Approximate
                 Binary Logarithms for Digital Filtering Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "2",
  pages =        "97--105",
  month =        feb,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222874",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671467",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Hamming:1970:DN
author: R. W. Hamming
title: On the Distribution of Numbers
journal: j-BELL-SYST-TECH-J
volume: 49
number: 8
pages: 1609--1625
month: oct
monthnumber: 10
year: 1970
CODEN: BSTJAN
DOI: https://doi.org/10.1002/j.1538-7305.1970.tb04281.x
ISSN: 0005-8580 (print), 2376-7154 (electronic) OR 00058580 (print), 23767154 (electronic)
ISSNL: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:55 MST 2010
bibtimestamp: 2010.11.09 11:15:55 MST
fjournal: The Bell System Technical Journal
acknowledgement: ack-nj
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: R. W. Hamming
rawtitle: On the Distribution of Numbers
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html; http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html; https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib; https://www.math.utah.edu/pub/tex/bib/bstj1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf; http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf

abstract:
This paper examines the distribution of the mantissas of floating-point numbers and shows how the arithmetic operations of a computer transform various distributions toward the limiting distribution $$ r(x) = 1 / (x ln b) qquad (1 / b leq x leq 1) $$ (where $b$ is the base of the number system). The paper also gives a number of applications to hardware, software, and general computing which show that this distribution is not merely an amusing curiosity. A brief examination of the distribution of exponents is included.

rawabstract:
This paper examines the distribution of the mantissas of floating-point numbers and shows how the arithmetic operations of a computer transform various distributions toward the limiting distribution $$ r(x) = 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where $b$ is the base of the number system). The paper also gives a number of applications to hardware, software, and general computing which show that this distribution is not merely an amusing curiosity. A brief examination of the distribution of exponents is included.

entry:
@Article{Hamming:1970:DN,
  author =       "R. W. Hamming",
  title =        "On the Distribution of Numbers",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "49",
  number =       "8",
  pages =        "1609--1625",
  month =        oct,
  year =         "1970",
  CODEN =        "BSTJAN",
  DOI =          "https://doi.org/10.1002/j.1538-7305.1970.tb04281.x",
  ISSN =         "0005-8580 (print), 2376-7154 (electronic)",
  ISSN-L =       "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/bstj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
  abstract =     "This paper examines the distribution of the mantissas
                 of floating-point numbers and shows how the arithmetic
                 operations of a computer transform various
                 distributions toward the limiting distribution $$ r(x)
                 = 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
                 $b$ is the base of the number system). The paper also
                 gives a number of applications to hardware, software,
                 and general computing which show that this distribution
                 is not merely an amusing curiosity. A brief examination
                 of the distribution of exponents is included.",
  acknowledgement = ack-nj # " and " # 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: Hansen:1970:APN
author: Rodney T. Hansen
title: Arithmetic of Pentagonal Numbers
journal: j-FIB-QUART
volume: 8
number: 1
pages: 83--86
month: feb
monthnumber: 2
year: 1970
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 18:05:23 MDT 2011
bibtimestamp: 2011.10.20 18:05:23 MDT
URL: http://www.fq.math.ca/Scanned/8-1/hansen.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Rodney T. Hansen
rawtitle: Arithmetic of Pentagonal Numbers
bibsource:
http://www.fq.math.ca/8-1.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Hansen:1970:APN,
  author =       "Rodney T. Hansen",
  title =        "Arithmetic of Pentagonal Numbers",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "1",
  pages =        "83--86",
  month =        feb,
  year =         "1970",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:23 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-1.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/8-1/hansen.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: fparith.bib
label: Harris:1970:NND
author: V. C. Harris
title: Note on the Number of Divisions Required in Finding the Greatest Common Divisor
journal: j-FIB-QUART
volume: 8
number: 1
pages: 104--??
month: feb
monthnumber: 2
year: 1970
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 18:05:23 MDT 2011
bibtimestamp: 2011.10.20 18:05:23 MDT
URL: http://www.fq.math.ca/Scanned/8-1/harris2.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: V. C. Harris
rawtitle: Note on the Number of Divisions Required in Finding the Greatest Common Divisor
bibsource:
http://www.fq.math.ca/8-1.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Harris:1970:NND,
  author =       "V. C. Harris",
  title =        "Note on the Number of Divisions Required in Finding
                 the Greatest Common Divisor",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "1",
  pages =        "104--??",
  month =        feb,
  year =         "1970",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:23 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-1.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/8-1/harris2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: mastersthesis
filename: fparith.bib
label: Harvey:1970:SSP
author: Michael P. Harvey
title: A system study and problem solution in polynomial evaluation
type: Thesis (M.S.)
school: California State College
address: Long Beach, CA, USA
pages: vi + 119
year: 1970
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Electronic digital computers.; Numerical calculations.; Polynomials.
remark: Title on spine: Automated floating point polynomial evaluation.
acknowledgement: ack-nhfb
rawauthor: Michael P. Harvey
rawtitle: A system study and problem solution in polynomial evaluation
entry:
@MastersThesis{Harvey:1970:SSP,
  author =       "Michael P. Harvey",
  title =        "A system study and problem solution in polynomial
                 evaluation",
  type =         "Thesis ({M.S.})",
  school =       "California State College",
  address =      "Long Beach, CA, USA",
  pages =        "vi + 119",
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers.; Numerical
                 calculations.; Polynomials.",
  remark =       "Title on spine: Automated floating point polynomial
                 evaluation.",
}


bibtype: techreport
filename: fparith.bib
label: Hillstrom:1970:PSF
author: K. E. Hillstrom
type: Report
number: ANL-7666
institution: inst-ANL
address: inst-ANL:adr
pages: vi + 119
year: 1970
bibdate: Fri Aug 20 09:29:37 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 09:29:37 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: K. E. Hillstrom
title:
Performance Statistics for the FORTRAN IV (H) and PL/I (Version 5) Libraries in the IBM OS / 360 Release 18

rawtitle:
Performance Statistics for the {FORTRAN IV (H)} and {PL/I} (Version 5) Libraries in the {IBM OS\slash 360 Release 18}

entry:
@TechReport{Hillstrom:1970:PSF,
  author =       "K. E. Hillstrom",
  title =        "Performance Statistics for the {FORTRAN IV (H)} and
                 {PL/I} (Version 5) Libraries in the {IBM OS\slash 360
                 Release 18}",
  type =         "Report",
  number =       "ANL-7666",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  year =         "1970",
  bibdate =      "Fri Aug 20 09:29:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Hornbuckle:1970:LMA
author: G. D. Hornbuckle and E. I. Ancona
title: The LX-1 Microprocessor and Its Application to Real-Time Signal Processing
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 710--720
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223021
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Hornbuckle.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-1
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. D. Hornbuckle and E. I. Ancona
rawtitle: The {LX-1} Microprocessor and Its Application to Real-Time Signal Processing
entry:
@Article{Hornbuckle:1970:LMA,
  author =       "G. D. Hornbuckle and E. I. Ancona",
  title =        "The {LX-1} Microprocessor and Its Application to
                 Real-Time Signal Processing",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "710--720",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223021",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Hornbuckle.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}


bibtype: article
filename: fparith.bib
label: Howell:1970:SLE
author: Jo Ann Howell and Robert T. Gregory
title: Solving linear equations using residue arithmetic --- Algorithm II
journal: j-BIT
volume: 10
pages: 23--37
year: 1970
CODEN: BITTEL, NBITAB
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65.35
MRnumber: MR0261777 (41 \#6389)
MRreviewer: J. Legras
bibdate: Thu Nov 8 14:50:19 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:19 ???
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Jo Ann Howell and Robert T. Gregory
rawtitle: Solving linear equations using residue arithmetic --- {Algorithm II}
entry:
@Article{Howell:1970:SLE,
  author =       "Jo Ann Howell and Robert T. Gregory",
  title =        "Solving linear equations using residue arithmetic ---
                 {Algorithm II}",
  journal =      j-BIT,
  volume =       "10",
  pages =        "23--37",
  year =         "1970",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.35",
  MRnumber =     "MR0261777 (41 \#6389)",
  MRreviewer =   "J. Legras",
  bibdate =      "Thu Nov 8 14:50:19 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: fparith.bib
label: Kailas:1970:AMC
author: M. V. Kailas
title: Another method of converting from hexadecimal to decimal
journal: j-CACM
volume: 13
number: 3
pages: 193--193
month: mar
monthnumber: 3
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Mar 25 13:26:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.03.25 13:26:09 MST
abstract: There is a simple paper-and-pencil method of converting a hexadecimal number N to decimal.
fjournal: Communications of the ACM
keywords: digital arithmetic
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
journalURL: https://dl.acm.org/loi/cacm
rawabstract: There is a simple paper-and-pencil method of converting a hexadecimal number N to decimal.
rawauthor: M. V. Kailas
rawtitle: Another method of converting from hexadecimal to decimal
entry:
@Article{Kailas:1970:AMC,
  author =       "M. V. Kailas",
  title =        "Another method of converting from hexadecimal to
                 decimal",
  journal =      j-CACM,
  volume =       "13",
  number =       "3",
  pages =        "193--193",
  month =        mar,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "There is a simple paper-and-pencil method of
                 converting a hexadecimal number N to decimal.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Knuth:1970:VNF
author: Donald E. Knuth
title: Von Neumann's First Computer Program
journal: j-COMP-SURV
volume: 2
number: 4
pages: 247--260
month: dec
monthnumber: 12
year: 1970
CODEN: CMSVAN
DOI: https://doi.org/10.1145/356580.356581
ISSN: 0010-4892 OR 00104892
ISSNL: 0360-0300 OR 03600300
bibdate: Sat Mar 23 15:03:00 2002
bibtimestamp: 2002.03.23 15:03:00 ???
note: Reprinted in cite Aspray:1987:PJN.
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: Donald E. Knuth
rawnote: Reprinted in \cite{Aspray:1987:PJN}.
rawtitle: {Von Neumann}'s First Computer Program
bibsource:
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/compsurv.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/HBP/ACMCS.bib; https://www.math.utah.edu/pub/tex/bib/compsurv.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Knuth:1970:VNF,
  author =       "Donald E. Knuth",
  title =        "{Von Neumann}'s First Computer Program",
  journal =      j-COMP-SURV,
  volume =       "2",
  number =       "4",
  pages =        "247--260",
  month =        dec,
  year =         "1970",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/356580.356581",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Sat Mar 23 15:03:00 2002",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/compsurv.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/HBP/ACMCS.bib;
                 https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Aspray:1987:PJN}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}


bibtype: article
filename: fparith.bib
label: Krishnamurthy:1970:OIS
author: E. V. Krishnamurthy
title: On Optimal Iterative Schemes For High-Speed Division
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 3
pages: 227--231
month: mar
monthnumber: 3
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.222901
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jan 08 23:09:36 2008
bibtimestamp: 2008.01.08 23:09:36 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. V. Krishnamurthy
rawtitle: On Optimal Iterative Schemes For High-Speed Division
entry:
@Article{Krishnamurthy:1970:OIS,
  author =       "E. V. Krishnamurthy",
  title =        "On Optimal Iterative Schemes For High-Speed Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "3",
  pages =        "227--231",
  month =        mar,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222901",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jan 08 23:09:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Krishnamurthy:1970:RTT
author: E. V. Krishnamurthy
title: On Range-Transformation Techniques for Division
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 2
pages: 157--160
month: feb
monthnumber: 2
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.222882
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 08:01:30 MDT 2011
bibtimestamp: 2011.07.13 08:01:30 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671475
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. V. Krishnamurthy
rawtitle: On Range-Transformation Techniques for Division
entry:
@Article{Krishnamurthy:1970:RTT,
  author =       "E. V. Krishnamurthy",
  title =        "On Range-Transformation Techniques for Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "2",
  pages =        "157--160",
  month =        feb,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222882",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671475",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Ling:1970:HSC
author: H. Ling
title: High-Speed Computer Multiplication Using a Multiple-Bit Decoding Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 706--709
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223020
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Ling.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-1
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. Ling
rawtitle: High-Speed Computer Multiplication Using a Multiple-Bit Decoding Algorithm
abstract:
This paper presents a method of performing the binary multiplication beyond the scheme of multiple ADD and SHIFT. The binary multiplication algorithm will be discussed first, followed by block decoding method, logic implementation, hardware consideration, and two examples which are at the end of the discussion.

rawabstract:
This paper presents a method of performing the binary multiplication beyond the scheme of multiple ADD and SHIFT. The binary multiplication algorithm will be discussed first, followed by block decoding method, logic implementation, hardware consideration, and two examples which are at the end of the discussion.

entry:
@Article{Ling:1970:HSC,
  author =       "H. Ling",
  title =        "High-Speed Computer Multiplication Using a
                 Multiple-Bit Decoding Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "706--709",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223020",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Ling.pdf",
  abstract =     "This paper presents a method of performing the binary
                 multiplication beyond the scheme of multiple ADD and
                 SHIFT. The binary multiplication algorithm will be
                 discussed first, followed by block decoding method,
                 logic implementation, hardware consideration, and two
                 examples which are at the end of the discussion.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}


bibtype: article
filename: fparith.bib
label: Linz:1970:AFP
author: Peter Linz
title: Accurate Floating-Point Summation
journal: j-CACM
volume: 13
number: 6
pages: 361--362
month: jun
monthnumber: 6
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.25
MRnumber: 44\#3468
MRreviewer: R. P. Brent
bibdate: Tue Mar 25 13:26:09 MST 1997
bibtimestamp: 1997.03.25 13:26:09 MST
fjournal: Communications of the ACM
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: New York University, NY, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
rawauthor: Peter Linz
rawtitle: Accurate Floating-Point Summation
bibsource:
Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1970.bib; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
This paper describes an alternate method for summing a set of floating-point numbers. Comparison of the error bound for this method with that of the standard summation method shows that it is considerably less sensitive to propagation of round-off error.

keywords:
accurate floating-point summation; computers, data processing; digital arithmetic; floating point arithmetic; floating-point addition; mathematics; numerical methods; round-off error; round-off errors; round-off propagation; summation

rawabstract:
This paper describes an alternate method for summing a set of floating-point numbers. Comparison of the error bound for this method with that of the standard summation method shows that it is considerably less sensitive to propagation of round-off error.

entry:
@Article{Linz:1970:AFP,
  author =       "Peter Linz",
  title =        "Accurate Floating-Point Summation",
  journal =      j-CACM,
  volume =       "13",
  number =       "6",
  pages =        "361--362",
  month =        jun,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "44\#3468",
  MRreviewer =   "R. P. Brent",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1970.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes an alternate method for summing a
                 set of floating-point numbers. Comparison of the error
                 bound for this method with that of the standard
                 summation method shows that it is considerably less
                 sensitive to propagation of round-off error.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "New York University, NY, USA",
  descriptors =  "Simulation; statistics; numeric calculation",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "accurate floating-point summation; computers, data
                 processing; digital arithmetic; floating point
                 arithmetic; floating-point addition; mathematics;
                 numerical methods; round-off error; round-off errors;
                 round-off propagation; summation",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Liu:1970:CEA
author: B. Liu and T. Kaneko
title: Correction to ``Error analysis of digital filters realized with floating-point arithmetic''
journal: j-PROC-IEEE
volume: 58
number: 3
pages: 376--376
month: mar
monthnumber: 3
year: 1970
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
note: See cite Liu:1969:EAD.
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: B. Liu and T. Kaneko
rawnote: See \cite{Liu:1969:EAD}.
rawtitle: Correction to {``Error analysis of digital filters realized with floating-point arithmetic''}
entry:
@Article{Liu:1970:CEA,
  author =       "B. Liu and T. Kaneko",
  title =        "Correction to {``Error analysis of digital filters
                 realized with floating-point arithmetic''}",
  journal =      j-PROC-IEEE,
  volume =       "58",
  number =       "3",
  pages =        "376--376",
  month =        mar,
  year =         "1970",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Liu:1969:EAD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}


bibtype: article
filename: fparith.bib
label: Long:1970:LAS
author: C. T. Long and J. H. Jordan
title: A Limited Arithmetic on Simple Continued Fractions --- II
journal: j-FIB-QUART
volume: 8
number: 2
pages: 135--157
month: mar
monthnumber: 3
year: 1970
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 18:05:25 MDT 2011
bibtimestamp: 2011.10.20 18:05:25 MDT
URL: http://www.fq.math.ca/Scanned/8-2/long.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: C. T. Long and J. H. Jordan
rawtitle: A Limited Arithmetic on Simple Continued Fractions --- {II}
bibsource:
http://www.fq.math.ca/8-2.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Long:1970:LAS,
  author =       "C. T. Long and J. H. Jordan",
  title =        "A Limited Arithmetic on Simple Continued Fractions ---
                 {II}",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "2",
  pages =        "135--157",
  month =        mar,
  year =         "1970",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:25 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-2.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/8-2/long.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: techreport
filename: fparith.bib
label: Malcolm:1970:AFA
author: Michael Malcolm
title: An algorithm for floating-point accumulation of sums with small relative error
number: STAN-CS-70-163
institution: Computer Science Department, Stanford University
address: Stanford, CA, USA
pages: 21
year: 1970
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: Reproduced by National Technical Information Service. AD 708 691.
acknowledgement: ack-nhfb
rawauthor: Michael Malcolm
rawtitle: An algorithm for floating-point accumulation of sums with small relative error
keywords:
accurate floating-point summation; Algorithms.; FORTRAN (Computer program language); Numerical calculations --- Computer programs.

entry:
@TechReport{Malcolm:1970:AFA,
  author =       "Michael Malcolm",
  title =        "An algorithm for floating-point accumulation of sums
                 with small relative error",
  number =       "STAN-CS-70-163",
  institution =  "Computer Science Department, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "21",
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Algorithms.;
                 FORTRAN (Computer program language); Numerical
                 calculations --- Computer programs.",
  remark =       "Reproduced by National Technical Information Service.
                 AD 708 691.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Marasa:1970:AAE
author: John D. Marasa
title: Accumulated arithmetic error in floating-point and alternative logarithmic number systems
type: Thesis (M.S.)
address: St. Louis, MO, USA
pages: vii + 88
year: 1970
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: Programming (Mathematics)
acknowledgement: ack-nhfb
rawauthor: John D. Marasa
rawtitle: Accumulated arithmetic error in floating-point and alternative logarithmic number systems
school:
Washington University, Sever Institute of Technology, Department of Applied Mathematics and Computer Science

entry:
@MastersThesis{Marasa:1970:AAE,
  author =       "John D. Marasa",
  title =        "Accumulated arithmetic error in floating-point and
                 alternative logarithmic number systems",
  type =         "Thesis ({M.S.})",
  school =       "Washington University, Sever Institute of Technology,
                 Department of Applied Mathematics and Computer
                 Science",
  address =      "St. Louis, MO, USA",
  pages =        "vii + 88",
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Programming (Mathematics)",
}


bibtype: article
filename: fparith.bib
label: Matula:1970:ECA
author: David W. Matula
title: The emergence of computational arithmetic as a component of the computer science curriculum
journal: j-SIGCSE
volume: 2
number: 3
pages: 41--44
month: nov
monthnumber: 11
year: 1970
CODEN: SIGSD3
DOI: https://doi.org/10.1145/873641.873650
ISSN: 0097-8418 (print), 2331-3927 (electronic) OR 00978418 (print), 23313927 (electronic)
ISSNL: 0097-8418 OR 00978418
bibdate: Sun Nov 18 08:53:42 MST 2012
bibtimestamp: 2012.11.18 08:53:42 MST
fjournal: SIGCSE Bulletin (ACM Special Interest Group on Computer Science Education)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J688
rawauthor: David W. Matula
rawtitle: The emergence of computational arithmetic as a component of the computer science curriculum
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigcse1970.bib

entry:
@Article{Matula:1970:ECA,
  author =       "David W. Matula",
  title =        "The emergence of computational arithmetic as a
                 component of the computer science curriculum",
  journal =      j-SIGCSE,
  volume =       "2",
  number =       "3",
  pages =        "41--44",
  month =        nov,
  year =         "1970",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/873641.873650",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sun Nov 18 08:53:42 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1970.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}


bibtype: article
filename: fparith.bib
label: Matula:1970:FFP
author: D. W. Matula
title: A Formalization of Floating-Point Numeric Base Conversion
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 681--692
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223017
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 08:01:35 MDT 2011
bibtimestamp: 2011.07.13 08:01:35 MDT
fjournal: IEEE Transactions on Computers
keywords: ARITH-1
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. W. Matula
rawtitle: A Formalization of Floating-Point Numeric Base Conversion
URL:
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Matula.pdf; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671610

abstract:
The process of converting arbitrary real numbers into a floating-point format is formalized as a mapping of the reals into a specified subset of real numbers. The structure of this subset, the set of $n$ significant digit base $b$ floating-point numbers, is analyzed and properties of conversion mappings are determined. For a restricted conversion mapping of the $n$ significant digit base $b$ numbers to the $m$ significant-digit base $d$ numbers, the one-to-one, onto, and order-preserving properties of the mapping are summarized. Multiple conversions consisting of a composition of individual conversion mappings are investigated and some results of the invariant points of such compound conversions are presented. The hardware and software implications of these results with regard to establishing goals and standards for floating-point formats and conversion procedures are considered.

rawabstract:
The process of converting arbitrary real numbers into a floating-point format is formalized as a mapping of the reals into a specified subset of real numbers. The structure of this subset, the set of $n$ significant digit base $b$ floating-point numbers, is analyzed and properties of conversion mappings are determined. For a restricted conversion mapping of the $n$ significant digit base $b$ numbers to the $m$ significant-digit base $d$ numbers, the one-to-one, onto, and order-preserving properties of the mapping are summarized. Multiple conversions consisting of a composition of individual conversion mappings are investigated and some results of the invariant points of such compound conversions are presented. The hardware and software implications of these results with regard to establishing goals and standards for floating-point formats and conversion procedures are considered.

entry:
@Article{Matula:1970:FFP,
  author =       "D. W. Matula",
  title =        "A Formalization of Floating-Point Numeric Base
                 Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "681--692",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223017",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:35 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Matula.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671610",
  abstract =     "The process of converting arbitrary real numbers into
                 a floating-point format is formalized as a mapping of
                 the reals into a specified subset of real numbers. The
                 structure of this subset, the set of $n$ significant
                 digit base $b$ floating-point numbers, is analyzed and
                 properties of conversion mappings are determined. For a
                 restricted conversion mapping of the $n$ significant
                 digit base $b$ numbers to the $m$ significant-digit
                 base $d$ numbers, the one-to-one, onto, and
                 order-preserving properties of the mapping are
                 summarized. Multiple conversions consisting of a
                 composition of individual conversion mappings are
                 investigated and some results of the invariant points
                 of such compound conversions are presented. The
                 hardware and software implications of these results
                 with regard to establishing goals and standards for
                 floating-point formats and conversion procedures are
                 considered.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}


bibtype: article
filename: fparith.bib
label: Mifsud:1970:MDA
author: C. J. Mifsud
title: A multiple-precision division algorithm
journal: j-CACM
volume: 13
number: 11
pages: 666--668
month: nov
monthnumber: 11
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Mar 25 13:26:09 MST 1997
bibtimestamp: 1997.03.25 13:26:09 MST
note: See addendum cite Mifsud:1973:AMP.
fjournal: Communications of the ACM
keywords: digital arithmetic
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Mitre Corp., McLean, VA, USA
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. J. Mifsud
rawnote: See addendum \cite{Mifsud:1973:AMP}.
rawtitle: A multiple-precision division algorithm
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Mifsud:1970:MDA,
  author =       "C. J. Mifsud",
  title =        "A multiple-precision division algorithm",
  journal =      j-CACM,
  volume =       "13",
  number =       "11",
  pages =        "666--668",
  month =        nov,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See addendum \cite{Mifsud:1973:AMP}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Mitre Corp., McLean, VA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Nickel:1970:KBS
author: K. Nickel
journal: j-Z-ANGE-MATH-MECH
volume: 50
pages: 369--373
year: 1970
CODEN: ZAMMAX
ISSN: 0044-2267 (print), 1521-4001 (electronic) OR 00442267 (print), 15214001 (electronic)
ISSNL: 0044-2267 OR 00442267
bibdate: Tue Aug 28 06:12:04 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.28 06:12:04 ???
fjournal: Zeitschrift fur Angewandte Mathematik und Mechanik
keywords: accurate floating-point summation
language: German
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001
rawauthor: K. Nickel
title:
Das Kahan--Babuskasche Summierungsverfahren in Triplex-ALGOL 60. (German) [The Kahan--Babuska summation method in Triplex-ALGOL 60]

rawtitle:
{Das Kahan--Babu{\v{s}}kasche Summierungsverfahren in Triplex-ALGOL 60}. ({German}) [{The Kahan--Babu{\v{s}}ka} summation method in {Triplex-ALGOL 60}]

entry:
@Article{Nickel:1970:KBS,
  author =       "K. Nickel",
  title =        "{Das Kahan--Babu{\v{s}}kasche Summierungsverfahren in
                 Triplex-ALGOL 60}. ({German}) [{The
                 Kahan--Babu{\v{s}}ka} summation method in
                 {Triplex-ALGOL 60}]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "50",
  pages =        "369--373",
  year =         "1970",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Tue Aug 28 06:12:04 2001",
  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",
  keywords =     "accurate floating-point summation",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Ninomiya:1970:BRS
author: Ichizo Ninomiya
title: Best Rational Starting Approximations and Improved Newton Iteration for the Square Root
journal: j-MATH-COMPUT
volume: 24
number: 110
pages: 391--404
month: apr
monthnumber: 4
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4130 (Interpolation and function approximation)
corpsource: Nagoya University, Chikua ku, Japan
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Ichizo Ninomiya
rawtitle: Best Rational Starting Approximations and Improved {Newton} Iteration for the Square Root
keywords:
computing procedure; function approximation; iterative methods; Newton iteration; rational approximation; square root

entry:
@Article{Ninomiya:1970:BRS,
  author =       "Ichizo Ninomiya",
  title =        "Best Rational Starting Approximations and Improved
                 {Newton} Iteration for the Square Root",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "391--404",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Nagoya University, Chikua ku, Japan",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computing procedure; function approximation; iterative
                 methods; Newton iteration; rational approximation;
                 square root",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Oppenheim:1970:RDF
author: A. Oppenheim
title: Realization of digital filters using block-floating-point arithmetic
journal: j-IEEE-TRANS-AUDIO-ELECTROACOUST
volume: 18
number: 2
pages: 130--136
month: jun
monthnumber: 6
year: 1970
CODEN: ITADAS
ISSN: 0018-9278 (print), 1558-2582 (electronic) OR 00189278 (print), 15582582 (electronic)
ISSNL: 0018-9278 OR 00189278
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Audio and Electroacoustics
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337
rawauthor: A. Oppenheim
rawtitle: Realization of digital filters using block-floating-point arithmetic
entry:
@Article{Oppenheim:1970:RDF,
  author =       "A. Oppenheim",
  title =        "Realization of digital filters using
                 block-floating-point arithmetic",
  journal =      j-IEEE-TRANS-AUDIO-ELECTROACOUST,
  volume =       "18",
  number =       "2",
  pages =        "130--136",
  month =        jun,
  year =         "1970",
  CODEN =        "ITADAS",
  ISSN =         "0018-9278 (print), 1558-2582 (electronic)",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
  summary =      "Recently, statistical models for the effects of
                 roundoff noise in fixed-point and floating-point
                 realizations of digital filters have been proposed and
                 verified, and a comparison between these realizations
                 presented. In this paper a structure for \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Phillips:1970:GLE
author: David L. Phillips
title: Generalized Logarithmic Error and Newton's Method for the $m$ th Root
journal: j-MATH-COMPUT
volume: 24
number: 110
pages: 383--389
month: apr
monthnumber: 4
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nj
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: David L. Phillips
rawtitle: Generalized Logarithmic Error and {Newton}'s Method for the $m$ th Root
entry:
@Article{Phillips:1970:GLE,
  author =       "David L. Phillips",
  title =        "Generalized Logarithmic Error and {Newton}'s Method
                 for the $m$ th Root",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "383--389",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Rao:1970:BEC
author: T. R. N. Rao
title: Biresidue Error-Correcting Codes for Computer Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 5
pages: 398--402
month: may
monthnumber: 5
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.222937
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 08:01:32 MDT 2011
bibtimestamp: 2011.07.13 08:01:32 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. R. N. Rao
rawtitle: Biresidue Error-Correcting Codes for Computer Arithmetic
entry:
@Article{Rao:1970:BEC,
  author =       "T. R. N. Rao",
  title =        "Biresidue Error-Correcting Codes for Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "5",
  pages =        "398--402",
  month =        may,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222937",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:32 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Rao:1970:BLR
author: T. R. N. Rao and A. K. Trehan
title: Binary Logic for Residue Arithmetic Using Magnitude Index
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 752--757
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223026
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Rao.pdf
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. R. N. Rao and A. K. Trehan
rawtitle: Binary Logic for Residue Arithmetic Using Magnitude Index
abstract:
We consider a residue number system using n pairwise relatively prime moduli $ m_1, ldots , m_n $ to represent any integer $X$ in the range $ M / 2 leq X > M / 2 $, when $ M = prod m_i $. The moduli $ m_i $ are chosen to be of the $ 2 - 1 $ type, in order that the residue arithmetic can be implemented by means of binary registers and binary logic. Further, for each residue number $X$, a magnitude index $ P_x $ is maintained for all arithmetic operations. We investigate the properties of such a system and derive the addition, subtraction, multiplication, sign determination, and overflow detection algorithms. The proposed organization is found to improve the operation times for sign detection and overflow detection operations, while rendering multiplication to be a difficult operation.

keywords:
ARITH-1; base extension; index generation logic; magnitude index; modular adders; naturalized form; overflow detection; residue multiplication; residue number system; scale by 2; sign determination

rawabstract:
We consider a residue number system using n pairwise relatively prime moduli $ m_1, \ldots {}, m_n $ to represent any integer $X$ in the range $ M / 2 \leq X > M / 2 $, when $ M = \prod m_i $. The moduli $ m_i $ are chosen to be of the $ 2 - 1 $ type, in order that the residue arithmetic can be implemented by means of binary registers and binary logic. Further, for each residue number $X$, a magnitude index $ P_x $ is maintained for all arithmetic operations. We investigate the properties of such a system and derive the addition, subtraction, multiplication, sign determination, and overflow detection algorithms. The proposed organization is found to improve the operation times for sign detection and overflow detection operations, while rendering multiplication to be a difficult operation.

entry:
@Article{Rao:1970:BLR,
  author =       "T. R. N. Rao and A. K. Trehan",
  title =        "Binary Logic for Residue Arithmetic Using Magnitude
                 Index",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "752--757",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223026",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Rao.pdf",
  abstract =     "We consider a residue number system using n pairwise
                 relatively prime moduli $ m_1, \ldots {}, m_n $ to
                 represent any integer $X$ in the range $ M / 2 \leq X >
                 M / 2 $, when $ M = \prod m_i $. The moduli $ m_i $ are
                 chosen to be of the $ 2 - 1 $ type, in order that the
                 residue arithmetic can be implemented by means of
                 binary registers and binary logic. Further, for each
                 residue number $X$, a magnitude index $ P_x $ is
                 maintained for all arithmetic operations. We
                 investigate the properties of such a system and derive
                 the addition, subtraction, multiplication, sign
                 determination, and overflow detection algorithms. The
                 proposed organization is found to improve the operation
                 times for sign detection and overflow detection
                 operations, while rendering multiplication to be a
                 difficult operation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1; base extension; index generation logic;
                 magnitude index; modular adders; naturalized form;
                 overflow detection; residue multiplication; residue
                 number system; scale by 2; sign determination",
}


bibtype: article
filename: fparith.bib
label: Robertson:1970:CBM
author: J. E. Robertson
title: The Correspondence Between Methods of Digital Division and Multiplier Recoding Procedures
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 692--701
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223018
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Robertson.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-1
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. E. Robertson
rawtitle: The Correspondence Between Methods of Digital Division and Multiplier Recoding Procedures
abstract:
This paper relates previous analyses of the binary SRT division to the theory of multiplier recoding. Since each binary quotient digit has three possible values, the quotient resulting from the SRT division is in recoded form; in this paper it is shown that the recoding is a function of the divisor, and the method for determining the characteristic Boolean function of the recoding is presented. The relationship between the division and the recoding is established by scaling the division in such a way that the scaled ``visor'' becomes a constant. Higher radix results are also discussed.

rawabstract:
This paper relates previous analyses of the binary SRT division to the theory of multiplier recoding. Since each binary quotient digit has three possible values, the quotient resulting from the SRT division is in recoded form; in this paper it is shown that the recoding is a function of the divisor, and the method for determining the characteristic Boolean function of the recoding is presented. The relationship between the division and the recoding is established by scaling the division in such a way that the scaled ``visor'' becomes a constant. Higher radix results are also discussed.

entry:
@Article{Robertson:1970:CBM,
  author =       "J. E. Robertson",
  title =        "The Correspondence Between Methods of Digital Division
                 and Multiplier Recoding Procedures",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "692--701",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223018",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Robertson.pdf",
  abstract =     "This paper relates previous analyses of the binary SRT
                 division to the theory of multiplier recoding. Since
                 each binary quotient digit has three possible values,
                 the quotient resulting from the SRT division is in
                 recoded form; in this paper it is shown that the
                 recoding is a function of the divisor, and the method
                 for determining the characteristic Boolean function of
                 the recoding is presented. The relationship between the
                 division and the recoding is established by scaling the
                 division in such a way that the scaled ``visor''
                 becomes a constant. Higher radix results are also
                 discussed.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}


bibtype: techreport
filename: fparith.bib
label: Rothmaier:1970:BQN
author: B. Rothmaier
type: Interner Bericht
number: Nr. 70/17
institution: Institut fur Informatik, Universitat Karlsruhe
year: 1970
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
acknowledgement: ack-nj
rawauthor: B. Rothmaier
title:
Die Berechnung der Quadratwurzel nebst Schranken auf Dualmaschinen toenglish The Computation of the Square Root together with [Interval] Bounds on Binary Machines endtoenglish 

rawtitle:
{Die Berechnung der Quadratwurzel nebst Schranken auf Dualmaschinen} \toenglish {The Computation of the Square Root together with [Interval] Bounds on Binary Machines} \endtoenglish

entry:
@TechReport{Rothmaier:1970:BQN,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der Quadratwurzel nebst Schranken auf
                 Dualmaschinen} \toenglish {The Computation of the
                 Square Root together with [Interval] Bounds on Binary
                 Machines} \endtoenglish",
  type =         "{Interner Bericht}",
  number =       "Nr. 70/17",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  pages =        "??",
  year =         "1970",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: fparith.bib
label: Rothmaier:1970:DSB
author: B. Rothmaier
type: Interner Bericht
number: Nr. 70/8
institution: Institut fur Informatik, Universitat Karlsruhe
year: 1970
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: B. Rothmaier
title:
Dokumentation der Standardfunktionen des Betriebssystems Hydra X8 toenglish Documentation of the Elementary Functions of the Operating System Hydra X8 endtoenglish 

rawtitle:
{Dokumentation der Standardfunktionen des Betriebssystems Hydra X8} \toenglish {Documentation} of the Elementary Functions of the Operating System {Hydra X8} \endtoenglish

entry:
@TechReport{Rothmaier:1970:DSB,
  author =       "B. Rothmaier",
  title =        "{Dokumentation der Standardfunktionen des
                 Betriebssystems Hydra X8} \toenglish {Documentation} of
                 the Elementary Functions of the Operating System {Hydra
                 X8} \endtoenglish",
  type =         "{Interner Bericht}",
  number =       "Nr. 70/8",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  pages =        "??",
  year =         "1970",
  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: article
filename: fparith.bib
label: Shively:1970:PFI
author: Richard R. Shively
title: Preface: First IEEE Conference on Computer Arithmetic, Minneapolis, Minnesota, June 16, 1969
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 679--680
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223016
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
fjournal: IEEE Transactions on Computers
keywords: ARITH-1
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Richard R. Shively
rawtitle: Preface: {First IEEE Conference on Computer Arithmetic, Minneapolis, Minnesota, June 16, 1969}
URL:
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_contents.pdf; http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Shively.pdf; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671609

entry:
@Article{Shively:1970:PFI,
  author =       "Richard R. Shively",
  title =        "Preface: {First IEEE Conference on Computer
                 Arithmetic, Minneapolis, Minnesota, June 16, 1969}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "679--680",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223016",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Shively.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671609",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}


bibtype: article
filename: fparith.bib
label: Sikdar:1970:DMM
author: K. Sikdar
title: Determination of Multipliers Mapping an Arbitrary Integer into a Range of Certain Type
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 12
pages: 1221--1222
month: dec
monthnumber: 12
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.222863
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 08:01:39 MDT 2011
bibtimestamp: 2011.07.13 08:01:39 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671456
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: K. Sikdar
rawtitle: Determination of Multipliers Mapping an Arbitrary Integer into a Range of Certain Type
entry:
@Article{Sikdar:1970:DMM,
  author =       "K. Sikdar",
  title =        "Determination of Multipliers Mapping an Arbitrary
                 Integer into a Range of Certain Type",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "12",
  pages =        "1221--1222",
  month =        dec,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222863",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671456",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Svoboda:1970:ADC
author: A. Svoboda
title: Adder With Distributed Control
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 749--751
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223025
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Svoboda.pdf
fjournal: IEEE Transactions on Computers
keywords: adder; adder for large number of numbers; ARITH-1; distributed control; reordering
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Svoboda
rawtitle: Adder With Distributed Control
abstract:
An adder is described for addition of a large number of binary numbers $ x_j, j = 1, 2, ldots , m $, where $ x_j = sum _i x_j, i 2^i, x_j, i = 0, 1, i = 0, 1, ldots , n - 1 $. The adder's algorithm has two parts: (1) the bits $ x_j, i $ are added independently for each binary order $ i : s_i = sum _j x_j, i leq m $ and the result expressed in the binary form $ s_i = sum _k a_i, k 2^k, a_i, k = 0, 1, k = 0, 1, ldots , p - 1 $ (where $ 2^p - 1 leq m < 2^p $) ; (2) the sum $ y = sum _j x_j $ is formed by adding terms $ s_i, k 2^i + k $ as contributions of the bit $ s_i, k $ to the total $y$. A hardware implementation of this algorithm is suggested where the sum $ s_i $ is obtained by a sequential circuit which reorders the values $ x_j, i' $ so that their sum $ s_i $, remains unchanged and so that after the reordering the new values $ x_j, i' $ obey the conditions $ x_j + 1, i leq x_j, i $ for every $ j = 1, 2, ldots , m - 1 $. The implementation with integrated circuits should be quite rewarding because the control of the circuit is done with independent control elements distributed all over the chip.

rawabstract:
An adder is described for addition of a large number of binary numbers $ x_j, j = 1, 2, \ldots {}, m $, where $ x_j = \sum_i x_{j, i} 2^i, x_{j, i} = 0, 1, i = 0, 1, \ldots {}, n - 1 $. The adder's algorithm has two parts: (1) the bits $ x_{j, i} $ are added independently for each binary order $ i : s_i = \sum_j x_{j, i} \leq m $ and the result expressed in the binary form $ s_i = \sum_k a_{i, k} 2^k, a_{i, k} = 0, 1, k = 0, 1, \ldots {}, p - 1 $ (where $ 2^{p - 1} \leq m < 2^p $) ; (2) the sum $ y = \sum_j x_j $ is formed by adding terms $ s_{i, k} {2^{i + k}} $ as contributions of the bit $ s_{i, k} $ to the total $y$. A hardware implementation of this algorithm is suggested where the sum $ s_i $ is obtained by a sequential circuit which reorders the values $ x_{j, i}' $ so that their sum $ s_i $, remains unchanged and so that after the reordering the new values $ x_{j, i}' $ obey the conditions $ x_{j + 1, i} \leq x_{j, i} $ for every $ j = 1, 2, \ldots {}, m - 1 $. The implementation with integrated circuits should be quite rewarding because the control of the circuit is done with independent control elements distributed all over the chip.

entry:
@Article{Svoboda:1970:ADC,
  author =       "A. Svoboda",
  title =        "Adder With Distributed Control",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "749--751",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223025",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Svoboda.pdf",
  abstract =     "An adder is described for addition of a large number
                 of binary numbers $ x_j, j = 1, 2, \ldots {}, m $,
                 where $ x_j = \sum_i x_{j, i} 2^i, x_{j, i} = 0, 1, i =
                 0, 1, \ldots {}, n - 1 $. The adder's algorithm has two
                 parts: (1) the bits $ x_{j, i} $ are added
                 independently for each binary order $ i : s_i = \sum_j
                 x_{j, i} \leq m $ and the result expressed in the
                 binary form $ s_i = \sum_k a_{i, k} 2^k, a_{i, k} = 0,
                 1, k = 0, 1, \ldots {}, p - 1 $ (where $ 2^{p - 1} \leq
                 m < 2^p $) ; (2) the sum $ y = \sum_j x_j $ is formed
                 by adding terms $ s_{i, k} {2^{i + k}} $ as
                 contributions of the bit $ s_{i, k} $ to the total $y$.
                 A hardware implementation of this algorithm is
                 suggested where the sum $ s_i $ is obtained by a
                 sequential circuit which reorders the values $ x_{j,
                 i}' $ so that their sum $ s_i $, remains unchanged and
                 so that after the reordering the new values $ x_{j, i}'
                 $ obey the conditions $ x_{j + 1, i} \leq x_{j, i} $
                 for every $ j = 1, 2, \ldots {}, m - 1 $. The
                 implementation with integrated circuits should be quite
                 rewarding because the control of the circuit is done
                 with independent control elements distributed all over
                 the chip.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "adder; adder for large number of numbers; ARITH-1;
                 distributed control; reordering",
}


bibtype: article
filename: fparith.bib
label: Taub:1970:ECS
author: D. M. Taub and C. E. Owen and B. P. Day
title: Experimental Computer for Schools
journal: Proceedings of the IEE
volume: 117
number: 2
pages: 303--312
month: feb
monthnumber: 2
year: 1970
bibdate: Fri Nov 28 19:30:38 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 19:30:38 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
rawauthor: D. M. Taub and C. E. Owen and B. P. Day
rawtitle: Experimental Computer for Schools
abstract:
The computer is a small desk-top machine designed for teaching schoolchildren how computers work. It works in decimal notation and has a powerful instruction set which includes 3-address floating-point instructions implemented as `extracode' subroutines. Addressing can be absolute, relative or indirect. For input it uses a capacitive touch keyboard, and for output and display a perfectly normal TV receiver is used. Another input/output device is an ordinary domestic tape recorder, used mainly for long term storage of programs. To make the operation of the machine easy to follow, it can be made to stop at certain stages in the processing of an instruction and automaticaly display the contents of all registers and storage locations relevant at that time. The paper gives a description of the machine and a discussion of the factors that hav influenced its design.

remark:
IBM Schools computer with scaled integer format, six decimal digits and exponent range of $ [ - 6, 0] $.

rawabstract:
The computer is a small desk-top machine designed for teaching schoolchildren how computers work. It works in decimal notation and has a powerful instruction set which includes 3-address floating-point instructions implemented as `extracode' subroutines. Addressing can be absolute, relative or indirect. For input it uses a capacitive touch keyboard, and for output and display a perfectly normal TV receiver is used. Another input/output device is an ordinary domestic tape recorder, used mainly for long term storage of programs. To make the operation of the machine easy to follow, it can be made to stop at certain stages in the processing of an instruction and automaticaly display the contents of all registers and storage locations relevant at that time. The paper gives a description of the machine and a discussion of the factors that hav influenced its design.

entry:
@Article{Taub:1970:ECS,
  author =       "D. M. Taub and C. E. Owen and B. P. Day",
  title =        "Experimental Computer for Schools",
  journal =      "Proceedings of the IEE",
  volume =       "117",
  number =       "2",
  pages =        "303--312",
  month =        feb,
  year =         "1970",
  bibdate =      "Fri Nov 28 19:30:38 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The computer is a small desk-top machine designed for
                 teaching schoolchildren how computers work. It works in
                 decimal notation and has a powerful instruction set
                 which includes 3-address floating-point instructions
                 implemented as `extracode' subroutines. Addressing can
                 be absolute, relative or indirect. For input it uses a
                 capacitive touch keyboard, and for output and display a
                 perfectly normal TV receiver is used. Another
                 input/output device is an ordinary domestic tape
                 recorder, used mainly for long term storage of
                 programs. To make the operation of the machine easy to
                 follow, it can be made to stop at certain stages in the
                 processing of an instruction and automaticaly display
                 the contents of all registers and storage locations
                 relevant at that time. The paper gives a description of
                 the machine and a discussion of the factors that hav
                 influenced its design.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "IBM Schools computer with scaled integer format, six
                 decimal digits and exponent range of $ [ - 6, 0] $.",
}


bibtype: book
filename: fparith.bib
label: Thornton:1970:DCC
author: James E. Thornton
title: Design of a Computer: the Control Data 6600
publisher: pub-SF
address: pub-SF:adr
pages: v + 181
year: 1970
ISBN: 0-07-057302-6, 0-07-057303-4 OR 0070573026, 0070573034
ISBN13: 978-0-07-057302-4, 978-0-07-057303-1 OR 9780070573024, 9780070573031
LCCN: TK7889.C6 T5 1970
bibdate: Wed Sep 14 22:45:51 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 22:45:51 ???
acknowledgement: ack-nhfb
rawauthor: James E. Thornton
rawtitle: Design of a Computer: the {Control Data 6600}
URL:
https://archive.computerhistory.org/resources/text/CDC/cdc.6600.thornton.design_of_a_computer_the_control_data_6600.1970.102630394.pdf

remark:
See Table V: Nonstandard Floating Point Arithmetic on page 79 for the rules governing Indefinite, Infinity, and Negative Zero operands.

TOC:
I: Introduction / 1 A. Justification for Large Computers / 1 B. Building Blocks / 4 C. The Approach / 5 II: Organization of the 6600 / 9 A. General / 9 B. Peripheral Subsystem / 10 C. Central Processor-CPU / 12 D. Central Storage / 15 E. Extended Core Storage / 17 III: Basic Circuit Properties / 19 A. The Silicon Transistor / 19 B. DCTL Logic Circuits / 21 C. Logic Symbols / 24 D. Transmission Lines / 28 E. Packaging / 32 IV: Central Storage System / 37 A. Storage Module / 37 B. Theory of Interleaved Storage / 44 C. Stunt Box / 47 D. Storage Bus System / 51 E. Extended Core Storage / 53 F. ECS Coupler and Controller / 55 V: Central Processor Functional Units / 57 A. Boolean Unit / 59 B. Fixed Add Unit / 63 C. Data Trunks / 69 D. Shift Unit / 71 E. Add Unit / 77 F. Multiply Unit / 88 G. Divide Unit / 101 H. Increment Unit / 105 I. Branch Unit / 111 J. ECS Coupler-Controller / 114 VI: Central Processor Control / 117 A. Exchange Jump / 117 B. Instruction Fetch / 120 C. Instruction Issue / 123 D. Scoreboard / 125 Register Entry/Exit Control / 134 F. Summary / 137 VII: Peripheral Subsystem / 141 A. Peripheral Processors / 141 B. Dead Start / 154 C. Disk Storage / 157 VIII: Systems Operation / 163 A. Files / 163 B. Tables / 165 C. Circular Buffer for 1/0 / 166 D. Job Processing / 167 E. System Monitor MTR / 168 F. Control Points / 169 G. Summary / 171 Appendix / 173 Index / 177

rawTOC:
I: Introduction / 1 \\ A. Justification for Large Computers / 1 \\ B. Building Blocks / 4 \\ C. The Approach / 5 \\ II: Organization of the 6600 / 9 \\ A. General / 9 \\ B. Peripheral Subsystem / 10 \\ C. Central Processor-CPU / 12 \\ D. Central Storage / 15 \\ E. Extended Core Storage / 17 \\ III: Basic Circuit Properties / 19 \\ A. The Silicon Transistor / 19 \\ B. DCTL Logic Circuits / 21 \\ C. Logic Symbols / 24 \\ D. Transmission Lines / 28 \\ E. Packaging / 32 \\ IV: Central Storage System / 37 \\ A. Storage Module / 37 \\ B. Theory of Interleaved Storage / 44 \\ C. Stunt Box / 47 \\ D. Storage Bus System / 51 \\ E. Extended Core Storage / 53 \\ F. ECS Coupler and Controller / 55 \\ V: Central Processor Functional Units / 57 \\ A. Boolean Unit / 59 \\ B. Fixed Add Unit / 63 \\ C. Data Trunks / 69 \\ D. Shift Unit / 71 \\ E. Add Unit / 77 \\ F. Multiply Unit / 88 \\ G. Divide Unit / 101 \\ H. Increment Unit / 105 \\ I. Branch Unit / 111 \\ J. ECS Coupler-Controller / 114 \\ VI: Central Processor Control / 117 \\ A. Exchange Jump / 117 \\ B. Instruction Fetch / 120 \\ C. Instruction Issue / 123 \\ D. Scoreboard / 125 \\ Register Entry/Exit Control / 134 \\ F. Summary / 137 \\ VII: Peripheral Subsystem / 141 A. Peripheral Processors / 141 \\ B. Dead Start / 154 \\ C. Disk Storage / 157 \\ VIII: Systems Operation / 163 \\ A. Files / 163 \\ B. Tables / 165 \\ C. Circular Buffer for 1/0 / 166 \\ D. Job Processing / 167 \\ E. System Monitor MTR / 168 \\ F. Control Points / 169 \\ G. Summary / 171 \\ Appendix / 173 \\ Index / 177

entry:
@Book{Thornton:1970:DCC,
  author =       "James E. Thornton",
  title =        "Design of a Computer: the {Control Data 6600}",
  publisher =    pub-SF,
  address =      pub-SF:adr,
  pages =        "v + 181",
  year =         "1970",
  ISBN =         "0-07-057302-6, 0-07-057303-4",
  ISBN-13 =      "978-0-07-057302-4, 978-0-07-057303-1",
  LCCN =         "TK7889.C6 T5 1970",
  bibdate =      "Wed Sep 14 22:45:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://archive.computerhistory.org/resources/text/CDC/cdc.6600.thornton.design_of_a_computer_the_control_data_6600.1970.102630394.pdf",
  acknowledgement = ack-nhfb,
  remark =       "See Table V: Nonstandard Floating Point Arithmetic on
                 page 79 for the rules governing Indefinite, Infinity,
                 and Negative Zero operands.",
  tableofcontents = "I: Introduction / 1 \\
                 A. Justification for Large Computers / 1 \\
                 B. Building Blocks / 4 \\
                 C. The Approach / 5 \\
                 II: Organization of the 6600 / 9 \\
                 A. General / 9 \\
                 B. Peripheral Subsystem / 10 \\
                 C. Central Processor-CPU / 12 \\
                 D. Central Storage / 15 \\
                 E. Extended Core Storage / 17 \\
                 III: Basic Circuit Properties / 19 \\
                 A. The Silicon Transistor / 19 \\
                 B. DCTL Logic Circuits / 21 \\
                 C. Logic Symbols / 24 \\
                 D. Transmission Lines / 28 \\
                 E. Packaging / 32 \\
                 IV: Central Storage System / 37 \\
                 A. Storage Module / 37 \\
                 B. Theory of Interleaved Storage / 44 \\
                 C. Stunt Box / 47 \\
                 D. Storage Bus System / 51 \\
                 E. Extended Core Storage / 53 \\
                 F. ECS Coupler and Controller / 55 \\
                 V: Central Processor Functional Units / 57 \\
                 A. Boolean Unit / 59 \\
                 B. Fixed Add Unit / 63 \\
                 C. Data Trunks / 69 \\
                 D. Shift Unit / 71 \\
                 E. Add Unit / 77 \\
                 F. Multiply Unit / 88 \\
                 G. Divide Unit / 101 \\
                 H. Increment Unit / 105 \\
                 I. Branch Unit / 111 \\
                 J. ECS Coupler-Controller / 114 \\
                 VI: Central Processor Control / 117 \\
                 A. Exchange Jump / 117 \\
                 B. Instruction Fetch / 120 \\
                 C. Instruction Issue / 123 \\
                 D. Scoreboard / 125 \\
                 Register Entry/Exit Control / 134 \\
                 F. Summary / 137 \\
                 VII: Peripheral Subsystem / 141 A. Peripheral
                 Processors / 141 \\
                 B. Dead Start / 154 \\
                 C. Disk Storage / 157 \\
                 VIII: Systems Operation / 163 \\
                 A. Files / 163 \\
                 B. Tables / 165 \\
                 C. Circular Buffer for 1/0 / 166 \\
                 D. Job Processing / 167 \\
                 E. System Monitor MTR / 168 \\
                 F. Control Points / 169 \\
                 G. Summary / 171 \\
                 Appendix / 173 \\
                 Index / 177",
}


bibtype: article
filename: fparith.bib
label: Tienari:1970:SMR
author: Martti Tienari
title: A Statistical Model of Roundoff Error for Varying Length Floating-Point Arithmetic
journal: j-BIT
volume: 10
number: 3
pages: 355--365
month: sep
monthnumber: 9
year: 1970
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01934204
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 68.00 (65.00)
MRnumber: 42\#7108
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=3&spage=355
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
reviewer: R. W. Hamming
rawauthor: Martti Tienari
rawtitle: A Statistical Model of Roundoff Error for Varying Length Floating-Point Arithmetic
entry:
@Article{Tienari:1970:SMR,
  author =       "Martti Tienari",
  title =        "A Statistical Model of Roundoff Error for Varying
                 Length Floating-Point Arithmetic",
  journal =      j-BIT,
  volume =       "10",
  number =       "3",
  pages =        "355--365",
  month =        sep,
  year =         "1970",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01934204",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "42\#7108",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=3&spage=355",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
  reviewer =     "R. W. Hamming",
}


bibtype: article
filename: fparith.bib
label: Tung:1970:SDD
author: Chin Tung
title: Signed-Digit Division Using Combinational Arithmetic Nets
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 746--748
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223024
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Tung.pdf
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Chin Tung
rawtitle: Signed-Digit Division Using Combinational Arithmetic Nets
abstract:
To meet the challenge created by the advent of large- scale integration, a unique microelectronic arithmetic building element and combinational arithmetic nets, composed of the building elements, have been studied and proposed for arithmetic processor design. A fast division algorithm, particularly suitable for floating- point arithmetic, has also been developed for signed-digit arithmetic. This algorithm is characterized by the need of preprocessing the divisor and then exact generation of quotient digits. This paper describes the implementation of this division algorithm with the arithmetic building element and combinational arithmetic nets. The intention here is to explore the feasibility of applying large-scale integration technology to arithmetic processors.

keywords:
ARITH-1; arithmetic building element; combinational arithmetic net; division; large-scale integration; microelectronic block; signed-digit number system

rawabstract:
To meet the challenge created by the advent of large- scale integration, a unique microelectronic arithmetic building element and combinational arithmetic nets, composed of the building elements, have been studied and proposed for arithmetic processor design. A fast division algorithm, particularly suitable for floating- point arithmetic, has also been developed for signed-digit arithmetic. This algorithm is characterized by the need of preprocessing the divisor and then exact generation of quotient digits. This paper describes the implementation of this division algorithm with the arithmetic building element and combinational arithmetic nets. The intention here is to explore the feasibility of applying large-scale integration technology to arithmetic processors.

entry:
@Article{Tung:1970:SDD,
  author =       "Chin Tung",
  title =        "Signed-Digit Division Using Combinational Arithmetic
                 Nets",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "746--748",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223024",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Tung.pdf",
  abstract =     "To meet the challenge created by the advent of large-
                 scale integration, a unique microelectronic arithmetic
                 building element and combinational arithmetic nets,
                 composed of the building elements, have been studied
                 and proposed for arithmetic processor design. A fast
                 division algorithm, particularly suitable for floating-
                 point arithmetic, has also been developed for
                 signed-digit arithmetic. This algorithm is
                 characterized by the need of preprocessing the divisor
                 and then exact generation of quotient digits. This
                 paper describes the implementation of this division
                 algorithm with the arithmetic building element and
                 combinational arithmetic nets. The intention here is to
                 explore the feasibility of applying large-scale
                 integration technology to arithmetic processors.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1; arithmetic building element; combinational
                 arithmetic net; division; large-scale integration;
                 microelectronic block; signed-digit number system",
}


bibtype: article
filename: fparith.bib
label: Usow:1970:CB
author: K. H. Usow
title: Certification Bibliography
journal: j-SIGNUM
volume: 5
number: 2
pages: 14--15
month: mar
monthnumber: 3
year: 1970
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Fri Aug 20 10:26:49 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 10:26:49 ???
fjournal: ACM SIGNUM Newsletter
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: K. H. Usow
rawtitle: Certification Bibliography
entry:
@Article{Usow:1970:CB,
  author =       "K. H. Usow",
  title =        "Certification Bibliography",
  journal =      j-SIGNUM,
  volume =       "5",
  number =       "2",
  pages =        "14--15",
  month =        mar,
  year =         "1970",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Fri Aug 20 10:26:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Waksman:1970:WAI
author: A. Waksman
title: On Winograd's Algorithm for Inner Products
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 4
pages: 360--361
month: apr
monthnumber: 4
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.222926
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Oct 09 18:54:12 2007
bibtimestamp: 2007.10.09 18:54:12 ???
fjournal: IEEE Transactions on Computers
keywords: fast matrix multiplication; product of matrices; sufficient number of arithmetical operations
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Waksman
rawtitle: On {Winograd}'s Algorithm for Inner Products
abstract:
This correspondence demonstrates an improvement on Winograd's algorithm for inner products as applied to the multiplication of two matrices.

rawabstract:
This correspondence demonstrates an improvement on Winograd's algorithm for inner products as applied to the multiplication of two matrices.

entry:
@Article{Waksman:1970:WAI,
  author =       "A. Waksman",
  title =        "On {Winograd}'s Algorithm for Inner Products",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "4",
  pages =        "360--361",
  month =        apr,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222926",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 09 18:54:12 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "This correspondence demonstrates an improvement on
                 Winograd's algorithm for inner products as applied to
                 the multiplication of two matrices.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "fast matrix multiplication; product of matrices;
                 sufficient number of arithmetical operations",
}


bibtype: article
filename: fparith.bib
label: Wilson:1970:OSA
author: M. Wayne Wilson
title: Optimal Starting Approximations for Generating Square Root for Slow or No Divide
journal: j-CACM
volume: 13
number: 9
pages: 559--560
month: sep
monthnumber: 9
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.50
MRnumber: 44\#2338
MRreviewer: J. E. {Dennis, Jr.}
bibdate: Thu Sep 1 10:15:43 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:43 ???
fjournal: Communications of the ACM
keywords: CACMA; digital arithmetic; ele; iterative methods; mathematics; numerical methods; optimisation
acknowledgement: ack-nj
classcodes: C5230 (Digital arithmetic methods)
corpsource: IBM, Houston, TX, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
rawauthor: M. Wayne Wilson
rawtitle: Optimal Starting Approximations for Generating Square Root for Slow or No Divide
abstract:
On computing machines with slow or no division, it is preferable to use an iterative scheme for the square root different from the classical Heron scheme. The problem of optimal initial approximants is considered, and some optimal polynomial initial approximations are tabulated.

rawabstract:
On computing machines with slow or no division, it is preferable to use an iterative scheme for the square root different from the classical Heron scheme. The problem of optimal initial approximants is considered, and some optimal polynomial initial approximations are tabulated.

entry:
@Article{Wilson:1970:OSA,
  author =       "M. Wayne Wilson",
  title =        "Optimal Starting Approximations for Generating Square
                 Root for Slow or No Divide",
  journal =      j-CACM,
  volume =       "13",
  number =       "9",
  pages =        "559--560",
  month =        sep,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "44\#2338",
  MRreviewer =   "J. E. {Dennis, Jr.}",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "On computing machines with slow or no division, it is
                 preferable to use an iterative scheme for the square
                 root different from the classical Heron scheme. The
                 problem of optimal initial approximants is considered,
                 and some optimal polynomial initial approximations are
                 tabulated.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, Houston, TX, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "CACMA; digital arithmetic; ele; iterative methods;
                 mathematics; numerical methods; optimisation",
}


bibtype: techreport
filename: fparith.bib
label: Yohe:1970:ACB
author: J. Michael Yohe
title: Accurate Conversion Between Number Bases
type: MRC Technical Summary Report
number: 1109
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: 559--560
month: oct
monthnumber: 10
year: 1970
bibdate: Sun Dec 30 21:39:41 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.30 21:39:41 ???
URL: https://apps.dtic.mil/sti/html/tr/AD0725091/
acknowledgement: ack-nhfb
rawauthor: J. Michael Yohe
rawtitle: Accurate Conversion Between Number Bases
abstract:
The author presents and proves algorithms for taking a number expressed in base gamma and finding, for a predetermined floating point representation in base beta, its least upper bound, greatest lower bound, and closest approximation.

rawabstract:
The author presents and proves algorithms for taking a number expressed in base gamma and finding, for a predetermined floating point representation in base beta, its least upper bound, greatest lower bound, and closest approximation.

entry:
@TechReport{Yohe:1970:ACB,
  author =       "J. Michael Yohe",
  title =        "Accurate Conversion Between Number Bases",
  type =         "{MRC} Technical Summary Report",
  number =       "1109",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        oct,
  year =         "1970",
  bibdate =      "Sun Dec 30 21:39:41 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://apps.dtic.mil/sti/html/tr/AD0725091/",
  abstract =     "The author presents and proves algorithms for taking a
                 number expressed in base gamma and finding, for a
                 predetermined floating point representation in base
                 beta, its least upper bound, greatest lower bound, and
                 closest approximation.",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Yohe:1970:BPF
author: J. Michael Yohe
title: Best possible floating point arithmetic
type: MRC Technical Summary Report
number: 1054
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: ii + 27
month: mar
monthnumber: 3
year: 1970
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
URL: https://apps.dtic.mil/sti/html/tr/AD0713699
keywords: Floating-point arithmetic.
remark: March 1970. Sponsored by Army Research Office, Durham, N.C.
acknowledgement: ack-nhfb
rawauthor: J. Michael Yohe
rawtitle: Best possible floating point arithmetic
abstract:
The report presents an algorithm for floating point arithmetic, using single-length arithmetic registers, which yields the most accurate approximation which can be expressed in the given floating point format, the greatest lower bound, or the least upper bound for the result of the operation, whichever is specified by the programmer. This makes the algorithm particularly useful for implementation of interval arithmetic.

rawabstract:
The report presents an algorithm for floating point arithmetic, using single-length arithmetic registers, which yields the most accurate approximation which can be expressed in the given floating point format, the greatest lower bound, or the least upper bound for the result of the operation, whichever is specified by the programmer. This makes the algorithm particularly useful for implementation of interval arithmetic.

entry:
@TechReport{Yohe:1970:BPF,
  author =       "J. Michael Yohe",
  title =        "Best possible floating point arithmetic",
  type =         "{MRC} Technical Summary Report",
  number =       "1054",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  pages =        "ii + 27",
  month =        mar,
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://apps.dtic.mil/sti/html/tr/AD0713699",
  abstract =     "The report presents an algorithm for floating point
                 arithmetic, using single-length arithmetic registers,
                 which yields the most accurate approximation which can
                 be expressed in the given floating point format, the
                 greatest lower bound, or the least upper bound for the
                 result of the operation, whichever is specified by the
                 programmer. This makes the algorithm particularly
                 useful for implementation of interval arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
  remark =       "March 1970. Sponsored by Army Research Office, Durham,
                 N.C.",
}


bibtype: techreport
filename: fparith.bib
label: Yohe:1970:RBC
author: J. Michael Yohe
title: Rigorous bounds on computed approximations to square roots and cube roots
type: MRC Technical Summary Report
number: 1088
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: ii + 27
year: 1970
bibdate: Sat Nov 01 07:35:34 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.01 07:35:34 ???
acknowledgement: ack-nhfb
rawauthor: J. Michael Yohe
rawtitle: Rigorous bounds on computed approximations to square roots and cube roots
remark:
From cite [page 586, column 2]Yohe:1973:RFP: ``In [this 1970 report], it is proved that on a binary computer with optimal directed rounding, the square root of a machine representable number can be calculated exactly if it is machine representable, and bracketed by two consecutive machine numbers if it is not machine representable; this is accomplished without using interval arithmetic. Similar, although not as tight, bounds are obtained for the cube root.

entry:
@TechReport{Yohe:1970:RBC,
  author =       "J. Michael Yohe",
  title =        "Rigorous bounds on computed approximations to square
                 roots and cube roots",
  type =         "{MRC} Technical Summary Report",
  number =       "1088",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  year =         "1970",
  bibdate =      "Sat Nov 01 07:35:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite[page 586, column 2]{Yohe:1973:RFP}: ``In
                 [this 1970 report], it is proved that on a binary
                 computer with optimal directed rounding, the square
                 root of a machine representable number can be
                 calculated exactly if it is machine representable, and
                 bracketed by two consecutive machine numbers if it is
                 not machine representable; this is accomplished without
                 using interval arithmetic. Similar, although not as
                 tight, bounds are obtained for the cube root.",
}


bibtype: article
filename: fparith.bib
label: Yong:1970:GBA
author: Lam Lay Yong
title: The Geometrical Basis of the Ancient Chinese Square-Root Method
journal: j-ISIS
volume: 61
number: 1
pages: 92--102
month: Spring
year: 1970
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:28:39 MDT 2013
bibtimestamp: 2013.07.30 21:28:39 MDT
URL: http://www.jstor.org/stable/229151
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: Lam Lay Yong
rawtitle: The Geometrical Basis of the {Ancient Chinese} Square-Root Method
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302287; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1970.bib

entry:
@Article{Yong:1970:GBA,
  author =       "Lam Lay Yong",
  title =        "The Geometrical Basis of the {Ancient Chinese}
                 Square-Root Method",
  journal =      j-ISIS,
  volume =       "61",
  number =       "1",
  pages =        "92--102",
  month =        "Spring",
  year =         "1970",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:28:39 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302287;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
  URL =          "http://www.jstor.org/stable/229151",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: article
filename: fparith.bib
label: Zohar:1970:NRC
author: S. Zohar
title: Negative Radix Conversion
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 3
pages: 222--226
month: mar
monthnumber: 3
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.222900
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 08:01:31 MDT 2011
bibtimestamp: 2011.07.13 08:01:31 MDT
note: See comments cite Pawlak:1971:ACN,Wadel:1971:CNR.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671493
fjournal: IEEE Transactions on Computers
keywords: negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Zohar
rawnote: See comments \cite{Pawlak:1971:ACN,Wadel:1971:CNR}.
rawtitle: Negative Radix Conversion
entry:
@Article{Zohar:1970:NRC,
  author =       "S. Zohar",
  title =        "Negative Radix Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "3",
  pages =        "222--226",
  month =        mar,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Pawlak:1971:ACN,Wadel:1971:CNR}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671493",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}


bibtype: book
filename: fparith.bib
label: Zuse:1970:CML
author: Konrad Zuse
title: Der Computer, mein Lebenswerk
publisher: Verlag moderne Industrie
address: Munchen, Germany
pages: 221
year: 1970
LCCN: QA76.2.Z8 A3
bibdate: Mon Nov 4 07:46:57 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.04 07:46:57 MST
keywords: computer engineers --- Germany --- biography; computers --- Germany --- history; Zuse, Konrad
acknowledgement: ack-nhfb
rawauthor: Konrad Zuse
rawtitle: {Der Computer, mein Lebenswerk}
entry:
@Book{Zuse:1970:CML,
  author =       "Konrad Zuse",
  title =        "{Der Computer, mein Lebenswerk}",
  publisher =    "Verlag moderne Industrie",
  address =      "M{\"u}nchen, Germany",
  pages =        "221",
  year =         "1970",
  LCCN =         "QA76.2.Z8 A3",
  bibdate =      "Mon Nov 4 07:46:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computer engineers --- Germany --- biography;
                 computers --- Germany --- history; Zuse, Konrad",
}


bibtype: article
filename: fparith.bib
label: Abdelmalek:1971:REA
author: Nabih N. Abdelmalek
title: Round-off Error Analysis for Gram--Schmidt Method and Solution of Linear Least Squares Problems
journal: j-BIT
volume: 11
number: 4
pages: 345--367
month: dec
monthnumber: 12
year: 1971
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01939404
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:12 MST 2006
bibtimestamp: 2006.01.04 18:52:12 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=4&spage=345
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Nabih N. Abdelmalek
rawtitle: Round-off Error Analysis for {Gram--Schmidt} Method and Solution of Linear Least Squares Problems
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Abdelmalek:1971:REA,
  author =       "Nabih N. Abdelmalek",
  title =        "Round-off Error Analysis for {Gram--Schmidt} Method
                 and Solution of Linear Least Squares Problems",
  journal =      j-BIT,
  volume =       "11",
  number =       "4",
  pages =        "345--367",
  month =        dec,
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01939404",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:12 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=4;
                 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=11&issue=4&spage=345",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: fparith.bib
label: Alway:1971:GFA
author: G. G. Alway
title: A general factorising algorithm
journal: j-COMP-J
volume: 14
number: 2
pages: 166--168
month: may
monthnumber: 5
year: 1971
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:51:53 MDT 2000
bibtimestamp: 2000.09.29 08:51:53 MDT
fjournal: The Computer Journal
keywords: computer algorithm; digital arithmetic; general factorising algorithm; primality of large numbers
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Nat. Phys. Lab., Teddington, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: G. G. Alway
rawtitle: A general factorising algorithm
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/140166.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/166.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/167.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/168.tif

entry:
@Article{Alway:1971:GFA,
  author =       "G. G. Alway",
  title =        "A general factorising algorithm",
  journal =      j-COMP-J,
  volume =       "14",
  number =       "2",
  pages =        "166--168",
  month =        may,
  year =         "1971",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:53 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/140166.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/166.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/167.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/168.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Nat. Phys. Lab., Teddington, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "computer algorithm; digital arithmetic; general
                 factorising algorithm; primality of large numbers",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: fparith.bib
label: Banerji:1971:RAC
author: D. K. Banerji
title: Residue arithmetic in computer design
institution: University of Waterloo
address: Waterloo, ON, Canada
pages: 166--168
year: 1971
bibdate: Thu Nov 18 09:13:45 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:13:45 ???
URL: http://books.google.com/books?id=YNVcPgAACAAJ
acknowledgement: ack-nhfb
rawauthor: D. K. Banerji
rawtitle: Residue arithmetic in computer design
entry:
@TechReport{Banerji:1971:RAC,
  author =       "D. K. Banerji",
  title =        "Residue arithmetic in computer design",
  institution =  "University of Waterloo",
  address =      "Waterloo, ON, Canada",
  year =         "1971",
  bibdate =      "Thu Nov 18 09:13:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://books.google.com/books?id=YNVcPgAACAAJ",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Bataille:1971:GCW
author: M. Bataille
title: The Gamma 60: The computer that was ahead of its time
journal: j-HONEYWELL-COMP-J
volume: 5
number: 3
pages: 99--105
year: 1971
CODEN: HNCJA3
ISSN: 0046-7847 OR 00467847
bibdate: Thu Nov 25 09:37:15 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.25 09:37:15 ???
fjournal: Honeywell Computer Journal
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: M. Bataille
rawtitle: The {Gamma 60}: The computer that was ahead of its time
remark:
The Gamma 60 decimal floating-point system provides 11 to 19 decimal digits with an exponent range of $ pm 40 $.

entry:
@Article{Bataille:1971:GCW,
  author =       "M. Bataille",
  title =        "The {Gamma 60}: The computer that was ahead of its
                 time",
  journal =      j-HONEYWELL-COMP-J,
  volume =       "5",
  number =       "3",
  pages =        "99--105",
  month =        "????",
  year =         "1971",
  CODEN =        "HNCJA3",
  ISSN =         "0046-7847",
  bibdate =      "Thu Nov 25 09:37:15 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Honeywell Computer Journal",
  keywords =     "decimal floating-point arithmetic",
  remark =       "The Gamma 60 decimal floating-point system provides 11
                 to 19 decimal digits with an exponent range of $ \pm 40
                 $.",
}


bibtype: article
filename: fparith.bib
label: Berg:1971:SAO
author: R. O. Berg and L. L. Kinney
title: Serial Adders with Overflow Correction
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 6
pages: 668--671
month: jun
monthnumber: 6
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223321
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:16 MDT 2011
bibtimestamp: 2011.07.13 06:38:16 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671914
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. O. Berg and L. L. Kinney
rawtitle: Serial Adders with Overflow Correction
entry:
@Article{Berg:1971:SAO,
  author =       "R. O. Berg and L. L. Kinney",
  title =        "Serial Adders with Overflow Correction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "6",
  pages =        "668--671",
  month =        jun,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223321",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:16 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671914",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Caprani:1971:ILR
author: Ole Caprani
title: Implementation of a Low Round-Off Summation Method
journal: j-BIT
volume: 11
number: 3
pages: 271--275
month: sep
monthnumber: 9
year: 1971
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01931808
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Sat Nov 14 09:14:57 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.11.14 09:14:57 ???
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=3&spage=271
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: accurate floating-point summation; floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Ole Caprani
rawtitle: Implementation of a Low Round-Off Summation Method
entry:
@Article{Caprani:1971:ILR,
  author =       "Ole Caprani",
  title =        "Implementation of a Low Round-Off Summation Method",
  journal =      j-BIT,
  volume =       "11",
  number =       "3",
  pages =        "271--275",
  month =        sep,
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01931808",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=3&spage=271",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
}


bibtype: misc
filename: fparith.bib
label: Chen:1971:BAU
author: Tien Chi Chen
pages: 271--275
day: 28
month: dec
monthnumber: 12
year: 1971
bibdate: Tue Jan 08 21:54:11 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.08 21:54:11 ???
URL: http://www.freepatentsonline.com/3631230.html
acknowledgement: ack-nhfb
howpublished: United States Patent 3,631,230
rawauthor: Tien Chi Chen
title:
Binary arithmetic unit implementing a multiplicative iteration for the exponential, logarithm, quotient and square root functions

abstract:
Apparatus and a method is described for efficiently achieving arithmetic evaluations for functions such as exponential, logarithm, quotient, and square root with a minimum use of multiplications or divisions. Basically, use is made of the fact that $ x(1 pm 2^-m) $ can be evaluated by a shift followed by an add. A pair of numbers $ (x_k, y_k) $ can represent a function $ x : f(x) = g(x_k, y_k) $, such that $ g(l, y_n) = y_n $ for logarithm, quotient and square root. Then, multiplication by shifting is applied to $ x_k $ with suitable adjustments on $ y_k $, until $ x_k $ is close to unity, at which time $ y_k $ represents the desired answer. The exponential is computed by essentially reversing the logarithm procedure. A termination algorithm further improves accuracy. The apparatus involves two registers for $ x_k $ and $ y_k $, a local memory, an adder and a shift register.

rawabstract:
Apparatus and a method is described for efficiently achieving arithmetic evaluations for functions such as exponential, logarithm, quotient, and square root with a minimum use of multiplications or divisions. Basically, use is made of the fact that $ x(1 \pm 2^{-m}) $ can be evaluated by a shift followed by an add. A pair of numbers $ (x_k, y_k) $ can represent a function $ x : f(x) = g(x_k, y_k) $, such that $ g(l, y_n) = y_n $ for logarithm, quotient and square root. Then, multiplication by shifting is applied to $ x_k $ with suitable adjustments on $ y_k $, until $ x_k $ is close to unity, at which time $ y_k $ represents the desired answer. The exponential is computed by essentially reversing the logarithm procedure. A termination algorithm further improves accuracy. The apparatus involves two registers for $ x_k $ and $ y_k $, a local memory, an adder and a shift register.

rawtitle:
Binary arithmetic unit implementing a multiplicative iteration for the exponential, logarithm, quotient and square root functions

entry:
@Misc{Chen:1971:BAU,
  author =       "Tien Chi Chen",
  title =        "Binary arithmetic unit implementing a multiplicative
                 iteration for the exponential, logarithm, quotient and
                 square root functions",
  howpublished = "United States Patent 3,631,230",
  day =          "28",
  month =        dec,
  year =         "1971",
  bibdate =      "Tue Jan 08 21:54:11 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/3631230.html",
  abstract =     "Apparatus and a method is described for efficiently
                 achieving arithmetic evaluations for functions such as
                 exponential, logarithm, quotient, and square root with
                 a minimum use of multiplications or divisions.
                 Basically, use is made of the fact that $ x(1 \pm
                 2^{-m}) $ can be evaluated by a shift followed by an
                 add. A pair of numbers $ (x_k, y_k) $ can represent a
                 function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
                 y_n) = y_n $ for logarithm, quotient and square root.
                 Then, multiplication by shifting is applied to $ x_k $
                 with suitable adjustments on $ y_k $, until $ x_k $ is
                 close to unity, at which time $ y_k $ represents the
                 desired answer. The exponential is computed by
                 essentially reversing the logarithm procedure. A
                 termination algorithm further improves accuracy. The
                 apparatus involves two registers for $ x_k $ and $ y_k
                 $, a local memory, an adder and a shift register.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Chen:1971:BMS
author: Tien Chi Chen
title: A Binary Multiplication Scheme Based on Squaring
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 6
pages: 678--680
month: jun
monthnumber: 6
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223325
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:16 MDT 2011
bibtimestamp: 2011.07.13 06:38:16 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671918
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Tien Chi Chen
rawtitle: A Binary Multiplication Scheme Based on Squaring
entry:
@Article{Chen:1971:BMS,
  author =       "Tien Chi Chen",
  title =        "A Binary Multiplication Scheme Based on Squaring",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "6",
  pages =        "678--680",
  month =        jun,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223325",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:16 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671918",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: misc
filename: fparith.bib
label: Chen:1971:DNC
author: Tien Chi Chen
title: Decimal Number Compression
pages: 4
day: 29
month: mar
monthnumber: 3
year: 1971
bibdate: Fri Nov 28 16:24:59 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:24:59 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
howpublished: Internal IBM memo to Dr. Irving T. Ho.
rawauthor: Tien Chi Chen
rawtitle: Decimal Number Compression
abstract:
The fact that four bits can represent 16 different states, but a decimal digit exploits only 10 of then (0--9) has been a valid criticism against decimal arithmetic.

rawabstract:
The fact that four bits can represent 16 different states, but a decimal digit exploits only 10 of then (0--9) has been a valid criticism against decimal arithmetic.

entry:
@Misc{Chen:1971:DNC,
  author =       "Tien Chi Chen",
  title =        "Decimal Number Compression",
  howpublished = "Internal IBM memo to Dr. Irving T. Ho.",
  pages =        "4",
  day =          "29",
  month =        mar,
  year =         "1971",
  bibdate =      "Fri Nov 28 16:24:59 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The fact that four bits can represent 16 different
                 states, but a decimal digit exploits only 10 of then
                 (0--9) has been a valid criticism against decimal
                 arithmetic.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Chen:1971:EAA
author: Tien Chi Chen
title: Efficient Arithmetic Apparatus and Method
journal: j-IBM-TDB
volume: 14
number: 1
pages: 328--330
month: jun
monthnumber: 6
year: 1971
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Tue Jan 08 22:33:33 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.08 22:33:33 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nhfb
rawauthor: Tien Chi Chen
rawtitle: Efficient Arithmetic Apparatus and Method
entry:
@Article{Chen:1971:EAA,
  author =       "Tien Chi Chen",
  title =        "Efficient Arithmetic Apparatus and Method",
  journal =      j-IBM-TDB,
  volume =       "14",
  number =       "1",
  pages =        "328--330",
  month =        jun,
  year =         "1971",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Tue Jan 08 22:33:33 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: incollection
filename: fparith.bib
label: Clark:1971:SCP
author: N. W. Clark and W. J. Cody and H. Kuki
title: Self-Contained Power Routines
crossref: Rice:1971:MS
pages: 399--415
year: 1971
bibdate: Thu Sep 15 18:56:49 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 18:56:49 ???
acknowledgement: ack-nj
rawauthor: N. W. Clark and W. J. Cody and H. Kuki
rawtitle: Self-Contained Power Routines
entry:
@InCollection{Clark:1971:SCP,
  author =       "N. W. Clark and W. J. Cody and H. Kuki",
  title =        "Self-Contained Power Routines",
  crossref =     "Rice:1971:MS",
  pages =        "399--415",
  year =         "1971",
  bibdate =      "Thu Sep 15 18:56:49 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: Cody:1971:DHC
author: W. J. Cody
title: Desirable Hardware Characteristics for Scientific Computation
journal: j-SIGNUM
volume: 6
number: 1
pages: 16--31
month: jan
monthnumber: 1
year: 1971
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1052614.1052616
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:49:57 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:49:57 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: W. J. Cody
rawtitle: Desirable Hardware Characteristics for Scientific Computation
entry:
@Article{Cody:1971:DHC,
  author =       "W. J. Cody",
  title =        "Desirable Hardware Characteristics for Scientific
                 Computation",
  journal =      j-SIGNUM,
  volume =       "6",
  number =       "1",
  pages =        "16--31",
  month =        jan,
  year =         "1971",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1052614.1052616",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:49:57 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  xxtitle =      "Hardware characteristics (pages missing from print)",
}


bibtype: incollection
filename: fparith.bib
label: Cody:1971:SEF
author: W. J. Cody
title: Software for the Elementary Functions
crossref: Rice:1971:MS
pages: 171--186
year: 1971
bibdate: Thu Sep 15 18:56:47 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 18:56:47 ???
acknowledgement: ack-nj
rawauthor: W. J. Cody
rawtitle: Software for the Elementary Functions
entry:
@InCollection{Cody:1971:SEF,
  author =       "W. J. Cody",
  title =        "Software for the Elementary Functions",
  crossref =     "Rice:1971:MS",
  pages =        "171--186",
  year =         "1971",
  bibdate =      "Thu Sep 15 18:56:47 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Dekker:1971:FPT
author: Theodorus J. Dekker
title: A Floating-Point Technique for Extending the Available Precision
journal: j-NUM-MATH
volume: 18
number: 3
pages: 224--242
month: jun
monthnumber: 6
year: 1971
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01397083
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 68A55
MRnumber: MR0299007 (45 \#8056)
bibdate: Mon May 26 11:49:34 MDT 1997
bibtimestamp: 1997.05.26 11:49:34 MDT
URL: http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN362160546_0018
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Math. Centre, Amsterdam, Netherlands
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: Theodorus J. Dekker
rawtitle: A Floating-Point Technique for Extending the Available Precision
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib; Parallel/par.lin.alg.bib

abstract:
A technique is described for expressing multilength floating-point arithmetic in terms of singlelength floating point arithmetic, i.e. the arithmetic for an available (say: single or double precision) floating-point number system. The basic algorithms are exact addition and multiplication of two singlelength floating-point numbers, delivering the result as a doublelength floating-point number. A straight-forward application of the technique yields a set of algorithms for doublelength arithmetic which are given as ALGOL 60 procedures.

keywords:
accurate floating-point summation; ALGOL 60 procedures; available precision; digital arithmetic; double precision; multilength; single; single length floating point arithmetic; subroutines

remark:
Report MR 118/70, Computation Department, Mathematical Centre, Amsterdam. Part of this research was done while the author was visiting Bell Telephone Laboratories, Murray Hill, New Jersey.

rawabstract:
A technique is described for expressing multilength floating-point arithmetic in terms of singlelength floating point arithmetic, i.e. the arithmetic for an available (say: single or double precision) floating-point number system. The basic algorithms are exact addition and multiplication of two singlelength floating-point numbers, delivering the result as a doublelength floating-point number. A straight-forward application of the technique yields a set of algorithms for doublelength arithmetic which are given as ALGOL 60 procedures.

entry:
@Article{Dekker:1971:FPT,
  author =       "Theodorus J. Dekker",
  title =        "A Floating-Point Technique for Extending the Available
                 Precision",
  journal =      j-NUM-MATH,
  volume =       "18",
  number =       "3",
  pages =        "224--242",
  month =        jun,
  year =         "1971",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01397083",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "68A55",
  MRnumber =     "MR0299007 (45 \#8056)",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib;
                 Parallel/par.lin.alg.bib",
  URL =          "http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN362160546_0018",
  abstract =     "A technique is described for expressing multilength
                 floating-point arithmetic in terms of singlelength
                 floating point arithmetic, i.e. the arithmetic for an
                 available (say: single or double precision)
                 floating-point number system. The basic algorithms are
                 exact addition and multiplication of two singlelength
                 floating-point numbers, delivering the result as a
                 doublelength floating-point number. A straight-forward
                 application of the technique yields a set of algorithms
                 for doublelength arithmetic which are given as ALGOL 60
                 procedures.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Math. Centre, Amsterdam, Netherlands",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "accurate floating-point summation; ALGOL 60
                 procedures; available precision; digital arithmetic;
                 double precision; multilength; single; single length
                 floating point arithmetic; subroutines",
  remark =       "Report MR 118/70, Computation Department, Mathematical
                 Centre, Amsterdam. Part of this research was done while
                 the author was visiting Bell Telephone Laboratories,
                 Murray Hill, New Jersey.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: DeLong:1971:UPA
author: Howard DeLong
title: Unsolved Problems in Arithmetic
journal: j-SCI-AMER
volume: 224
number: 3
pages: 50--60
month: mar
monthnumber: 3
year: 1971
CODEN: SCAMAC
DOI: https://doi.org/10.1038/scientificamerican0371-50
ISSN: 0036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)
ISSNL: 0036-8733 OR 00368733
bibdate: Wed May 22 12:00:01 MDT 2013
bibtimestamp: 2013.05.22 12:00:01 MDT
URL: http://www.nature.com/scientificamerican/journal/v224/n3/pdf/scientificamerican0371-50.pdf
fjournal: Scientific American
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/scientificamerican
rawauthor: Howard DeLong
rawtitle: Unsolved Problems in Arithmetic
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1970.bib

entry:
@Article{DeLong:1971:UPA,
  author =       "Howard DeLong",
  title =        "Unsolved Problems in Arithmetic",
  journal =      j-SCI-AMER,
  volume =       "224",
  number =       "3",
  pages =        "50--60",
  month =        mar,
  year =         "1971",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican0371-50",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 12:00:01 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1970.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v224/n3/pdf/scientificamerican0371-50.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}


bibtype: article
filename: fparith.bib
label: Dutka:1971:SRD
author: Jacques Dutka
title: The Square Root of $2$ to $ 1, 000, 000 $ Decimals
journal: j-MATH-COMPUT
volume: 25
number: 116
pages: 927--930
month: oct
monthnumber: 10
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Jacques Dutka
rawtitle: The Square Root of $2$ to $ 1, 000, 000 $ Decimals
entry:
@Article{Dutka:1971:SRD,
  author =       "Jacques Dutka",
  title =        "The Square Root of $2$ to $ 1, 000, 000 $ Decimals",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "927--930",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Gentleman:1971:OMC
author: W. Morven Gentleman
title: Optimal multiplication chains for computing a power of a symbolic polynomial
journal: j-SIGSAM
number: 18
pages: 23--30
month: apr
monthnumber: 4
year: 1971
CODEN: SIGSBZ
DOI: https://doi.org/10.1145/1093425.1093426
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Tue Jun 17 19:14:25 MDT 2008
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.06.17 19:14:25 MDT
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
issue: 18
rawauthor: W. Morven Gentleman
rawtitle: Optimal multiplication chains for computing a power of a symbolic polynomial
abstract:
This paper shows that in a certain model of symbolic manipulation of algebraic formulae, the simple method of computing a power of a symbolic polynomial by repeated multiplication by the original polynomial is, in essence, the optimal method.

rawabstract:
This paper shows that in a certain model of symbolic manipulation of algebraic formulae, the simple method of computing a power of a symbolic polynomial by repeated multiplication by the original polynomial is, in essence, the optimal method.

entry:
@Article{Gentleman:1971:OMC,
  author =       "W. Morven Gentleman",
  title =        "Optimal multiplication chains for computing a power of
                 a symbolic polynomial",
  journal =      j-SIGSAM,
  volume =       "??",
  number =       "18",
  pages =        "23--30",
  month =        apr,
  year =         "1971",
  CODEN =        "SIGSBZ",
  DOI =          "https://doi.org/10.1145/1093425.1093426",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Tue Jun 17 19:14:25 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper shows that in a certain model of symbolic
                 manipulation of algebraic formulae, the simple method
                 of computing a power of a symbolic polynomial by
                 repeated multiplication by the original polynomial is,
                 in essence, the optimal method.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  issue =        "18",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: techreport
filename: fparith.bib
label: Ghest:1971:TCD
author: R. C. Ghest
title: A Two's Complement Digital Multiplier, the Am25S05
type: Technical report
institution: Advanced Micro Devices
address: Sunnyvale, CA, USA
year: 1971
bibdate: Fri Nov 09 18:50:36 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 18:50:36 ???
acknowledgement: ack-nhfb
rawauthor: R. C. Ghest
rawtitle: A Two's Complement Digital Multiplier, the {Am25S05}
entry:
@TechReport{Ghest:1971:TCD,
  author =       "R. C. Ghest",
  title =        "A Two's Complement Digital Multiplier, the {Am25S05}",
  type =         "Technical report",
  institution =  "Advanced Micro Devices",
  address =      "Sunnyvale, CA, USA",
  pages =        "????",
  year =         "1971",
  bibdate =      "Fri Nov 09 18:50:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Ginsberg:1971:NID
author: Myron Ginsberg
booktitle: Proceedings of the First Annual Rocky Mountain Symposium on Microprocessors
title: Numerical influences on the design of floating-point arithmetic for microcomputers
pages: 24--72
year: 1971
bibdate: Fri Nov 09 18:52:22 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 18:52:22 ???
acknowledgement: ack-nhfb
rawauthor: Myron Ginsberg
rawbooktitle: Proceedings of the First Annual Rocky Mountain Symposium on Microprocessors
rawtitle: Numerical influences on the design of floating-point arithmetic for microcomputers
entry:
@InProceedings{Ginsberg:1971:NID,
  author =       "Myron Ginsberg",
  booktitle =    "Proceedings of the First Annual Rocky Mountain
                 Symposium on Microprocessors",
  title =        "Numerical influences on the design of floating-point
                 arithmetic for microcomputers",
  publisher =    "????",
  address =      "????",
  pages =        "24--72",
  year =         "1971",
  bibdate =      "Fri Nov 09 18:52:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Glaser:1971:HBO
author: Anton Glaser
title: History of Binary and Other Nondecimal Numeration
publisher: Anton Glaser
address: Southampton, PA, USA
pages: ix + 196
year: 1971
ISBN: 0-9600324-1-X OR 096003241X
ISBN13: 978-0-9600324-1-9 OR 9780960032419
LCCN: QA141.2 .G55
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 revised edition cite Glaser:1981:HBO.
remark: Based on the author's thesis, Temple University, with title: History of modern numeration systems.
subject: Numeration; History
acknowledgement: ack-nhfb
authordates: 1924--
rawauthor: Anton Glaser
rawnote: See also revised edition \cite{Glaser:1981:HBO}.
rawtitle: History of Binary and Other Nondecimal Numeration
TOC:
Before Leibniz Leibniz (1646--1716) The rest of the 1700s The nineteenth century The twentieth century up to the computer age Applications to computers Contemporary literature

rawTOC:
Before Leibniz \\ Leibniz (1646--1716) \\ The rest of the 1700s \\ The nineteenth century \\ The twentieth century up to the computer age \\ Applications to computers \\ Contemporary literature

entry:
@Book{Glaser:1971:HBO,
  author =       "Anton Glaser",
  title =        "History of Binary and Other Nondecimal Numeration",
  publisher =    "Anton Glaser",
  address =      "Southampton, PA, USA",
  pages =        "ix + 196",
  year =         "1971",
  ISBN =         "0-9600324-1-X",
  ISBN-13 =      "978-0-9600324-1-9",
  LCCN =         "QA141.2 .G55",
  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 revised edition \cite{Glaser:1981:HBO}.",
  acknowledgement = ack-nhfb,
  author-dates = "1924--",
  remark =       "Based on the author's thesis, Temple University, with
                 title: History of modern numeration systems.",
  subject =      "Numeration; History",
  tableofcontents = "Before Leibniz \\
                 Leibniz (1646--1716) \\
                 The rest of the 1700s \\
                 The nineteenth century \\
                 The twentieth century up to the computer age \\
                 Applications to computers \\
                 Contemporary literature",
}


bibtype: article
filename: fparith.bib
label: Golub:1971:CAC
author: G. H. Golub and L. B. Smith
title: Chebyshev Approximation of Continuous Functions by a Chebyshev System of Functions
journal: j-CACM
volume: 14
number: 11
pages: 737--746
month: nov
monthnumber: 11
year: 1971
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Aug 15 09:54:14 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.15 09:54:14 ???
note: ACM Algorithm 414.
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: G. H. Golub and L. B. Smith
rawnote: ACM Algorithm 414.
rawtitle: {Chebyshev} Approximation of Continuous Functions by a {Chebyshev} System of Functions
entry:
@Article{Golub:1971:CAC,
  author =       "G. H. Golub and L. B. Smith",
  title =        "{Chebyshev} Approximation of Continuous Functions by a
                 {Chebyshev} System of Functions",
  journal =      j-CACM,
  volume =       "14",
  number =       "11",
  pages =        "737--746",
  month =        nov,
  year =         "1971",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Aug 15 09:54:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM Algorithm 414.",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: techreport
filename: fparith.bib
label: Haavie:1971:SMA
author: T. Haa vie
title: Some Methods for Automatic Integration and their Implementation on the CERN CDC 65 / 6600 Computers
type: Report
number: CERN 71-26
institution: CERN
address: Geneva, Switzerland
pages: 737--746
day: 1
month: dec
monthnumber: 12
year: 1971
bibdate: Thu Jan 04 13:15:46 2024
bibtimestamp: 2024.01.04 13:15:46 ???
URL: https://cds.cern.ch/record/190218/files/CERN-71-26.pdf
keywords: automatic integration; CDC arithmetic; Clenshaw / Curtis; Romberg; rounding corrections
acknowledgement: ack-nhfb
onlinedate: iv + 43
rawauthor: T. H{\aa}vie
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Two schemes for automatic integration using modified Romberg and Clenshaw--Curtis quadratures are discussed. The experience gained testing FORTRAN routines, using both rounded and unrounded arithmetic, on a set of 20 test examples are reported.

remark:
The report gives results, and recommendations, for default (unrounded) and rounded arithmetic computation in the peculiar arithmetic of the CDC 6000 / 7000 family computers, for single precision (48-bit significand, about 14 decimal digits) and double precision (96-bit significand, almost 29 decimal digits). Unlike Wirth's compiler work cite Wirth:1972:PCG, it does not get down to instruction set details, or discuss the problems of integer arithmetic.

rawabstract:
Two schemes for automatic integration using modified Romberg and Clenshaw--Curtis quadratures are discussed. The experience gained testing FORTRAN routines, using both rounded and unrounded arithmetic, on a set of 20 test examples are reported.

rawtitle:
Some Methods for Automatic Integration and their Implementation on the {CERN CDC 65\slash 6600} Computers

entry:
@TechReport{Haavie:1971:SMA,
  author =       "T. H{\aa}vie",
  title =        "Some Methods for Automatic Integration and their
                 Implementation on the {CERN CDC 65\slash 6600}
                 Computers",
  type =         "Report",
  number =       "CERN 71-26",
  institution =  "CERN",
  address =      "Geneva, Switzerland",
  day =          "1",
  month =        dec,
  year =         "1971",
  bibdate =      "Thu Jan 04 13:15:46 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://cds.cern.ch/record/190218/files/CERN-71-26.pdf",
  abstract =     "Two schemes for automatic integration using modified
                 Romberg and Clenshaw--Curtis quadratures are discussed.
                 The experience gained testing FORTRAN routines, using
                 both rounded and unrounded arithmetic, on a set of 20
                 test examples are reported.",
  acknowledgement = ack-nhfb,
  keywords =     "automatic integration; CDC arithmetic; Clenshaw\slash
                 Curtis; Romberg; rounding corrections",
  onlinedate =   "iv + 43",
  remark =       "The report gives results, and recommendations, for
                 default (unrounded) and rounded arithmetic computation
                 in the peculiar arithmetic of the CDC 6000\slash 7000
                 family computers, for single precision (48-bit
                 significand, about 14 decimal digits) and double
                 precision (96-bit significand, almost 29 decimal
                 digits). Unlike Wirth's compiler work
                 \cite{Wirth:1972:PCG}, it does not get down to
                 instruction set details, or discuss the problems of
                 integer arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Honey:1971:CCD
author: D. W. Honey
journal: j-COMP-J
volume: 14
number: 4
pages: 443--443
month: nov
monthnumber: 11
year: 1971
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:51:58 MDT 2000
bibtimestamp: 2000.09.29 08:51:58 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: D. W. Honey
title:
Correspondence: Calculation of a double-length square root from a double length number using single precision techniques

bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif

rawtitle:
Correspondence: Calculation of a double-length square root from a double length number using single precision techniques

entry:
@Article{Honey:1971:CCD,
  author =       "D. W. Honey",
  title =        "Correspondence: Calculation of a double-length square
                 root from a double length number using single precision
                 techniques",
  journal =      j-COMP-J,
  volume =       "14",
  number =       "4",
  pages =        "443--443",
  month =        nov,
  year =         "1971",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:58 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Kagan:1971:FPS
author: Claude A. R. Kagan
title: Floating point sub-language of a string language
journal: j-SIGPLAN
volume: 6
number: 10
pages: 20--22
month: nov
monthnumber: 11
year: 1971
CODEN: SINODQ
DOI: https://doi.org/10.1145/1317448.1317449
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sat Dec 2 08:35:10 MST 2017
bibtimestamp: 2017.12.02 08:35:10 MST
URL: https://dl.acm.org/citation.cfm?id=1317449
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Claude A. R. Kagan
rawtitle: Floating point sub-language of a string language
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigplan1970.bib

abstract:
The facilities for floating point computation within the framework of a string language currently operating on the PDP-10 at the Western Electric Company Engineering Research Center are considered to be a sublanguage. This sublanguage is accessed through use of the * (asterisk) as a function marker in lieu of the colon, and such use causes execution of all of the available arithmetic functions as well as a family of additional functions whose names are the same as those used in Fortran. The list of functions that will execute in this sublanguage is displayed through execution of ** (LF), expression.

rawabstract:
The facilities for floating point computation within the framework of a string language currently operating on the PDP-10 at the Western Electric Company Engineering Research Center are considered to be a sublanguage. This sublanguage is accessed through use of the * (asterisk) as a function marker in lieu of the colon, and such use causes execution of all of the available arithmetic functions as well as a family of additional functions whose names are the same as those used in Fortran. The list of functions that will execute in this sublanguage is displayed through execution of ** (LF), expression.

entry:
@Article{Kagan:1971:FPS,
  author =       "Claude A. R. Kagan",
  title =        "Floating point sub-language of a string language",
  journal =      j-SIGPLAN,
  volume =       "6",
  number =       "10",
  pages =        "20--22",
  month =        nov,
  year =         "1971",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/1317448.1317449",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat Dec 2 08:35:10 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan1970.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=1317449",
  abstract =     "The facilities for floating point computation within
                 the framework of a string language currently operating
                 on the PDP-10 at the Western Electric Company
                 Engineering Research Center are considered to be a
                 sublanguage. This sublanguage is accessed through use
                 of the * (asterisk) as a function marker in lieu of the
                 colon, and such use causes execution of all of the
                 available arithmetic functions as well as a family of
                 additional functions whose names are the same as those
                 used in Fortran. The list of functions that will
                 execute in this sublanguage is displayed through
                 execution of ** (LF), expression.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: inproceedings
filename: fparith.bib
label: Kahan:1971:SEA
author: W. M. Kahan
title: A Survey of Error Analysis
crossref: Freiman:1971:PIC
pages: 1214--1239
year: 1971
MRclass: 65G05
MRnumber: MR0458845 (56 \#17045)
bibdate: Tue Aug 28 05:24:53 2001
bibtimestamp: 2001.08.28 05:24:53 ???
series: Information Processing 71
URL: http://dblp.uni-trier.de/db/conf/ifip/ifip71-2.html#Kahan71
keywords: accurate floating-point summation
acknowledgement: ack-jr
rawauthor: W. M. Kahan
rawtitle: A Survey of Error Analysis
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

remark:
This paper contains the modified compensating summation algorithm wherein `e = (temp - s) + y' is replaced by `f = 0; if (sign(temp) == sign(y)) f = (0.46*s - s) + s e = ((temp - f) - (s - f)) + y', cited in e.g., cite Dalhquist:1974:NM,Higham:1993:AFP.

entry:
@InProceedings{Kahan:1971:SEA,
  author =       "W. M. Kahan",
  title =        "A Survey of Error Analysis",
  crossref =     "Freiman:1971:PIC",
  pages =        "1214--1239",
  year =         "1971",
  MRclass =      "65G05",
  MRnumber =     "MR0458845 (56 \#17045)",
  bibdate =      "Tue Aug 28 05:24:53 2001",
  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",
  series =       "Information Processing 71",
  URL =          "http://dblp.uni-trier.de/db/conf/ifip/ifip71-2.html#Kahan71",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  keywords =     "accurate floating-point summation",
  remark =       "This paper contains the modified compensating
                 summation algorithm wherein `e = (temp - s) + y' is
                 replaced by `f = 0; if (sign(temp) == sign(y)) {f =
                 (0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
                 cited in e.g.,
                 \cite{Dalhquist:1974:NM,Higham:1993:AFP}.",
}


bibtype: article
filename: fparith.bib
label: Kan:1971:EAD
author: E. Kan and J. Aggarwal
title: Error analysis of digital filter employing floating-point arithmetic
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 18
number: 6
pages: 678--686
month: nov
monthnumber: 11
year: 1971
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
note: See correction cite Kan:1973:CEA.
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: E. Kan and J. Aggarwal
rawnote: See correction \cite{Kan:1973:CEA}.
rawtitle: Error analysis of digital filter employing floating-point arithmetic
entry:
@Article{Kan:1971:EAD,
  author =       "E. Kan and J. Aggarwal",
  title =        "Error analysis of digital filter employing
                 floating-point arithmetic",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "18",
  number =       "6",
  pages =        "678--686",
  month =        nov,
  year =         "1971",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Kan:1973:CEA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The error accumulation in a digital filter employing
                 floating-point arithmetic is studied. Sources of errors
                 are considered to originate from (1) roundoff in the
                 arithmetic operations, (2) quantization of both the
                 input and the initial states, and (3) \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Kingsbury:1971:DFU
author: N. G. Kingsbury and P. J. W. Rayner
title: Digital filtering using logarithmic arithmetic
journal: j-ELECT-LETTERS
volume: 7
number: 2
pages: 56--58
day: 28
month: jan
monthnumber: 1
year: 1971
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19710039
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Mon May 30 07:32:20 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2016.05.30 07:32:20 ???
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: N. G. Kingsbury and P. J. W. Rayner
rawtitle: Digital filtering using logarithmic arithmetic
entry:
@Article{Kingsbury:1971:DFU,
  author =       "N. G. Kingsbury and P. J. W. Rayner",
  title =        "Digital filtering using logarithmic arithmetic",
  journal =      j-ELECT-LETTERS,
  volume =       "7",
  number =       "2",
  pages =        "56--58",
  day =          "28",
  month =        jan,
  year =         "1971",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19710039",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Mon May 30 07:32:20 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}


bibtype: article
filename: fparith.bib
label: Krishnamurthy:1971:CTW
author: E. V. Krishnamurthy
title: Complementary Two-Way Algorithms for Negative Radix Conversions
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 5
pages: 543--550
month: may
monthnumber: 5
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223288
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:14 MDT 2011
bibtimestamp: 2011.07.13 06:38:14 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671881
fjournal: IEEE Transactions on Computers
keywords: negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. V. Krishnamurthy
rawtitle: Complementary Two-Way Algorithms for Negative Radix Conversions
entry:
@Article{Krishnamurthy:1971:CTW,
  author =       "E. V. Krishnamurthy",
  title =        "Complementary Two-Way Algorithms for Negative Radix
                 Conversions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "5",
  pages =        "543--550",
  month =        may,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223288",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671881",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Krishnamurthy:1971:EIR
author: E. V. Krishnamurthy
title: Economical Iterative and Range-Transformation Schemes for Division
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 4
pages: 470--472
month: apr
monthnumber: 4
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223270
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:14 MDT 2011
bibtimestamp: 2011.07.13 06:38:14 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671863
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. V. Krishnamurthy
rawtitle: Economical Iterative and Range-Transformation Schemes for Division
entry:
@Article{Krishnamurthy:1971:EIR,
  author =       "E. V. Krishnamurthy",
  title =        "Economical Iterative and Range-Transformation Schemes
                 for Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "4",
  pages =        "470--472",
  month =        apr,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223270",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671863",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Kuki:1971:FEP
author: H. Kuki and J. Ascoly
title: FORTRAN extended-precision library
journal: j-IBM-SYS-J
volume: 10
number: 1
pages: 39--61
year: 1971
CODEN: IBMSA7
ISSN: 0018-8670 OR 00188670
bibdate: Thu Sep 15 18:51:32 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 18:51:32 ???
fjournal: IBM Systems Journal
acknowledgement: ack-nj
rawauthor: H. Kuki and J. Ascoly
rawtitle: {FORTRAN} extended-precision library
entry:
@Article{Kuki:1971:FEP,
  author =       "H. Kuki and J. Ascoly",
  title =        "{FORTRAN} extended-precision library",
  journal =      j-IBM-SYS-J,
  volume =       "10",
  number =       "1",
  pages =        "39--61",
  year =         "1971",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:51:32 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Systems Journal",
  xxmonth =      "(none)",
}


bibtype: incollection
filename: fparith.bib
label: Kuki:1971:MFS
author: H. Kuki
crossref: Rice:1971:MS
pages: 187--199
year: 1971
bibdate: Fri Sep 16 16:27:40 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 16:27:40 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nj
rawauthor: H. Kuki
title:
Mathematical Function Subprograms for Basic System Libraries --- Objectives, Constraints, and Trade-Off

rawtitle:
Mathematical Function Subprograms for Basic System Libraries\emdash Objectives, Constraints, and Trade-Off

entry:
@InCollection{Kuki:1971:MFS,
  author =       "H. Kuki",
  title =        "Mathematical Function Subprograms for Basic System
                 Libraries\emdash Objectives, Constraints, and
                 Trade-Off",
  crossref =     "Rice:1971:MS",
  pages =        "187--199",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:27:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Kulisch:1971:AAR
author: Ulrich W. Kulisch
title: An axiomatic approach to rounded computations
journal: j-NUM-MATH
volume: 18
number: 1
pages: 1--17
month: feb
monthnumber: 2
year: 1971
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01398455
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 16:12:48 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.10.17 16:12:48 MDT
note: See also cite Kulisch:1969:AAR.
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Ulrich W. Kulisch
rawnote: See also \cite{Kulisch:1969:AAR}.
rawtitle: An axiomatic approach to rounded computations
abstract:
The present paper is intended to give an axiomatic approach to rounded computations. A rounding is defined as a monotone mapping of an ordered set into a subset, which in general is called a lower respectively an upper screen. The first chapter deals with roundings in ordered sets. In the second chapter further properties of roundings in linearly ordered sets are studied. The third chapter deals with the two most important applications, the approximation of the real arithmetic on a finite screen and the approximation of the real interval arithmetic on an upper screen. Beyond these examples various further applications are possible.

rawabstract:
The present paper is intended to give an axiomatic approach to rounded computations. A rounding is defined as a monotone mapping of an ordered set into a subset, which in general is called a lower respectively an upper screen. The first chapter deals with roundings in ordered sets. In the second chapter further properties of roundings in linearly ordered sets are studied. The third chapter deals with the two most important applications, the approximation of the real arithmetic on a finite screen and the approximation of the real interval arithmetic on an upper screen. Beyond these examples various further applications are possible.

entry:
@Article{Kulisch:1971:AAR,
  author =       "Ulrich W. Kulisch",
  title =        "An axiomatic approach to rounded computations",
  journal =      j-NUM-MATH,
  volume =       "18",
  number =       "1",
  pages =        "1--17",
  month =        feb,
  year =         "1971",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01398455",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Kulisch:1969:AAR}.",
  abstract =     "The present paper is intended to give an axiomatic
                 approach to rounded computations. A rounding is defined
                 as a monotone mapping of an ordered set into a subset,
                 which in general is called a lower respectively an
                 upper screen. The first chapter deals with roundings in
                 ordered sets. In the second chapter further properties
                 of roundings in linearly ordered sets are studied. The
                 third chapter deals with the two most important
                 applications, the approximation of the real arithmetic
                 on a finite screen and the approximation of the real
                 interval arithmetic on an upper screen. Beyond these
                 examples various further applications are possible.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: fparith.bib
label: Kupka:1971:SRA
author: I. Kupka
title: Simulation of real arithmetic and real functions in finite sets
journal: j-NUM-MATH
volume: 17
number: 2
pages: 143--152
year: 1971
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
language: German
acknowledgement: ack-nhfb
corpsource: Univ. Hamburg, West Germany
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: I. Kupka
rawtitle: Simulation of real arithmetic and real functions in finite sets
keywords:
error estimation; errors; estimation theory; finite set; floating point arithmetic; real functions; simulation

entry:
@Article{Kupka:1971:SRA,
  author =       "I. Kupka",
  title =        "Simulation of real arithmetic and real functions in
                 finite sets",
  journal =      j-NUM-MATH,
  volume =       "17",
  number =       "2",
  pages =        "143--152",
  year =         "1971",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C1220 (Simulation, modelling and identification);
                 C4110 (Error analysis in numerical methods)",
  corpsource =   "Univ. Hamburg, West Germany",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "error estimation; errors; estimation theory; finite
                 set; floating point arithmetic; real functions;
                 simulation",
  language =     "German",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: fparith.bib
label: Lindsay:1971:RAF
author: D. S. Lindsay
title: A rounded arithmetic FORTRAN compiler for CDC 6000 machines
type: Report
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
month: dec
monthnumber: 12
year: 1971
bibdate: Thu Jan 04 13:08:56 2024
bibtimestamp: 2024.01.04 13:08:56 ???
keywords: rounding corrections
acknowledgement: ack-nhfb
rawauthor: D. S. Lindsay
rawtitle: A rounded arithmetic {FORTRAN} compiler for {CDC 6000} machines
bibsource:
https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
No copy of this report seems to be available online; it is cited in cite [p. 34]Wirth:1972:PCG. See the remarks in that entry about the challenges of the CDC arithmetic system.

entry:
@TechReport{Lindsay:1971:RAF,
  author =       "D. S. Lindsay",
  title =        "A rounded arithmetic {FORTRAN} compiler for {CDC 6000}
                 machines",
  type =         "Report",
  number =       "????",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "????",
  month =        dec,
  year =         "1971",
  bibdate =      "Thu Jan 04 13:08:56 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "rounding corrections",
  remark =       "No copy of this report seems to be available online;
                 it is cited in \cite[p. 34]{Wirth:1972:PCG}. See the
                 remarks in that entry about the challenges of the CDC
                 arithmetic system.",
}


bibtype: article
filename: fparith.bib
label: Majithia:1971:CAN
author: J. C. Majithia and R. Kitai
title: A Cellular Array for the Nonrestoring Extraction of Square Roots
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 12
pages: 1617--1618
month: dec
monthnumber: 12
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223191
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:22 MDT 2011
bibtimestamp: 2011.07.13 06:38:22 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. C. Majithia and R. Kitai
rawtitle: A Cellular Array for the Nonrestoring Extraction of Square Roots
entry:
@Article{Majithia:1971:CAN,
  author =       "J. C. Majithia and R. Kitai",
  title =        "A Cellular Array for the Nonrestoring Extraction of
                 Square Roots",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1617--1618",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223191",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Majithia:1971:IAM
author: J. C. Majithia and R. Kitai
title: An Iterative Array for Multiplication of Signed Binary Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 2
pages: 214--216
month: feb
monthnumber: 2
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223216
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:12 MDT 2011
bibtimestamp: 2011.07.13 06:38:12 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671809
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. C. Majithia and R. Kitai
rawtitle: An Iterative Array for Multiplication of Signed Binary Numbers
entry:
@Article{Majithia:1971:IAM,
  author =       "J. C. Majithia and R. Kitai",
  title =        "An Iterative Array for Multiplication of Signed Binary
                 Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "2",
  pages =        "214--216",
  month =        feb,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223216",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671809",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Malcolm:1971:AFP
author: Michael A. Malcolm
title: On Accurate Floating-Point Summation
journal: j-CACM
volume: 14
number: 11
pages: 731--736
month: nov
monthnumber: 11
year: 1971
CODEN: CACMA2
DOI: https://doi.org/10.1145/362854.362889
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65G05 (68-XX)
MRnumber: 47 4434
MRreviewer: P. Brock
bibdate: Mon Jan 22 07:01:06 MST 2001
bibtimestamp: 2001.01.22 07:01:06 MST
fjournal: Communications of the ACM
keywords: accurate floating-point summation; digital arithmetic; error analysis
acknowledgement: ack-nj
classcodes: C5230 (Digital arithmetic methods)
corpsource: Stanford University, CA, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: P Practical
rawauthor: Michael A. Malcolm
rawtitle: On Accurate Floating-Point Summation
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Malcolm71; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Malcolm:1971:AFP,
  author =       "Michael A. Malcolm",
  title =        "On Accurate Floating-Point Summation",
  journal =      j-CACM,
  volume =       "14",
  number =       "11",
  pages =        "731--736",
  month =        nov,
  year =         "1971",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362854.362889",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05 (68-XX)",
  MRnumber =     "47 4434",
  MRreviewer =   "P. Brock",
  bibdate =      "Mon Jan 22 07:01:06 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Malcolm71;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Stanford University, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "accurate floating-point summation; digital arithmetic;
                 error analysis",
  oldlabel =     "Malcolm71",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm71",
}


bibtype: techreport
filename: fparith.bib
label: Malcolm:1971:ARP
author: Michael A. Malcolm
title: Algorithm to reveal properties of floating-point arithmetic
institution: Stanford University
address: Stanford, Ca.
pages: 8
year: 1971
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: AD-727 104
keywords: Algorithms.; Floating-point arithmetic.
remark: ``STAN-CS-71-211.''
acknowledgement: ack-nhfb
rawauthor: Michael A. Malcolm
rawtitle: Algorithm to reveal properties of floating-point arithmetic
entry:
@TechReport{Malcolm:1971:ARP,
  author =       "Michael A. Malcolm",
  title =        "Algorithm to reveal properties of floating-point
                 arithmetic",
  institution =  "Stanford University",
  address =      "Stanford, Ca.",
  pages =        "8",
  year =         "1971",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "AD-727 104",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Floating-point arithmetic.",
  remark =       "``STAN-CS-71-211.''",
}


bibtype: article
filename: fparith.bib
label: Morris:1971:TFP
author: R. Morris
title: Tapered Floating Point: a New Floating-Point Representation
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 12
pages: 1578--1579
month: dec
monthnumber: 12
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223174
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:22 MDT 2011
bibtimestamp: 2011.07.13 06:38:22 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671767
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. Morris
rawtitle: Tapered Floating Point: a New Floating-Point Representation
entry:
@Article{Morris:1971:TFP,
  author =       "R. Morris",
  title =        "Tapered Floating Point: a New Floating-Point
                 Representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1578--1579",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223174",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671767",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Mullet:1971:NME
author: Gary M. Mullet and Tracy W. Murray
title: A New Method for Examining Rounding Error in Least-Squares Regression Computer Programs
journal: j-J-AM-STAT-ASSOC
volume: 66
number: 335
pages: 496--498
month: sep
monthnumber: 9
year: 1971
CODEN: JSTNAL
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
bibdate: Wed Jan 25 08:05:44 MST 2012
bibtimestamp: 2012.01.25 08:05:44 MST
URL: http://www.jstor.org/stable/2283514
fjournal: Journal of the American Statistical Association
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uasa20
rawauthor: Gary M. Mullet and Tracy W. Murray
rawtitle: A New Method for Examining Rounding Error in Least-Squares Regression Computer Programs
bibsource:
http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314211; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib

entry:
@Article{Mullet:1971:NME,
  author =       "Gary M. Mullet and Tracy W. Murray",
  title =        "A New Method for Examining Rounding Error in
                 Least-Squares Regression Computer Programs",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "66",
  number =       "335",
  pages =        "496--498",
  month =        sep,
  year =         "1971",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:44 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314211;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  URL =          "http://www.jstor.org/stable/2283514",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}


bibtype: article
filename: fparith.bib
label: Nicoud:1971:IAR
author: Jean-Daniel Nicoud
title: Iterative Arrays for Radix Conversion
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 12
pages: 1479--1489
month: dec
monthnumber: 12
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223160
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Oct 10 13:44:30 2007
bibtimestamp: 2007.10.10 13:44:30 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jean-Daniel Nicoud
rawtitle: Iterative Arrays for Radix Conversion
abstract:
The general study of the conversion of a number from the radix p to the radix q number system leads to four different algorithms for integers, and to four similar ones for fractions. Most transform algorithms can be implemented by iterative arrays of cells characterized by simple equations. Such arrays are very attractive with present-time large-scale integration technology. Two kinds of cells, that is, two iterative arrays, are sufficient for the near instantaneous conversion of fixed-point numbers from radix p to radix q, or vice versa. For the important special case of binary-decimal conversion, the structure of the cells is studied, and different realizations using the BCD code are described. One of them is specially suited for an LSI realization in MOS technology. The advantages of other codes are discussed. In particular, the use of the biquinary code allows the realization of the fastest cells, with only one gate delay for each line of cells.

keywords:
base conversion; binary-decimal conversion; cellular arrays; code conversion; iterative arrays; large-scale integration; MOS technology; number systems; radix conversion algorithms

rawabstract:
The general study of the conversion of a number from the radix p to the radix q number system leads to four different algorithms for integers, and to four similar ones for fractions. Most transform algorithms can be implemented by iterative arrays of cells characterized by simple equations. Such arrays are very attractive with present-time large-scale integration technology. Two kinds of cells, that is, two iterative arrays, are sufficient for the near instantaneous conversion of fixed-point numbers from radix p to radix q, or vice versa. For the important special case of binary-decimal conversion, the structure of the cells is studied, and different realizations using the BCD code are described. One of them is specially suited for an LSI realization in MOS technology. The advantages of other codes are discussed. In particular, the use of the biquinary code allows the realization of the fastest cells, with only one gate delay for each line of cells.

entry:
@Article{Nicoud:1971:IAR,
  author =       "Jean-Daniel Nicoud",
  title =        "Iterative Arrays for Radix Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1479--1489",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223160",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Oct 10 13:44:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "The general study of the conversion of a number from
                 the radix p to the radix q number system leads to four
                 different algorithms for integers, and to four similar
                 ones for fractions. Most transform algorithms can be
                 implemented by iterative arrays of cells characterized
                 by simple equations. Such arrays are very attractive
                 with present-time large-scale integration technology.
                 Two kinds of cells, that is, two iterative arrays, are
                 sufficient for the near instantaneous conversion of
                 fixed-point numbers from radix p to radix q, or vice
                 versa. For the important special case of binary-decimal
                 conversion, the structure of the cells is studied, and
                 different realizations using the BCD code are
                 described. One of them is specially suited for an LSI
                 realization in MOS technology. The advantages of other
                 codes are discussed. In particular, the use of the
                 biquinary code allows the realization of the fastest
                 cells, with only one gate delay for each line of
                 cells.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "base conversion; binary-decimal conversion; cellular
                 arrays; code conversion; iterative arrays; large-scale
                 integration; MOS technology; number systems; radix
                 conversion algorithms",
}


bibtype: article
filename: fparith.bib
label: Paker:1971:BFP
author: Y. Paker
title: A Binary Floating-Point Resistor
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 1
pages: 7--11
month: jan
monthnumber: 1
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223074
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:11 MDT 2011
bibtimestamp: 2011.07.13 06:38:11 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671667
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Y. Paker
rawtitle: A Binary Floating-Point Resistor
entry:
@Article{Paker:1971:BFP,
  author =       "Y. Paker",
  title =        "A Binary Floating-Point Resistor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "1",
  pages =        "7--11",
  month =        jan,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223074",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671667",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Paus:1971:FPA
author: Dag Paus
title: Floating point arithmetikk til Nord-2B
type: Hovedoppgave i fysikk
institution: Universitetet i Oslo
address: Oslo, Norway
pages: 156
year: 1971
bibdate: Thu May 09 08:11:14 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:11:14 ???
language: Norwegian
acknowledgement: ack-nhfb
rawauthor: Dag Paus
rawtitle: Floating point arithmetikk til {Nord-2B}
entry:
@TechReport{Paus:1971:FPA,
  author =       "Dag Paus",
  title =        "Floating point arithmetikk til {Nord-2B}",
  type =         "Hovedoppgave i fysikk",
  institution =  "Universitetet i Oslo",
  address =      "Oslo, Norway",
  pages =        "156",
  year =         "1971",
  bibdate =      "Thu May 09 08:11:14 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Norwegian",
}


bibtype: article
filename: fparith.bib
label: Pawlak:1971:ACN
author: Z. Pawlak
title: Another Comment on ``Negative Radix Conversion''
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 5
pages: 587--587
month: may
monthnumber: 5
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223301
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:15 MDT 2011
bibtimestamp: 2011.07.13 06:38:15 MDT
note: See cite Wadel:1971:CNR,Zohar:1970:NRC.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671894
fjournal: IEEE Transactions on Computers
keywords: negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Z. Pawlak
rawnote: See \cite{Wadel:1971:CNR,Zohar:1970:NRC}.
rawtitle: Another Comment on {``Negative Radix Conversion''}
entry:
@Article{Pawlak:1971:ACN,
  author =       "Z. Pawlak",
  title =        "Another Comment on {``Negative Radix Conversion''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "5",
  pages =        "587--587",
  month =        may,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223301",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Wadel:1971:CNR,Zohar:1970:NRC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671894",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Pezaris:1971:BBA
author: S. D. Pezaris
title: A 40ns 17-bit by 17-bit array multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 4
pages: 442--447 (??)
month: apr
monthnumber: 4
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223261
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:12:55 2007
bibtimestamp: 2007.11.09 19:12:55 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. D. Pezaris
rawtitle: A 40ns 17-bit by 17-bit array multiplier
entry:
@Article{Pezaris:1971:BBA,
  author =       "S. D. Pezaris",
  title =        "A 40ns 17-bit by 17-bit array multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "4",
  pages =        "442--447 (??)",
  month =        apr,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223261",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:12:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Pezaris:1971:NBB
author: S. D. Pezaris
title: A 40-ns 17-Bit by 17-Bit Array Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 4
pages: 442--447
month: apr
monthnumber: 4
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223261
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:14 MDT 2011
bibtimestamp: 2011.07.13 06:38:14 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671854
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. D. Pezaris
rawtitle: A 40-ns 17-Bit by 17-Bit Array Multiplier
entry:
@Article{Pezaris:1971:NBB,
  author =       "S. D. Pezaris",
  title =        "A 40-ns 17-Bit by 17-Bit Array Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "4",
  pages =        "442--447",
  month =        apr,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223261",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671854",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Rhyne:1971:SPN
author: V. T. Rhyne
title: A Simple Postcorrection for Nonrestoring Division
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 2
pages: 213--214
month: feb
monthnumber: 2
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223215
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:12 MDT 2011
bibtimestamp: 2011.07.13 06:38:12 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671808
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. T. Rhyne
rawtitle: A Simple Postcorrection for Nonrestoring Division
entry:
@Article{Rhyne:1971:SPN,
  author =       "V. T. Rhyne",
  title =        "A Simple Postcorrection for Nonrestoring Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "2",
  pages =        "213--214",
  month =        feb,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223215",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671808",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: phdthesis
filename: fparith.bib
label: Rothmaier:1971:BEF
author: B. Rothmaier
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1971
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: B. Rothmaier
title:
Die Berechnung der elementaren Funktionen mit beliebiger Genauigkeit toenglish The Computation of Elementary Functions with Arbitrary Accuracy endtoenglish 

rawtitle:
{Die Berechnung der elementaren Funktionen mit beliebiger Genauigkeit} \toenglish {The Computation of Elementary Functions with Arbitrary Accuracy} \endtoenglish

entry:
@PhdThesis{Rothmaier:1971:BEF,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der elementaren Funktionen mit
                 beliebiger Genauigkeit} \toenglish {The Computation of
                 Elementary Functions with Arbitrary Accuracy}
                 \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1971",
  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: article
filename: fparith.bib
label: Sarkar:1971:EPP
author: B. P. Sarkar and E. V. Krishnamurthy
title: Economic Pseudodivision Processes for Obtaining Square Root, Logarithm, and Arctan
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 12
pages: 1589--1593
month: dec
monthnumber: 12
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223178
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:22 MDT 2011
bibtimestamp: 2011.07.13 06:38:22 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671771
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. P. Sarkar and E. V. Krishnamurthy
rawtitle: Economic Pseudodivision Processes for Obtaining Square Root, Logarithm, and Arctan
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

entry:
@Article{Sarkar:1971:EPP,
  author =       "B. P. Sarkar and E. V. Krishnamurthy",
  title =        "Economic Pseudodivision Processes for Obtaining Square
                 Root, Logarithm, and Arctan",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1589--1593",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223178",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671771",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Schmookler:1971:HSD
author: Martin S. Schmookler and Arnold Weinberger
title: High speed decimal addition
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 8
pages: 862--867
month: aug
monthnumber: 8
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223362
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 28 19:10:32 2003
bibtimestamp: 2003.11.28 19:10:32 ???
fjournal: IEEE Transactions on Computers
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Martin S. Schmookler and Arnold Weinberger
rawtitle: High speed decimal addition
abstract:
Parallel decimal arithmetic capability is becoming increasingly attractive with new applications of computers in a multiprogramming environment. The direct production of decimal sums offers a significant improvement in addition over methods requiring decimal correction. These techniques are illustrated in the eight-digit adder which appears in the System/360 Model 195.

rawabstract:
Parallel decimal arithmetic capability is becoming increasingly attractive with new applications of computers in a multiprogramming environment. The direct production of decimal sums offers a significant improvement in addition over methods requiring decimal correction. These techniques are illustrated in the eight-digit adder which appears in the System/360 Model 195.

entry:
@Article{Schmookler:1971:HSD,
  author =       "Martin S. Schmookler and Arnold Weinberger",
  title =        "High speed decimal addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "8",
  pages =        "862--867",
  month =        aug,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223362",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 28 19:10:32 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "Parallel decimal arithmetic capability is becoming
                 increasingly attractive with new applications of
                 computers in a multiprogramming environment. The direct
                 production of decimal sums offers a significant
                 improvement in addition over methods requiring decimal
                 correction. These techniques are illustrated in the
                 eight-digit adder which appears in the System/360 Model
                 195.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Schonhage:1971:SMG
author: A. Schonhage and V. Strassen
title: Schnelle Multiplikation gross er Zahlen. (German) [Fast multiplication of large numbers]
journal: j-COMPUTING
volume: 7
number: 3--4
pages: 281--292
year: 1971
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Thu Jan 04 08:42:36 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date)
bibtimestamp: 2001.01.04 08:42:36 ???
note: Check pages??
fjournal: Computing: Archiv fur informatik und numerik
keywords: algorithm; binary numbers; logical nets; multitape Turing machines; product
language: German
acknowledgement: ack-ec
affiliation: University, Konstanz, West Germany
journalURL: http://link.springer.com/journal/607
rawauthor: A. Sch{\"o}nhage and V. Strassen
rawnote: Check pages??
rawtitle: {Schnelle Multiplikation gro{\ss}er Zahlen}. ({German}) [{Fast} multiplication of large numbers]
entry:
@Article{Schonhage:1971:SMG,
  author =       "A. Sch{\"o}nhage and V. Strassen",
  title =        "{Schnelle Multiplikation gro{\ss}er Zahlen}.
                 ({German}) [{Fast} multiplication of large numbers]",
  journal =      j-COMPUTING,
  volume =       "7",
  number =       "3--4",
  pages =        "281--292",
  year =         "1971",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Thu Jan 04 08:42:36 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  note =         "Check pages??",
  acknowledgement = ack-ec # " and " # ack-nhfb,
  affiliation =  "University, Konstanz, West Germany",
  classification = "C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "algorithm; binary numbers; logical nets; multitape
                 Turing machines; product",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Shepherd:1971:RSL
author: B. J. Shepherd
title: Right Shift for Low-Cost Multiply and Divide
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 12
pages: 1586--1589
month: dec
monthnumber: 12
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223177
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:22 MDT 2011
bibtimestamp: 2011.07.13 06:38:22 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671770
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. J. Shepherd
rawtitle: Right Shift for Low-Cost Multiply and Divide
entry:
@Article{Shepherd:1971:RSL,
  author =       "B. J. Shepherd",
  title =        "Right Shift for Low-Cost Multiply and Divide",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1586--1589",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223177",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671770",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: Stein:1971:IMA
author: Marvin L. Stein and William D. Munro
title: Introduction to machine arithmetic
publisher: pub-AW
address: pub-AW:adr
pages: viii + 295
year: 1971
LCCN: QA76.5 .S752
bibdate: Fri Nov 9 19:20:08 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.11.09 19:20:08 MST
subject: Electronic digital computers; Arithmetic
acknowledgement: ack-nhfb
rawauthor: Marvin L. Stein and William D. Munro
rawtitle: Introduction to machine arithmetic
entry:
@Book{Stein:1971:IMA,
  author =       "Marvin L. Stein and William D. Munro",
  title =        "Introduction to machine arithmetic",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "viii + 295",
  year =         "1971",
  LCCN =         "QA76.5 .S752",
  bibdate =      "Fri Nov 9 19:20:08 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "Electronic digital computers; Arithmetic",
}


bibtype: article
filename: fparith.bib
label: Stein:1971:SMA
author: M. L. Stein and W. D. Munro
title: Scaling Machine Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 6
pages: 675--678
month: jun
monthnumber: 6
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223324
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:16 MDT 2011
bibtimestamp: 2011.07.13 06:38:16 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671917
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. L. Stein and W. D. Munro
rawtitle: Scaling Machine Arithmetic
entry:
@Article{Stein:1971:SMA,
  author =       "M. L. Stein and W. D. Munro",
  title =        "Scaling Machine Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "6",
  pages =        "675--678",
  month =        jun,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223324",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:16 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671917",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Wadel:1971:CNR
author: L. B. Wadel
title: Comment on ``Negative Radix Conversion''
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 5
pages: 587--587
month: may
monthnumber: 5
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223300
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:15 MDT 2011
bibtimestamp: 2011.07.13 06:38:15 MDT
note: See cite Pawlak:1971:ACN,Zohar:1970:NRC.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671893
fjournal: IEEE Transactions on Computers
keywords: negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. B. Wadel
rawnote: See \cite{Pawlak:1971:ACN,Zohar:1970:NRC}.
rawtitle: Comment on {``Negative Radix Conversion''}
entry:
@Article{Wadel:1971:CNR,
  author =       "L. B. Wadel",
  title =        "Comment on {``Negative Radix Conversion''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "5",
  pages =        "587--587",
  month =        may,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223300",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Pawlak:1971:ACN,Zohar:1970:NRC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671893",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Walker:1971:BS
author: R. J. Walker
title: Binary Summation
journal: j-CACM
volume: 14
number: 6
pages: 417--417
month: jun
monthnumber: 6
year: 1971
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:27:52 MST 2001
bibtimestamp: 2001.01.22 07:27:52 MST
fjournal: Communications of the ACM
keywords: binary summation; digital arithmetic; floating point; roundoff errors; space; storage
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Cornell University, Ithaca, NY, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: R. J. Walker
rawtitle: Binary Summation
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Walker71; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Walker:1971:BS,
  author =       "R. J. Walker",
  title =        "Binary Summation",
  journal =      j-CACM,
  volume =       "14",
  number =       "6",
  pages =        "417--417",
  month =        jun,
  year =         "1971",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:27:52 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Walker71;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Cornell University, Ithaca, NY, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "binary summation; digital arithmetic; floating point;
                 roundoff errors; space; storage",
  oldlabel =     "Walker71",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Walker71",
}


bibtype: inproceedings
filename: fparith.bib
label: Walther:1971:UAE
author: J. S. Walther
title: A unified algorithm for elementary functions
crossref: AFIPS:1971:ACP
volume: 38
pages: 379--385
year: 1971
DOI: https://doi.org/10.1145/1478786.1478840
bibdate: Thu Sep 1 10:15:31 1994
bibtimestamp: 1994.09.01 10:15:31 ???
acknowledgement: ack-nj
rawauthor: J. S. Walther
rawtitle: A unified algorithm for elementary functions
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, ln, exp and square-root. The basis for the algorithm is coordinate rotation in a linear, circular, or hyperbolic coordinate system depending on which function is to be calculated. The only operations required are shifting, adding, subtracting and the recall of prestored constants. The limited domain of convergence of the algorithm is calculated, leading to a discussion of the modifications required to extend the domain for floating-point calculations

rawabstract:
This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, ln, exp and square-root. The basis for the algorithm is coordinate rotation in a linear, circular, or hyperbolic coordinate system depending on which function is to be calculated. The only operations required are shifting, adding, subtracting and the recall of prestored constants. The limited domain of convergence of the algorithm is calculated, leading to a discussion of the modifications required to extend the domain for floating-point calculations

entry:
@InProceedings{Walther:1971:UAE,
  author =       "J. S. Walther",
  title =        "A unified algorithm for elementary functions",
  crossref =     "AFIPS:1971:ACP",
  volume =       "38",
  pages =        "379--385",
  year =         "1971",
  DOI =          "https://doi.org/10.1145/1478786.1478840",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes a single unified algorithm for
                 the calculation of elementary functions including
                 multiplication, division, sin, cos, tan, arctan, sinh,
                 cosh, tanh, arctanh, ln, exp and square-root. The basis
                 for the algorithm is coordinate rotation in a linear,
                 circular, or hyperbolic coordinate system depending on
                 which function is to be calculated. The only operations
                 required are shifting, adding, subtracting and the
                 recall of prestored constants. The limited domain of
                 convergence of the algorithm is calculated, leading to
                 a discussion of the modifications required to extend
                 the domain for floating-point calculations",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Wlodarski:1971:FLN
author: J. Wlodarski
title: Fibonacci and Lucas Numbers Tend to Obey Benford's Law
journal: j-FIB-QUART
volume: 9
number: 1
pages: 87--88
month: feb
monthnumber: 2
year: 1971
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 18:05:33 MDT 2011
bibtimestamp: 2011.10.20 18:05:33 MDT
URL: http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf
fjournal: The Fibonacci Quarterly
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: J. Wlodarski
rawtitle: {Fibonacci} and {Lucas} Numbers Tend to Obey {Benford's Law}
bibsource:
http://www.fq.math.ca/9-1.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Wlodarski:1971:FLN,
  author =       "J. Wlodarski",
  title =        "{Fibonacci} and {Lucas} Numbers Tend to Obey
                 {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "9",
  number =       "1",
  pages =        "87--88",
  month =        feb,
  year =         "1971",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:33 MDT 2011",
  bibsource =    "http://www.fq.math.ca/9-1.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/9-1/wlodarski2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: inproceedings
filename: fparith.bib
label: Yohe:1971:R
author: J. Michael Yohe
booktitle: Proceedings of the 1971 Army Numerical Analysis and Computers Conference
title: Rounding
publisher: US Army Research Office
address: Durham, NC, USA
pages: 213--223
year: 1971
bibdate: Sun Dec 30 21:37:46 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.30 21:37:46 ???
note: ARO-D Report 71-4
acknowledgement: ack-nhfb
rawauthor: J. Michael Yohe
rawbooktitle: Proceedings of the 1971 Army Numerical Analysis and Computers Conference
rawnote: ARO-D Report 71-4
rawtitle: Rounding
entry:
@InProceedings{Yohe:1971:R,
  author =       "J. Michael Yohe",
  booktitle =    "Proceedings of the 1971 Army Numerical Analysis and
                 Computers Conference",
  title =        "Rounding",
  publisher =    "US Army Research Office",
  address =      "Durham, NC, USA",
  pages =        "213--223",
  year =         "1971",
  LCCN =         "????",
  bibdate =      "Sun Dec 30 21:37:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ARO-D Report 71-4",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Abdelmagid:1972:DFP
author: Mohamed Nabil Fouad Abdelmagid
title: Design of a floating point arithmetic unit
type: Thesis (M.S.)
school: Illinois Institute of Technology
address: Chicago, IL.
pages: v + 60
year: 1972
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: Mohamed Nabil Fouad Abdelmagid
rawtitle: Design of a floating point arithmetic unit
entry:
@MastersThesis{Abdelmagid:1972:DFP,
  author =       "Mohamed Nabil Fouad Abdelmagid",
  title =        "Design of a floating point arithmetic unit",
  type =         "Thesis ({M.S.})",
  school =       "Illinois Institute of Technology",
  address =      "Chicago, IL.",
  pages =        "v + 60",
  year =         "1972",
  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: Ahmad:1972:ISH
author: M. Ahmad
title: Iterative schemes for high speed division
journal: j-COMP-J
volume: 15
number: 4
pages: 333--336
month: nov
monthnumber: 11
year: 1972
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:52:07 MDT 2000
bibtimestamp: 2000.09.29 08:52:07 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Univ. Manchester, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: A Application; T Theoretical or Mathematical
rawauthor: M. Ahmad
rawtitle: Iterative schemes for high speed division
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/150333.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/333.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/334.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/335.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/336.tif

keywords:
digital arithmetic; digital computers; high speed division; iterative methods; iterative schemes; multiplicative

entry:
@Article{Ahmad:1972:ISH,
  author =       "M. Ahmad",
  title =        "Iterative schemes for high speed division",
  journal =      j-COMP-J,
  volume =       "15",
  number =       "4",
  pages =        "333--336",
  month =        nov,
  year =         "1972",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:52:07 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/150333.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/333.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/334.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/335.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/336.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. Manchester, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "digital arithmetic; digital computers; high speed
                 division; iterative methods; iterative schemes;
                 multiplicative",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Bandyopadhyay:1972:IAM
author: S. Bandyopadhyay and S. Basu and A. K. Choudhury
title: An Iterative Array for Multiplication of Signed Binary Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 8
pages: 921--922
month: aug
monthnumber: 8
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009055
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:46 MDT 2011
bibtimestamp: 2011.07.12 18:58:46 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009055
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Bandyopadhyay and S. Basu and A. K. Choudhury
rawtitle: An Iterative Array for Multiplication of Signed Binary Numbers
entry:
@Article{Bandyopadhyay:1972:IAM,
  author =       "S. Bandyopadhyay and S. Basu and A. K. Choudhury",
  title =        "An Iterative Array for Multiplication of Signed Binary
                 Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "921--922",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009055",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009055",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Banerji:1972:TAR
author: D. K. Banerji and J. A. Brzozowski
title: On Translation Algorithms in Residue Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 12
pages: 1281--1285
month: dec
monthnumber: 12
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1972.223499
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:48 MDT 2011
bibtimestamp: 2011.07.12 18:58:48 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. K. Banerji and J. A. Brzozowski
rawtitle: On Translation Algorithms in Residue Number Systems
URL:
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35066; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672092

abstract:
This paper considers translation problems in residue number systems. The conversion from a fixed-base representation to a residue representation can be done using residue adders only; we show that relatively simple combinational logic can be used to replace one level of residue addition. In the reverse translation problem, we examine the conditions under which base extension can be used to compute the fixed-base digits from a residue code number, and we study the efficiency of the algorithm.

keywords:
base extension; input translation; modular arithmetic; output translation; residue arithmetic; residue number systems

rawabstract:
This paper considers translation problems in residue number systems. The conversion from a fixed-base representation to a residue representation can be done using residue adders only; we show that relatively simple combinational logic can be used to replace one level of residue addition. In the reverse translation problem, we examine the conditions under which base extension can be used to compute the fixed-base digits from a residue code number, and we study the efficiency of the algorithm.

entry:
@Article{Banerji:1972:TAR,
  author =       "D. K. Banerji and J. A. Brzozowski",
  title =        "On Translation Algorithms in Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "12",
  pages =        "1281--1285",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1972.223499",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35066;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672092",
  abstract =     "This paper considers translation problems in residue
                 number systems. The conversion from a fixed-base
                 representation to a residue representation can be done
                 using residue adders only; we show that relatively
                 simple combinational logic can be used to replace one
                 level of residue addition. In the reverse translation
                 problem, we examine the conditions under which base
                 extension can be used to compute the fixed-base digits
                 from a residue code number, and we study the efficiency
                 of the algorithm.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "base extension; input translation; modular arithmetic;
                 output translation; residue arithmetic; residue number
                 systems",
}


bibtype: article
filename: fparith.bib
label: Brakefield:1972:OFP
author: James C. Brakefield
title: An optimal floating point format
journal: j-COMP-ARCH-NEWS
volume: 1
number: 4
pages: 16--17
month: oct
monthnumber: 10
year: 1972
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Fri May 12 09:41:08 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.12 09:41:08 MDT
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigarch
rawauthor: James C. Brakefield
rawtitle: An optimal floating point format
entry:
@Article{Brakefield:1972:OFP,
  author =       "James C. Brakefield",
  title =        "An optimal floating point format",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "1",
  number =       "4",
  pages =        "16--17",
  month =        oct,
  year =         "1972",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:41:08 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}


bibtype: article
filename: fparith.bib
label: Chen:1972:ACE
author: Tien Chi Chen
title: Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots
journal: j-IBM-JRD
volume: 16
number: 4
pages: 380--388
month: jul
monthnumber: 7
year: 1972
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65D20
MRnumber: 49 \#1738
bibdate: Tue Mar 25 14:26:59 MST 1997
bibtimestamp: 1997.03.25 14:26:59 MST
URL: http://www.research.ibm.com/journal/rd/164/chen.pdf
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: IBM, San Jose, CA, USA
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: F. Gotze
treatment: P Practical
rawauthor: Tien Chi Chen
rawtitle: Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
It is shown how a relatively simple device can evaluate exponentials, logarithms, ratios and square roots for fraction arguments, employing only shifts, adds, high-speed table lookups, and bit counting. The scheme is based on the cotransformation of a number pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is invariant; when $x$ is driven towards a known value $ x_w $, $y$ is driven towards the result. For an $N$-bit fraction about $ N / 4 $ iterations are required, each involving two or three adds; then a termination algorithm, based on an add and an abbreviated multiply, completes the process, for a total cost of about one conventional multiply time. Convergence, errors and simulation using APL are discussed.

keywords:
adds; APL; bit counting; convergence; cotransformation; digital arithmetic; errors; exponentials; high speed table; iteration; logarithms; lookups; ratios; shifts; simulation; square roots; termination algorithm

rawabstract:
It is shown how a relatively simple device can evaluate exponentials, logarithms, ratios and square roots for fraction arguments, employing only shifts, adds, high-speed table lookups, and bit counting. The scheme is based on the cotransformation of a number pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is invariant; when $x$ is driven towards a known value $ x_w $, $y$ is driven towards the result. For an $N$-bit fraction about $ N / 4 $ iterations are required, each involving two or three adds; then a termination algorithm, based on an add and an abbreviated multiply, completes the process, for a total cost of about one conventional multiply time. Convergence, errors and simulation using APL are discussed.

entry:
@Article{Chen:1972:ACE,
  author =       "Tien Chi Chen",
  title =        "Automatic Computation of Exponentials, Logarithms,
                 Ratios and Square Roots",
  journal =      j-IBM-JRD,
  volume =       "16",
  number =       "4",
  pages =        "380--388",
  month =        jul,
  year =         "1972",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65D20",
  MRnumber =     "49 \#1738",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/164/chen.pdf",
  abstract =     "It is shown how a relatively simple device can
                 evaluate exponentials, logarithms, ratios and square
                 roots for fraction arguments, employing only shifts,
                 adds, high-speed table lookups, and bit counting. The
                 scheme is based on the cotransformation of a number
                 pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
                 invariant; when $x$ is driven towards a known value $
                 x_w $, $y$ is driven towards the result. For an $N$-bit
                 fraction about $ N / 4 $ iterations are required, each
                 involving two or three adds; then a termination
                 algorithm, based on an add and an abbreviated multiply,
                 completes the process, for a total cost of about one
                 conventional multiply time. Convergence, errors and
                 simulation using APL are discussed.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, San Jose, CA, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "adds; APL; bit counting; convergence;
                 cotransformation; digital arithmetic; errors;
                 exponentials; high speed table; iteration; logarithms;
                 lookups; ratios; shifts; simulation; square roots;
                 termination algorithm",
  reviewer =     "F. Gotze",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Chiang:1972:NAB
author: A. C. L. Chiang and I. S. Reed
title: Notes on the Arithmetic BN Modulo A Codes
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 8
pages: 891--894
month: aug
monthnumber: 8
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009046
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:46 MDT 2011
bibtimestamp: 2011.07.12 18:58:46 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009046
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. C. L. Chiang and I. S. Reed
rawtitle: Notes on the Arithmetic {BN} Modulo {A} Codes
entry:
@Article{Chiang:1972:NAB,
  author =       "A. C. L. Chiang and I. S. Reed",
  title =        "Notes on the Arithmetic {BN} Modulo {A} Codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "891--894",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009046",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009046",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Chien:1972:ECH
author: R. T. Chien and Se June Hong
title: Error Correction in High-Speed Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 5
pages: 433--438
month: may
monthnumber: 5
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1972.223538
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:43 MDT 2011
bibtimestamp: 2011.07.12 18:58:43 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672131
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. T. Chien and Se June Hong
rawtitle: Error Correction in High-Speed Arithmetic
entry:
@Article{Chien:1972:ECH,
  author =       "R. T. Chien and Se June Hong",
  title =        "Error Correction in High-Speed Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "5",
  pages =        "433--438",
  month =        may,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223538",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672131",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Chinal:1972:SCP
author: J. P. Chinal
title: Some Comments on Postcorrections for Nonrestoring Division
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 12
pages: 1385--1394
month: dec
monthnumber: 12
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1972.223511
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:49 MDT 2011
bibtimestamp: 2011.07.12 18:58:49 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672104
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. P. Chinal
rawtitle: Some Comments on Postcorrections for Nonrestoring Division
entry:
@Article{Chinal:1972:SCP,
  author =       "J. P. Chinal",
  title =        "Some Comments on Postcorrections for Nonrestoring
                 Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "12",
  pages =        "1385--1394",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223511",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672104",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: DeMori:1972:PSS
author: R. De Mori and A. Serra
title: A Parallel Structure for Signed-Number Multiplication and Addition
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 12
pages: 1453--1454
month: dec
monthnumber: 12
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1972.223525
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:49 MDT 2011
bibtimestamp: 2011.07.12 18:58:49 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672118
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. {De Mori} and A. Serra
rawtitle: A Parallel Structure for Signed-Number Multiplication and Addition
entry:
@Article{DeMori:1972:PSS,
  author =       "R. {De Mori} and A. Serra",
  title =        "A Parallel Structure for Signed-Number Multiplication
                 and Addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "12",
  pages =        "1453--1454",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223525",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672118",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Fenwick:1972:BRD
author: Peter M. Fenwick
title: A Binary Representation for Decimal Numbers
journal: j-AUSTRALIAN-COMP-J
volume: 4
number: 4
pages: 146--149
month: nov
monthnumber: 11
year: 1972
CODEN: ACMJB2
ISSN: 0004-8917 OR 00048917
bibdate: Fri Nov 28 11:31:38 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:31:38 ???
fjournal: Australian Computer Journal
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Peter M. Fenwick
rawtitle: A Binary Representation for Decimal Numbers
entry:
@Article{Fenwick:1972:BRD,
  author =       "Peter M. Fenwick",
  title =        "A Binary Representation for Decimal Numbers",
  journal =      j-AUSTRALIAN-COMP-J,
  volume =       "4",
  number =       "4",
  pages =        "146--149",
  month =        nov,
  year =         "1972",
  CODEN =        "ACMJB2",
  ISSN =         "0004-8917",
  bibdate =      "Fri Nov 28 11:31:38 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Computer Journal",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Fettweis:1972:CBM
author: A. Fettweis
title: On the connection between multiplier word length limitation and roundoff noise in digital filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 19
number: 5
pages: 486--491
month: sep
monthnumber: 9
year: 1972
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: A. Fettweis
rawtitle: On the connection between multiplier word length limitation and roundoff noise in digital filters
entry:
@Article{Fettweis:1972:CBM,
  author =       "A. Fettweis",
  title =        "On the connection between multiplier word length
                 limitation and roundoff noise in digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "19",
  number =       "5",
  pages =        "486--491",
  month =        sep,
  year =         "1972",
  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 =      "It is shown that for digital filters there exists a
                 direct and an indirect connection between the
                 generation of roundoff noise by a multiplier and the
                 effect that the coefficient word length limitation of
                 this multiplier has upon the response \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Franklin:1972:ZDA
author: J. W. Franklin
title: Zoned Decimal Arithmetic
journal: j-IBM-TDB
volume: 15
number: 7
pages: 2123--2124
month: dec
monthnumber: 12
year: 1972
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: J. W. Franklin
rawtitle: Zoned Decimal Arithmetic
entry:
@Article{Franklin:1972:ZDA,
  author =       "J. W. Franklin",
  title =        "Zoned Decimal Arithmetic",
  journal =      j-IBM-TDB,
  volume =       "15",
  number =       "7",
  pages =        "2123--2124",
  month =        dec,
  year =         "1972",
  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: book
filename: fparith.bib
label: Goldstine:1972:CPN
author: Herman H. Goldstine
title: The Computer: From Pascal to von Neumann
publisher: pub-PRINCETON
address: pub-PRINCETON:adr
pages: xii + 378
year: 1972
ISBN: 0-691-02367-0; 0-691-08104-2 OR 0691023670; 0691081042
ISBN13: 978-0-691-02367-0; 978-0-691-08104-5 OR 9780691023670; 9780691081045
bibdate: Mon Jun 06 19:17:03 2005
bibtimestamp: 2005.06.06 19:17:03 ???
acknowledgement: ack-nhfb
rawauthor: Herman H. Goldstine
rawtitle: The Computer: {From Pascal} to {von Neumann}
bibsource:
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/TUBScsd/1972.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

note:
Second printing, 1973. Paperback edition 1980. Fifth printing, 1993 with new preface. Reprint 2000 by Books on Demand, Ann Arbor, MI, USA.

rawnote:
Second printing, 1973. Paperback edition 1980. Fifth printing, 1993 with new preface. Reprint 2000 by Books on Demand, Ann Arbor, MI, USA.

entry:
@Book{Goldstine:1972:CPN,
  author =       "Herman H. Goldstine",
  title =        "The Computer: {From Pascal} to {von Neumann}",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xii + 378",
  year =         "1972",
  ISBN =         "0-691-02367-0; 0-691-08104-2",
  ISBN-13 =      "978-0-691-02367-0; 978-0-691-08104-5",
  bibdate =      "Mon Jun 06 19:17:03 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/TUBScsd/1972.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",
  note =         "Second printing, 1973. Paperback edition 1980. Fifth
                 printing, 1993 with new preface. Reprint 2000 by Books
                 on Demand, Ann Arbor, MI, USA.",
  acknowledgement = ack-nhfb,
  descriptor =   "Computer, ENIAC, Entwicklung, Geschichte, Pascal, Von
                 Neumann",
  kwds =         "book, history, computer",
}


bibtype: techreport
filename: fparith.bib
label: Gosper:1972:HCF
author: R. W. Gosper
title: HAKMEM 101: Continued Fractions
type: Memo
number: AIM 239
institution: MIT AI Laboratory
address: Cambridge, MA, USA
pages: 37--44
year: 1972
bibdate: Fri Nov 30 06:37:23 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.30 06:37:23 ???
URL: http://www.inwap.com/pdp10/hbaker/hakmem/cf.html#item101a
acknowledgement: ack-nhfb
rawauthor: R. W. Gosper
rawtitle: {HAKMEM} 101: Continued Fractions
remark:
From the document: ``The familiar transcendental functions of rational arguments also have simple continued fractions, but these are generally not regular and cannot be reconstructed from numerical values by a simple algorithm, since nonregular representations aren't unique. The point is, however, that numbers like e, pi, sqrt(2), sin 0.5, sqrt(7), arctan sqrt(7), etc. can be expressed to unlimited precision by simple programs which produce the terms on demand.'' Also: ``Rational number arithmetic often loses because numerators and denominators grow so large as to require icky multiprecision. Algorithms for arithmetic on continued fractions seem generally unknown. The next items describe how to arithmetically combine continued fractions to produce new ones, one term at a time.'' and ``Continued fractions let us perform numerical calculations a little at a time without ever introducing any error, such as roundoff or truncation. As if this weren't enough, the calculations provide automatic error analysis, and obviate most forms of successive approximation.''

entry:
@TechReport{Gosper:1972:HCF,
  author =       "R. W. Gosper",
  title =        "{HAKMEM} 101: Continued Fractions",
  type =         "Memo",
  number =       "AIM 239",
  institution =  "MIT AI Laboratory",
  address =      "Cambridge, MA, USA",
  pages =        "37--44",
  year =         "1972",
  bibdate =      "Fri Nov 30 06:37:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.inwap.com/pdp10/hbaker/hakmem/cf.html#item101a",
  acknowledgement = ack-nhfb,
  remark =       "From the document: ``The familiar transcendental
                 functions of rational arguments also have simple
                 continued fractions, but these are generally not
                 regular and cannot be reconstructed from numerical
                 values by a simple algorithm, since nonregular
                 representations aren't unique. The point is, however,
                 that numbers like e, pi, sqrt(2), sin 0.5, sqrt(7),
                 arctan sqrt(7), etc. can be expressed to unlimited
                 precision by simple programs which produce the terms on
                 demand.'' Also: ``Rational number arithmetic often
                 loses because numerators and denominators grow so large
                 as to require icky multiprecision. Algorithms for
                 arithmetic on continued fractions seem generally
                 unknown. The next items describe how to arithmetically
                 combine continued fractions to produce new ones, one
                 term at a time.'' and ``Continued fractions let us
                 perform numerical calculations a little at a time
                 without ever introducing any error, such as roundoff or
                 truncation. As if this weren't enough, the calculations
                 provide automatic error analysis, and obviate most
                 forms of successive approximation.''",
}


bibtype: article
filename: fparith.bib
label: Gregory:1972:CFP
author: James Gregory
title: A Comparison of Floating Point Summation Methods
journal: j-CACM
volume: 15
number: 9
pages: 838--838
month: sep
monthnumber: 9
year: 1972
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:46:23 MST 2001
bibtimestamp: 2001.01.22 06:46:23 MST
fjournal: Communications of the ACM
acknowledgement: ack-nj
classcodes: C5230 (Digital arithmetic methods)
corpsource: Argonne Nat. Lab., IL, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: James Gregory
rawtitle: A Comparison of Floating Point Summation Methods
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Gregory72; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
accurate floating-point summation; comparison; digital arithmetic; error; error propagation; floating point summation methods; truncation

entry:
@Article{Gregory:1972:CFP,
  author =       "James Gregory",
  title =        "A Comparison of Floating Point Summation Methods",
  journal =      j-CACM,
  volume =       "15",
  number =       "9",
  pages =        "838--838",
  month =        sep,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:46:23 MST 2001",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Gregory72;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  descriptors =  "Simulation; statistics; numeric calculation",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "accurate floating-point summation; comparison; digital
                 arithmetic; error; error propagation; floating point
                 summation methods; truncation",
  oldlabel =     "Gregory72",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gregory72",
}


bibtype: article
filename: fparith.bib
label: Gregory:1972:URA
author: Robert Todd Gregory
title: The use of residue arithmetic with automatic digital computers
journal: Delta (Waukesha)
volume: 3
number: 2
pages: 1--27
year: 1972 / 1973
MRclass: 68A10
MRnumber: MR0321348 (47 \#9881)
MRreviewer: A. D. Booth
bibdate: Thu Nov 8 14:50:21 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:21 ???
acknowledgement: ack-nhfb
rawauthor: Robert Todd Gregory
rawtitle: The use of residue arithmetic with automatic digital computers
entry:
@Article{Gregory:1972:URA,
  author =       "Robert Todd Gregory",
  title =        "The use of residue arithmetic with automatic digital
                 computers",
  journal =      "Delta (Waukesha)",
  volume =       "3",
  number =       "2",
  pages =        "1--27",
  year =         "1972\slash 1973",
  MRclass =      "68A10",
  MRnumber =     "MR0321348 (47 \#9881)",
  MRreviewer =   "A. D. Booth",
  bibdate =      "Thu Nov 8 14:50:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Hallin:1972:PAF
author: T. G. Hallin and M. J. Flynn
title: Pipelining of Arithmetic Functions
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 8
pages: 880--886
month: aug
monthnumber: 8
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009044
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 18:57:52 2007
bibtimestamp: 2007.11.09 18:57:52 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. G. Hallin and M. J. Flynn
rawtitle: Pipelining of Arithmetic Functions
entry:
@Article{Hallin:1972:PAF,
  author =       "T. G. Hallin and M. J. Flynn",
  title =        "Pipelining of Arithmetic Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "880--886",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009044",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 18:57:52 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Heising:1972:MM
author: W. Heising and M. O. Rabin and Shmuel Winograd
title: Multiplication Method
journal: j-IBM-TDB
volume: 15
number: 4
pages: 1147--1148
month: sep
monthnumber: 9
year: 1972
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
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: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: W. Heising and M. O. Rabin and Shmuel Winograd
rawtitle: Multiplication Method
entry:
@Article{Heising:1972:MM,
  author =       "W. Heising and M. O. Rabin and Shmuel Winograd",
  title =        "Multiplication Method",
  journal =      j-IBM-TDB,
  volume =       "15",
  number =       "4",
  pages =        "1147--1148",
  month =        sep,
  year =         "1972",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  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 =     "IBM Technical Disclosure Bulletin",
}


bibtype: manual
filename: fparith.bib
label: IBM:1972:ISR
author: International Business Machines Corporation
organization: IBM Corporation
address: White Plains, NY, USA
pages: 18
year: 1972
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: IBM 360 (Computer)
remark: ``GX20-1787-0.''
acknowledgement: ack-nhfb
rawauthor: {International Business Machines Corporation}
title:
IBM System / 360 reference data: direct evaluation of floating point numbers in hexadecimal: debugging aid

rawtitle:
{IBM System\slash 360} reference data: direct evaluation of floating point numbers in hexadecimal: debugging aid

entry:
@Manual{IBM:1972:ISR,
  author =       "{International Business Machines Corporation}",
  title =        "{IBM System\slash 360} reference data: direct
                 evaluation of floating point numbers in hexadecimal:
                 debugging aid",
  organization = "IBM Corporation",
  address =      "White Plains, NY, USA",
  pages =        "18",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "IBM 360 (Computer)",
  remark =       "``GX20-1787-0.''",
}


bibtype: article
filename: fparith.bib
label: Kamal:1972:HSM
author: A. A. Kamal and M. A. N. Ghannam
title: High-Speed Multiplication Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 9
pages: 1017--1021
month: sep
monthnumber: 9
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009082
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:46 MDT 2011
bibtimestamp: 2011.07.12 18:58:46 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009082
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. A. Kamal and M. A. N. Ghannam
rawtitle: High-Speed Multiplication Systems
entry:
@Article{Kamal:1972:HSM,
  author =       "A. A. Kamal and M. A. N. Ghannam",
  title =        "High-Speed Multiplication Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "9",
  pages =        "1017--1021",
  month =        sep,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009082",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009082",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Liu:1972:REF
author: B. Liu and M. Van Valkenburg
title: On roundoff error of fixed-point digital filters using sign-magnitude truncation
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 19
pages: 536--537
month: sep
monthnumber: 9
year: 1972
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: B. Liu and M. {Van Valkenburg}
rawtitle: On roundoff error of fixed-point digital filters using sign-magnitude truncation
entry:
@Article{Liu:1972:REF,
  author =       "B. Liu and M. {Van Valkenburg}",
  title =        "On roundoff error of fixed-point digital filters using
                 sign-magnitude truncation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "19",
  pages =        "536--537",
  month =        sep,
  year =         "1972",
  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 =      "This correspondence gives the statistical mean squared
                 error at the output of a digital filter due to roundoff
                 accumulation when fixed-point arithmetic with
                 sign-magnitude truncation is \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Loevenbruck:1972:CNR
author: A. P. Loevenbruck
title: Conversion of Number Representations
journal: j-IBM-TDB
volume: 15
number: 7
pages: 2148--2151
month: dec
monthnumber: 12
year: 1972
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:16:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:10 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: A. P. Loevenbruck
rawtitle: Conversion of Number Representations
entry:
@Article{Loevenbruck:1972:CNR,
  author =       "A. P. Loevenbruck",
  title =        "Conversion of Number Representations",
  journal =      j-IBM-TDB,
  volume =       "15",
  number =       "7",
  pages =        "2148--2151",
  month =        dec,
  year =         "1972",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: fparith.bib
label: Majithia:1972:CAE
author: J. C. Majithia
title: Cellular Array for Extraction of Squares and Square Roots of Binary Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 9
pages: 1023--1024
month: sep
monthnumber: 9
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009084
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:46 MDT 2011
bibtimestamp: 2011.07.12 18:58:46 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. C. Majithia
rawtitle: Cellular Array for Extraction of Squares and Square Roots of Binary Numbers
entry:
@Article{Majithia:1972:CAE,
  author =       "J. C. Majithia",
  title =        "Cellular Array for Extraction of Squares and Square
                 Roots of Binary Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "9",
  pages =        "1023--1024",
  month =        sep,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009084",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Malcolm:1972:ARP
author: Michael A. Malcolm
title: Algorithms to Reveal Properties of Floating-Point Arithmetic
journal: j-CACM
volume: 15
number: 11
pages: 949--951
month: nov
monthnumber: 11
year: 1972
CODEN: CACMA2
DOI: https://doi.org/10.1145/355606.361870
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:14:16 1994
bibtimestamp: 1994.09.01 10:14:16 ???
note: See also cite Gentleman:1974:MAR.
fjournal: Communications of the ACM
acknowledgement: ack-nj
classcodes: C5230 (Digital arithmetic methods)
corpsource: Stanford University, CA, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
treatment: T Theoretical or Mathematical
rawauthor: Michael A. Malcolm
rawnote: See also \cite{Gentleman:1974:MAR}.
rawtitle: Algorithms to Reveal Properties of Floating-Point Arithmetic
bibsource:
Compendex database; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Malcolm72; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Two algorithms are presented in the form of Fortran subroutines. Each subroutine computes the radix and number of digits of the floating-point numbers and whether rounding or chopping is done by the machine on which it is run. The methods are shown to work on any ``reasonable'' floating-point computer.

keywords:
chopping; computer programming; computer programming languages --- Fortran; digital arithmetic; digits; floating point arithmetic; Fortran subroutines; mathematical techniques --- Digital Arithmetic; number of; properties; radix; rounding

rawabstract:
Two algorithms are presented in the form of Fortran subroutines. Each subroutine computes the radix and number of digits of the floating-point numbers and whether rounding or chopping is done by the machine on which it is run. The methods are shown to work on any ``reasonable'' floating-point computer.

entry:
@Article{Malcolm:1972:ARP,
  author =       "Michael A. Malcolm",
  title =        "Algorithms to Reveal Properties of Floating-Point
                 Arithmetic",
  journal =      j-CACM,
  volume =       "15",
  number =       "11",
  pages =        "949--951",
  month =        nov,
  year =         "1972",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355606.361870",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:14:16 1994",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Malcolm72;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Gentleman:1974:MAR}.",
  abstract =     "Two algorithms are presented in the form of Fortran
                 subroutines. Each subroutine computes the radix and
                 number of digits of the floating-point numbers and
                 whether rounding or chopping is done by the machine on
                 which it is run. The methods are shown to work on any
                 ``reasonable'' floating-point computer.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723",
  corpsource =   "Stanford University, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "chopping; computer programming; computer programming
                 languages --- Fortran; digital arithmetic; digits;
                 floating point arithmetic; Fortran subroutines;
                 mathematical techniques --- Digital Arithmetic; number
                 of; properties; radix; rounding",
  oldlabel =     "Malcolm72",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm72",
}


bibtype: article
filename: fparith.bib
label: Mandelbaum:1972:ECR
author: David Mandelbaum
title: Error correction in residue arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-21
pages: 538--545
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009006
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 94A10 (94A20)
MRnumber: MR0345709 (49 \#10440)
MRreviewer: P. Deussen
bibdate: Thu Nov 8 14:50:21 2007
bibtimestamp: 2007.11.08 14:50:21 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: David Mandelbaum
rawtitle: Error correction in residue arithmetic
entry:
@Article{Mandelbaum:1972:ECR,
  author =       "David Mandelbaum",
  title =        "Error correction in residue arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  pages =        "538--545",
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009006",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "94A10 (94A20)",
  MRnumber =     "MR0345709 (49 \#10440)",
  MRreviewer =   "P. Deussen",
  bibdate =      "Thu Nov 8 14:50:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Manos:1972:CCA
author: Paul Manos and L. Richard Turner
type: NASA Technical Note
number: TN D-6698
institution: NASA
address: Washington, DC, USA
pages: iii + 68
month: mar
monthnumber: 3
year: 1972
bibdate: Mon May 22 11:27:24 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.22 11:27:24 ???
URL: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf
acknowledgement: ack-nhfb
rawauthor: Paul Manos and L. Richard Turner
title:
Constrained Chebyshev approximations to some elementary functions suitable for evaluation with floating-point arithmetic

rawtitle:
Constrained {Chebyshev} approximations to some elementary functions suitable for evaluation with floating-point arithmetic

entry:
@TechReport{Manos:1972:CCA,
  author =       "Paul Manos and L. Richard Turner",
  title =        "Constrained {Chebyshev} approximations to some
                 elementary functions suitable for evaluation with
                 floating-point arithmetic",
  type =         "{NASA} Technical Note",
  number =       "TN D-6698",
  institution =  "NASA",
  address =      "Washington, DC, USA",
  pages =        "iii + 68",
  month =        mar,
  year =         "1972",
  bibdate =      "Mon May 22 11:27:24 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Maple:1972:FPA
author: Christopher Marion Maple
title: A floating point analog to digital and digital to analog converter
type: Thesis (B.S.)
school: Massachusetts Institute of Technology. Dept. of Electrical Engineering
address: Cambridge, MA, USA
pages: 18
year: 1972
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: Christopher Marion Maple
rawtitle: A floating point analog to digital and digital to analog converter
entry:
@MastersThesis{Maple:1972:FPA,
  author =       "Christopher Marion Maple",
  title =        "A floating point analog to digital and digital to
                 analog converter",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical Engineering",
  address =      "Cambridge, MA, USA",
  pages =        "18",
  year =         "1972",
  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: Marino:1972:NAA
author: D. Marino
journal: j-IEEE-TRANS-COMPUT
volume: 21
number: 12
pages: 1416--1421
month: dec
monthnumber: 12
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1972.223516
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 08 08:05:51 1994
bibtimestamp: 1994.09.08 08:05:51 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Marino
title:
New Algorithms for the Approximate Evaluation in Hardware of Binary Logarithms and Elementary Functions

rawtitle:
New Algorithms for the Approximate Evaluation in Hardware of Binary Logarithms and Elementary Functions

entry:
@Article{Marino:1972:NAA,
  author =       "D. Marino",
  title =        "New Algorithms for the Approximate Evaluation in
                 Hardware of Binary Logarithms and Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "21",
  number =       "12",
  pages =        "1416--1421",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223516",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 08:05:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1972:NTF
author: David W. Matula
title: Number Theoretic Foundations of Finite Precision Arithmetic
crossref: Zaremba:1972:ANT
pages: 479--489
year: 1972
bibdate: Fri Oct 19 22:58:55 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.19 22:58:55 ???
acknowledgement: ack-nhfb
rawauthor: David W. Matula
rawtitle: Number Theoretic Foundations of Finite Precision Arithmetic
keywords:
base conversion; finite-precision rational arithmetic; number theory; overflow; radix conversion; tape updating problem

entry:
@InProceedings{Matula:1972:NTF,
  author =       "David W. Matula",
  title =        "Number Theoretic Foundations of Finite Precision
                 Arithmetic",
  crossref =     "Zaremba:1972:ANT",
  pages =        "479--489",
  year =         "1972",
  bibdate =      "Fri Oct 19 22:58:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "base conversion; finite-precision rational arithmetic;
                 number theory; overflow; radix conversion; tape
                 updating problem",
}


bibtype: techreport
filename: fparith.bib
label: Metropolis:1972:ABCa
author: N. Metropolis
title: Analyzed Binary Computing
type: Technical Report
number: LA-DC--72-783; CONF-720916--2
institution: inst-LASL
address: inst-LASL:adr
pages: 4
day: 12
month: sep
monthnumber: 9
year: 1972
bibdate: Tue Mar 20 11:25:24 2007
bibtimestamp: 2007.03.20 11:25:24 ???
URL: http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4647144&query_id=0
acknowledgement: ack-nhfb
rawauthor: N. Metropolis
rawtitle: Analyzed Binary Computing
entry:
@TechReport{Metropolis:1972:ABCa,
  author =       "N. Metropolis",
  title =        "Analyzed Binary Computing",
  type =         "Technical Report",
  number =       "LA-DC--72-783; CONF-720916--2",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  pages =        "4",
  day =          "12",
  month =        sep,
  year =         "1972",
  bibdate =      "Tue Mar 20 11:25:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4647144&query_id=0",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Metropolis:1972:ABCb
author: N. Metropolis
title: Analyzed Binary Computing
crossref: IEEE:1972:IAD
pages: 81--84
year: 1972
bibdate: Wed Mar 21 09:24:37 2007
bibtimestamp: 2007.03.21 09:24:37 ???
acknowledgement: ack-nhfb
rawauthor: N. Metropolis
rawtitle: Analyzed Binary Computing
abstract:
A single format for the representation of numbers in a computer is proposed to accommodate both exact and inexact quantities. A consistent set of rules is described for addition (subtraction), multiplication and division of such quantities, both within their separate types, as well as in combination. Error correlation aside, the propagation of inherent errors is monitored in operations with at least one imprecise value. A definitive algorithm must, of course take into account any correlations of inherent errors; these correlations must be recognized and incorporated into the algorithm by the numerical analyst, not by the logical designer of the computer.

rawabstract:
A single format for the representation of numbers in a computer is proposed to accommodate both exact and inexact quantities. A consistent set of rules is described for addition (subtraction), multiplication and division of such quantities, both within their separate types, as well as in combination. Error correlation aside, the propagation of inherent errors is monitored in operations with at least one imprecise value. A definitive algorithm must, of course take into account any correlations of inherent errors; these correlations must be recognized and incorporated into the algorithm by the numerical analyst, not by the logical designer of the computer.

entry:
@InProceedings{Metropolis:1972:ABCb,
  author =       "N. Metropolis",
  title =        "Analyzed Binary Computing",
  crossref =     "IEEE:1972:IAD",
  pages =        "81--84",
  year =         "1972",
  bibdate =      "Wed Mar 21 09:24:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A single format for the representation of numbers in a
                 computer is proposed to accommodate both exact and
                 inexact quantities. A consistent set of rules is
                 described for addition (subtraction), multiplication
                 and division of such quantities, both within their
                 separate types, as well as in combination. Error
                 correlation aside, the propagation of inherent errors
                 is monitored in operations with at least one imprecise
                 value. A definitive algorithm must, of course take into
                 account any correlations of inherent errors; these
                 correlations must be recognized and incorporated into
                 the algorithm by the numerical analyst, not by the
                 logical designer of the computer.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Metropolis:1972:ABCc
author: Nicholas C. Metropolis
title: Analyzed binary computing
crossref: IEEE:1972:ITS
pages: 1--14
year: 1972
DOI: https://doi.org/10.1109/ARITH.1972.6153912
bibdate: Tue Mar 5 08:31:37 MST 2013
bibtimestamp: 2013.03.05 08:31:37 MST
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6148543
rawauthor: Nicholas C. Metropolis
rawtitle: Analyzed binary computing
entry:
@InProceedings{Metropolis:1972:ABCc,
  author =       "Nicholas C. Metropolis",
  title =        "Analyzed binary computing",
  crossref =     "IEEE:1972:ITS",
  pages =        "1--14",
  year =         "1972",
  DOI =          "https://doi.org/10.1109/ARITH.1972.6153912",
  bibdate =      "Tue Mar 5 08:31:37 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6148543",
}


bibtype: mastersthesis
filename: fparith.bib
label: Miller:1972:DFD
author: Peter Edwin Miller
type: Thesis (M.S.)
school: Ohio State University
address: Columbus, OH, USA
pages: 83
year: 1972
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: Arithmetic --- Computer programs; PDP-9 (Computer)
acknowledgement: ack-nhfb
rawauthor: Peter Edwin Miller
title:
The design of a floating-point, double-precision arithmetic unit for the Digital Equipment Corporation's PDP-9 computer

rawtitle:
The design of a floating-point, double-precision arithmetic unit for the {Digital Equipment Corporation}'s {PDP-9} computer

entry:
@MastersThesis{Miller:1972:DFD,
  author =       "Peter Edwin Miller",
  title =        "The design of a floating-point, double-precision
                 arithmetic unit for the {Digital Equipment
                 Corporation}'s {PDP-9} computer",
  type =         "Thesis ({M.S.})",
  school =       "Ohio State University",
  address =      "Columbus, OH, USA",
  pages =        "83",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic --- Computer programs; PDP-9 (Computer)",
}


bibtype: inproceedings
filename: fparith.bib
label: Neely:1972:CSN
author: Peter M. Neely
title: On conventions for systems of numerical representation
crossref: ACM:1972:PAA
pages: 644--561
year: 1972
bibdate: Fri Nov 28 11:28:06 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:28:06 ???
acknowledgement: ack-nhfb
rawauthor: Peter M. Neely
rawtitle: On conventions for systems of numerical representation
abstract:
Present conventions for numeric representation are considered inadequate to serve the needs of applied computing. Thus an augmented digital number system is proposed for use in programming languages and in digital computers. Special symbols are proposed for numbers too large, too small or too close to zero to be represented in the normal digital number system, or which are undefined. Properties of mappings among and between digital number systems are used to justify the augments chosen. Finally a suggestion is made for a new floating point word format that will serve all the above needs and will greatly extend the exponent range of floating point numbers.

rawabstract:
Present conventions for numeric representation are considered inadequate to serve the needs of applied computing. Thus an augmented digital number system is proposed for use in programming languages and in digital computers. Special symbols are proposed for numbers too large, too small or too close to zero to be represented in the normal digital number system, or which are undefined. Properties of mappings among and between digital number systems are used to justify the augments chosen. Finally a suggestion is made for a new floating point word format that will serve all the above needs and will greatly extend the exponent range of floating point numbers.

entry:
@InProceedings{Neely:1972:CSN,
  author =       "Peter M. Neely",
  title =        "On conventions for systems of numerical
                 representation",
  crossref =     "ACM:1972:PAA",
  pages =        "644--561",
  year =         "1972",
  bibdate =      "Fri Nov 28 11:28:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Present conventions for numeric representation are
                 considered inadequate to serve the needs of applied
                 computing. Thus an augmented digital number system is
                 proposed for use in programming languages and in
                 digital computers. Special symbols are proposed for
                 numbers too large, too small or too close to zero to be
                 represented in the normal digital number system, or
                 which are undefined. Properties of mappings among and
                 between digital number systems are used to justify the
                 augments chosen. Finally a suggestion is made for a new
                 floating point word format that will serve all the
                 above needs and will greatly extend the exponent range
                 of floating point numbers.",
  acknowledgement = ack-nhfb,
}


