# bibtab

bibtype: book
filename: fparith.bib
label: Heck:1996:IM
author: Andre Heck
title: Introduction to Maple
publisher: pub-SV
address: pub-SV:adr
edition: Second
pages: xx + 699
year: 1996
DOI: https://doi.org/10.1007/978-1-4684-0484-5
LCCN: QA155.7.E4H43 1993
MRclass: 65-01, 65B10, 65D18, 65Dxx, 65Fxx, 65Lxx, 68-01, 68N15, 68W30, 68NXX
MRnumber: MR1405611 (97c:68076)
bibdate: Tue Jun 06 17:57:02 1995
bibtimestamp: 1995.06.06 17:57:02 ???
acknowledgement: ack-nhfb
rawauthor: Andr{\'e} Heck
rawtitle: Introduction to {Maple}
ISBN:
0-387-94535-0 (hardcover), 1-4684-0484-9, 1-4684-0486-5 OR 0387945350 (hardcover), 1468404849, 1468404865

ISBN13:
978-0-387-94535-4 (hardcover), 978-1-4684-0484-5, 978-1-4684-0486-9 OR 9780387945354 (hardcover), 9781468404845, 9781468404869

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

abstract:
The first edition of this book has been very well received by the community. The new version 4 of Maple V contains so many new mathematical features and improvements in the user interface that Waterloo Maple Inc. markets it as ``the Power Edition.'' These two facts have made it necessary to write a second edition within a short period of the first. I corrected typographical errors, rephrased text, updated and improved many examples, and added much new material. Hardly any chapter has been left untouched. Substantially changed or added sections and chapters address the assume facility, I/O, approximation theory, integration, composite data types, simplification, graphics, differential equations, and matrix algebra. Tables summarize features, command options, etc., and constitute a quick reference. The enlarged index of the book has been carefully compiled to make locating search items quick and easy. Many new examples have been included showing how to use Maple as a problem solver, how to assist the system during computations, and how to extend its built-in facilities. About the Maple Version Used: The second edition of this book is fully revised and updated to Maple V Release 4. More precisely, the second edition of this book was produced with Maple V Release 4, beta 3 on a SUN SPARCstation 20, Model 71. There should be hardly any difference between this beta version and the final release; only minor differences in the user interface are not excluded.

TOC:
Preface to the Second Edition / v Preface to the First Edition / ix List of Tables / xix 1 Introduction to Computer Algebra / 1 1.1 What is Computer Algebra? / 1 1.2 Computer Algebra Systems / 2 1.3 Some Properties of Computer Algebra Systems / 5 1.4 Advantages of Computer Algebra / 11 1.5 Limitations of Computer Algebra / 24 1.6 Design of Maple / 30 2 The First Steps: Calculus on Numbers / 35 2.1 Getting Started / 35 2.2 Getting Help / 38 2.3 Integers and Rational Numbers / 44 2.4 Irrational Numbers and Floating-Point Numbers / 48 2.5 Algebraic Numbers / 54 2.6 Complex Numbers / 59 2.7 Exercises / 63 3 Variables and Names / 65 3.1 Assignment and Unassignment / 65 3.2 Evaluation / 73 3.3 Names of Variables / 77 3.4 Basic Data Types / 82 3.5 Attributes / 86 3.6 Properties / 87 3.7 Exercises / 92 4 Getting Around with Maple / 95 4.1 Maple Input and Output / 95 4.2 The Maple Library / 101 4.3 Reading and Writing Files / 105 4.4 Importing and Exporting Numerical Data / 110 4.5 Low-Level I/O / 113 4.6 Code Generation / 123 4.7 Changing Maple to Your Own Taste / 129 4.8 Exercises / 133 5 Polynomials and Rational Functions / 135 5.1 Univariate Polynomials / 135 5.2 Multivariate Polynomials / 140 5.3 Rational Functions / 142 5.4 Conversions / 144 5.5 Exercises / 147 6 Internal Data Representation and Substitution / 149 6.1 Internal Representation of Polynomials / 149 6.2 Generalized Rational Expressions / 155 6.3 Substitution / 158 6.4 Exercises / 170 7 Manipulation of Polynomials and Rational Expressions / 173 7.1 Expansion / 173 7.2 Factorization / 176 7.3 Canonical Form and Normal Form / 179 7.4 Normalization / 181 7.5 Collection / 183 7.6 Sorting / 186 7.7 Exercises / 186 8 Functions / 189 8.1 Mathematical Functions / 189 8.2 Arrow Operators / 193 8.3 Piecewise Defined Functions / 195 8.4 Maple Procedures / 202 8.5 Recursive Procedure Definitions / 204 8.6 unapply / 209 8.7 Operations on Functions / 210 8.8 Anonymous Functions / 211 8.9 Exercises / 212 9 Differentiation / 213 9.1 Symbolic Differentiation / 213 9.2 Automatic Differentiation / 221 9.3 Exercises / 224 10 Integration and Summation / 227 10.1 Indefinite Integration / 227 10.2 Definite Integration / 236 10.3 Numerical Integration / 241 10.4 Integral Transforms / 242 10.5 Assisting Maple's Integrator / 252 10.6 Summation / 256 10.7 Exercises / 261 11 Series, Approximation, and Limits / 267 11.1 Truncated Series / 267 11.2 Approximation of Functions / 278 11.3 Power Series / 285 11.4 Limits / 288 11.5 Exercises / 291 12 Composite Data Types / 293 12.1 Sequence / 293 12.2 Set / 296 12.3 List / 298 12.4 Array / 304 12.5 Table / 310 12.6 Last Name Evaluation / 314 12.7 Function Call / 317 12.8 Conversion Between Composite Data Types / 319 12.9 Exercises / 322 13 The Assume Facility / 325 13.1 The Need for an Assume Facility / 325 13.2 Basics of assume / 329 13.3 An Algebra of Properties / 332 13.4 Implementation of assume / 335 13.5 Exercises / 340 13.6 Hierarchy of Properties / 340 14 Simplification / 343 14.1 Automatic Simplification / 344 14.2 expand / 346 14.3 combine / 353 14.4 simplify / 358 14.5 convert / 364 14.6 Trigonometrie Simplification / 367 14.7 Simplification w.r.t. Side Relations / 370 14.8 Control Over Simplification / 374 14.9 Defining Your Own Simplification Routines / 378 14.10 Exercises / 383 14.11 Simplification Chart / 385 15 Graphics / 387 15.1 Some Basic Two-Dimensional Plots / 389 15.2 Options of plot / 393 15.3 The Structure of Two-Dimensional Graphics / 406 15.4 The plottools Package / 412 15.5 Special Two-Dimensional Plots / 416 15.6 Two-Dimensional Geometry / 429 15.7 Plot Aliasing / 432 15.8 A Common Mistake / 433 15.9 Some Basic Three-Dimensional Plots / 434 15.10 Options of plot3d / 436 15.11 The Structure of Three-Dimensional Graphics / 444 15.12 Special Three-Dimensional Plots / 449 15.13 Data Plotting / 457 15.14 Animation / 467 15.15 List of Plot Options / 469 15.16 Exercises / 475 16 Solving Equations / 479 16.1 Equations in One Unknown / 479 16.2 Abbreviations in solve / 480 16.3 Some Difficulties / 481 16.4 Systems of Equations / 488 16.5 The Grobner Basis Method / 499 16.6 Inequalities / 505 16.7 Numerical Solvers / 507 16.8 Other Solvers in Maple / 509 16.9 Exercises / 515 17 Differential Equations / 519 17.1 First Glance at ODEs / 519 17.2 Analytic Solutions / 520 17.3 Taylor Series Method / 532 17.4 Power Series Method / 534 17.5 Numerical Solutions / 536 17.6 DEtools / 548 17.7 Perturbation Methods / 555 17.8 Partial Differential Equations / 567 17.9 Lie Point Symmetries of PDEs / 569 17.10 Exercises / 572 18 Linear Algebra: The linaig Package / 575 18.1 Loading the linaig Package / 575 18.2 Creating New Vectors and Matrices / 576 18.3 Vector and Matrix Arithmetic / 580 18.4 Basic Matrix Functions / 584 18.5 Structural Operations / 589 18.6 Vector Operations / 592 18.7 Standard Forms of Matrices / 592 18.8 Exercises / 597 19 Linear Algebra: Applications / 601 19.1 Kinematics of the Stanford Manipulator / 601 19.2 A Three-Compartment Model of Cadmium Transfer / 606 19.3 Molecular-Orbital Huckel Theory / 618 19.4 Vector Analysis / 623 19.5 Moore--Penrose Inverse / 631 19.6 Exercises / 633 References / 635 Index / 651

rawabstract:
The first edition of this book has been very well received by the community. The new version 4 of Maple V contains so many new mathematical features and improvements in the user interface that Waterloo Maple Inc. markets it as ``the Power Edition.'' These two facts have made it necessary to write a second edition within a short period of the first. I corrected typographical errors, rephrased text, updated and improved many examples, and added much new material. Hardly any chapter has been left untouched. Substantially changed or added sections and chapters address the assume facility, I/O, approximation theory, integration, composite data types, simplification, graphics, differential equations, and matrix algebra. Tables summarize features, command options, etc., and constitute a quick reference. The enlarged index of the book has been carefully compiled to make locating search items quick and easy. Many new examples have been included showing how to use Maple as a problem solver, how to assist the system during computations, and how to extend its built-in facilities. About the Maple Version Used: The second edition of this book is fully revised and updated to Maple V Release 4. More precisely, the second edition of this book was produced with Maple V Release 4, beta 3 on a SUN SPARCstation 20, Model 71. There should be hardly any difference between this beta version and the final release; only minor differences in the user interface are not excluded.

rawTOC:
Preface to the Second Edition / v \\ Preface to the First Edition / ix \\ List of Tables / xix \\ 1 Introduction to Computer Algebra / 1 \\ 1.1 What is Computer Algebra? / 1 \\ 1.2 Computer Algebra Systems / 2 \\ 1.3 Some Properties of Computer Algebra Systems / 5 \\ 1.4 Advantages of Computer Algebra / 11 \\ 1.5 Limitations of Computer Algebra / 24 \\ 1.6 Design of Maple / 30 \\ 2 The First Steps: Calculus on Numbers / 35 \\ 2.1 Getting Started / 35 \\ 2.2 Getting Help / 38 \\ 2.3 Integers and Rational Numbers / 44 \\ 2.4 Irrational Numbers and Floating-Point Numbers / 48 \\ 2.5 Algebraic Numbers / 54 \\ 2.6 Complex Numbers / 59 \\ 2.7 Exercises / 63 \\ 3 Variables and Names / 65 \\ 3.1 Assignment and Unassignment / 65 \\ 3.2 Evaluation / 73 \\ 3.3 Names of Variables / 77 \\ 3.4 Basic Data Types / 82 \\ 3.5 Attributes / 86 \\ 3.6 Properties / 87 \\ 3.7 Exercises / 92 \\ 4 Getting Around with Maple / 95 \\ 4.1 Maple Input and Output / 95 \\ 4.2 The Maple Library / 101 \\ 4.3 Reading and Writing Files / 105 \\ 4.4 Importing and Exporting Numerical Data / 110 \\ 4.5 Low-Level I/O / 113 \\ 4.6 Code Generation / 123 \\ 4.7 Changing Maple to Your Own Taste / 129 \\ 4.8 Exercises / 133 \\ 5 Polynomials and Rational Functions / 135 \\ 5.1 Univariate Polynomials / 135 \\ 5.2 Multivariate Polynomials / 140 \\ 5.3 Rational Functions / 142 \\ 5.4 Conversions / 144 \\ 5.5 Exercises / 147 \\ 6 Internal Data Representation and Substitution / 149 \\ 6.1 Internal Representation of Polynomials / 149 \\ 6.2 Generalized Rational Expressions / 155 \\ 6.3 Substitution / 158 \\ 6.4 Exercises / 170 \\ 7 Manipulation of Polynomials and Rational Expressions / 173 \\ 7.1 Expansion / 173 \\ 7.2 Factorization / 176 \\ 7.3 Canonical Form and Normal Form / 179 \\ 7.4 Normalization / 181 \\ 7.5 Collection / 183 \\ 7.6 Sorting / 186 \\ 7.7 Exercises / 186 \\ 8 Functions / 189 \\ 8.1 Mathematical Functions / 189 \\ 8.2 Arrow Operators / 193 \\ 8.3 Piecewise Defined Functions / 195 \\ 8.4 Maple Procedures / 202 \\ 8.5 Recursive Procedure Definitions / 204 \\ 8.6 unapply / 209 \\ 8.7 Operations on Functions / 210 \\ 8.8 Anonymous Functions / 211 \\ 8.9 Exercises / 212 \\ 9 Differentiation / 213 \\ 9.1 Symbolic Differentiation / 213 \\ 9.2 Automatic Differentiation / 221 \\ 9.3 Exercises / 224 \\ 10 Integration and Summation / 227 \\ 10.1 Indefinite Integration / 227 \\ 10.2 Definite Integration / 236 \\ 10.3 Numerical Integration / 241 \\ 10.4 Integral Transforms / 242 \\ 10.5 Assisting Maple's Integrator / 252 \\ 10.6 Summation / 256 \\ 10.7 Exercises / 261 \\ 11 Series, Approximation, and Limits / 267 \\ 11.1 Truncated Series / 267 \\ 11.2 Approximation of Functions / 278 \\ 11.3 Power Series / 285 \\ 11.4 Limits / 288 \\ 11.5 Exercises / 291 \\ 12 Composite Data Types / 293 \\ 12.1 Sequence / 293 \\ 12.2 Set / 296 \\ 12.3 List / 298 \\ 12.4 Array / 304 \\ 12.5 Table / 310 \\ 12.6 Last Name Evaluation / 314 \\ 12.7 Function Call / 317 \\ 12.8 Conversion Between Composite Data Types / 319 \\ 12.9 Exercises / 322 \\ 13 The Assume Facility / 325 \\ 13.1 The Need for an Assume Facility / 325 \\ 13.2 Basics of assume / 329 \\ 13.3 An Algebra of Properties / 332 \\ 13.4 Implementation of assume / 335 \\ 13.5 Exercises / 340 \\ 13.6 Hierarchy of Properties / 340 \\ 14 Simplification / 343 \\ 14.1 Automatic Simplification / 344 \\ 14.2 expand / 346 \\ 14.3 combine / 353 \\ 14.4 simplify / 358 \\ 14.5 convert / 364 \\ 14.6 Trigonometrie Simplification / 367 \\ 14.7 Simplification w.r.t. Side Relations / 370 \\ 14.8 Control Over Simplification / 374 \\ 14.9 Defining Your Own Simplification Routines / 378 \\ 14.10 Exercises / 383 \\ 14.11 Simplification Chart / 385 \\ 15 Graphics / 387 \\ 15.1 Some Basic Two-Dimensional Plots / 389 \\ 15.2 Options of plot / 393 \\ 15.3 The Structure of Two-Dimensional Graphics / 406 \\ 15.4 The plottools Package / 412 \\ 15.5 Special Two-Dimensional Plots / 416 \\ 15.6 Two-Dimensional Geometry / 429 \\ 15.7 Plot Aliasing / 432 \\ 15.8 A Common Mistake / 433 \\ 15.9 Some Basic Three-Dimensional Plots / 434 \\ 15.10 Options of plot3d / 436 \\ 15.11 The Structure of Three-Dimensional Graphics / 444 \\ 15.12 Special Three-Dimensional Plots / 449 \\ 15.13 Data Plotting / 457 \\ 15.14 Animation / 467 \\ 15.15 List of Plot Options / 469 \\ 15.16 Exercises / 475 \\ 16 Solving Equations / 479 \\ 16.1 Equations in One Unknown / 479 \\ 16.2 Abbreviations in solve / 480 \\ 16.3 Some Difficulties / 481 \\ 16.4 Systems of Equations / 488 \\ 16.5 The Gr{\"o}bner Basis Method / 499 \\ 16.6 Inequalities / 505 \\ 16.7 Numerical Solvers / 507 \\ 16.8 Other Solvers in Maple / 509 \\ 16.9 Exercises / 515 \\ 17 Differential Equations / 519 \\ 17.1 First Glance at ODEs / 519 \\ 17.2 Analytic Solutions / 520 \\ 17.3 Taylor Series Method / 532 \\ 17.4 Power Series Method / 534 \\ 17.5 Numerical Solutions / 536 \\ 17.6 DEtools / 548 \\ 17.7 Perturbation Methods / 555 \\ 17.8 Partial Differential Equations / 567 \\ 17.9 Lie Point Symmetries of PDEs / 569 \\ 17.10 Exercises / 572 \\ 18 Linear Algebra: The linaig Package / 575 \\ 18.1 Loading the linaig Package / 575 \\ 18.2 Creating New Vectors and Matrices / 576 \\ 18.3 Vector and Matrix Arithmetic / 580 \\ 18.4 Basic Matrix Functions / 584 \\ 18.5 Structural Operations / 589 \\ 18.6 Vector Operations / 592 \\ 18.7 Standard Forms of Matrices / 592 \\ 18.8 Exercises / 597 \\ 19 Linear Algebra: Applications / 601 \\ 19.1 Kinematics of the Stanford Manipulator / 601 \\ 19.2 A Three-Compartment Model of Cadmium Transfer / 606 \\ 19.3 Molecular-Orbital H{\"u}ckel Theory / 618 \\ 19.4 Vector Analysis / 623 \\ 19.5 Moore--Penrose Inverse / 631 \\ 19.6 Exercises / 633 \\ References / 635 \\ Index / 651

entry:
@Book{Heck:1996:IM,
  author =       "Andr{\'e} Heck",
  title =        "Introduction to {Maple}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xx + 699",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4684-0484-5",
  ISBN =         "0-387-94535-0 (hardcover), 1-4684-0484-9,
                 1-4684-0486-5",
  ISBN-13 =      "978-0-387-94535-4 (hardcover), 978-1-4684-0484-5,
                 978-1-4684-0486-9",
  LCCN =         "QA155.7.E4H43 1993",
  MRclass =      "65-01, 65B10, 65D18, 65Dxx, 65Fxx, 65Lxx, 68-01,
                 68N15, 68W30, 68NXX",
  MRnumber =     "MR1405611 (97c:68076)",
  bibdate =      "Tue Jun 06 17:57:02 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$39.00",
  abstract =     "The first edition of this book has been very well
                 received by the community. The new version 4 of Maple V
                 contains so many new mathematical features and
                 improvements in the user interface that Waterloo Maple
                 Inc. markets it as ``the Power Edition.'' These two
                 facts have made it necessary to write a second edition
                 within a short period of the first. I corrected
                 typographical errors, rephrased text, updated and
                 improved many examples, and added much new material.
                 Hardly any chapter has been left untouched.
                 Substantially changed or added sections and chapters
                 address the assume facility, I/O, approximation theory,
                 integration, composite data types, simplification,
                 graphics, differential equations, and matrix algebra.
                 Tables summarize features, command options, etc., and
                 constitute a quick reference. The enlarged index of the
                 book has been carefully compiled to make locating
                 search items quick and easy. Many new examples have
                 been included showing how to use Maple as a problem
                 solver, how to assist the system during computations,
                 and how to extend its built-in facilities. About the
                 Maple Version Used: The second edition of this book is
                 fully revised and updated to Maple V Release 4. More
                 precisely, the second edition of this book was produced
                 with Maple V Release 4, beta 3 on a SUN SPARCstation
                 20, Model 71. There should be hardly any difference
                 between this beta version and the final release; only
                 minor differences in the user interface are not
                 excluded.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface to the Second Edition / v \\
                 Preface to the First Edition / ix \\
                 List of Tables / xix \\
                 1 Introduction to Computer Algebra / 1 \\
                 1.1 What is Computer Algebra? / 1 \\
                 1.2 Computer Algebra Systems / 2 \\
                 1.3 Some Properties of Computer Algebra Systems / 5 \\
                 1.4 Advantages of Computer Algebra / 11 \\
                 1.5 Limitations of Computer Algebra / 24 \\
                 1.6 Design of Maple / 30 \\
                 2 The First Steps: Calculus on Numbers / 35 \\
                 2.1 Getting Started / 35 \\
                 2.2 Getting Help / 38 \\
                 2.3 Integers and Rational Numbers / 44 \\
                 2.4 Irrational Numbers and Floating-Point Numbers / 48
                 \\
                 2.5 Algebraic Numbers / 54 \\
                 2.6 Complex Numbers / 59 \\
                 2.7 Exercises / 63 \\
                 3 Variables and Names / 65 \\
                 3.1 Assignment and Unassignment / 65 \\
                 3.2 Evaluation / 73 \\
                 3.3 Names of Variables / 77 \\
                 3.4 Basic Data Types / 82 \\
                 3.5 Attributes / 86 \\
                 3.6 Properties / 87 \\
                 3.7 Exercises / 92 \\
                 4 Getting Around with Maple / 95 \\
                 4.1 Maple Input and Output / 95 \\
                 4.2 The Maple Library / 101 \\
                 4.3 Reading and Writing Files / 105 \\
                 4.4 Importing and Exporting Numerical Data / 110 \\
                 4.5 Low-Level I/O / 113 \\
                 4.6 Code Generation / 123 \\
                 4.7 Changing Maple to Your Own Taste / 129 \\
                 4.8 Exercises / 133 \\
                 5 Polynomials and Rational Functions / 135 \\
                 5.1 Univariate Polynomials / 135 \\
                 5.2 Multivariate Polynomials / 140 \\
                 5.3 Rational Functions / 142 \\
                 5.4 Conversions / 144 \\
                 5.5 Exercises / 147 \\
                 6 Internal Data Representation and Substitution / 149
                 \\
                 6.1 Internal Representation of Polynomials / 149 \\
                 6.2 Generalized Rational Expressions / 155 \\
                 6.3 Substitution / 158 \\
                 6.4 Exercises / 170 \\
                 7 Manipulation of Polynomials and Rational Expressions
                 / 173 \\
                 7.1 Expansion / 173 \\
                 7.2 Factorization / 176 \\
                 7.3 Canonical Form and Normal Form / 179 \\
                 7.4 Normalization / 181 \\
                 7.5 Collection / 183 \\
                 7.6 Sorting / 186 \\
                 7.7 Exercises / 186 \\
                 8 Functions / 189 \\
                 8.1 Mathematical Functions / 189 \\
                 8.2 Arrow Operators / 193 \\
                 8.3 Piecewise Defined Functions / 195 \\
                 8.4 Maple Procedures / 202 \\
                 8.5 Recursive Procedure Definitions / 204 \\
                 8.6 unapply / 209 \\
                 8.7 Operations on Functions / 210 \\
                 8.8 Anonymous Functions / 211 \\
                 8.9 Exercises / 212 \\
                 9 Differentiation / 213 \\
                 9.1 Symbolic Differentiation / 213 \\
                 9.2 Automatic Differentiation / 221 \\
                 9.3 Exercises / 224 \\
                 10 Integration and Summation / 227 \\
                 10.1 Indefinite Integration / 227 \\
                 10.2 Definite Integration / 236 \\
                 10.3 Numerical Integration / 241 \\
                 10.4 Integral Transforms / 242 \\
                 10.5 Assisting Maple's Integrator / 252 \\
                 10.6 Summation / 256 \\
                 10.7 Exercises / 261 \\
                 11 Series, Approximation, and Limits / 267 \\
                 11.1 Truncated Series / 267 \\
                 11.2 Approximation of Functions / 278 \\
                 11.3 Power Series / 285 \\
                 11.4 Limits / 288 \\
                 11.5 Exercises / 291 \\
                 12 Composite Data Types / 293 \\
                 12.1 Sequence / 293 \\
                 12.2 Set / 296 \\
                 12.3 List / 298 \\
                 12.4 Array / 304 \\
                 12.5 Table / 310 \\
                 12.6 Last Name Evaluation / 314 \\
                 12.7 Function Call / 317 \\
                 12.8 Conversion Between Composite Data Types / 319 \\
                 12.9 Exercises / 322 \\
                 13 The Assume Facility / 325 \\
                 13.1 The Need for an Assume Facility / 325 \\
                 13.2 Basics of assume / 329 \\
                 13.3 An Algebra of Properties / 332 \\
                 13.4 Implementation of assume / 335 \\
                 13.5 Exercises / 340 \\
                 13.6 Hierarchy of Properties / 340 \\
                 14 Simplification / 343 \\
                 14.1 Automatic Simplification / 344 \\
                 14.2 expand / 346 \\
                 14.3 combine / 353 \\
                 14.4 simplify / 358 \\
                 14.5 convert / 364 \\
                 14.6 Trigonometrie Simplification / 367 \\
                 14.7 Simplification w.r.t. Side Relations / 370 \\
                 14.8 Control Over Simplification / 374 \\
                 14.9 Defining Your Own Simplification Routines / 378
                 \\
                 14.10 Exercises / 383 \\
                 14.11 Simplification Chart / 385 \\
                 15 Graphics / 387 \\
                 15.1 Some Basic Two-Dimensional Plots / 389 \\
                 15.2 Options of plot / 393 \\
                 15.3 The Structure of Two-Dimensional Graphics / 406
                 \\
                 15.4 The plottools Package / 412 \\
                 15.5 Special Two-Dimensional Plots / 416 \\
                 15.6 Two-Dimensional Geometry / 429 \\
                 15.7 Plot Aliasing / 432 \\
                 15.8 A Common Mistake / 433 \\
                 15.9 Some Basic Three-Dimensional Plots / 434 \\
                 15.10 Options of plot3d / 436 \\
                 15.11 The Structure of Three-Dimensional Graphics / 444
                 \\
                 15.12 Special Three-Dimensional Plots / 449 \\
                 15.13 Data Plotting / 457 \\
                 15.14 Animation / 467 \\
                 15.15 List of Plot Options / 469 \\
                 15.16 Exercises / 475 \\
                 16 Solving Equations / 479 \\
                 16.1 Equations in One Unknown / 479 \\
                 16.2 Abbreviations in solve / 480 \\
                 16.3 Some Difficulties / 481 \\
                 16.4 Systems of Equations / 488 \\
                 16.5 The Gr{\"o}bner Basis Method / 499 \\
                 16.6 Inequalities / 505 \\
                 16.7 Numerical Solvers / 507 \\
                 16.8 Other Solvers in Maple / 509 \\
                 16.9 Exercises / 515 \\
                 17 Differential Equations / 519 \\
                 17.1 First Glance at ODEs / 519 \\
                 17.2 Analytic Solutions / 520 \\
                 17.3 Taylor Series Method / 532 \\
                 17.4 Power Series Method / 534 \\
                 17.5 Numerical Solutions / 536 \\
                 17.6 DEtools / 548 \\
                 17.7 Perturbation Methods / 555 \\
                 17.8 Partial Differential Equations / 567 \\
                 17.9 Lie Point Symmetries of PDEs / 569 \\
                 17.10 Exercises / 572 \\
                 18 Linear Algebra: The linaig Package / 575 \\
                 18.1 Loading the linaig Package / 575 \\
                 18.2 Creating New Vectors and Matrices / 576 \\
                 18.3 Vector and Matrix Arithmetic / 580 \\
                 18.4 Basic Matrix Functions / 584 \\
                 18.5 Structural Operations / 589 \\
                 18.6 Vector Operations / 592 \\
                 18.7 Standard Forms of Matrices / 592 \\
                 18.8 Exercises / 597 \\
                 19 Linear Algebra: Applications / 601 \\
                 19.1 Kinematics of the Stanford Manipulator / 601 \\
                 19.2 A Three-Compartment Model of Cadmium Transfer /
                 606 \\
                 19.3 Molecular-Orbital H{\"u}ckel Theory / 618 \\
                 19.4 Vector Analysis / 623 \\
                 19.5 Moore--Penrose Inverse / 631 \\
                 19.6 Exercises / 633 \\
                 References / 635 \\
                 Index / 651",
}


bibtype: article
filename: fparith.bib
label: Hecker:1996:LGF
author: Chris Hecker
title: Let's get to the (floating) point
journal: Game Developer
volume: 2
pages: 19--24
month: feb
monthnumber: 2
year: 1996
ISSN: 1073-922X OR 1073922X
bibdate: Fri Jan 06 07:46:23 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.06 07:46:23 ???
note: accurate floating-point summation; splitting of floating-point numbers into high and low parts
acknowledgement: ack-nhfb
rawauthor: Chris Hecker
rawnote: accurate floating-point summation; splitting of floating-point numbers into high and low parts
rawtitle: Let's get to the (floating) point
URL:
http://chrishecker.com/images/f/fb/Gdmfp.pdf; https://www.gamasutra.com/php-bin/store.php?item_id=220&category=22&book=

entry:
@Article{Hecker:1996:LGF,
  author =       "Chris Hecker",
  title =        "Let's get to the (floating) point",
  journal =      "Game Developer",
  volume =       "2",
  number =       "??",
  pages =        "19--24",
  month =        feb # "\slash " # mar,
  year =         "1996",
  ISSN =         "1073-922X",
  bibdate =      "Fri Jan 06 07:46:23 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "accurate floating-point summation; splitting of
                 floating-point numbers into high and low parts",
  URL =          "http://chrishecker.com/images/f/fb/Gdmfp.pdf;
                 https://www.gamasutra.com/php-bin/store.php?item_id=220&category=22&book=",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Heikes:1996:DFP
author: Craig Heikes and Glenn Colon-Bonet
title: A Dual Floating Point Coprocessor with an FMAC Architecture
crossref: Wuorinen:1996:DTP
pages: 354--355
year: 1996
bibdate: Fri Jun 24 10:49:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 10:49:14 ???
acknowledgement: ack-nhfb
rawauthor: Craig Heikes and Glenn Colon-Bonet
rawtitle: A Dual Floating Point Coprocessor with an {FMAC} Architecture
entry:
@InProceedings{Heikes:1996:DFP,
  author =       "Craig Heikes and Glenn Colon-Bonet",
  title =        "A Dual Floating Point Coprocessor with an {FMAC}
                 Architecture",
  crossref =     "Wuorinen:1996:DTP",
  pages =        "354--355",
  year =         "1996",
  bibdate =      "Fri Jun 24 10:49:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Heindl:1996:MVC
author: G. Heindl
crossref: Alefeld:1996:SCV
pages: 207--213
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: G. Heindl
title:
A Method for Verified Computing of Inner and Outer Approximations of the Interval Hull of a Tolerance Polyhedron

rawtitle:
A Method for Verified Computing of Inner and Outer Approximations of the Interval Hull of a Tolerance Polyhedron

entry:
@InProceedings{Heindl:1996:MVC,
  author =       "G. Heindl",
  title =        "A Method for Verified Computing of Inner and Outer
                 Approximations of the Interval Hull of a Tolerance
                 Polyhedron",
  crossref =     "Alefeld:1996:SCV",
  pages =        "207--213",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Heinrich:1996:AAF
author: Peter Heinrich
title: Algorithm Alley: a Fast Integer Square Root
journal: j-DDJ
volume: 21
number: 4
pages: 113--114, 130
month: apr
monthnumber: 4
year: 1996
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibsource: http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Peter Heinrich
rawtitle: Algorithm Alley: a Fast Integer Square Root
entry:
@Article{Heinrich:1996:AAF,
  author =       "Peter Heinrich",
  title =        "Algorithm Alley: a Fast Integer Square Root",
  journal =      j-DDJ,
  volume =       "21",
  number =       "4",
  pages =        "113--114, 130",
  month =        apr,
  year =         "1996",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: inproceedings
filename: fparith.bib
label: Herzberger:1996:OCC
author: J. Herzberger
crossref: Alefeld:1996:SCV
pages: 154--159
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: J. Herzberger
title:
On the $R$-Order of Convergence of a Class of Simultaneous Methods for the Inclusions of Polynomial Roots

rawtitle:
On the {$R$}-Order of Convergence of a Class of Simultaneous Methods for the Inclusions of Polynomial Roots

entry:
@InProceedings{Herzberger:1996:OCC,
  author =       "J. Herzberger",
  title =        "On the {$R$}-Order of Convergence of a Class of
                 Simultaneous Methods for the Inclusions of Polynomial
                 Roots",
  crossref =     "Alefeld:1996:SCV",
  pages =        "154--159",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Hickey:1996:FSP
author: Timothy J. Hickey and Qun Ju
title: Fast, Sound, and Precise Narrowing of the Exponential Function
type: Technical report
institution: Computer Science Department, Brandeis University
address: Waltham, MA, USA 02254
pages: 154--159
month: mar
monthnumber: 3
year: 1996
bibdate: Sat Nov 05 15:42:23 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.05 15:42:23 ???
URL: http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz
acknowledgement: ack-nhfb
rawauthor: Timothy J. Hickey and Qun Ju
rawtitle: Fast, Sound, and Precise Narrowing of the Exponential Function
entry:
@TechReport{Hickey:1996:FSP,
  author =       "Timothy J. Hickey and Qun Ju",
  title =        "Fast, Sound, and Precise Narrowing of the Exponential
                 Function",
  type =         "Technical report",
  institution =  "Computer Science Department, Brandeis University",
  address =      "Waltham, MA, USA 02254",
  month =        mar,
  year =         "1996",
  bibdate =      "Sat Nov 05 15:42:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Higham:1996:ASN
author: Nicholas J. Higham
title: Accuracy and Stability of Numerical Algorithms
publisher: pub-SIAM
address: pub-SIAM:adr
pages: xxviii + 688
year: 1996
ISBN: 0-89871-355-2 (paperback) OR 0898713552 (paperback)
ISBN13: 978-0-89871-355-8 (paperback) OR 9780898713558 (paperback)
LCCN: QA297.H53 1996
MRclass: 65Fxx, 15-04, 65-02, 65G50
bibdate: Tue Jan 30 11:01:35 1996
bibtimestamp: 1996.01.30 11:01:35 ???
URL: http://www.ma.man.ac.uk/~higham/asna.html
remark: Typeset with LaTeX 2e.
acknowledgement: ack-njh
rawauthor: Nicholas J. Higham
rawtitle: Accuracy and Stability of Numerical Algorithms
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/texbook2.bib

TOC:
Principles of Finite Precision Computation Relative Error and Significant Digits Sources of Errors Precision Versus Accuracy Backward and Forward Errors Conditioning Cancellation Solving a Quadratic Equation Computing the Sample Variance Solving Linear Equations Accumulation of Rounding Errors Instability Without Cancellation Increasing the Precision Cancellation of Rounding Errors Rounding Errors Can Be Beneficial Stability of an Algorithm Depends on the Problem Rounding Errors Are Not Random Designing Stable Algorithms Misconceptions Rounding Errors in Numerical Analysis Floating Point Arithmetic Floating Point Number System Model of Arithmetic IEEE Arithmetic Aberrant Arithmetics Exact Subtraction Fused Multiply-Add Operation Choice of Base and Distribution of Numbers Statistical Distribution of Rounding Errors Alternative Number Systems Elementary Functions Accuracy Tests Inner and Outer Products The Purpose of Rounding Error Analysis Running Error Analysis Notation for Error Analysis Matrix Multiplication Complex Arithmetic Miscellany Error Analysis Demystified Other Approaches Summation Summation Methods Error Analysis Compensated Summation Other Summation Methods Statistical Estimates of Accuracy Choice of Method Polynomials Horner's Method Evaluating Derivatives The Newton Form and Polynomial Interpolation Matrix Polynomials Norms Vector Norms

rawTOC:
Principles of Finite Precision Computation \\ Relative Error and Significant Digits \\ Sources of Errors \\ Precision Versus Accuracy \\ Backward and Forward Errors \\ Conditioning \\ Cancellation \\ Solving a Quadratic Equation \\ Computing the Sample Variance \\ Solving Linear Equations \\ Accumulation of Rounding Errors \\ Instability Without Cancellation \\ Increasing the Precision \\ Cancellation of Rounding Errors \\ Rounding Errors Can Be Beneficial \\ Stability of an Algorithm Depends on the Problem \\ Rounding Errors Are Not Random \\ Designing Stable Algorithms \\ Misconceptions \\ Rounding Errors in Numerical Analysis \\ Floating Point Arithmetic \\ Floating Point Number System \\ Model of Arithmetic \\ IEEE Arithmetic \\ Aberrant Arithmetics \\ Exact Subtraction \\ Fused Multiply-Add Operation \\ Choice of Base and Distribution of Numbers \\ Statistical Distribution of Rounding Errors \\ Alternative Number Systems \\ Elementary Functions \\ Accuracy Tests \\ Inner and Outer Products \\ The Purpose of Rounding Error Analysis \\ Running Error Analysis \\ Notation for Error Analysis \\ Matrix Multiplication \\ Complex Arithmetic \\ Miscellany \\ Error Analysis Demystified \\ Other Approaches \\ Summation \\ Summation Methods \\ Error Analysis \\ Compensated Summation \\ Other Summation Methods \\ Statistical Estimates of Accuracy \\ Choice of Method \\ Polynomials \\ Horner's Method \\ Evaluating Derivatives \\ The Newton Form and Polynomial Interpolation \\ Matrix Polynomials \\ Norms \\ Vector Norms

entry:
@Book{Higham:1996:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxviii + 688",
  year =         "1996",
  ISBN =         "0-89871-355-2 (paperback)",
  ISBN-13 =      "978-0-89871-355-8 (paperback)",
  LCCN =         "QA297.H53 1996",
  MRclass =      "65Fxx, 15-04, 65-02, 65G50",
  bibdate =      "Tue Jan 30 11:01:35 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$39.00",
  URL =          "http://www.ma.man.ac.uk/~higham/asna.html",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  remark =       "Typeset with \LaTeX2e.",
  tableofcontents = "Principles of Finite Precision Computation \\
                 Relative Error and Significant Digits \\
                 Sources of Errors \\
                 Precision Versus Accuracy \\
                 Backward and Forward Errors \\
                 Conditioning \\
                 Cancellation \\
                 Solving a Quadratic Equation \\
                 Computing the Sample Variance \\
                 Solving Linear Equations \\
                 Accumulation of Rounding Errors \\
                 Instability Without Cancellation \\
                 Increasing the Precision \\
                 Cancellation of Rounding Errors \\
                 Rounding Errors Can Be Beneficial \\
                 Stability of an Algorithm Depends on the Problem \\
                 Rounding Errors Are Not Random \\
                 Designing Stable Algorithms \\
                 Misconceptions \\
                 Rounding Errors in Numerical Analysis \\
                 Floating Point Arithmetic \\
                 Floating Point Number System \\
                 Model of Arithmetic \\
                 IEEE Arithmetic \\
                 Aberrant Arithmetics \\
                 Exact Subtraction \\
                 Fused Multiply-Add Operation \\
                 Choice of Base and Distribution of Numbers \\
                 Statistical Distribution of Rounding Errors \\
                 Alternative Number Systems \\
                 Elementary Functions \\
                 Accuracy Tests \\
                 Inner and Outer Products \\
                 The Purpose of Rounding Error Analysis \\
                 Running Error Analysis \\
                 Notation for Error Analysis \\
                 Matrix Multiplication \\
                 Complex Arithmetic \\
                 Miscellany \\
                 Error Analysis Demystified \\
                 Other Approaches \\
                 Summation \\
                 Summation Methods \\
                 Error Analysis \\
                 Compensated Summation \\
                 Other Summation Methods \\
                 Statistical Estimates of Accuracy \\
                 Choice of Method \\
                 Polynomials \\
                 Horner's Method \\
                 Evaluating Derivatives \\
                 The Newton Form and Polynomial Interpolation \\
                 Matrix Polynomials \\
                 Norms \\
                 Vector Norms",
}


bibtype: article
filename: fparith.bib
label: Hong:1996:NMM
author: Seong-Min Hong and Sang-Yeop Oh and Hyunsoo Yoon
title: New Modular Multiplication Algorithms for Fast Modular Exponentiation
journal: j-LECT-NOTES-COMP-SCI
volume: 1070
pages: 166--??
year: 1996
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Mon Feb 4 12:02:22 MST 2002
bibtimestamp: 2002.02.04 12:02:22 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Seong-Min Hong and Sang-Yeop Oh and Hyunsoo Yoon
rawtitle: New Modular Multiplication Algorithms for Fast Modular Exponentiation
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1070.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1070/10700166.htm; http://link.springer-ny.com/link/service/series/0558/papers/1070/10700166.pdf

entry:
@Article{Hong:1996:NMM,
  author =       "Seong-Min Hong and Sang-Yeop Oh and Hyunsoo Yoon",
  title =        "New Modular Multiplication Algorithms for Fast Modular
                 Exponentiation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1070",
  pages =        "166--??",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Feb 4 12:02:22 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1070.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1070/10700166.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1070/10700166.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Hyvoenen:1996:SCE
author: E. Hyvoenen and S. De Pascale
title: Shared Computations for Efficient Interval Functions Evaluation
crossref: Alefeld:1996:SCV
pages: 38--44
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: E. Hyvoenen and S. De Pascale
rawtitle: Shared Computations for Efficient Interval Functions Evaluation
entry:
@InProceedings{Hyvoenen:1996:SCE,
  author =       "E. Hyvoenen and S. De Pascale",
  title =        "Shared Computations for Efficient Interval Functions
                 Evaluation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "38--44",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Inacio:1996:DDF
author: Christopher Inacio and Denise Ombres
title: The DSP decision: fixed point or floating?
journal: j-IEEE-SPECTRUM
volume: 33
number: 9
pages: 72--74
month: sep
monthnumber: 9
year: 1996
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.535397
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Thu Sep 01 16:15:25 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.09.01 16:15:25 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Christopher Inacio and Denise Ombres
rawtitle: The {DSP} decision: fixed point or floating?
entry:
@Article{Inacio:1996:DDF,
  author =       "Christopher Inacio and Denise Ombres",
  title =        "The {DSP} decision: fixed point or floating?",
  journal =      j-IEEE-SPECTRUM,
  volume =       "33",
  number =       "9",
  pages =        "72--74",
  month =        sep,
  year =         "1996",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.535397",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:15:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
}


bibtype: article
filename: fparith.bib
label: ISO:1996:TRF
author: ISO / IEC JTC1 / SC22 / WG5 --- N1231
title: Technical report for floating-point exception handling
journal: j-FORTRAN-FORUM
volume: 15
number: 3
pages: 1--28
month: dec
monthnumber: 12
year: 1996
ISSN: 1061-7264 (print), 1931-1311 (electronic) OR 10617264 (print), 19311311 (electronic)
ISSNL: 1061-7264 OR 10617264
bibdate: Wed Feb 6 18:50:06 MST 2002
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.06 18:50:06 MST
note: 7th October 1996.
fjournal: ACM Fortran Forum
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/toc.cfm?id=J286
issue: 47
rawauthor: {ISO\slash IEC JTC1\slash SC22\slash WG5 --- N1231}
rawnote: 7th October 1996.
rawtitle: Technical report for floating-point exception handling
entry:
@Article{ISO:1996:TRF,
  author =       "{ISO\slash IEC JTC1\slash SC22\slash WG5 --- N1231}",
  title =        "Technical report for floating-point exception
                 handling",
  journal =      j-FORTRAN-FORUM,
  volume =       "15",
  number =       "3",
  pages =        "1--28",
  month =        dec,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Wed Feb 6 18:50:06 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "7th October 1996.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "47",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}


bibtype: article
filename: fparith.bib
label: Ito:1996:SRI
author: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
title: Square rooting by iterative multiply-additions
journal: j-INFO-PROC-LETT
volume: 60
number: 5
pages: 267--269
day: 8
month: dec
monthnumber: 12
year: 1996
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68M07
MRnumber: 97i:68014
bibdate: Wed Nov 11 12:16:26 MST 1998
bibtimestamp: 1998.11.11 12:16:26 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
corpsource: Department of Inf. Sci., Kyoto University, Japan
journalURL: http://www.sciencedirect.com/science/journal/00200190
treatment: T Theoretical or Mathematical
rawauthor: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
rawtitle: Square rooting by iterative multiply-additions
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
computer arithmetic; convergence of numerical methods; digital arithmetic; iterative methods; iterative multiply-additions; linear converging ratio; multiplicative methods; Newton--Raphson method; read-only storage; ROM sizes; square root algorithm

entry:
@Article{Ito:1996:SRI,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Square rooting by iterative multiply-additions",
  journal =      j-INFO-PROC-LETT,
  volume =       "60",
  number =       "5",
  pages =        "267--269",
  day =          "8",
  month =        dec,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07",
  MRnumber =     "97i:68014",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Inf. Sci., Kyoto University, Japan",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "computer arithmetic; convergence of numerical methods;
                 digital arithmetic; iterative methods; iterative
                 multiply-additions; linear converging ratio;
                 multiplicative methods; Newton--Raphson method;
                 read-only storage; ROM sizes; square root algorithm",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Jayasuriya:1996:MAU
author: Kumara Jayasuriya
title: Multiprecision arithmetic using fast Hartley transforms
journal: j-APPL-MATH-COMP
volume: 75
number: 2--3
pages: 239--251
day: 15
month: mar
monthnumber: 3
year: 1996
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/0096-3003(96)90067-3
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:02:36 MST 2012
bibtimestamp: 2012.11.20 21:02:36 MST
URL: http://www.sciencedirect.com/science/article/pii/0096300396900673
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: Kumara Jayasuriya
rawtitle: Multiprecision arithmetic using fast {Hartley} transforms
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Jayasuriya:1996:MAU,
  author =       "Kumara Jayasuriya",
  title =        "Multiprecision arithmetic using fast {Hartley}
                 transforms",
  journal =      j-APPL-MATH-COMP,
  volume =       "75",
  number =       "2--3",
  pages =        "239--251",
  day =          "15",
  month =        mar,
  year =         "1996",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(96)90067-3",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0096300396900673",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}


bibtype: article
filename: fparith.bib
label: Jessani:1996:FPU
author: R. M. Jessani and C. H. Olson
title: The floating point unit of the PowerPC 603e microprocessor
journal: j-IBM-JRD
volume: 40
number: 5
pages: 559--566
month: sep
monthnumber: 9
year: 1996
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Tue Mar 25 14:26:59 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.03.25 14:26:59 MST
URL: http://www.almaden.ibm.com/journal/rd40-5.html#four
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
corpsource: Somerset Design Center, Motorola Inc., Austin, TX, USA
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
treatment: A Application; P Practical
rawauthor: R. M. Jessani and C. H. Olson
rawtitle: The floating point unit of the {PowerPC 603e} microprocessor
abstract:
The IBM PowerPC 603e* floating-point unit (FPU) is an on-chip functional unit to support IEEE 754 standard single- and double-precision binary floating-point arithmetic operations. The design objectives are to be a low-cost, low-power, high-performance engine in a single-chip superscalar microprocessor. Using less than 15 mm$^2$ of the available silicon area on the chip (the size of the PowerPC 603e microprocessor is 98 mm$^2$) and operating at the peak clock frequency of 100 MHz, an average single-pumping multiply-add-fuse instruction has one-cycle throughput and four-cycle latency. An average double-pumping multiply-add-fuse instruction has two-cycle throughput and five-cycle latency. The estimated performance at 100 MHz is 105 against the SPECfp92** benchmark.

keywords:
add-fuse instruction; design objectives; digital arithmetic; double-pumping multiply-add-fuse; floating point unit; functional unit; IEEE 754 standard; instruction; microprocessor chips; on-chip; peak clock frequency; PowerPC 603e microprocessor; silicon area; single-pumping multiply-

classcodes:
B1265F (Microprocessors and microcomputers); C5130 (Microprocessor chips); C5230 (Digital arithmetic methods)

rawabstract:
The IBM PowerPC 603e* floating-point unit (FPU) is an on-chip functional unit to support IEEE 754 standard single- and double-precision binary floating-point arithmetic operations. The design objectives are to be a low-cost, low-power, high-performance engine in a single-chip superscalar microprocessor. Using less than 15 mm$^2$ of the available silicon area on the chip (the size of the PowerPC 603e microprocessor is 98 mm$^2$) and operating at the peak clock frequency of 100 MHz, an average single-pumping multiply-add-fuse instruction has one-cycle throughput and four-cycle latency. An average double-pumping multiply-add-fuse instruction has two-cycle throughput and five-cycle latency. The estimated performance at 100 MHz is 105 against the SPECfp92** benchmark.

entry:
@Article{Jessani:1996:FPU,
  author =       "R. M. Jessani and C. H. Olson",
  title =        "The floating point unit of the {PowerPC 603e}
                 microprocessor",
  journal =      j-IBM-JRD,
  volume =       "40",
  number =       "5",
  pages =        "559--566",
  month =        sep,
  year =         "1996",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd40-5.html#four",
  abstract =     "The IBM PowerPC 603e* floating-point unit (FPU) is an
                 on-chip functional unit to support IEEE 754 standard
                 single- and double-precision binary floating-point
                 arithmetic operations. The design objectives are to be
                 a low-cost, low-power, high-performance engine in a
                 single-chip superscalar microprocessor. Using less than
                 15 mm$^2$ of the available silicon area on the chip
                 (the size of the PowerPC 603e microprocessor is 98
                 mm$^2$) and operating at the peak clock frequency of
                 100 MHz, an average single-pumping multiply-add-fuse
                 instruction has one-cycle throughput and four-cycle
                 latency. An average double-pumping multiply-add-fuse
                 instruction has two-cycle throughput and five-cycle
                 latency. The estimated performance at 100 MHz is 105
                 against the SPECfp92** benchmark.",
  acknowledgement = ack-nhfb,
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Somerset Design Center, Motorola Inc., Austin, TX,
                 USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "add-fuse instruction; design objectives; digital
                 arithmetic; double-pumping multiply-add-fuse; floating
                 point unit; functional unit; IEEE 754 standard;
                 instruction; microprocessor chips; on-chip; peak clock
                 frequency; PowerPC 603e microprocessor; silicon area;
                 single-pumping multiply-",
  treatment =    "A Application; P Practical",
  xxlibnote =    "Issue missing from UofUtah Marriott Library",
}


bibtype: inproceedings
filename: fparith.bib
label: Jullien:1996:VDS
author: Graham A. Jullien
title: VLSI Digital Signal Processing: Some Arithmetic Issues
crossref: Luk:1996:PSC
pages: 1--13
year: 1996
DOI: https://doi.org/10.1117/12.255423
bibdate: Tue Jun 14 18:18:32 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:18:32 ???
URL: http://www.atips.ca/research/documents/ca/aa/1996_keynote.pdf
remark: Keynote address: VLSI Arithmetic and DSP Implementations.
acknowledgement: ack-nhfb
rawauthor: Graham A. Jullien
rawtitle: {VLSI} Digital Signal Processing: Some Arithmetic Issues
entry:
@InProceedings{Jullien:1996:VDS,
  author =       "Graham A. Jullien",
  title =        "{VLSI} Digital Signal Processing: Some Arithmetic
                 Issues",
  crossref =     "Luk:1996:PSC",
  pages =        "1--13",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255423",
  bibdate =      "Tue Jun 14 18:18:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.atips.ca/research/documents/ca/aa/1996_keynote.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Keynote address: VLSI Arithmetic and DSP
                 Implementations.",
}


bibtype: misc
filename: fparith.bib
label: Kahan:1996:BEC
author: W. Kahan
title: The baleful effect of computer benchmarks upon applied mathematics, physics, and chemistry
pages: 1--13
year: 1996
bibdate: Sat Apr 28 18:52:17 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 18:52:17 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/baleful.ps
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: W. Kahan
rawtitle: The baleful effect of computer benchmarks upon applied mathematics, physics, and chemistry
entry:
@Misc{Kahan:1996:BEC,
  author =       "W. Kahan",
  title =        "The baleful effect of computer benchmarks upon applied
                 mathematics, physics, and chemistry",
  howpublished = "World-Wide Web document.",
  year =         "1996",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/baleful.ps",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Kahan:1996:LNS
author: W. Kahan
title: Lecture notes on the status of IEEE Standard 754 for binary floating-point arithmetic
pages: 1--13
year: 1996
bibdate: Sat Apr 28 18:52:17 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 18:52:17 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: W. Kahan
rawtitle: Lecture notes on the status of {IEEE Standard 754} for binary floating-point arithmetic
entry:
@Misc{Kahan:1996:LNS,
  author =       "W. Kahan",
  title =        "Lecture notes on the status of {IEEE Standard 754} for
                 binary floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  year =         "1996",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps",
  acknowledgement = ack-nhfb,
}


bibtype: unpublished
filename: fparith.bib
label: Kahan:1996:WCY
author: W. Kahan
title: What can you learn about floating-point arithmetic in one hour?
institution: inst-BERKELEY-EECS
address: inst-BERKELEY-EECS:adr
pages: 23
year: 1996
bibdate: Mon Apr 25 17:58:22 2005
bibtimestamp: 2005.04.25 17:58:22 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/cs267fp.ps
acknowledgement: ack-nhfb
key: Kah96a
rawauthor: W. Kahan
rawtitle: What can you learn about floating-point arithmetic in one hour?
note:
Postscript version accessible electronically at path =http://http.cs.berkeley.edu/~wkahan/ieee754status=.

rawnote:
Postscript version accessible electronically at \path=http://http.cs.berkeley.edu/~wkahan/ieee754status=.

entry:
@Unpublished{Kahan:1996:WCY,
  author =       "W. Kahan",
  key =          "Kah96a",
  title =        "What can you learn about floating-point arithmetic in
                 one hour?",
  institution =  inst-BERKELEY-EECS,
  address =      inst-BERKELEY-EECS:adr,
  pages =        "23",
  year =         "1996",
  bibdate =      "Mon Apr 25 17:58:22 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Postscript version accessible electronically at
                 \path=http://http.cs.berkeley.edu/~wkahan/ieee754status=.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/cs267fp.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kalantari:1996:HOI
author: B. Kalantari and I. Kalantari
title: High order iterative methods for approximating square roots
journal: j-BIT-NUM-MATH
volume: 36
number: 2
pages: 395--399
month: jun
monthnumber: 6
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01731991
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D15 (65H99)
MRnumber: 97k:65039
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: B. Kalantari and I. Kalantari
rawtitle: High order iterative methods for approximating square roots
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395

entry:
@Article{Kalantari:1996:HOI,
  author =       "B. Kalantari and I. Kalantari",
  title =        "High order iterative methods for approximating square
                 roots",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "395--399",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731991",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D15 (65H99)",
  MRnumber =     "97k:65039",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: fparith.bib
label: Kalliojarvi:1996:REB
author: K. Kalliojarvi and J. Astola
title: Roundoff errors in block-floating-point systems
journal: j-IEEE-TRANS-SIG-PROC
volume: 44
number: 4
pages: 783--790
month: apr
monthnumber: 4
year: 1996
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
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 Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: K. Kalliojarvi and J. Astola
rawtitle: Roundoff errors in block-floating-point systems
entry:
@Article{Kalliojarvi:1996:REB,
  author =       "K. Kalliojarvi and J. Astola",
  title =        "Roundoff errors in block-floating-point systems",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "44",
  number =       "4",
  pages =        "783--790",
  month =        apr,
  year =         "1996",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  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 Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "Block-floating-point representation is a special case
                 of floating-point representation, where several numbers
                 have a joint exponent term. In this paper, roundoff
                 errors in signal processing systems utilizing
                 block-floating-point representation are \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Kane:1996:PRA
author: Gerry Kane
title: PA-RISC 2.0 Architecture
publisher: pub-PHPTR
address: pub-PHPTR:adr
pages: various
year: 1996
ISBN: 0-13-182734-0 OR 0131827340
ISBN13: 978-0-13-182734-9 OR 9780131827349
LCCN: QA76.8.H48K36 1996
bibdate: Tue Jan 09 12:34:37 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 2001.01.09 12:34:37 ???
keywords: Hewlett--Packard computers; PA-RISC microprocessors
acknowledgement: ack-nhfb
rawauthor: Gerry Kane
rawtitle: {PA-RISC 2.0} Architecture
URL:
http://devresource.hp.com/devresource/Docs/Refs/PA2_0/index.html; http://devresource.hp.com/devresource/Docs/Refs/PA2_0/updates/index.html

abstract:
This is the authoritative definition of Hewlett-Packard's 2.0 PA-RISC architecture, one of the most mature and efficient RISC (Reduced Instruction Set Computer) processor architectures in the industry. PA-RISC is the foundation for machines proving especially well-suited for such markets as high performance graphics, mission critical transaction processing, and emerging multimedia applications such as interactive video services.

TOC:
1: Overview 2: Processing Resources 3: Addressing and Access Control 4: Control Flow 5: Interruptions 6: Instruction Set Overview 7: Instruction Descriptions 8: Floating-point Coprocessor 9: Floating-Point Instruction Set 10: Floating-Point Exceptions 11: Performance Monitor Coprocessor B: Instruction Formats C: Operation Codes D: Conditions E: Instruction Notation Control Structures F: TLB and Cache Control G: Memory Ordering Model H: Address Formation Details I: Programming Notes PA-RISC 2 Instruction Completers and Pseudo-Ops

rawabstract:
This is the authoritative definition of Hewlett-Packard's 2.0 PA-RISC architecture, one of the most mature and efficient RISC (Reduced Instruction Set Computer) processor architectures in the industry. PA-RISC is the foundation for machines proving especially well-suited for such markets as high performance graphics, mission critical transaction processing, and emerging multimedia applications such as interactive video services.

rawTOC:
1: Overview \\ 2: Processing Resources \\ 3: Addressing and Access Control \\ 4: Control Flow \\ 5: Interruptions \\ 6: Instruction Set Overview \\ 7: Instruction Descriptions \\ 8: Floating-point Coprocessor \\ 9: Floating-Point Instruction Set \\ 10: Floating-Point Exceptions \\ 11: Performance Monitor Coprocessor \\ B: Instruction Formats \\ C: Operation Codes \\ D: Conditions \\ E: Instruction Notation Control Structures \\ F: TLB and Cache Control \\ G: Memory Ordering Model \\ H: Address Formation Details \\ I: Programming Notes \\ PA-RISC 2 Instruction Completers and Pseudo-Ops

entry:
@Book{Kane:1996:PRA,
  author =       "Gerry Kane",
  title =        "{PA-RISC 2.0} Architecture",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "various",
  year =         "1996",
  ISBN =         "0-13-182734-0",
  ISBN-13 =      "978-0-13-182734-9",
  LCCN =         "QA76.8.H48K36 1996",
  bibdate =      "Tue Jan 09 12:34:37 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$34.40",
  URL =          "http://devresource.hp.com/devresource/Docs/Refs/PA2_0/index.html;
                 http://devresource.hp.com/devresource/Docs/Refs/PA2_0/updates/index.html",
  abstract =     "This is the authoritative definition of
                 Hewlett-Packard's 2.0 PA-RISC architecture, one of the
                 most mature and efficient RISC (Reduced Instruction Set
                 Computer) processor architectures in the industry.
                 PA-RISC is the foundation for machines proving
                 especially well-suited for such markets as high
                 performance graphics, mission critical transaction
                 processing, and emerging multimedia applications such
                 as interactive video services.",
  acknowledgement = ack-nhfb,
  keywords =     "Hewlett--Packard computers; PA-RISC microprocessors",
  tableofcontents = "1: Overview \\
                 2: Processing Resources \\
                 3: Addressing and Access Control \\
                 4: Control Flow \\
                 5: Interruptions \\
                 6: Instruction Set Overview \\
                 7: Instruction Descriptions \\
                 8: Floating-point Coprocessor \\
                 9: Floating-Point Instruction Set \\
                 10: Floating-Point Exceptions \\
                 11: Performance Monitor Coprocessor \\
                 B: Instruction Formats \\
                 C: Operation Codes \\
                 D: Conditions \\
                 E: Instruction Notation Control Structures \\
                 F: TLB and Cache Control \\
                 G: Memory Ordering Model \\
                 H: Address Formation Details \\
                 I: Programming Notes \\
                 PA-RISC 2 Instruction Completers and Pseudo-Ops",
}


bibtype: article
filename: fparith.bib
label: Katti:1996:NRA
author: Rajendra S. Katti
title: A new residue arithmetic error correction scheme
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 1
pages: 13--19
month: jan
monthnumber: 1
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.481482
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 68M07
MRnumber: MR1372160 (96j:68011)
bibdate: Wed Jul 6 19:47:08 MDT 2011
bibtimestamp: 2011.07.06 19:47:08 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=481482
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Rajendra S. Katti
rawtitle: A new residue arithmetic error correction scheme
entry:
@Article{Katti:1996:NRA,
  author =       "Rajendra S. Katti",
  title =        "A new residue arithmetic error correction scheme",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "1",
  pages =        "13--19",
  month =        jan,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.481482",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07",
  MRnumber =     "MR1372160 (96j:68011)",
  bibdate =      "Wed Jul 6 19:47:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=481482",
  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: Kearfott:1996:OPI
author: R. B. Kearfott and X. Shi
title: Optimal Preconditioners for Interval Gauss--Seidel Methods
crossref: Alefeld:1996:SCV
pages: 173--178
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: R. B. Kearfott and X. Shi
rawtitle: Optimal Preconditioners for Interval {Gauss--Seidel} Methods
entry:
@InProceedings{Kearfott:1996:OPI,
  author =       "R. B. Kearfott and X. Shi",
  title =        "Optimal Preconditioners for Interval {Gauss--Seidel}
                 Methods",
  crossref =     "Alefeld:1996:SCV",
  pages =        "173--178",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kearfott:1996:TNS
author: R. B. Kearfott
crossref: Alefeld:1996:SCV
pages: 160--172
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: R. B. Kearfott
title:
Treating Non-Smooth Functions as Smooth Functions in Global Optimization and Nonlinear Systems Solvers

rawtitle:
Treating Non-Smooth Functions as Smooth Functions in Global Optimization and Nonlinear Systems Solvers

entry:
@InProceedings{Kearfott:1996:TNS,
  author =       "R. B. Kearfott",
  title =        "Treating Non-Smooth Functions as Smooth Functions in
                 Global Optimization and Nonlinear Systems Solvers",
  crossref =     "Alefeld:1996:SCV",
  pages =        "160--172",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Koeber:1996:IIF
author: M. Koeber
title: Inclusion of the Inverse of a Functions in $n$ Variables
crossref: Alefeld:1996:SCV
pages: 179--185
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. Koeber
rawtitle: Inclusion of the Inverse of a Functions in $n$ Variables
entry:
@InProceedings{Koeber:1996:IIF,
  author =       "M. Koeber",
  title =        "Inclusion of the Inverse of a Functions in $n$
                 Variables",
  crossref =     "Alefeld:1996:SCV",
  pages =        "179--185",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kowaleski:1996:DEP
title: A dual execution pipelined floating-point CMOS processor
crossref: Wuorinen:1996:DTP
pages: 358--359
year: 1996
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawtitle: A dual execution pipelined floating-point {CMOS} processor
author:
J. A. Kowaleski and G. M. Wolrich and T. C. Fischer and R. J. Dupcak and P. L. Kroesen and T. Pham and A. Olesin

rawauthor:
J. A. Kowaleski and G. M. Wolrich and T. C. Fischer and R. J. Dupcak and P. L. Kroesen and T. Pham and A. Olesin

entry:
@InProceedings{Kowaleski:1996:DEP,
  author =       "J. A. Kowaleski and G. M. Wolrich and T. C. Fischer
                 and R. J. Dupcak and P. L. Kroesen and T. Pham and A.
                 Olesin",
  title =        "A dual execution pipelined floating-point {CMOS}
                 processor",
  crossref =     "Wuorinen:1996:DTP",
  pages =        "358--359",
  year =         "1996",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kraemer:1996:CNI
author: W. Kraemer and S. Wedner
title: Computing Narrow Inclusions for Cauchy Principal Value Integrals
crossref: Alefeld:1996:SCV
pages: 45--51
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: W. Kraemer and S. Wedner
rawtitle: Computing Narrow Inclusions for {Cauchy} Principal Value Integrals
entry:
@InProceedings{Kraemer:1996:CNI,
  author =       "W. Kraemer and S. Wedner",
  title =        "Computing Narrow Inclusions for {Cauchy} Principal
                 Value Integrals",
  crossref =     "Alefeld:1996:SCV",
  pages =        "45--51",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kreinovich:1996:CCI
author: V. Kreinovich and A. Lakeyev and J. Rohn
crossref: Alefeld:1996:SCV
pages: 293--306
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: V. Kreinovich and A. Lakeyev and J. Rohn
title:
Computational Complexity of Interval Algebraic Problems: Some Are Feasible and Some Are Computationally Intractable --- a Survey

rawtitle:
Computational Complexity of Interval Algebraic Problems: Some Are Feasible and Some Are Computationally Intractable --- a Survey

entry:
@InProceedings{Kreinovich:1996:CCI,
  author =       "V. Kreinovich and A. Lakeyev and J. Rohn",
  title =        "Computational Complexity of Interval Algebraic
                 Problems: Some Are Feasible and Some Are
                 Computationally Intractable --- a Survey",
  crossref =     "Alefeld:1996:SCV",
  pages =        "293--306",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ley:1996:PDU
author: Eduardo Ley
title: On the Peculiar Distribution of the U.S. Stock Indexes' Digits
journal: j-AMER-STAT
volume: 50
number: 4
pages: 311--313
month: nov
monthnumber: 11
year: 1996
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Mon Nov 14 15:09:04 2011
bibtimestamp: 2011.11.14 15:09:04 ???
URL: http://www.jstor.org/stable/2684926
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: Eduardo Ley
rawtitle: On the Peculiar Distribution of the {U.S.} Stock Indexes' Digits
bibsource:
https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Ley:1996:PDU,
  author =       "Eduardo Ley",
  title =        "On the Peculiar Distribution of the {U.S.} Stock
                 Indexes' Digits",
  journal =      j-AMER-STAT,
  volume =       "50",
  number =       "4",
  pages =        "311--313",
  month =        nov,
  year =         "1996",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Nov 14 15:09:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2684926",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: inproceedings
filename: fparith.bib
label: Li:1996:NNR
author: Yamin Li and Wanming Chu
title: A new non-restoring square root algorithm and its VLSI implementations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 538--544
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Yamin Li and Wanming Chu
rawtitle: A new non-restoring square root algorithm and its {VLSI} implementations
booktitle:
Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '96

rawbooktitle:
Proceedings of the {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors: {ICCD '96}

entry:
@InProceedings{Li:1996:NNR,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD '96}",
  title =        "A new non-restoring square root algorithm and its
                 {VLSI} implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "538--544",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a new non-restoring square root algorithm
                 that is very efficient to implement. The new algorithm
                 presented here has the following features unlike other
                 square root algorithms. First, the focus of the
                 ``non-restoring'' is on the {\&} \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Lions:1996:AFF
title: Ariane 5 Flight 501 failure, report by the Inquiry Board
type: Technical Report
institution: European Space Agency
address: Paris, France
pages: 538--544
year: 1996
bibdate: Sat Apr 01 07:39:11 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2017.04.01 07:39:11 ???
URL: http://sunnyday.mit.edu/accidents/Ariane5accidentreport.html
acknowledgement: ack-nhfb
rawtitle: {Ariane 5 Flight 501} failure, report by the {Inquiry Board}
author:
Jacques-Louis Lions and Mauro Balduccini and Yvan Choquer and Remy Hergott and Bernard Humbert and Eric Lefort

note:
From the foreword: ``On 4 June 1996, the maiden flight of the Ariane 5 launcher ended in a failure. Only about 40 seconds after initiation of the flight sequence, at an altitude of about 3700 m, the launcher veered off its flight path, broke up and exploded. Engineers from the Ariane 5 project teams of CNES and Industry immediately started to investigate the failure.'' From the report: ``The internal SRI software exception was caused during execution of a data conversion from 64-bit floating point to 16-bit signed integer value. The floating point number which was converted had a value greater than what could be represented by a 16-bit signed integer. This resulted in an Operand Error. The data conversion instructions (in Ada code) were not protected from causing an Operand Error, although other conversions of comparable variables in the same place in the code were protected.''

remark:
Report of an arithmetic error that put an expensive space missile off course, requiring its destruction in the air. Presumably-reliable code in Ada adapted from an earlier missile generated had not been updated for the new design.

rawauthor:
Jacques-Louis Lions and Mauro Balduccini and Yvan Choquer and Remy Hergott and Bernard Humbert and Eric Lefort

rawnote:
From the foreword: ``On 4 June 1996, the maiden flight of the Ariane 5 launcher ended in a failure. Only about 40 seconds after initiation of the flight sequence, at an altitude of about 3700 m, the launcher veered off its flight path, broke up and exploded. Engineers from the Ariane 5 project teams of CNES and Industry immediately started to investigate the failure.'' From the report: ``The internal SRI software exception was caused during execution of a data conversion from 64-bit floating point to 16-bit signed integer value. The floating point number which was converted had a value greater than what could be represented by a 16-bit signed integer. This resulted in an Operand Error. The data conversion instructions (in Ada code) were not protected from causing an Operand Error, although other conversions of comparable variables in the same place in the code were protected.''

entry:
@TechReport{Lions:1996:AFF,
  author =       "Jacques-Louis Lions and Mauro Balduccini and Yvan
                 Choquer and Remy Hergott and Bernard Humbert and Eric
                 Lefort",
  title =        "{Ariane 5 Flight 501} failure, report by the {Inquiry
                 Board}",
  type =         "Technical Report",
  institution =  "European Space Agency",
  address =      "Paris, France",
  year =         "1996",
  bibdate =      "Sat Apr 01 07:39:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the foreword: ``On 4 June 1996, the maiden flight
                 of the Ariane 5 launcher ended in a failure. Only about
                 40 seconds after initiation of the flight sequence, at
                 an altitude of about 3700 m, the launcher veered off
                 its flight path, broke up and exploded. Engineers from
                 the Ariane 5 project teams of CNES and Industry
                 immediately started to investigate the failure.'' From
                 the report: ``The internal SRI software exception was
                 caused during execution of a data conversion from
                 64-bit floating point to 16-bit signed integer value.
                 The floating point number which was converted had a
                 value greater than what could be represented by a
                 16-bit signed integer. This resulted in an Operand
                 Error. The data conversion instructions (in Ada code)
                 were not protected from causing an Operand Error,
                 although other conversions of comparable variables in
                 the same place in the code were protected.''",
  URL =          "http://sunnyday.mit.edu/accidents/Ariane5accidentreport.html",
  acknowledgement = ack-nhfb,
  remark =       "Report of an arithmetic error that put an expensive
                 space missile off course, requiring its destruction in
                 the air. Presumably-reliable code in Ada adapted from
                 an earlier missile generated had not been updated for
                 the new design.",
}


bibtype: article
filename: fparith.bib
label: Lo:1996:CBC
author: Jien-Chung Lo and S. Thanawastien and T. R. N. Rao
title: Correction to ``Berger Check Prediction for Array Multipliers and Array Dividers''
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 383--383
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1996.485579
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:10 MDT 2011
bibtimestamp: 2011.07.06 19:47:10 MDT
note: See cite Lo:1993:BCP.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485579
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jien-Chung Lo and S. Thanawastien and T. R. N. Rao
rawnote: See \cite{Lo:1993:BCP}.
rawtitle: Correction to {``Berger Check Prediction for Array Multipliers and Array Dividers''}
entry:
@Article{Lo:1996:CBC,
  author =       "Jien-Chung Lo and S. Thanawastien and T. R. N. Rao",
  title =        "Correction to {``Berger Check Prediction for Array
                 Multipliers and Array Dividers''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "383--383",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1996.485579",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Lo:1993:BCP}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485579",
  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: Louca:1996:IIS
author: L. Louca and T. A. Cook and W. H. Johnson
title: Implementation of IEEE single precision floating point addition and multiplication on FPGAs
crossref: Pocek:1996:ISF
pages: 107--116
year: 1996
DOI: https://doi.org/10.1109/FPGA.1996.564761
bibdate: Sat Oct 9 12:52:57 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.09 12:52:57 ???
acknowledgement: ack-nhfb
rawauthor: L. Louca and T. A. Cook and W. H. Johnson
rawtitle: Implementation of {IEEE} single precision floating point addition and multiplication on {FPGAs}
abstract:
Floating point operations are hard to implement on FPGAs because of the complexity of their algorithms. On the other hand, many scientific problems require floating point arithmetic with high levels of accuracy in their calculations. Therefore, we have explored FPGA implementations of addition and multiplication for IEEE single precision floating-point numbers. Customizations were performed where this was possible in order to save chip area, or get the most out of our prototype board. The implementations tradeoff area and speed for accuracy. The adder is a bit-parallel adder, and the multiplier is a digit-serial multiplier. Prototypes have been implemented on Altera FLEX8000s, and peak rates of 7 MFlops for 32-bit addition and 2.3 MFlops for 32-bit multiplication have been obtained.

rawabstract:
Floating point operations are hard to implement on FPGAs because of the complexity of their algorithms. On the other hand, many scientific problems require floating point arithmetic with high levels of accuracy in their calculations. Therefore, we have explored FPGA implementations of addition and multiplication for IEEE single precision floating-point numbers. Customizations were performed where this was possible in order to save chip area, or get the most out of our prototype board. The implementations tradeoff area and speed for accuracy. The adder is a bit-parallel adder, and the multiplier is a digit-serial multiplier. Prototypes have been implemented on Altera FLEX8000s, and peak rates of 7 MFlops for 32-bit addition and 2.3 MFlops for 32-bit multiplication have been obtained.

entry:
@InProceedings{Louca:1996:IIS,
  author =       "L. Louca and T. A. Cook and W. H. Johnson",
  title =        "Implementation of {IEEE} single precision floating
                 point addition and multiplication on {FPGAs}",
  crossref =     "Pocek:1996:ISF",
  pages =        "107--116",
  year =         "1996",
  DOI =          "https://doi.org/10.1109/FPGA.1996.564761",
  bibdate =      "Sat Oct 9 12:52:57 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point operations are hard to implement on
                 FPGAs because of the complexity of their algorithms. On
                 the other hand, many scientific problems require
                 floating point arithmetic with high levels of accuracy
                 in their calculations. Therefore, we have explored FPGA
                 implementations of addition and multiplication for IEEE
                 single precision floating-point numbers. Customizations
                 were performed where this was possible in order to save
                 chip area, or get the most out of our prototype board.
                 The implementations tradeoff area and speed for
                 accuracy. The adder is a bit-parallel adder, and the
                 multiplier is a digit-serial multiplier. Prototypes
                 have been implemented on Altera FLEX8000s, and peak
                 rates of 7 MFlops for 32-bit addition and 2.3 MFlops
                 for 32-bit multiplication have been obtained.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Lozier:1996:EBL
author: Daniel W. Lozier and P. R. Turner
title: Error-Bounding in Level-Index Computer Arithmetic
crossref: Alefeld:1996:NME
pages: 138--145
year: 1996
bibdate: Fri Jul 09 07:20:57 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.07.09 07:20:57 ???
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/oldenburg95.ps.Z
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier and P. R. Turner
rawtitle: Error-Bounding in Level-Index Computer Arithmetic
entry:
@InProceedings{Lozier:1996:EBL,
  author =       "Daniel W. Lozier and P. R. Turner",
  title =        "Error-Bounding in Level-Index Computer Arithmetic",
  crossref =     "Alefeld:1996:NME",
  pages =        "138--145",
  year =         "1996",
  bibdate =      "Fri Jul 09 07:20:57 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/oldenburg95.ps.Z",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Luther:1996:CAG
author: W. Luther and W. Otten
title: The Complex Arithmetic-Geometric Mean and Multiple-Precision Matrix Functions
crossref: Alefeld:1996:SCV
pages: 52--58
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: W. Luther and W. Otten
rawtitle: The Complex Arithmetic-Geometric Mean and Multiple-Precision Matrix Functions
entry:
@InProceedings{Luther:1996:CAG,
  author =       "W. Luther and W. Otten",
  title =        "The Complex Arithmetic-Geometric Mean and
                 Multiple-Precision Matrix Functions",
  crossref =     "Alefeld:1996:SCV",
  pages =        "52--58",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: MacDonald:1996:NSS
author: D. A. MacDonald
title: A note on the summation of slowly convergent alternating series
journal: j-BIT-NUM-MATH
volume: 36
number: 4
pages: 766--774
month: dec
monthnumber: 12
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01733790
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 40A25 (65B10 65B15)
MRnumber: 98c:40001
MRreviewer: Vanna Zanelli
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: D. A. MacDonald
rawtitle: A note on the summation of slowly convergent alternating series
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&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.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=4&spage=766

abstract:
The kth term of the infinite series $ sum nolimits _k = 0^infty ( - 1)^k [ln (k + 2)]^ - 0.1 $ is larger than $ 0.5 $ whenever $ k < k_0 $, where $ k_0 + 1 = e^1024 $. To sum this series correct to order $ 10^-1 $ using direct summation seems an impossible task, notwithstanding the power of modern computers. This note will present an alternative approach to those classical methods (the Euler transformation is one) which can accurately sum such series. The theory to be presented has the added advantage of providing accurate bounds for the error in the approximate result. The method used will be Euler--Maclaurin summation, revitalised by computer algebra.

keywords:
accurate floating-point summation; Euler--Maclaurin formula; slowly convergent alternating series; summation

rawabstract:
The kth term of the infinite series $ \sum \nolimits_{k = 0}^\infty {( - 1)^k [\ln (k + 2)]^{ - 0.1} } $ is larger than $ 0.5 $ whenever $ k < k_0 $, where $ k_0 + 1 = e^{1024} $. To sum this series correct to order $ 10^{-1} $ using direct summation seems an impossible task, notwithstanding the power of modern computers. This note will present an alternative approach to those classical methods (the Euler transformation is one) which can accurately sum such series. The theory to be presented has the added advantage of providing accurate bounds for the error in the approximate result. The method used will be Euler--Maclaurin summation, revitalised by computer algebra.

entry:
@Article{MacDonald:1996:NSS,
  author =       "D. A. MacDonald",
  title =        "A note on the summation of slowly convergent
                 alternating series",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "4",
  pages =        "766--774",
  month =        dec,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01733790",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "40A25 (65B10 65B15)",
  MRnumber =     "98c:40001",
  MRreviewer =   "Vanna Zanelli",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&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.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=4&spage=766",
  abstract =     "The kth term of the infinite series $ \sum
                 \nolimits_{k = 0}^\infty {( - 1)^k [\ln (k + 2)]^{ -
                 0.1} } $ is larger than $ 0.5 $ whenever $ k < k_0 $,
                 where $ k_0 + 1 = e^{1024} $. To sum this series
                 correct to order $ 10^{-1} $ using direct summation
                 seems an impossible task, notwithstanding the power of
                 modern computers. This note will present an alternative
                 approach to those classical methods (the Euler
                 transformation is one) which can accurately sum such
                 series. The theory to be presented has the added
                 advantage of providing accurate bounds for the error in
                 the approximate result. The method used will be
                 Euler--Maclaurin summation, revitalised by computer
                 algebra.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; Euler--Maclaurin
                 formula; slowly convergent alternating series;
                 summation",
}


bibtype: article
filename: fparith.bib
label: Macpherson:1996:RAP
author: George W. Macpherson
title: A reusable Ada package for scientific dimensional integrity
journal: j-SIGADA-LETTERS
volume: 16
number: 3
pages: 56--69
month: may
monthnumber: 5
year: 1996
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:57 MDT 2003
bibtimestamp: 2003.08.09 09:05:57 MDT
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
corpsource: CACI Inc.-Federal, Colorado Springs, CO, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: George W. Macpherson
rawtitle: A reusable {Ada} package for scientific dimensional integrity
keywords:
Ada; Ada programming language; arithmetic operations; ASSIGN function; checking; computational reliability; data integrity; declaration; digital arithmetic; entries; exponents; floating point numeric value; fundamental physical units; generic package; information hiding; integer; length; limited private; mass; multiplication operation; numeric; operator; overloading; PHYSICAL QUANTITY type; physics computing; relational operations; reusability; reusable Ada package; scientific dimensional integrity; software; software modifiability; software packages; software reliability; software reusability; strong typing; symbol creation; time; types; units; units (measurement); values; variables

classcodes:
A0650M (Computing devices and techniques); A0620F (Measurement units); C7320 (Physics and chemistry computing); C6130 (Data handling techniques); C5230 (Digital arithmetic methods)

entry:
@Article{Macpherson:1996:RAP,
  author =       "George W. Macpherson",
  title =        "A reusable {Ada} package for scientific dimensional
                 integrity",
  journal =      j-SIGADA-LETTERS,
  volume =       "16",
  number =       "3",
  pages =        "56--69",
  month =        may # "\slash " # jun,
  year =         "1996",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:57 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "A0650M (Computing devices and techniques); A0620F
                 (Measurement units); C7320 (Physics and chemistry
                 computing); C6130 (Data handling techniques); C5230
                 (Digital arithmetic methods)",
  corpsource =   "CACI Inc.-Federal, Colorado Springs, CO, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; Ada programming language; arithmetic operations;
                 ASSIGN function; checking; computational reliability;
                 data integrity; declaration; digital arithmetic;
                 entries; exponents; floating point numeric value;
                 fundamental physical units; generic package;
                 information hiding; integer; length; limited private;
                 mass; multiplication operation; numeric; operator;
                 overloading; PHYSICAL QUANTITY type; physics computing;
                 relational operations; reusability; reusable Ada
                 package; scientific dimensional integrity; software;
                 software modifiability; software packages; software
                 reliability; software reusability; strong typing;
                 symbol creation; time; types; units; units
                 (measurement); values; variables",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Maeder:1996:MPLa
author: Roman E. Maeder
title: The Mathematica Programmer: Long Integers: Basic Arithmetic and Data Types
journal: j-MATHEMATICA-J
volume: 6
number: 2
pages: 32--40
month: Spring
year: 1996
ISSN: 1047-5974 (print), 1097-1610 (electronic) OR 10475974 (print), 10971610 (electronic)
ISSNL: 1047-5974 OR 10475974
bibdate: Sat Nov 6 13:34:10 MDT 2010
bibsource: http://www.mathematica-journal.com/issue/v6i2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.06 13:34:10 MDT
fjournal: Mathematica Journal
acknowledgement: ack-nhfb
journalURL: http://www.mathematica-journal.com/
rawauthor: Roman E. Maeder
rawtitle: The {Mathematica} Programmer: Long Integers: Basic Arithmetic and Data Types
URL:
http://www.mathematica-journal.com/issue/v6i2/columns/maeder/index.html; http://www.mathematica-journal.com/issue/v6i2/columns/maeder/maeder62.pdf

abstract:
Long-integer arithmetic is a fundamental part of symbolic computation. This article introduces the fundamentals of long-integer calculations by implementing a prototype system in Mathematica. Our code is strictly procedural and could be translated into C or assembler easily. The tools needed are arrays that behave like arrays in procedural languages, as well as tools for software testing and debugging.

rawabstract:
Long-integer arithmetic is a fundamental part of symbolic computation. This article introduces the fundamentals of long-integer calculations by implementing a prototype system in Mathematica. Our code is strictly procedural and could be translated into C or assembler easily. The tools needed are arrays that behave like arrays in procedural languages, as well as tools for software testing and debugging.

entry:
@Article{Maeder:1996:MPLa,
  author =       "Roman E. Maeder",
  title =        "The {Mathematica} Programmer: Long Integers: Basic
                 Arithmetic and Data Types",
  journal =      j-MATHEMATICA-J,
  volume =       "6",
  number =       "2",
  pages =        "32--40",
  month =        "Spring",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:10 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v6i2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathematica-journal.com/issue/v6i2/columns/maeder/index.html;
                 http://www.mathematica-journal.com/issue/v6i2/columns/maeder/maeder62.pdf",
  abstract =     "Long-integer arithmetic is a fundamental part of
                 symbolic computation. This article introduces the
                 fundamentals of long-integer calculations by
                 implementing a prototype system in Mathematica. Our
                 code is strictly procedural and could be translated
                 into C or assembler easily. The tools needed are arrays
                 that behave like arrays in procedural languages, as
                 well as tools for software testing and debugging.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}


bibtype: article
filename: fparith.bib
label: Maeder:1996:MPLb
author: Roman E. Maeder
title: The Mathematica Programmer: Long Integers: Efficient Algorithms
journal: j-MATHEMATICA-J
volume: 6
number: 3
pages: 37--43
month: Summer
year: 1996
ISSN: 1047-5974 (print), 1097-1610 (electronic) OR 10475974 (print), 10971610 (electronic)
ISSNL: 1047-5974 OR 10475974
bibdate: Sat Nov 6 13:34:12 MDT 2010
bibsource: http://www.mathematica-journal.com/issue/v6i3/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.06 13:34:12 MDT
fjournal: Mathematica Journal
acknowledgement: ack-nhfb
journalURL: http://www.mathematica-journal.com/
rawauthor: Roman E. Maeder
rawtitle: The {Mathematica} Programmer: Long Integers: Efficient Algorithms
URL:
http://www.mathematica-journal.com/issue/v6i3/columns/maeder/contents/63maeder.pdf; http://www.mathematica-journal.com/issue/v6i3/columns/maeder/index.html

abstract:
This is the second part of an article on long-integer arithmetic. It discusses the data type for long integers and investigates a few asymptotically efficient algorithms for multiplication and division. We will not discuss all our code in detail, but point out a few important ideas.

rawabstract:
This is the second part of an article on long-integer arithmetic. It discusses the data type for long integers and investigates a few asymptotically efficient algorithms for multiplication and division. We will not discuss all our code in detail, but point out a few important ideas.

entry:
@Article{Maeder:1996:MPLb,
  author =       "Roman E. Maeder",
  title =        "The {Mathematica} Programmer: Long Integers: Efficient
                 Algorithms",
  journal =      j-MATHEMATICA-J,
  volume =       "6",
  number =       "3",
  pages =        "37--43",
  month =        "Summer",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:12 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v6i3/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathematica-journal.com/issue/v6i3/columns/maeder/contents/63maeder.pdf;
                 http://www.mathematica-journal.com/issue/v6i3/columns/maeder/index.html",
  abstract =     "This is the second part of an article on long-integer
                 arithmetic. It discusses the data type for long
                 integers and investigates a few asymptotically
                 efficient algorithms for multiplication and division.
                 We will not discuss all our code in detail, but point
                 out a few important ideas.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}


bibtype: article
filename: fparith.bib
label: Makino:1996:MBF
author: H. Makino and H. Suzuki and H. Morinaka and Y. Nakase and K. Mashiko and T. Sumi
title: A 286 MHz 64-b floating point multiplier with enhanced CG operation
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 31
number: 4
pages: 504--513
month: apr
monthnumber: 4
year: 1996
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: H. Makino and H. Suzuki and H. Morinaka and Y. Nakase and K. Mashiko and T. Sumi
rawtitle: A {286 MHz} 64-b floating point multiplier with enhanced {CG} operation
entry:
@Article{Makino:1996:MBF,
  author =       "H. Makino and H. Suzuki and H. Morinaka and Y. Nakase
                 and K. Mashiko and T. Sumi",
  title =        "A {286 MHz} 64-b floating point multiplier with
                 enhanced {CG} operation",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "31",
  number =       "4",
  pages =        "504--513",
  month =        apr,
  year =         "1996",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  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 Journal of Solid-State Circuits",
  summary =      "This paper presents a high speed 64-b floating point
                 (FP) multiplier that has a useful function for computer
                 graphics (CG). The critical path delay is minimized by
                 using high speed logic gates and limiting the stage
                 number of series transmission gate \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Manickavasagam:1996:ATI
author: SenthilKumar Manickavasagam
title: ``$ a + b $'' arithmetic: theory and implementation
type: Thesis (M.S.)
school: Electrical Engineering and Computer Science, Ohio University
address: Athens, OH, USA
pages: xi + 152
year: 1996
bibdate: Mon Mar 05 14:33:56 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.05 14:33:56 ???
acknowledgement: ack-nhfb
rawauthor: SenthilKumar Manickavasagam
rawtitle: ``$ a + b $'' arithmetic: theory and implementation
entry:
@MastersThesis{Manickavasagam:1996:ATI,
  author =       "SenthilKumar Manickavasagam",
  title =        "``$ a + b $'' arithmetic: theory and implementation",
  type =         "Thesis ({M.S.})",
  school =       "Electrical Engineering and Computer Science, Ohio
                 University",
  address =      "Athens, OH, USA",
  pages =        "xi + 152",
  year =         "1996",
  bibdate =      "Mon Mar 05 14:33:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Manning:1996:FS
author: Evan Manning
title: Floating-point Summation
journal: j-CCCUJ
volume: 14
number: 9
pages: 51--??
month: sep
monthnumber: 9
year: 1996
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Wed Nov 6 07:30:58 MST 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.11.06 07:30:58 MST
fjournal: C/C++ Users Journal
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: Evan Manning
rawtitle: Floating-point Summation
entry:
@Article{Manning:1996:FS,
  author =       "Evan Manning",
  title =        "Floating-point Summation",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "9",
  pages =        "51--??",
  month =        sep,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Wed Nov 6 07:30:58 MST 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
  keywords =     "accurate floating-point summation",
}


bibtype: inproceedings
filename: fparith.bib
label: Markov:1996:FIA
author: S. M. Markov
title: On the Foundations of Interval Arithmetic
crossref: Alefeld:1996:SCV
pages: 307--313
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: S. M. Markov
rawtitle: On the Foundations of Interval Arithmetic
entry:
@InProceedings{Markov:1996:FIA,
  author =       "S. M. Markov",
  title =        "On the Foundations of Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "307--313",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Mayer:1996:SEI
author: G. Mayer
title: Success in Epsilon-Inflation
crossref: Alefeld:1996:SCV
pages: 98--104
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: G. Mayer
rawtitle: Success in Epsilon-Inflation
entry:
@InProceedings{Mayer:1996:SEI,
  author =       "G. Mayer",
  title =        "Success in Epsilon-Inflation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "98--104",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Mikov:1996:LSA
author: Alexander I. Mikov
title: Large-scale addition of machine real numbers: Accuracy estimates
journal: j-THEOR-COMP-SCI
volume: 162
number: 1
pages: 151--170
day: 05
month: aug
monthnumber: 8
year: 1996
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Mon Jul 19 22:20:05 MDT 1999
bibtimestamp: 1999.07.19 22:20:05 MDT
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
corpsource: Department of Computer Science, Perm State University, Russia
journalURL: http://www.sciencedirect.com/science/journal/03043975/
treatment: T Theoretical or Mathematical
rawauthor: Alexander I. Mikov
rawtitle: Large-scale addition of machine real numbers: {Accuracy} estimates
bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_free/browse/browse.cgi?year=1996&volume=162&issue=1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/tcs1995.bib

URL:
http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_sub/browse/browse.cgi?year=1996&volume=162&issue=1&aid=2194

keywords:
accuracy estimates; digital arithmetic; floating-point arithmetic; large-scale addition; machine real numbers; positive independent random variables; random variables; real distribution interval; roundoff error

entry:
@Article{Mikov:1996:LSA,
  author =       "Alexander I. Mikov",
  title =        "Large-scale addition of machine real numbers:
                 {Accuracy} estimates",
  journal =      j-THEOR-COMP-SCI,
  volume =       "162",
  number =       "1",
  pages =        "151--170",
  day =          "05",
  month =        aug,
  year =         "1996",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Mon Jul 19 22:20:05 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_free/browse/browse.cgi?year=1996&volume=162&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs1995.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_sub/browse/browse.cgi?year=1996&volume=162&issue=1&aid=2194",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Computer Science, Perm State University,
                 Russia",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  keywords =     "accuracy estimates; digital arithmetic; floating-point
                 arithmetic; large-scale addition; machine real numbers;
                 positive independent random variables; random
                 variables; real distribution interval; roundoff error",
  pubcountry =   "Netherlands",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Miner:1996:VIC
author: Paul S. Miner and James F. Leathrum, Jr.
title: Verification of IEEE Compliant Subtractive Division Algorithms
crossref: Srivas:1996:FMC
pages: 64--78
year: 1996
bibdate: Wed Nov 24 12:01:07 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 12:01:07 ???
URL: http://www.ece.odu.edu/~leathrum/Formal_Methods/computer_arithmetic/fmcad.ps
acknowledgement: ack-nhfb
rawauthor: Paul S. Miner and James F. {Leathrum, Jr.}
rawtitle: Verification of {IEEE} Compliant Subtractive Division Algorithms
remark:
fmcad.ps actually contains two separate versions of this article, and must be split manually before printing.

entry:
@InProceedings{Miner:1996:VIC,
  author =       "Paul S. Miner and James F. {Leathrum, Jr.}",
  title =        "Verification of {IEEE} Compliant Subtractive Division
                 Algorithms",
  crossref =     "Srivas:1996:FMC",
  pages =        "64--78",
  year =         "1996",
  bibdate =      "Wed Nov 24 12:01:07 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ece.odu.edu/~leathrum/Formal_Methods/computer_arithmetic/fmcad.ps",
  acknowledgement = ack-nhfb,
  remark =       "fmcad.ps actually contains two separate versions of
                 this article, and must be split manually before
                 printing.",
}


bibtype: techreport
filename: fparith.bib
label: Moler:1996:CCF
author: Cleve B. Moler
title: Cleve's Corner: Floating points: IEEE Standard unifies arithmetic model
type: Technical note
institution: inst-MATHWORKS
address: inst-MATHWORKS:adr
pages: 3
month: Fall
year: 1996
bibdate: Thu Oct 24 07:16:21 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 07:16:21 ???
URL: http://www.mathworks.com/company/newsletter/pdf/Fall96Cleve.pdf
keywords: Matlab
acknowledgement: ack-nhfb
rawauthor: Cleve B. Moler
rawtitle: {Cleve}'s Corner: {Floating} points: {IEEE Standard} unifies arithmetic model
entry:
@TechReport{Moler:1996:CCF,
  author =       "Cleve B. Moler",
  title =        "{Cleve}'s Corner: {Floating} points: {IEEE Standard}
                 unifies arithmetic model",
  type =         "Technical note",
  institution =  inst-MATHWORKS,
  address =      inst-MATHWORKS:adr,
  pages =        "3",
  month =        "Fall",
  year =         "1996",
  bibdate =      "Thu Oct 24 07:16:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathworks.com/company/newsletter/pdf/Fall96Cleve.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Matlab",
}


bibtype: inproceedings
filename: fparith.bib
label: Mraz:1996:ELB
author: F. Mraz
title: The Exact Lower Bound of Optimal Values in Interval LP
crossref: Alefeld:1996:SCV
pages: 214--220
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: F. Mraz
rawtitle: The Exact Lower Bound of Optimal Values in Interval {LP}
entry:
@InProceedings{Mraz:1996:ELB,
  author =       "F. Mraz",
  title =        "The Exact Lower Bound of Optimal Values in Interval
                 {LP}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "214--220",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Mrozek:1996:IPC
author: M. Mrozek
title: Inheritable Properties and Computer Assisted Proofs in Dynamics
crossref: Alefeld:1996:SCV
pages: 245--257
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. Mrozek
rawtitle: Inheritable Properties and Computer Assisted Proofs in Dynamics
entry:
@InProceedings{Mrozek:1996:IPC,
  author =       "M. Mrozek",
  title =        "Inheritable Properties and Computer Assisted Proofs in
                 Dynamics",
  crossref =     "Alefeld:1996:SCV",
  pages =        "245--257",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Muller:1996:CES
author: Michael Muller and Christine Rub and Wolfgang Rulling
title: A circuit for exact summation of floating-point numbers
journal: j-INFO-PROC-LETT
volume: 57
number: 3
pages: 159--163
day: 12
month: feb
monthnumber: 2
year: 1996
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Sat Nov 7 17:55:43 MST 1998
bibtimestamp: 1998.11.07 17:55:43 MST
fjournal: Information Processing Letters
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Michael M{\"u}ller and Christine R{\"u}b and Wolfgang R{\"u}lling
rawtitle: A circuit for exact summation of floating-point numbers
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Muller:1996:CES,
  author =       "Michael M{\"u}ller and Christine R{\"u}b and Wolfgang
                 R{\"u}lling",
  title =        "A circuit for exact summation of floating-point
                 numbers",
  journal =      j-INFO-PROC-LETT,
  volume =       "57",
  number =       "3",
  pages =        "159--163",
  day =          "12",
  month =        feb,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sat Nov 7 17:55:43 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "accurate floating-point summation",
}


bibtype: inproceedings
filename: fparith.bib
label: Muller:1996:TER
author: Jean-Michel Muller and A. Tisserand
title: Towards Exact Rounding of the Elementary Functions
crossref: Alefeld:1996:SCV
pages: 59--71
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: Jean-Michel Muller and A. Tisserand
rawtitle: Towards Exact Rounding of the Elementary Functions
entry:
@InProceedings{Muller:1996:TER,
  author =       "Jean-Michel Muller and A. Tisserand",
  title =        "Towards Exact Rounding of the Elementary Functions",
  crossref =     "Alefeld:1996:SCV",
  pages =        "59--71",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Nakao:1996:GEB
author: M. T. Nakao and N. Yamamoto and Y. Watanabe
title: Guaranteed Error Bounds for Finite Element Solutions of the Stokes Problem
crossref: Alefeld:1996:SCV
pages: 258--264
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. T. Nakao and N. Yamamoto and Y. Watanabe
rawtitle: Guaranteed Error Bounds for Finite Element Solutions of the {Stokes} Problem
entry:
@InProceedings{Nakao:1996:GEB,
  author =       "M. T. Nakao and N. Yamamoto and Y. Watanabe",
  title =        "Guaranteed Error Bounds for Finite Element Solutions
                 of the {Stokes} Problem",
  crossref =     "Alefeld:1996:SCV",
  pages =        "258--264",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Nonnenmacher:1996:LCS
author: A. Nonnenmacher and D. A. Mlynski
title: Liquid Crystal Simulation Using Automatic Differentiation and Interval Arithmetic
crossref: Alefeld:1996:SCV
pages: 334--340
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: A. Nonnenmacher and D. A. Mlynski
rawtitle: Liquid Crystal Simulation Using Automatic Differentiation and Interval Arithmetic
entry:
@InProceedings{Nonnenmacher:1996:LCS,
  author =       "A. Nonnenmacher and D. A. Mlynski",
  title =        "Liquid Crystal Simulation Using Automatic
                 Differentiation and Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "334--340",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Oberman:1996:DIH
author: Stuart Franklin Oberman
title: Design Issues in High Performance Floating Point Arithmetic Units
type: Thesis (Ph.D.)
school: Department of Electrical Engineering, Stanford University
address: Stanford, CA, USA
pages: xiv + 151
month: nov
monthnumber: 11
year: 1996
bibdate: Fri Mar 27 10:14:18 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.27 10:14:18 ???
acknowledgement: ack-nhfb
rawauthor: Stuart Franklin Oberman
rawtitle: Design Issues in High Performance Floating Point Arithmetic Units
URL:
ftp://umunhum.stanford.edu/tr/oberman.nov96.thesis.ps.Z; https://www.proquest.com/pqdtglobal/docview/304386888

entry:
@PhdThesis{Oberman:1996:DIH,
  author =       "Stuart Franklin Oberman",
  title =        "Design Issues in High Performance Floating Point
                 Arithmetic Units",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "xiv + 151",
  month =        nov,
  year =         "1996",
  bibdate =      "Fri Mar 27 10:14:18 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://umunhum.stanford.edu/tr/oberman.nov96.thesis.ps.Z;
                 https://www.proquest.com/pqdtglobal/docview/304386888",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Oberman:1996:FIR
author: Stuart F. Oberman and Michael J. Flynn
title: Fast IEEE Rounding for Division by Functional Iteration
type: Technical Report
number: CSL-TR-96-700
institution: Stanford University
address: Stanford, CA, USA
pages: v + 16
month: jul
monthnumber: 7
year: 1996
bibdate: Sun Dec 10 13:50:59 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.10 13:50:59 ???
URL: http://i.stanford.edu/pub/cstr/reports/csl/tr/96/700/CSL-TR-96-700.pdf
keywords: division, Goldschmidt's algorithm, IEEE rounding, Newton--Raphson, variable latency
acknowledgement: ack-nhfb
rawauthor: Stuart F. Oberman and Michael J. Flynn
rawtitle: Fast {IEEE} Rounding for Division by Functional Iteration
abstract:
A class of high performance division algorithms is functional iteration. Division by functional iteration uses multiplication as the fundamental operator. The main advantage of division by functional iteration is quadratic convergence to the quotient. However, unlike non-restoring division algorithms such as SRT division, functional iteration does not directly provide a final remainder. This makes fast and exact rounding difficult. This paper clarifies the methodology for correct IEEE compliant rounding for quadratically-converging division algorithms. It proposes an extension to previously reported techniques of using extended precision in the computation to reduce the frequency of back multiplications required to obtain the final remainder. Further, a technique applicable to all IEEE rounding modes is presented which replaces the final subtraction for remainder computation with very simple combinational logic.

rawabstract:
A class of high performance division algorithms is functional iteration. Division by functional iteration uses multiplication as the fundamental operator. The main advantage of division by functional iteration is quadratic convergence to the quotient. However, unlike non-restoring division algorithms such as SRT division, functional iteration does not directly provide a final remainder. This makes fast and exact rounding difficult. This paper clarifies the methodology for correct IEEE compliant rounding for quadratically-converging division algorithms. It proposes an extension to previously reported techniques of using extended precision in the computation to reduce the frequency of back multiplications required to obtain the final remainder. Further, a technique applicable to all IEEE rounding modes is presented which replaces the final subtraction for remainder computation with very simple combinational logic.

entry:
@TechReport{Oberman:1996:FIR,
  author =       "Stuart F. Oberman and Michael J. Flynn",
  title =        "Fast {IEEE} Rounding for Division by Functional
                 Iteration",
  type =         "Technical Report",
  number =       "CSL-TR-96-700",
  institution =  "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "v + 16",
  month =        jul,
  year =         "1996",
  bibdate =      "Sun Dec 10 13:50:59 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://i.stanford.edu/pub/cstr/reports/csl/tr/96/700/CSL-TR-96-700.pdf",
  abstract =     "A class of high performance division algorithms is
                 functional iteration. Division by functional iteration
                 uses multiplication as the fundamental operator. The
                 main advantage of division by functional iteration is
                 quadratic convergence to the quotient. However, unlike
                 non-restoring division algorithms such as SRT division,
                 functional iteration does not directly provide a final
                 remainder. This makes fast and exact rounding
                 difficult. This paper clarifies the methodology for
                 correct IEEE compliant rounding for
                 quadratically-converging division algorithms. It
                 proposes an extension to previously reported techniques
                 of using extended precision in the computation to
                 reduce the frequency of back multiplications required
                 to obtain the final remainder. Further, a technique
                 applicable to all IEEE rounding modes is presented
                 which replaces the final subtraction for remainder
                 computation with very simple combinational logic.",
  acknowledgement = ack-nhfb,
  keywords =     "division, Goldschmidt's algorithm, IEEE rounding,
                 Newton--Raphson, variable latency",
}


bibtype: inproceedings
filename: fparith.bib
label: Oberman:1996:IDO
author: Stuart F. Oberman and Michael J. Flynn
title: Implementing Division and Other Floating-Point Operations: a System Perspective
crossref: Alefeld:1996:SCV
pages: 18--24
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
URL: ftp://arith.stanford.edu/tr/scan_system.ps.Z
acknowledgement: ack-nhfb
rawauthor: Stuart F. Oberman and Michael J. Flynn
rawtitle: Implementing Division and Other Floating-Point Operations: a System Perspective
entry:
@InProceedings{Oberman:1996:IDO,
  author =       "Stuart F. Oberman and Michael J. Flynn",
  title =        "Implementing Division and Other Floating-Point
                 Operations: a System Perspective",
  crossref =     "Alefeld:1996:SCV",
  pages =        "18--24",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/scan_system.ps.Z",
  acknowledgement = ack-nhfb,
  summary =      "Modern computer applications have increased in their
                 computation complexity in recent years. The
                 industry-wide usage of performance benchmarks, such as
                 SPECmarks forces processor designers to pay particular
                 attention to floating-point (FP) computation.
                 Furthermore, special purpose applications, such as high
                 performance graphics rendering systems, have placed
                 further demands on processors. The development of high
                 speed FP hardware is a requirement to meet these
                 increasing computation demands.",
}


bibtype: article
filename: fparith.bib
label: Oberman:1996:RDL
author: S. F. Oberman and M. J. Flynn
title: Reducing division latency with reciprocal caches
journal: j-RELIABLE-COMPUTING
volume: 2
number: 2
pages: 147--153
month: apr
monthnumber: 4
year: 1996
CODEN: RCOMF8
ISSN: 1385-3139 (print), 1573-1340 (electronic) OR 13853139 (print), 15731340 (electronic)
ISSNL: 1385-3139 OR 13853139
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
URL: ftp://arith.stanford.edu/tr/scan_recip.ps.Z
fjournal: Reliable Computing = Nadezhnye vychisleniia
acknowledgement: ack-sfo
journalURL: http://link.springer.com/journal/11155
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: Reducing division latency with reciprocal caches
entry:
@Article{Oberman:1996:RDL,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Reducing division latency with reciprocal caches",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "2",
  number =       "2",
  pages =        "147--153",
  month =        apr,
  year =         "1996",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/scan_recip.ps.Z",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}


bibtype: article
filename: fparith.bib
label: Oberman:1996:VLP
author: S. F. Oberman and M. J. Flynn
title: A Variable Latency Pipelined Floating-Point Adder
journal: j-LECT-NOTES-COMP-SCI
volume: 1124
pages: 183--192
year: 1996
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Fri Mar 27 10:07:13 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.27 10:07:13 ???
URL: ftp://arith.stanford.edu/tr/fpadd_euro.ps.Z
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: A Variable Latency Pipelined Floating-Point Adder
entry:
@Article{Oberman:1996:VLP,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "A Variable Latency Pipelined Floating-Point Adder",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1124",
  pages =        "183--192",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Mar 27 10:07:13 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/fpadd_euro.ps.Z",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Oklobdzija:1996:MSO
author: V. G. Oklobdzija and D. Villeger and S. S. Liu
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 294--306
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.485568
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:09 MDT 2011
bibtimestamp: 2011.07.06 19:47:09 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485568
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. G. Oklobdzija and D. Villeger and S. S. Liu
title:
A method for speed optimized partial product reduction and generation of fast parallel multipliers using an algorithmic approach

rawtitle:
A method for speed optimized partial product reduction and generation of fast parallel multipliers using an algorithmic approach

entry:
@Article{Oklobdzija:1996:MSO,
  author =       "V. G. Oklobdzija and D. Villeger and S. S. Liu",
  title =        "A method for speed optimized partial product reduction
                 and generation of fast parallel multipliers using an
                 algorithmic approach",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "294--306",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485568",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485568",
  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",
}


bibtype: article
filename: fparith.bib
label: Paar:1996:NAP
author: C. Paar
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 7
pages: 856--861
month: jul
monthnumber: 7
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.508323
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:12 MDT 2011
bibtimestamp: 2011.07.06 19:47:12 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=508323
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. Paar
title:
A new architecture for a parallel finite field multiplier with low complexity based on composite fields

rawtitle:
A new architecture for a parallel finite field multiplier with low complexity based on composite fields

entry:
@Article{Paar:1996:NAP,
  author =       "C. Paar",
  title =        "A new architecture for a parallel finite field
                 multiplier with low complexity based on composite
                 fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "7",
  pages =        "856--861",
  month =        jul,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.508323",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=508323",
  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: Parhami:1996:CHS
author: B. Parhami and S. Kawahito and M. Ishida and T. Nakamura and M. Kameyama and T. Higuchi
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 5
pages: 637--639
month: may
monthnumber: 5
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.509918
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:11 MDT 2011
bibtimestamp: 2011.07.06 19:47:11 MDT
note: See cite Kawahito:1994:HSA.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509918
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. Parhami and S. Kawahito and M. Ishida and T. Nakamura and M. Kameyama and T. Higuchi
rawnote: See \cite{Kawahito:1994:HSA}.
title:
Comments on ``High-speed area-efficient multiplier design using multiple-valued current-mode circuits''

rawtitle:
Comments on {``High-speed area-efficient multiplier design using multiple-valued current-mode circuits''}

entry:
@Article{Parhami:1996:CHS,
  author =       "B. Parhami and S. Kawahito and M. Ishida and T.
                 Nakamura and M. Kameyama and T. Higuchi",
  title =        "Comments on {``High-speed area-efficient multiplier
                 design using multiple-valued current-mode circuits''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "5",
  pages =        "637--639",
  month =        may,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.509918",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Kawahito:1994:HSA}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509918",
  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: Park:1996:OHW
author: Edwards Park
journal: j-SMITHSONIAN
volume: 26
number: 11
pages: 20--??
day: 01
month: feb
monthnumber: 2
year: 1996
CODEN: SMSNA5
ISSN: 0037-7333 (print), 1930-5508 (electronic) OR 00377333 (print), 19305508 (electronic)
ISSNL: 0037-7333 OR 00377333
bibdate: Fri Jun 21 14:38:22 MDT 1996
bibtimestamp: 1996.06.21 14:38:22 MDT
fjournal: Smithsonian
acknowledgement: ack-nhfb
rawauthor: Edwards Park
title:
The Object at Hand: What a difference the Difference Engine made: from Charles Babbage's calculator emerged today's computer

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
The Object at Hand: What a difference the {Difference Engine} made: from {Charles Babbage}'s calculator emerged today's computer

entry:
@Article{Park:1996:OHW,
  author =       "Edwards Park",
  title =        "The Object at Hand: What a difference the {Difference
                 Engine} made: from {Charles Babbage}'s calculator
                 emerged today's computer",
  journal =      j-SMITHSONIAN,
  volume =       "26",
  number =       "11",
  pages =        "20--??",
  day =          "01",
  month =        feb,
  year =         "1996",
  CODEN =        "SMSNA5",
  ISSN =         "0037-7333 (print), 1930-5508 (electronic)",
  ISSN-L =       "0037-7333",
  bibdate =      "Fri Jun 21 14:38:22 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Smithsonian",
}


bibtype: article
filename: fparith.bib
label: Park:1996:PAG
author: Taegeun Park
title: A Parallel Algorithm for Global Routing Using an Associative Processor
journal: j-J-PAR-DIST-COMP
volume: 38
number: 1
pages: 51--62
day: 10
month: oct
monthnumber: 10
year: 1996
CODEN: JPDCER
DOI: https://doi.org/10.1006/jpdc.1996.0128
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Thu Mar 9 09:19:01 MST 2000
bibtimestamp: 2000.03.09 09:19:01 MST
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Design Lab., Hyundai Electron. Ind., Kyoungki, South Korea
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: A Application; P Practical
rawauthor: Taegeun Park
rawtitle: A Parallel Algorithm for Global Routing Using an Associative Processor
URL:
http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production; http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production/pdf

keywords:
addressable storage; array; associative processing; associative processor; benchmark problems; computational complexity; content-; content-addressable memory; control section; digital arithmetic; global routing; layout process; matching; minimisation; minimum-; multiple data device; O(d) complexity; parallel algorithm; parallel algorithms; parallel arithmetic; problem; processing elements; randomly generated data; row logic; rudimentary logic; search-oriented applications; selective; single instruction; weight path

entry:
@Article{Park:1996:PAG,
  author =       "Taegeun Park",
  title =        "A Parallel Algorithm for Global Routing Using an
                 Associative Processor",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "38",
  number =       "1",
  pages =        "51--62",
  day =          "10",
  month =        oct,
  year =         "1996",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1996.0128",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:19:01 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C1180 (Optimisation techniques); C4240C
                 (Computational complexity); C4240P (Parallel
                 programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C5340 (Associative storage)",
  corpsource =   "Design Lab., Hyundai Electron. Ind., Kyoungki, South
                 Korea",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "addressable storage; array; associative processing;
                 associative processor; benchmark problems;
                 computational complexity; content-; content-addressable
                 memory; control section; digital arithmetic; global
                 routing; layout process; matching; minimisation;
                 minimum-; multiple data device; O(d) complexity;
                 parallel algorithm; parallel algorithms; parallel
                 arithmetic; problem; processing elements; randomly
                 generated data; row logic; rudimentary logic;
                 search-oriented applications; selective; single
                 instruction; weight path",
  treatment =    "A Application; P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Petunin:1996:UMI
author: D. Petunin and A. Semenov
title: The Use of Multi-Intervals in the UniCalc Solver
crossref: Alefeld:1996:SCV
pages: 91--97
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: D. Petunin and A. Semenov
rawtitle: The Use of Multi-Intervals in the {UniCalc} Solver
entry:
@InProceedings{Petunin:1996:UMI,
  author =       "D. Petunin and A. Semenov",
  title =        "The Use of Multi-Intervals in the {UniCalc} Solver",
  crossref =     "Alefeld:1996:SCV",
  pages =        "91--97",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Plum:1996:ETP
author: M. Plum
title: Enclosure for Two-Point Boundary Value Problems Near Bifurcation Points
crossref: Alefeld:1996:SCV
pages: 265--279
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. Plum
rawtitle: Enclosure for Two-Point Boundary Value Problems Near Bifurcation Points
entry:
@InProceedings{Plum:1996:ETP,
  author =       "M. Plum",
  title =        "Enclosure for Two-Point Boundary Value Problems Near
                 Bifurcation Points",
  crossref =     "Alefeld:1996:SCV",
  pages =        "265--279",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Popova:1996:IOI
author: E. D. Popova
title: Interval operations involving NaNs
journal: j-RELIABLE-COMPUTING
volume: 2
number: 2
pages: 161--166
month: jun
monthnumber: 6
year: 1996
CODEN: RCOMF8
ISSN: 1385-3139 (print), 1573-1340 (electronic) OR 13853139 (print), 15731340 (electronic)
ISSNL: 1385-3139 OR 13853139
bibdate: Sat Feb 4 17:45:55 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2012.02.04 17:45:55 ???
fjournal: Reliable Computing = Nadezhnye vychisleniia
acknowledgement: ack-vk
journalURL: http://link.springer.com/journal/11155
rawauthor: E. D. Popova
rawtitle: Interval operations involving {NaNs}
entry:
@Article{Popova:1996:IOI,
  author =       "E. D. Popova",
  title =        "Interval operations involving {NaNs}",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "2",
  number =       "2",
  pages =        "161--166",
  month =        jun,
  year =         "1996",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Sat Feb 4 17:45:55 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-vk,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}


bibtype: article
filename: fparith.bib
label: Posch:1996:DRN
author: K. C. Posch and R. Posch
title: Division in residue number systems involving length indicators
journal: j-J-COMPUT-APPL-MATH
volume: 66
number: 1--2
pages: 411--419
day: 31
month: jan
monthnumber: 1
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:48 MST 2017
bibtimestamp: 2017.02.25 12:27:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795001646
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: K. C. Posch and R. Posch
rawtitle: Division in residue number systems involving length indicators
entry:
@Article{Posch:1996:DRN,
  author =       "K. C. Posch and R. Posch",
  title =        "Division in residue number systems involving length
                 indicators",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "66",
  number =       "1--2",
  pages =        "411--419",
  day =          "31",
  month =        jan,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001646",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: fparith.bib
label: Price:1996:RA
author: David T. Price
title: Remark on Algorithm 715
journal: j-TOMS
volume: 22
number: 2
pages: 258--258
month: jun
monthnumber: 6
year: 1996
CODEN: ACMSCU
DOI: https://doi.org/10.1145/229473.236186
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Feb 8 10:28:55 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.02.08 10:28:55 ???
note: See cite Cody:1993:ASE
URL: http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p258-price/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: David T. Price
rawnote: See \cite{Cody:1993:ASE}
rawtitle: Remark on {Algorithm 715}
entry:
@Article{Price:1996:RA,
  author =       "David T. Price",
  title =        "Remark on {Algorithm 715}",
  journal =      j-TOMS,
  volume =       "22",
  number =       "2",
  pages =        "258--258",
  month =        jun,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/229473.236186",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Cody:1993:ASE}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p258-price/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1996:NHS
author: Vishwas M. Rao and Behrouz Nowrouzian
title: Novel high-speed bit-parallel multiply accumulate arithmetic architecture
crossref: Luk:1996:PSC
pages: 26--38
year: 1996
DOI: https://doi.org/10.1117/12.255442
bibdate: Tue Jun 14 18:26:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:26:06 ???
acknowledgement: ack-nhfb
rawauthor: Vishwas M. Rao and Behrouz Nowrouzian
rawtitle: Novel high-speed bit-parallel multiply accumulate arithmetic architecture
entry:
@InProceedings{Rao:1996:NHS,
  author =       "Vishwas M. Rao and Behrouz Nowrouzian",
  title =        "Novel high-speed bit-parallel multiply accumulate
                 arithmetic architecture",
  crossref =     "Luk:1996:PSC",
  pages =        "26--38",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255442",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1996:RTS
author: V. M. Rao and B. Nowrouzian
booktitle: Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996
title: Rounding techniques for signed binary arithmetic
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 294--297
year: 1996
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: V. M. Rao and B. Nowrouzian
rawbooktitle: Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996
rawtitle: Rounding techniques for signed binary arithmetic
abstract:
This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.

rawabstract:
This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.

entry:
@InProceedings{Rao:1996:RTS,
  author =       "V. M. Rao and B. Nowrouzian",
  booktitle =    "Canadian Conference on Electrical and Computer
                 Engineering. 26--29 May 1996",
  title =        "Rounding techniques for signed binary arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "294--297",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper is concerned with the derivation of the
                 relationship that exists between the number truncation
                 in two's complement (TC) arithmetic and the
                 corresponding truncation in signed-binary (SB)
                 arithmetic. The resulting relationship is subsequently
                 exploited and applied to the development of a pair of
                 novel techniques for SB rounding. These techniques are
                 then translated into algorithm suitable for two-level
                 logic implementation. Finally, the resulting algorithms
                 are applied to the design and implementation of a
                 high-speed SB-kernel based TC multiply-accumulate
                 arithmetic architecture.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Ratz:1996:BRS
author: D. Ratz
title: On Branching Rules in Second-Order Branch-and-Bound Methods for Global Optimization
crossref: Alefeld:1996:SCV
pages: 221--227
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: D. Ratz
rawtitle: On Branching Rules in Second-Order Branch-and-Bound Methods for Global Optimization
entry:
@InProceedings{Ratz:1996:BRS,
  author =       "D. Ratz",
  title =        "On Branching Rules in Second-Order Branch-and-Bound
                 Methods for Global Optimization",
  crossref =     "Alefeld:1996:SCV",
  pages =        "221--227",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Reid:1996:RFF
author: J. K. Reid
title: Remark on ``Fast Floating-Point Processing in Common Lisp''
journal: j-TOMS
volume: 22
number: 4
pages: 496--497
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
DOI: https://doi.org/10.1145/235815.235824
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 9 10:21:08 1999
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.03.09 10:21:08 ???
note: See cite Fateman:1995:FFP.
URL: http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p496-reid/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Rutherford Appleton Lab
journalURL: https://dl.acm.org/loi/toms
journalabr: ACM Trans Math Software
rawauthor: J. K. Reid
rawnote: See \cite{Fateman:1995:FFP}.
rawtitle: Remark on ``{Fast Floating-Point Processing in Common Lisp}''
abstract:
We explain why we feel that the comparison between Common Lisp and Fortran in a recent article by Fateman et al. in this journal is not entirely fair.

keywords:
Common Lisp language; Control structures; Digital arithmetic; Floating point computation; fortran (programming language); Lisp (programming language); Standards

subject:
bf D.3.2: Software, PROGRAMMING LANGUAGES, General, Standards. bf D.3.3: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Modules, packages.

rawabstract:
We explain why we feel that the comparison between Common Lisp and Fortran in a recent article by Fateman et al. in this journal is not entirely fair.

entry:
@Article{Reid:1996:RFF,
  author =       "J. K. Reid",
  title =        "Remark on ``{Fast Floating-Point Processing in Common
                 Lisp}''",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "496--497",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235824",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:21:08 1999",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fateman:1995:FFP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p496-reid/",
  abstract =     "We explain why we feel that the comparison between
                 Common Lisp and Fortran in a recent article by Fateman
                 et al. in this journal is not entirely fair.",
  acknowledgement = ack-nhfb # " and " # ack-rfb,
  affiliation =  "Rutherford Appleton Lab",
  classification = "721.1; 723.1.1; 902.2; 921.6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  journalabr =   "ACM Trans Math Software",
  keywords =     "Common Lisp language; Control structures; Digital
                 arithmetic; Floating point computation; fortran
                 (programming language); Lisp (programming language);
                 Standards",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, General,
                 Standards. {\bf D.3.3}: Software, PROGRAMMING
                 LANGUAGES, Language Constructs and Features, Modules,
                 packages.",
}


bibtype: inproceedings
filename: fparith.bib
label: Rump:1996:DBR
author: Siegfried M. Rump
title: The Distance Between Regularity and Strong Regularity
crossref: Alefeld:1996:SCV
pages: 105--117
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: Siegfried M. Rump
rawtitle: The Distance Between Regularity and Strong Regularity
entry:
@InProceedings{Rump:1996:DBR,
  author =       "Siegfried M. Rump",
  title =        "The Distance Between Regularity and Strong
                 Regularity",
  crossref =     "Alefeld:1996:SCV",
  pages =        "105--117",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Sarma:1996:HRT
author: D. Das Sarma and D. W. Matula
title: Hardware Reciprocal Table Compression / Decompression Techniques
crossref: Alefeld:1996:SCV
pages: 11--17
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: D. Das Sarma and D. W. Matula
rawtitle: Hardware Reciprocal Table Compression\slash Decompression Techniques
entry:
@InProceedings{Sarma:1996:HRT,
  author =       "D. Das Sarma and D. W. Matula",
  title =        "Hardware Reciprocal Table Compression\slash
                 Decompression Techniques",
  crossref =     "Alefeld:1996:SCV",
  pages =        "11--17",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Saunders:1996:TGF
author: Kevin Saunders
title: Third generation floating point DSP design
type: Report
number: 800 XY/N-1
institution: University of Bristol. Department of Aerospace Engineering
address: Bristol, UK
pages: 11--17
year: 1996
bibdate: Thu May 09 08:52:59 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:52:59 ???
acknowledgement: ack-nhfb
rawauthor: Kevin Saunders
rawtitle: Third generation floating point {DSP} design
entry:
@TechReport{Saunders:1996:TGF,
  author =       "Kevin Saunders",
  title =        "Third generation floating point {DSP} design",
  type =         "Report",
  number =       "800 XY/N-1",
  institution =  "University of Bristol. Department of Aerospace
                 Engineering",
  address =      "Bristol, UK",
  year =         "1996",
  bibdate =      "Thu May 09 08:52:59 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Schatzman:1996:ADF
author: James C. Schatzman
title: Accuracy of the discrete Fourier transform and the fast Fourier transform
journal: j-SIAM-J-SCI-COMP
volume: 17
number: 5
pages: 1150--1166
month: sep
monthnumber: 9
year: 1996
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827593247023
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
MRclass: 65T20 (42A65 42C10 68Q25)
MRnumber: 97e:65155
bibdate: Fri Dec 4 14:47:53 MST 1998
bibtimestamp: 1998.12.04 14:47:53 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/24702
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
ajournal: SIAM J. Sci. Comput.
journalURL: http://epubs.siam.org/sisc
rawauthor: James C. Schatzman
rawtitle: Accuracy of the discrete {Fourier} transform and the fast {Fourier} transform
bibsource:
http://epubs.siam.org/toc/sjoce3/17/5; 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/siamjscicomput.bib

remark:
This article analyzes errors in computing one-dimensional Fourier transforms, the fast way (FFT) and the slow way. The author identifies two main causes of accuracy loss in the computed transforms: (1) inaccurate sine and cosine functions, and (2) failure to use accurate summation methods, such as Kahan's compensated summation.

entry:
@Article{Schatzman:1996:ADF,
  author =       "James C. Schatzman",
  title =        "Accuracy of the discrete {Fourier} transform and the
                 fast {Fourier} transform",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "17",
  number =       "5",
  pages =        "1150--1166",
  month =        sep,
  year =         "1996",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827593247023",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65T20 (42A65 42C10 68Q25)",
  MRnumber =     "97e:65155",
  bibdate =      "Fri Dec 4 14:47:53 MST 1998",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/17/5;
                 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/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/24702",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM J. Sci. Comput.",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  remark =       "This article analyzes errors in computing
                 one-dimensional Fourier transforms, the fast way (FFT)
                 and the slow way. The author identifies two main causes
                 of accuracy loss in the computed transforms: (1)
                 inaccurate sine and cosine functions, and (2) failure
                 to use accurate summation methods, such as Kahan's
                 compensated summation.",
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1996:HDI
author: M. J. Schulte and K. C. Bickerstaff and E. E. Swartzlander, Jr.
title: Hardware Designs for Interval Multiplication
pages: 85--87
year: 1996
bibdate: Sun Mar 04 10:51:30 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 10:51:30 ???
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and K. C. Bickerstaff and E. E. {Swartzlander, Jr.}
rawtitle: Hardware Designs for Interval Multiplication
booktitle:
Proceedings of the II Workshop on Computer Arithmetic, Interval and Symbolic Computation, Recife, Brazil, August, 1996

rawbooktitle:
Proceedings of the {II} Workshop on Computer Arithmetic, Interval and Symbolic Computation, Recife, Brazil, August, 1996

entry:
@InProceedings{Schulte:1996:HDI,
  author =       "M. J. Schulte and K. C. Bickerstaff and E. E.
                 {Swartzlander, Jr.}",
  editor =       "????",
  booktitle =    "Proceedings of the {II} Workshop on Computer
                 Arithmetic, Interval and Symbolic Computation, Recife,
                 Brazil, August, 1996",
  title =        "Hardware Designs for Interval Multiplication",
  publisher =    "????",
  address =      "????",
  pages =        "85--87",
  year =         "1996",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 10:51:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1996:PAS
author: M. J. Schulte and E. E. Swartzlander
title: A Processor for Accurate, Self-Validating Computing
crossref: Alefeld:1996:SCV
pages: 25--31
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and E. E. Swartzlander
rawtitle: A Processor for Accurate, Self-Validating Computing
entry:
@InProceedings{Schulte:1996:PAS,
  author =       "M. J. Schulte and E. E. Swartzlander",
  title =        "A Processor for Accurate, Self-Validating Computing",
  crossref =     "Alefeld:1996:SCV",
  pages =        "25--31",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Schwandt:1996:GCI
author: H. Schwandt
crossref: Alefeld:1996:SCV
pages: 280--286
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: H. Schwandt
title:
Globally Convergent Iterative Domain Decomposition Methods for the Parallel Solution of a Class of Nonlinear Systems of Equations

rawtitle:
Globally Convergent Iterative Domain Decomposition Methods for the Parallel Solution of a Class of Nonlinear Systems of Equations

entry:
@InProceedings{Schwandt:1996:GCI,
  author =       "H. Schwandt",
  title =        "Globally Convergent Iterative Domain Decomposition
                 Methods for the Parallel Solution of a Class of
                 Nonlinear Systems of Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "280--286",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Schwarz:1996:HSA
author: Eric M. Schwarz and Michael J. Flynn
title: Hardware Starting Approximation Method and Its Application to the Square Root Operation
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 12
pages: 1356--1369
month: dec
monthnumber: 12
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.545966
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:15 MDT 2011
bibtimestamp: 2011.07.06 19:47:15 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=545966
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Eric M. Schwarz and Michael J. Flynn
rawtitle: Hardware Starting Approximation Method and Its Application to the Square Root Operation
entry:
@Article{Schwarz:1996:HSA,
  author =       "Eric M. Schwarz and Michael J. Flynn",
  title =        "Hardware Starting Approximation Method and Its
                 Application to the Square Root Operation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "12",
  pages =        "1356--1369",
  month =        dec,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.545966",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=545966",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Quadratically converging algorithms for high-order
                 arithmetic operations typically are accelerated by a
                 starting approximation. The higher the precision of the
                 starting approximation, the less number of iterations
                 required for convergence. \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Sezgin:1996:SIR
author: F. Sezgin
title: Some improvements for a random number generator with single-precision floating-point arithmetic
journal: j-COMP-GEOSCI
volume: 22
number: 4
pages: 453--455
month: may
monthnumber: 5
year: 1996
CODEN: CGEODT, CGOSDN
ISSN: 0098-3004 (print), 1873-7803 (electronic) OR 00983004 (print), 18737803 (electronic)
ISSNL: 0098-3004 OR 00983004
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
fjournal: Computers and Geosciences
acknowledgement: ack-nhfb
rawauthor: F. Sezgin
rawtitle: Some improvements for a random number generator with single-precision floating-point arithmetic
entry:
@Article{Sezgin:1996:SIR,
  author =       "F. Sezgin",
  title =        "Some improvements for a random number generator with
                 single-precision floating-point arithmetic",
  journal =      j-COMP-GEOSCI,
  volume =       "22",
  number =       "4",
  pages =        "453--455",
  month =        may,
  year =         "1996",
  CODEN =        "CGEODT, CGOSDN",
  ISSN =         "0098-3004 (print), 1873-7803 (electronic)",
  ISSN-L =       "0098-3004",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Geosciences",
  pagecount =    "3",
}


bibtype: inproceedings
filename: fparith.bib
label: Shary:1996:NAA
author: S. P. Shary
title: A New Approach to the Analysis of Static Systems Under Internal Uncertainty
crossref: Alefeld:1996:SCV
pages: 118--132
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: S. P. Shary
rawtitle: A New Approach to the Analysis of Static Systems Under Internal Uncertainty
entry:
@InProceedings{Shary:1996:NAA,
  author =       "S. P. Shary",
  title =        "A New Approach to the Analysis of Static Systems Under
                 Internal Uncertainty",
  crossref =     "Alefeld:1996:SCV",
  pages =        "118--132",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Shewchuk:1996:APF
author: Jonathan Richard Shewchuk
title: Adaptive precision floating-point arithmetic and fast robust geometric predicates
type: Report
number: CMU-CS-96-140
institution: Department of Computer Science, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 53
year: 1996
bibdate: Fri Jan 06 11:59:17 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.06 11:59:17 ???
keywords: floating-point arithmetic; multiple-precision arithmetic
acknowledgement: ack-nhfb
rawauthor: Jonathan Richard Shewchuk
rawtitle: Adaptive precision floating-point arithmetic and fast robust geometric predicates
abstract:
Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small.par These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floating-point numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness.

rawabstract:
Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small.\par These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floating-point numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness.

entry:
@TechReport{Shewchuk:1996:APF,
  author =       "Jonathan Richard Shewchuk",
  title =        "Adaptive precision floating-point arithmetic and fast
                 robust geometric predicates",
  type =         "Report",
  number =       "CMU-CS-96-140",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "53",
  year =         "1996",
  bibdate =      "Fri Jan 06 11:59:17 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Exact computer arithmetic has a variety of uses
                 including, but not limited to, the robust
                 implementation of geometric algorithms. This report has
                 three purposes. The first is to offer fast
                 software-level algorithms for exact addition and
                 multiplication of arbitrary precision floating-point
                 values. The second is to propose a technique for
                 adaptive-precision arithmetic that can often speed
                 these algorithms when one wishes to perform
                 multiprecision calculations that do not always require
                 exact arithmetic, but must satisfy some error bound.
                 The third is to provide a practical demonstration of
                 these techniques, in the form of implementations of
                 several common geometric calculations whose required
                 degree of accuracy depends on their inputs. These
                 robust geometric predicates are adaptive; their running
                 time depends on the degree of uncertainty of the
                 result, and is usually small.\par

                 These algorithms work on computers whose floating-point
                 arithmetic uses radix two and exact rounding, including
                 machines complying with the IEEE 754 standard. The
                 inputs to the predicates may be arbitrary single or
                 double precision floating-point numbers. C code is
                 publicly available for the 2D and 3D orientation and
                 incircle tests, and robust Delaunay triangulation using
                 these tests. Timings of the implementations demonstrate
                 their effectiveness.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; multiple-precision
                 arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Shewchuk:1996:RAF
author: Jonathan Richard Shewchuk
booktitle: Proceedings of the 12th Annual ACM Symposium on Computational Geometry
title: Robust Adaptive Floating-Point Geometric Predicates
publisher: pub-ACM
address: pub-ACM:adr
pages: 141--150
year: 1996
DOI: https://doi.org/10.1145/237218.237337
bibdate: Sat May 1 15:33:15 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.05.01 15:33:15 ???
URL: http://www.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-predicates.ps
acknowledgement: ack-nhfb
rawauthor: Jonathan Richard Shewchuk
rawbooktitle: {Proceedings of the 12th Annual ACM Symposium on Computational Geometry}
rawtitle: Robust Adaptive Floating-Point Geometric Predicates
entry:
@InProceedings{Shewchuk:1996:RAF,
  author =       "Jonathan Richard Shewchuk",
  booktitle =    "{Proceedings of the 12th Annual ACM Symposium on
                 Computational Geometry}",
  title =        "Robust Adaptive Floating-Point Geometric Predicates",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "141--150",
  year =         "1996",
  DOI =          "https://doi.org/10.1145/237218.237337",
  bibdate =      "Sat May 1 15:33:15 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-predicates.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Shewchuk:1996:TEQ
author: J. R. Shewchuk
editor: Ming C. Lin and Dinesh Manocha
booktitle: Applied Computational Geometry: Towards Geometric Engineering
title: Triangle: Engineering a $2$D Quality Mesh Generator and Delaunay Triangulator
journal: j-LECT-NOTES-COMP-SCI
volume: 1148
pages: 203--222
year: 1996
CODEN: LNCSD9
DOI: https://doi.org/10.1007/BFb0014497
ISBN: 3-540-61785-X (softcover), 3-540-70680-1 (e-book) OR 354061785X (softcover), 3540706801 (ebook)
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Dec 21 09:47:26 1996
bibtimestamp: 1996.12.21 09:47:26 ???
URL: https://link.springer.com/chapter/10.1007/BFb0014497
fjournal: Lecture Notes in Computer Science
keywords: Delaunay triangulation; exact arithmetic; refinement algorithm; refinement stage; roundoff error
remark: First ACM Workshop on Applied Computational Geometry.
acknowledgement: ack-nhfb
bookURL: https://link.springer.com/book/10.1007/BFb0014474
journalURL: http://link.springer.com/bookseries/558
rawauthor: J. R. Shewchuk
rawbooktitle: Applied Computational Geometry: Towards Geometric Engineering
raweditor: Ming C. Lin and Dinesh Manocha
rawtitle: {Triangle}: Engineering a {$2$D} Quality Mesh Generator and {Delaunay} Triangulator
ISBN13:
978-3-540-61785-3 (softcover), 978-3-540-70680-9 (e-book) OR 9783540617853 (softcover), 9783540706809 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/lncs1996b.bib

entry:
@Article{Shewchuk:1996:TEQ,
  author =       "J. R. Shewchuk",
  editor =       "Ming C. Lin and Dinesh Manocha",
  booktitle =    "Applied Computational Geometry: Towards Geometric
                 Engineering",
  title =        "{Triangle}: Engineering a {$2$D} Quality Mesh
                 Generator and {Delaunay} Triangulator",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1148",
  pages =        "203--222",
  year =         "1996",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/BFb0014497",
  ISBN =         "3-540-61785-X (softcover), 3-540-70680-1 (e-book)",
  ISBN-13 =      "978-3-540-61785-3 (softcover), 978-3-540-70680-9
                 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Dec 21 09:47:26 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs1996b.bib",
  URL =          "https://link.springer.com/chapter/10.1007/BFb0014497",
  acknowledgement = ack-nhfb,
  book-URL =     "https://link.springer.com/book/10.1007/BFb0014474",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "Delaunay triangulation; exact arithmetic; refinement
                 algorithm; refinement stage; roundoff error",
  remark =       "First ACM Workshop on Applied Computational
                 Geometry.",
}


bibtype: article
filename: fparith.bib
label: Shirayanagi:1996:FPG
author: Kiyoshi Shirayanagi
title: Floating point Grobner bases
journal: j-MATH-COMPUT-SIMUL
volume: 42
number: 4--6
pages: 509--528
month: nov
monthnumber: 11
year: 1996
CODEN: MCSIDR
DOI: https://doi.org/10.1016/S0378-4754(96)00027-4
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Mon Aug 18 12:50:38 MDT 2025
bibtimestamp: 2025.08.18 12:50:38 MDT
URL: https://www.sciencedirect.com/science/article/pii/S0378475496000274
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: Kiyoshi Shirayanagi
rawtitle: Floating point {Gr{\"o}bner} bases
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1990.bib

entry:
@Article{Shirayanagi:1996:FPG,
  author =       "Kiyoshi Shirayanagi",
  title =        "Floating point {Gr{\"o}bner} bases",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "42",
  number =       "4--6",
  pages =        "509--528",
  month =        nov,
  year =         "1996",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/S0378-4754(96)00027-4",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 12:50:38 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1990.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0378475496000274",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: inproceedings
filename: fparith.bib
label: Shokin:1996:IPI
author: Y. I. Shokin
title: On Interval Problems, Interval Algorithms and Their Computational Complexity
crossref: Alefeld:1996:SCV
pages: 314--328
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: Y. I. Shokin
rawtitle: On Interval Problems, Interval Algorithms and Their Computational Complexity
entry:
@InProceedings{Shokin:1996:IPI,
  author =       "Y. I. Shokin",
  title =        "On Interval Problems, Interval Algorithms and Their
                 Computational Complexity",
  crossref =     "Alefeld:1996:SCV",
  pages =        "314--328",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Sinclair:1996:ORS
author: R. Sinclair
title: Optimization of reciprocals and square roots on the i860 microprocessor
journal: j-INT-J-HIGH-SPEED-COMPUTING
volume: 8
number: 1
pages: 57--64
year: 1996
CODEN: IHSCEZ
ISSN: 0129-0533 OR 01290533
bibdate: Mon Feb 25 11:19:22 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Article1st database
bibtimestamp: 2002.02.25 11:19:22 MST
fjournal: International Journal of High Speed Computing
acknowledgement: ack-nhfb
journalURL: http://www.worldscientific.com/worldscinet/ijhsc
rawauthor: R. Sinclair
rawtitle: Optimization of reciprocals and square roots on the {i860} microprocessor
entry:
@Article{Sinclair:1996:ORS,
  author =       "R. Sinclair",
  title =        "Optimization of reciprocals and square roots on the
                 {i860} microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "8",
  number =       "1",
  pages =        "57--64",
  year =         "1996",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Mon Feb 25 11:19:22 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Article1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}


bibtype: article
filename: fparith.bib
label: Singer:1996:EAP
author: Benjamin Singer and George Saon
title: An efficient algorithm for parallel integer multiplication
journal: j-J-NETW-COMPUT-APPL
volume: 19
number: 4
pages: 415--418
month: oct
monthnumber: 10
year: 1996
CODEN: JNCAF3
ISSN: 1084-8045 (print), 1095-8592 (electronic) OR 10848045 (print), 10958592 (electronic)
ISSNL: 1084-8045 OR 10848045
bibdate: Wed Jan 28 15:41:22 MST 2015
bibtimestamp: 2015.01.28 15:41:22 MST
URL: http://www.sciencedirect.com/science/article/pii/S1084804596900296
fjournal: Journal of Network and Computer Applications
acknowledgement: ack-nhfb
ajournal: J. Netw. Comput. Appl.
journalURL: http://www.sciencedirect.com/science/journal/10848045
rawauthor: Benjamin Singer and George Saon
rawtitle: An efficient algorithm for parallel integer multiplication
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jnetwcomputappl.bib

entry:
@Article{Singer:1996:EAP,
  author =       "Benjamin Singer and George Saon",
  title =        "An efficient algorithm for parallel integer
                 multiplication",
  journal =      j-J-NETW-COMPUT-APPL,
  volume =       "19",
  number =       "4",
  pages =        "415--418",
  month =        oct,
  year =         "1996",
  CODEN =        "JNCAF3",
  ISSN =         "1084-8045 (print), 1095-8592 (electronic)",
  ISSN-L =       "1084-8045",
  bibdate =      "Wed Jan 28 15:41:22 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnetwcomputappl.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1084804596900296",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Netw. Comput. Appl.",
  fjournal =     "Journal of Network and Computer Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/10848045",
}


bibtype: article
filename: fparith.bib
label: Soderquist:1996:AFT
author: Peter Soderquist and Miriam Leeser
title: Area and Performance Tradeoffs in Floating-Point Divide and Square-Root Implementations
journal: j-COMP-SURV
volume: 28
number: 3
pages: 518--564
month: sep
monthnumber: 9
year: 1996
CODEN: CMSVAN
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Wed Nov 13 06:52:01 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.11.13 06:52:01 MST
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: Peter Soderquist and Miriam Leeser
rawtitle: Area and Performance Tradeoffs in Floating-Point Divide and Square-Root Implementations
entry:
@Article{Soderquist:1996:AFT,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Area and Performance Tradeoffs in Floating-Point
                 Divide and Square-Root Implementations",
  journal =      j-COMP-SURV,
  volume =       "28",
  number =       "3",
  pages =        "518--564",
  month =        sep,
  year =         "1996",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Wed Nov 13 06:52:01 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}


bibtype: article
filename: fparith.bib
label: Soderquist:1996:APT
author: Peter Soderquist and Miriam Leeser
title: Area and Performance Tradeoffs in Floating-Point Divide and Square-Root Implementations
journal: j-COMP-SURV
volume: 28
number: 3
pages: 518--564
month: sep
monthnumber: 9
year: 1996
CODEN: CMSVAN
DOI: https://doi.org/10.1145/243439.243481
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Thu Jun 19 09:54:32 MDT 2008
bibtimestamp: 2008.06.19 09:54:32 MDT
URL: http://www.acm.org/pubs/citations/journals/surveys/1996-28-3/p518-soderquist/
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: Peter Soderquist and Miriam Leeser
rawtitle: Area and Performance Tradeoffs in Floating-Point Divide and Square-Root Implementations
bibsource:
http://www.acm.org/pubs/contents/journals/surveys/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Floating-point divide and square-root operations are essential to many scientific and engineering applications, and are required in all computer systems that support the IEEE floating-point standard. Yet many current microprocessors provide only weak support for these operations. The latency and throughput of division are typically far inferior to those of floating-point addition and multiplication, and square-root performance is often even lower. This article argues the case for high-performance division and square root. It also explains the algorithms and implementations of the primary techniques, subtractive and multiplicative methods, employed in microprocessor floating-point units with their associated area/performance tradeoffs. Case studies of representative floating-point unit configurations are presented, supported by simulation results using a carefully selected benchmark, Givens rotation, to show the dynamic performance impact of the various implementation alternatives. The topology of the implementation is found to be an important performance factor. Multiplicative algorithms, such as the Newton--Raphson method and Goldschmidt's algorithm, can achieve low latencies. However, these implementations serialize multiply, divide, and square root operations through a single pipeline, which can lead to low throughput. While this hardware sharing yields low size requirements for baseline implementations, lower-latency versions require many times more area. For these reasons, multiplicative implementations are best suited to cases where subtractive methods are precluded by area constraints, and modest performance on divide and square root operations is tolerable. Subtractive algorithms, exemplified by radix-4 SRT and radix-16 SRT, can be made to execute in parallel with other floating-point operations.

keywords:
area and performance tradeoffs; arithmetic and logic structures; computer arithmetic.; computer system implementation; design studies. bf c.5.3: computer systems organization; design styles; division; floating-point; FPU; general; microcomputers; microprocessors. bf g.1.0: mathematics of computing; numerical analysis; parallel. bf c.4: computer systems organization; performance of systems; square root; SRT; bf b.2.1: hardware

subject:
bf B.2.1: Hardware, ARITHMETIC AND LOGIC STRUCTURES, Design Styles, Parallel. bf C.4: Computer Systems Organization, PERFORMANCE OF SYSTEMS, Design studies. bf C.5.3: Computer Systems Organization, COMPUTER SYSTEM IMPLEMENTATION, Microcomputers, Microprocessors. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.

rawabstract:
Floating-point divide and square-root operations are essential to many scientific and engineering applications, and are required in all computer systems that support the IEEE floating-point standard. Yet many current microprocessors provide only weak support for these operations. The latency and throughput of division are typically far inferior to those of floating-point addition and multiplication, and square-root performance is often even lower. This article argues the case for high-performance division and square root. It also explains the algorithms and implementations of the primary techniques, subtractive and multiplicative methods, employed in microprocessor floating-point units with their associated area/performance tradeoffs. Case studies of representative floating-point unit configurations are presented, supported by simulation results using a carefully selected benchmark, Givens rotation, to show the dynamic performance impact of the various implementation alternatives. The topology of the implementation is found to be an important performance factor. Multiplicative algorithms, such as the Newton--Raphson method and Goldschmidt's algorithm, can achieve low latencies. However, these implementations serialize multiply, divide, and square root operations through a single pipeline, which can lead to low throughput. While this hardware sharing yields low size requirements for baseline implementations, lower-latency versions require many times more area. For these reasons, multiplicative implementations are best suited to cases where subtractive methods are precluded by area constraints, and modest performance on divide and square root operations is tolerable. Subtractive algorithms, exemplified by radix-4 SRT and radix-16 SRT, can be made to execute in parallel with other floating-point operations.

entry:
@Article{Soderquist:1996:APT,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Area and Performance Tradeoffs in Floating-Point
                 Divide and Square-Root Implementations",
  journal =      j-COMP-SURV,
  volume =       "28",
  number =       "3",
  pages =        "518--564",
  month =        sep,
  year =         "1996",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/243439.243481",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:54:32 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/surveys/1996-28-3/p518-soderquist/",
  abstract =     "Floating-point divide and square-root operations are
                 essential to many scientific and engineering
                 applications, and are required in all computer systems
                 that support the IEEE floating-point standard. Yet many
                 current microprocessors provide only weak support for
                 these operations. The latency and throughput of
                 division are typically far inferior to those of
                 floating-point addition and multiplication, and
                 square-root performance is often even lower. This
                 article argues the case for high-performance division
                 and square root. It also explains the algorithms and
                 implementations of the primary techniques, subtractive
                 and multiplicative methods, employed in microprocessor
                 floating-point units with their associated
                 area/performance tradeoffs. Case studies of
                 representative floating-point unit configurations are
                 presented, supported by simulation results using a
                 carefully selected benchmark, Givens rotation, to show
                 the dynamic performance impact of the various
                 implementation alternatives. The topology of the
                 implementation is found to be an important performance
                 factor. Multiplicative algorithms, such as the
                 Newton--Raphson method and Goldschmidt's algorithm, can
                 achieve low latencies. However, these implementations
                 serialize multiply, divide, and square root operations
                 through a single pipeline, which can lead to low
                 throughput. While this hardware sharing yields low size
                 requirements for baseline implementations,
                 lower-latency versions require many times more area.
                 For these reasons, multiplicative implementations are
                 best suited to cases where subtractive methods are
                 precluded by area constraints, and modest performance
                 on divide and square root operations is tolerable.
                 Subtractive algorithms, exemplified by radix-4 SRT and
                 radix-16 SRT, can be made to execute in parallel with
                 other floating-point operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  keywords =     "area and performance tradeoffs; arithmetic and logic
                 structures; computer arithmetic.; computer system
                 implementation; design studies. {\bf c.5.3}: computer
                 systems organization; design styles; division;
                 floating-point; FPU; general; microcomputers;
                 microprocessors. {\bf g.1.0}: mathematics of computing;
                 numerical analysis; parallel. {\bf c.4}: computer
                 systems organization; performance of systems; square
                 root; SRT; {\bf b.2.1}: hardware",
  subject =      "{\bf B.2.1}: Hardware, ARITHMETIC AND LOGIC
                 STRUCTURES, Design Styles, Parallel. {\bf C.4}:
                 Computer Systems Organization, PERFORMANCE OF SYSTEMS,
                 Design studies. {\bf C.5.3}: Computer Systems
                 Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, Microprocessors. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic.",
}


bibtype: incollection
filename: fparith.bib
label: Steele:1996:EL
author: Guy L. Steele Jr. and Richard P. Gabriel
title: The evolution of Lisp
crossref: Bergin:1996:HPL
pages: 233--330
year: 1996
bibdate: Wed Jan 29 17:01:12 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 17:01:12 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Guy L. {Steele Jr.} and Richard P. Gabriel
rawtitle: The evolution of {Lisp}
remark:
From cite Steele:2004:RHP: ``In early 1971, he [White] began to analyze the machine-language algorithm used in the implementation of MacLisp (described in this report) to convert PDP-10 floating-point numbers into decimal notation.''

entry:
@InCollection{Steele:1996:EL,
  author =       "Guy L. {Steele Jr.} and Richard P. Gabriel",
  title =        "The evolution of {Lisp}",
  crossref =     "Bergin:1996:HPL",
  pages =        "233--330",
  year =         "1996",
  bibdate =      "Wed Jan 29 17:01:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``In early 1971, he
                 [White] began to analyze the machine-language algorithm
                 used in the implementation of MacLisp (described in
                 this report) to convert PDP-10 floating-point numbers
                 into decimal notation.''",
}


bibtype: book
filename: fparith.bib
label: Stewart:1996:ANA
author: G. W. (Gilbert W.) Stewart
publisher: pub-SIAM
address: pub-SIAM:adr
pages: x + 200
year: 1996
DOI: https://doi.org/10.1137/1.9781611971491
ISBN: 0-89871-362-5 (paperback) OR 0898713625 (paperback)
ISBN13: 978-0-89871-362-6 (paperback) OR 9780898713626 (paperback)
LCCN: QA297 .S785 1996
MRclass: 65-01
MRnumber: 1372060
bibdate: Tue May 27 08:35:41 MDT 2014
bibtimestamp: 2014.05.27 08:35:41 MDT
keywords: numerical analysis
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: G. W. (Gilbert W.) Stewart
title:
Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the University of Maryland at College Park and recorded after the fact

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib; z3950.loc.gov:7090/Voyager

URL:
http://www.loc.gov/catdir/enhancements/fy0726/95047768-d.html; http://www.loc.gov/catdir/enhancements/fy0726/95047768-t.html

TOC:
Part I. Nonlinear Equations Lecture 1. By the Dawn's Early Light Interval Bisection Relative Error Lecture 2. Newton's Method Reciprocals and Square Roots Local Convergence Analysis Slow Death Lecture 3. A Quasi-Newton Method Rates of Convergence Iterating for a Fixed Point Multiple Zeros Ending with a Proposition Lecture 4. The Secant Method Convergence Rate of Convergence Multipoint Methods Muller's Method The Linear-Fractional Method Lecture 5. A Hybrid Method Errors, Accuracy, and Condition Numbers Part II. Computer Arithmetic: Lecture 6. Floating-Point Numbers Overflow and Underflow Rounding Error Floating-point Arithmetic Lecture 7. Computing Sums Backward Error Analysis Perturbation Analysis Cheap and Chippy Chopping Lecture 8. Cancellation The Quadratic Equation That Fatal Bit of Rounding Error Envoi Part III. Linear Equations Lecture 9. Matrices, Vectors, and Scalars Operations with Matrices Rank-One Matrices Partitioned Matrices Lecture 10. Theory of Linear Systems Computational Generalities Triangular Systems Operation Counts Lecture 11. Memory Considerations Row Oriented Algorithms A Column Oriented Algorithm General Observations on Row and Column Orientation Basic Linear Algebra Subprograms Lecture 12. Positive Definite Matrices The Cholesky Decomposition Economics Lecture 13. Inner-Product Form of the Cholesky Algorithm Gaussian Elimination Lecture 14. Pivoting BLAS Upper Hessenberg and Tridiagonal Systems Lecture 15. Vector Norms Matrix Norms Relative Error Sensitivity of Linear Systems Lecture 16. The Condition of Linear Systems Artificial Ill Conditioning Rounding Error and Gaussian Elimination Comments on the Analysis Lecture 17. The Wonderful Residual: A Project Introduction More on Norms The Wonderful Residual Matrices with Known Condition Invert and Multiply Cramer's Rule Submission Part IV. Polynomial Interpolation Lecture 18. Quadratic Interpolation Shifting Polynomial Interpolation Lagrange Polynomials and Existence Uniqueness Lecture 19. Synthetic Division The Newton Form of the Interpolant Evaluation Existence Divided Differences Lecture 20. Error in Interpolation Error Bounds Convergence Chebyshev Points Part V. Numerical Integration and Differentiation Lecture 21. Numerical Integration Change of Intervals The Trapezoidal Rule The Composite Trapezoidal Rule Newton-Cotes Formulas Undetermined Coefficients and Simpson's Rule Lecture 22. The Composite Simpson's Rule Errors in Simpson's Rule Weighting Functions Gaussian Quadrature Lecture 23. The Setting Orthogonal Polynomials Existence Zeros of Orthogonal Polynomials Gaussian Quadrature Error and Convergence Examples Lecture 24. Numerical Differentiation and Integration Formulas From Power Series Limitations Bibliography

rawtitle:
Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the {University of Maryland at College Park} and recorded after the fact

rawTOC:
Part I. Nonlinear Equations \\ \\ Lecture 1. By the Dawn's Early Light \\ Interval Bisection \\ Relative Error \\ \\ Lecture 2. Newton's Method \\ Reciprocals and Square Roots \\ Local Convergence Analysis \\ Slow Death \\ \\ Lecture 3. A Quasi-Newton Method \\ Rates of Convergence \\ Iterating for a Fixed Point \\ Multiple Zeros \\ Ending with a Proposition \\ \\ Lecture 4. The Secant Method \\ Convergence \\ Rate of Convergence \\ Multipoint Methods \\ Muller's Method \\ The Linear-Fractional Method \\ \\ Lecture 5. A Hybrid Method \\ Errors, Accuracy, and Condition Numbers \\ \\ Part II. Computer Arithmetic: \\ \\ Lecture 6. Floating-Point Numbers \\ Overflow and Underflow \\ Rounding Error \\ Floating-point Arithmetic \\ \\ Lecture 7. Computing Sums \\ Backward Error Analysis \\ Perturbation Analysis \\ Cheap and Chippy Chopping \\ \\ Lecture 8. Cancellation \\ The Quadratic Equation \\ That Fatal Bit of Rounding Error \\ Envoi \\ \\ Part III. Linear Equations \\ \\ Lecture 9. Matrices, Vectors, and Scalars \\ Operations with Matrices \\ Rank-One Matrices \\ Partitioned Matrices \\ \\ Lecture 10. Theory of Linear Systems \\ Computational Generalities \\ Triangular Systems \\ Operation Counts \\ \\ Lecture 11. Memory Considerations \\ Row Oriented Algorithms \\ A Column Oriented Algorithm \\ General Observations on Row and Column Orientation \\ Basic Linear Algebra Subprograms \\ \\ Lecture 12. Positive Definite Matrices \\ The Cholesky Decomposition \\ Economics \\ \\ Lecture 13. Inner-Product Form of the Cholesky Algorithm \\ Gaussian Elimination \\ \\ Lecture 14. Pivoting \\ BLAS \\ Upper Hessenberg and Tridiagonal Systems \\ \\ Lecture 15. Vector Norms \\ Matrix Norms \\ Relative Error \\ Sensitivity of Linear Systems \\ \\ Lecture 16. The Condition of Linear Systems \\ Artificial Ill Conditioning \\ Rounding Error and Gaussian Elimination \\ Comments on the Analysis \\ \\ Lecture 17. The Wonderful Residual: A Project \\ Introduction \\ More on Norms \\ The Wonderful Residual \\ Matrices with Known Condition \\ Invert and Multiply \\ Cramer's Rule \\ Submission \\ \\ Part IV. Polynomial Interpolation \\ \\ Lecture 18. Quadratic Interpolation \\ Shifting \\ Polynomial Interpolation \\ Lagrange Polynomials and Existence \\ Uniqueness \\ \\ Lecture 19. Synthetic Division \\ The Newton Form of the Interpolant \\ Evaluation \\ Existence \\ Divided Differences \\ \\ Lecture 20. Error in Interpolation \\ Error Bounds \\ Convergence \\ Chebyshev Points \\ \\ Part V. Numerical Integration and Differentiation \\ \\ Lecture 21. Numerical Integration \\ Change of Intervals \\ The Trapezoidal Rule \\ The Composite Trapezoidal Rule \\ Newton-Cotes Formulas \\ Undetermined Coefficients and Simpson's Rule \\ \\ Lecture 22. The Composite Simpson's Rule \\ Errors in Simpson's Rule \\ Weighting Functions \\ Gaussian Quadrature \\ \\ Lecture 23. The Setting \\ Orthogonal Polynomials \\ Existence \\ Zeros of Orthogonal Polynomials \\ Gaussian Quadrature \\ Error and Convergence \\ Examples \\ \\ Lecture 24. Numerical Differentiation and Integration \\ Formulas From Power Series \\ Limitations \\ Bibliography

entry:
@Book{Stewart:1996:ANA,
  author =       "G. W. (Gilbert W.) Stewart",
  title =        "Afternotes on numerical analysis: a series of lectures
                 on elementary numerical analysis presented at the
                 {University of Maryland at College Park} and recorded
                 after the fact",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "x + 200",
  year =         "1996",
  DOI =          "https://doi.org/10.1137/1.9781611971491",
  ISBN =         "0-89871-362-5 (paperback)",
  ISBN-13 =      "978-0-89871-362-6 (paperback)",
  LCCN =         "QA297 .S785 1996",
  MRclass =      "65-01",
  MRnumber =     "1372060",
  bibdate =      "Tue May 27 08:35:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0726/95047768-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0726/95047768-t.html",
  acknowledgement = ack-nhfb,
  keywords =     "numerical analysis",
  subject =      "Numerical analysis",
  tableofcontents = "Part I. Nonlinear Equations \\
                 \\
                 Lecture 1. By the Dawn's Early Light \\
                 Interval Bisection \\
                 Relative Error \\
                 \\
                 Lecture 2. Newton's Method \\
                 Reciprocals and Square Roots \\
                 Local Convergence Analysis \\
                 Slow Death \\
                 \\
                 Lecture 3. A Quasi-Newton Method \\
                 Rates of Convergence \\
                 Iterating for a Fixed Point \\
                 Multiple Zeros \\
                 Ending with a Proposition \\
                 \\
                 Lecture 4. The Secant Method \\
                 Convergence \\
                 Rate of Convergence \\
                 Multipoint Methods \\
                 Muller's Method \\
                 The Linear-Fractional Method \\
                 \\
                 Lecture 5. A Hybrid Method \\
                 Errors, Accuracy, and Condition Numbers \\
                 \\
                 Part II. Computer Arithmetic: \\
                 \\
                 Lecture 6. Floating-Point Numbers \\
                 Overflow and Underflow \\
                 Rounding Error \\
                 Floating-point Arithmetic \\
                 \\
                 Lecture 7. Computing Sums \\
                 Backward Error Analysis \\
                 Perturbation Analysis \\
                 Cheap and Chippy Chopping \\
                 \\
                 Lecture 8. Cancellation \\
                 The Quadratic Equation \\
                 That Fatal Bit of Rounding Error \\
                 Envoi \\
                 \\
                 Part III. Linear Equations \\
                 \\
                 Lecture 9. Matrices, Vectors, and Scalars \\
                 Operations with Matrices \\
                 Rank-One Matrices \\
                 Partitioned Matrices \\
                 \\
                 Lecture 10. Theory of Linear Systems \\
                 Computational Generalities \\
                 Triangular Systems \\
                 Operation Counts \\
                 \\
                 Lecture 11. Memory Considerations \\
                 Row Oriented Algorithms \\
                 A Column Oriented Algorithm \\
                 General Observations on Row and Column Orientation \\
                 Basic Linear Algebra Subprograms \\
                 \\
                 Lecture 12. Positive Definite Matrices \\
                 The Cholesky Decomposition \\
                 Economics \\
                 \\
                 Lecture 13. Inner-Product Form of the Cholesky
                 Algorithm \\
                 Gaussian Elimination \\
                 \\
                 Lecture 14. Pivoting \\
                 BLAS \\
                 Upper Hessenberg and Tridiagonal Systems \\
                 \\
                 Lecture 15. Vector Norms \\
                 Matrix Norms \\
                 Relative Error \\
                 Sensitivity of Linear Systems \\
                 \\
                 Lecture 16. The Condition of Linear Systems \\
                 Artificial Ill Conditioning \\
                 Rounding Error and Gaussian Elimination \\
                 Comments on the Analysis \\
                 \\
                 Lecture 17. The Wonderful Residual: A Project \\
                 Introduction \\
                 More on Norms \\
                 The Wonderful Residual \\
                 Matrices with Known Condition \\
                 Invert and Multiply \\
                 Cramer's Rule \\
                 Submission \\
                 \\
                 Part IV. Polynomial Interpolation \\
                 \\
                 Lecture 18. Quadratic Interpolation \\
                 Shifting \\
                 Polynomial Interpolation \\
                 Lagrange Polynomials and Existence \\
                 Uniqueness \\
                 \\
                 Lecture 19. Synthetic Division \\
                 The Newton Form of the Interpolant \\
                 Evaluation \\
                 Existence \\
                 Divided Differences \\
                 \\
                 Lecture 20. Error in Interpolation \\
                 Error Bounds \\
                 Convergence \\
                 Chebyshev Points \\
                 \\
                 Part V. Numerical Integration and Differentiation \\
                 \\
                 Lecture 21. Numerical Integration \\
                 Change of Intervals \\
                 The Trapezoidal Rule \\
                 The Composite Trapezoidal Rule \\
                 Newton-Cotes Formulas \\
                 Undetermined Coefficients and Simpson's Rule \\
                 \\
                 Lecture 22. The Composite Simpson's Rule \\
                 Errors in Simpson's Rule \\
                 Weighting Functions \\
                 Gaussian Quadrature \\
                 \\
                 Lecture 23. The Setting \\
                 Orthogonal Polynomials \\
                 Existence \\
                 Zeros of Orthogonal Polynomials \\
                 Gaussian Quadrature \\
                 Error and Convergence \\
                 Examples \\
                 \\
                 Lecture 24. Numerical Differentiation and Integration
                 \\
                 Formulas From Power Series \\
                 Limitations \\
                 Bibliography",
}


bibtype: article
filename: fparith.bib
label: Suzuki:1996:LZA
author: H. Suzuki and H. Morinaka and H. Makino and Y. Nakase and K. Mashiko and T. Sumi
title: Leading-zero anticipatory logic for high-speed floating point addition
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 31
number: 8
pages: 1157--1164
month: aug
monthnumber: 8
year: 1996
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
note: See comments cite Oklobdzija:1997:CLZ.
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: H. Suzuki and H. Morinaka and H. Makino and Y. Nakase and K. Mashiko and T. Sumi
rawnote: See comments \cite{Oklobdzija:1997:CLZ}.
rawtitle: Leading-zero anticipatory logic for high-speed floating point addition
entry:
@Article{Suzuki:1996:LZA,
  author =       "H. Suzuki and H. Morinaka and H. Makino and Y. Nakase
                 and K. Mashiko and T. Sumi",
  title =        "Leading-zero anticipatory logic for high-speed
                 floating point addition",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "31",
  number =       "8",
  pages =        "1157--1164",
  month =        aug,
  year =         "1996",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Oklobdzija:1997:CLZ}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "This paper describes a new leading-zero anticipatory
                 (LZA) logic for high-speed floating-point addition
                 (FADD). This logic carries out the pre-decoding for
                 normalization concurrently with addition for the
                 significand. It also performs the shift operation
                 \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Tan:1996:MPF
author: Kien Beng Tan
title: A micro-power, floating point analog-to-digital converter
type: Thesis (M.S.)
school: Department of Electrical Engineering, University of California, Los Angeles
address: Los Angeles, CA, USA
year: 1996
bibdate: Thu Oct 24 14:19:35 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 14:19:35 MDT
keywords: dissertations, academic -- UCLA -- Electrical Engineering
acknowledgement: ack-nhfb
rawauthor: Kien Beng Tan
rawtitle: A micro-power, floating point analog-to-digital converter
entry:
@MastersThesis{Tan:1996:MPF,
  author =       "Kien Beng Tan",
  title =        "A micro-power, floating point analog-to-digital
                 converter",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "????",
  year =         "1996",
  bibdate =      "Thu Oct 24 14:19:35 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations, academic -- UCLA -- Electrical
                 Engineering",
}


bibtype: inproceedings
filename: fparith.bib
label: Tatsaki:1996:AIC
author: A. Tatsaki
title: An adaptive image coder based on residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 700--703
year: 1996
DOI: https://doi.org/10.1109/ICECS.1996.584458
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Tatsaki
rawtitle: An adaptive image coder based on residue number system
booktitle:
Proceedings of the Third IEEE International Conference on Electronics, Circuits, and Systems, 1996. ICECS 96

rawbooktitle:
Proceedings of the Third {IEEE} International Conference on Electronics, Circuits, and Systems, 1996. {ICECS 96}

entry:
@InProceedings{Tatsaki:1996:AIC,
  author =       "A. Tatsaki",
  booktitle =    "Proceedings of the Third {IEEE} International
                 Conference on Electronics, Circuits, and Systems, 1996.
                 {ICECS 96}",
  title =        "An adaptive image coder based on residue number
                 system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "700--703",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.1996.584458",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "An efficient coder for adaptive lossy compression of
                 still images is presented. It is based on a
                 computational efficient extraction of the details of
                 image blocks. The Discrete Cosine Transform and an
                 efficient Lattice Vector Quantizer based on the
                 \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Trott:1996:AWL
author: Aaron Gregory Trott
type: M.S.E.E. thesis
school: Mississippi State University
address: Mississippi State, MS 39762, USA
pages: 103
year: 1996
bibdate: Fri Feb 1 09:20:32 MST 2013
bibtimestamp: 2013.02.01 09:20:32 MST
URL: http://search.proquest.com/docview/304273691
subject: Electrical engineering; Aerospace materials
acknowledgement: ack-nhfb
advisor: Robert J. Moorhead
rawauthor: Aaron Gregory Trott
title:
The application of wavelets to lossless compression and progressive transmission of floating point data in three-dimensional curvilinear grids

bibsource:
http://search.proquest.com/; https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
The application of wavelets to lossless compression and progressive transmission of floating point data in three-dimensional curvilinear grids

entry:
@MastersThesis{Trott:1996:AWL,
  author =       "Aaron Gregory Trott",
  title =        "The application of wavelets to lossless compression
                 and progressive transmission of floating point data in
                 three-dimensional curvilinear grids",
  type =         "{M.S.E.E.} thesis",
  school =       "Mississippi State University",
  address =      "Mississippi State, MS 39762, USA",
  pages =        "103",
  year =         "1996",
  bibdate =      "Fri Feb 1 09:20:32 MST 2013",
  bibsource =    "http://search.proquest.com/;
                 https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://search.proquest.com/docview/304273691",
  acknowledgement = ack-nhfb,
  advisor =      "Robert J. Moorhead",
  classification = "0538: Aerospace materials; 0544: Electrical
                 engineering",
  dissertation-thesis-number = "1379238",
  subject =      "Electrical engineering; Aerospace materials",
}


bibtype: misc
filename: fparith.bib
label: Urano:1996:MAN
author: M. Urano and T. Taniguchi
title: Method and apparatus for normalization of a floating point binary number
pages: 103
day: 30
month: apr
monthnumber: 4
year: 1996
bibdate: Fri Nov 28 15:31:26 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 15:31:26 ???
note: U.S. Patent No. 5,513,362.
acknowledgement: ack-mfc
rawauthor: M. Urano and T. Taniguchi
rawnote: U.S. Patent No. 5,513,362.
rawtitle: Method and apparatus for normalization of a floating point binary number
entry:
@Misc{Urano:1996:MAN,
  author =       "M. Urano and T. Taniguchi",
  title =        "Method and apparatus for normalization of a floating
                 point binary number",
  day =          "30",
  month =        apr,
  year =         "1996",
  bibdate =      "Fri Nov 28 15:31:26 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,513,362.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Vassilladis:1996:ARA
author: S. Vassilladis and S. Contofana and K. Bertels
title: $2$-$1$ addition and related arithmetic operations with threshold logic
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 9
pages: 1062--1067
month: sep
monthnumber: 9
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.537130
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:13 MDT 2011
bibtimestamp: 2011.07.06 19:47:13 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537130
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Vassilladis and S. Contofana and K. Bertels
rawtitle: $2$-$1$ addition and related arithmetic operations with threshold logic
entry:
@Article{Vassilladis:1996:ARA,
  author =       "S. Vassilladis and S. Contofana and K. Bertels",
  title =        "$2$-$1$ addition and related arithmetic operations
                 with threshold logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "9",
  pages =        "1062--1067",
  month =        sep,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.537130",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537130",
  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: Venners:1996:FPA
author: Bill Venners
title: Under the Hood: Floating-point arithmetic
journal: j-JAVAWORLD
volume: 1
number: 9
pages: 1062--1067
month: nov
monthnumber: 11
year: 1996
ISSN: 1091-8906 OR 10918906
bibdate: Thu Aug 13 08:48:26 MDT 1998
bibsource: http://www.javaworld.com/javaworld/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.08.13 08:48:26 MDT
URL: http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.htm
acknowledgement: ack-nhfb
rawauthor: Bill Venners
rawtitle: Under the Hood: Floating-point arithmetic
entry:
@Article{Venners:1996:FPA,
  author =       "Bill Venners",
  title =        "Under the Hood: Floating-point arithmetic",
  journal =      j-JAVAWORLD,
  volume =       "1",
  number =       "9",
  month =        nov,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1091-8906",
  bibdate =      "Thu Aug 13 08:48:26 MDT 1998",
  bibsource =    "http://www.javaworld.com/javaworld/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.htm",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: vonMatt:1996:RES
author: Urs von Matt and G. W. Stewart
title: Rounding errors in solving block Hessenberg systems
journal: j-MATH-COMPUT
volume: 65
number: 213
pages: 115--135
month: jan
monthnumber: 1
year: 1996
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65F05 (65G05)
MRnumber: 96e:65019
MRreviewer: Alfonso Laratta
bibdate: Fri Jul 16 10:38:30 MDT 1999
bibtimestamp: 1999.07.16 10:38:30 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00667-9&u=/mcom/1996-65-213/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4140 (Linear algebra); C1110 (Algebra); C4240 (Programming and algorithm theory)
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Urs {von Matt} and G. W. Stewart
rawtitle: Rounding errors in solving block {Hessenberg} systems
bibsource:
http://www.ams.org/mcom/1996-65-213; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

keywords:
algebra; algorithm; algorithm theory; block diagonally dominant; block Hessenberg; block Hessenberg system; divide and conquer methods; divide-and-conquer; linear; linear system solution; linear systems; M-matrices; matrices; matrix algebra; rounding error analysis; rounding errors; solution; stable solution

entry:
@Article{vonMatt:1996:RES,
  author =       "Urs {von Matt} and G. W. Stewart",
  title =        "Rounding errors in solving block {Hessenberg}
                 systems",
  journal =      j-MATH-COMPUT,
  volume =       "65",
  number =       "213",
  pages =        "115--135",
  month =        jan,
  year =         "1996",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "96e:65019",
  MRreviewer =   "Alfonso Laratta",
  bibdate =      "Fri Jul 16 10:38:30 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1996-65-213;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00667-9&u=/mcom/1996-65-213/",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4140 (Linear algebra); C1110 (Algebra); C4240
                 (Programming and algorithm theory)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algebra; algorithm; algorithm theory; block diagonally
                 dominant; block Hessenberg; block Hessenberg system;
                 divide and conquer methods; divide-and-conquer; linear;
                 linear system solution; linear systems; M-matrices;
                 matrices; matrix algebra; rounding error analysis;
                 rounding errors; solution; stable solution",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Vrahatis:1996:GBM
author: M. N. Vrahatis
title: A Generalized Bisection Method for Large and Imprecise Problems
crossref: Alefeld:1996:SCV
pages: 186--192
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. N. Vrahatis
rawtitle: A Generalized Bisection Method for Large and Imprecise Problems
entry:
@InProceedings{Vrahatis:1996:GBM,
  author =       "M. N. Vrahatis",
  title =        "A Generalized Bisection Method for Large and Imprecise
                 Problems",
  crossref =     "Alefeld:1996:SCV",
  pages =        "186--192",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Werner:1996:CIW
author: K. Werner
title: Calculations of the Inverse Weierstrass Functions in an Arbitrary Machine Arithmetic
crossref: Alefeld:1996:SCV
pages: 72--78
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: K. Werner
rawtitle: Calculations of the Inverse {Weierstrass} Functions in an Arbitrary Machine Arithmetic
entry:
@InProceedings{Werner:1996:CIW,
  author =       "K. Werner",
  title =        "Calculations of the Inverse {Weierstrass} Functions in
                 an Arbitrary Machine Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "72--78",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Wiethoff:1996:PAE
author: A. Wiethoff
title: A Parallel Algorithm for Enclosing All Zeros of a Nonlinear System of Equations
crossref: Alefeld:1996:SCV
pages: 193--199
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: A. Wiethoff
rawtitle: A Parallel Algorithm for Enclosing All Zeros of a Nonlinear System of Equations
entry:
@InProceedings{Wiethoff:1996:PAE,
  author =       "A. Wiethoff",
  title =        "A Parallel Algorithm for Enclosing All Zeros of a
                 Nonlinear System of Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "193--199",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Williams:1996:TMF
author: K. B. Williams
journal: j-CCCUJ
volume: 14
number: 12
pages: 49--54, 58--65
month: dec
monthnumber: 12
year: 1996
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Mon Apr 10 06:32:36 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.04.10 06:32:36 ???
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawauthor: K. B. Williams
title:
Testing Math Functions: When requirements are tight, we must carefully examine all potential sources of error. Make sure your math library isn't the weak link in the chain

note:
Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.

rawnote:
Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.

rawtitle:
Testing Math Functions: {When} requirements are tight, we must carefully examine all potential sources of error. {Make} sure your math library isn't the weak link in the chain

entry:
@Article{Williams:1996:TMF,
  author =       "K. B. Williams",
  title =        "Testing Math Functions: {When} requirements are tight,
                 we must carefully examine all potential sources of
                 error. {Make} sure your math library isn't the weak
                 link in the chain",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "12",
  pages =        "49--54, 58--65",
  month =        dec,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Mon Apr 10 06:32:36 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Describes a package that extends the
                 Cody-Waite-Plauger work on the ELEFUNT package for the
                 testing of the elementary functions, including the
                 inverse hyperbolic functions, cube root, and Bessel
                 functions of the first and second kinds. The C++
                 package implements 192-bit extended precision versions
                 of all of the functions, so that accurate results are
                 available for comparison with the normal
                 double-precision results.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: incollection
filename: fparith.bib
label: Zachary:1996:ESD
author: Joseph L. Zachary
title: Eratosthenes: Significant Digits and Interval Arithmetic
crossref: Zachary:1996:ISP
pages: 29--43
year: 1996
DOI: https://doi.org/10.1007/978-1-4612-2366-5_3
bibdate: Sat Feb 16 15:23:11 2013
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2013.02.16 15:23:11 ???
acknowledgement: ack-nhfb
rawauthor: Joseph L. Zachary
rawtitle: {Eratosthenes}: Significant Digits and Interval Arithmetic
entry:
@InCollection{Zachary:1996:ESD,
  author =       "Joseph L. Zachary",
  title =        "{Eratosthenes}: Significant Digits and Interval
                 Arithmetic",
  crossref =     "Zachary:1996:ISP",
  pages =        "29--43",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4612-2366-5_3",
  bibdate =      "Sat Feb 16 15:23:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Zachary:1996:SHA
author: Joseph L. Zachary
title: Stairway to Heaven: Accumulation of Roundoff Error
crossref: Zachary:1996:ISP
pages: 45--61
year: 1996
DOI: https://doi.org/10.1007/978-1-4612-2366-5_4
bibdate: Sat Feb 16 15:30:56 2013
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2013.02.16 15:30:56 ???
acknowledgement: ack-nhfb
rawauthor: Joseph L. Zachary
rawtitle: Stairway to Heaven: Accumulation of Roundoff Error
entry:
@InCollection{Zachary:1996:SHA,
  author =       "Joseph L. Zachary",
  title =        "Stairway to Heaven: Accumulation of Roundoff Error",
  crossref =     "Zachary:1996:ISP",
  pages =        "45--61",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4612-2366-5_4",
  bibdate =      "Sat Feb 16 15:30:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Zgliczynski:1996:RVC
author: P. Zgliczynski
title: Rigorous Verification of Chaos in the Roessler Equations
crossref: Alefeld:1996:SCV
pages: 287--292
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: P. Zgliczynski
rawtitle: Rigorous Verification of Chaos in the {Roessler} Equations
entry:
@InProceedings{Zgliczynski:1996:RVC,
  author =       "P. Zgliczynski",
  title =        "Rigorous Verification of Chaos in the {Roessler}
                 Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "287--292",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Al-Twaijry:1997:APO
author: Hesham Abdulaziz Al-Twaijry
title: Area And Performance Optimized CMOS Multipliers
type: Ph.D. thesis
school: Department of Electrical Engineering, Stanford University
address: Stanford, CA, USA
month: aug
monthnumber: 8
year: 1997
bibdate: Mon Dec 24 10:02:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 10:02:37 ???
acknowledgement: ack-nhfb
rawauthor: Hesham Abdulaziz Al-Twaijry
rawtitle: Area And Performance Optimized {CMOS} Multipliers
entry:
@PhdThesis{Al-Twaijry:1997:APO,
  author =       "Hesham Abdulaziz Al-Twaijry",
  title =        "Area And Performance Optimized {CMOS} Multipliers",
  type =         "{Ph.D.} thesis",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  month =        aug,
  year =         "1997",
  bibdate =      "Mon Dec 24 10:02:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Allaart:1997:ISC
author: Pieter C. Allaart
title: An Invariant-Sum Characterization of Benford's Law
journal: j-J-APPL-PROBAB
volume: 34
number: 1
pages: 288--291
month: mar
monthnumber: 3
year: 1997
CODEN: JPRBAM
DOI: https://doi.org/10.2307/3215195
ISSN: 0021-9002 (print), 1475-6072 (electronic) OR 00219002 (print), 14756072 (electronic)
ISSNL: 0021-9002 OR 00219002
bibdate: Fri Mar 30 11:25:14 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.30 11:25:14 ???
fjournal: Journal of Applied Probability
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00219002.html; http://projecteuclid.org/euclid.jap/
rawauthor: Pieter C. Allaart
rawtitle: An Invariant-Sum Characterization of {Benford's Law}
URL:
http://links.jstor.org/sici?sici=0021-9002%28199703%2934%3A1%3C288%3AAICOBL%3E2.0.CO%3B2-S&size=LARGE

abstract:
The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit $ d (d = 1, 2, cdots , 9) $ is approximately constant. In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first digits $ d_1, cdots , d_k $ is constant for every fixed $k$.

rawabstract:
The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit $ d (d = 1, 2, \cdots, 9) $ is approximately constant. In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first digits $ d_1, \cdots, d_k $ is constant for every fixed $k$.

entry:
@Article{Allaart:1997:ISC,
  author =       "Pieter C. Allaart",
  title =        "An Invariant-Sum Characterization of {Benford's Law}",
  journal =      j-J-APPL-PROBAB,
  volume =       "34",
  number =       "1",
  pages =        "288--291",
  month =        mar,
  year =         "1997",
  CODEN =        "JPRBAM",
  DOI =          "https://doi.org/10.2307/3215195",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  bibdate =      "Fri Mar 30 11:25:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0021-9002%28199703%2934%3A1%3C288%3AAICOBL%3E2.0.CO%3B2-S&size=LARGE",
  abstract =     "The accountant Nigrini remarked that in tables of data
                 distributed according to Benford's law, the sum of all
                 elements with first digit $ d (d = 1, 2, \cdots, 9) $
                 is approximately constant. In this note, a mathematical
                 formulation of Nigrini's observation is given and it is
                 shown that Benford's law is the unique probability
                 distribution such that the expected sum of all elements
                 with first digits $ d_1, \cdots, d_k $ is constant for
                 every fixed $k$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: techreport
filename: fparith.bib
label: Althaus:1997:MNF
author: Ernst Althaus and Kurt Mehlhorn
title: Maximum network flow with floating point arithmetic
type: Forschungsbericht
number: MPI-I-97-1-022
institution: Max-Planck-Institut fur Informatik
address: Saarbrucken, Germany
pages: 5
year: 1997
ISSN: 0946-011X OR 0946011X
bibdate: Thu May 09 08:55:36 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:55:36 ???
acknowledgement: ack-nhfb
rawauthor: Ernst Althaus and Kurt Mehlhorn
rawtitle: Maximum network flow with floating point arithmetic
entry:
@TechReport{Althaus:1997:MNF,
  author =       "Ernst Althaus and Kurt Mehlhorn",
  title =        "Maximum network flow with floating point arithmetic",
  type =         "Forschungsbericht",
  number =       "MPI-I-97-1-022",
  institution =  "Max-Planck-Institut f{\"u}r Informatik",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "5",
  year =         "1997",
  ISSN =         "0946-011X",
  bibdate =      "Thu May 09 08:55:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Anonymous:1997:BRPk
author: Anonymous
journal: j-COMPUT-MATH-APPL
volume: 34
number: 10
pages: 141--141
month: nov
monthnumber: 11
year: 1997
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:40 MST 2017
bibtimestamp: 2017.03.01 21:48:40 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122197902650
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Anonymous
title:
Book Review: booktitle Primes of the form $ x^2 + n y^2 $: Fermat, class field theory, and complex multiplication: David A. Cox. John Wiley & Sons, New York. (1989). 351 pages. $49.95, pounds 29.95

rawtitle:
Book Review: {{\booktitle{Primes of the form $ x^2 + n y^2 $: Fermat, class field theory, and complex multiplication}}: David A. Cox. John Wiley \& Sons, New York. (1989). 351 pages. \$49.95, \pounds 29.95}

entry:
@Article{Anonymous:1997:BRPk,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Primes of the form $ x^2 + n
                 y^2 $: Fermat, class field theory, and complex
                 multiplication}}: David A. Cox. John Wiley \& Sons, New
                 York. (1989). 351 pages. \$49.95, \pounds 29.95}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "34",
  number =       "10",
  pages =        "141--141",
  month =        nov,
  year =         "1997",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:40 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122197902650",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1997:SIS
author: Anonymous
title: SCAN-97 International Symposium on Scientific Computing Computer Arithmetic and Validated Numerics
journal: j-J-COMPUT-APPL-MATH
volume: 81
number: 2
pages: N13--N14
day: 8
month: jul
monthnumber: 7
year: 1997
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:02 MST 2017
bibtimestamp: 2017.02.25 12:36:02 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042797900741
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Anonymous
rawtitle:
{SCAN-97} International Symposium on Scientific Computing Computer Arithmetic and Validated Numerics

entry:
@Article{Anonymous:1997:SIS,
  author =       "Anonymous",
  title =        "{SCAN-97} International Symposium on Scientific
                 Computing Computer Arithmetic and Validated Numerics",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "81",
  number =       "2",
  pages =        "N13--N14",
  day =          "8",
  month =        jul,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042797900741",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: fparith.bib
label: Aoki:1997:RCR
author: Takafumi Aoki and Hiroaki Amada and Tatsuo Higuchi
title: Real / Complex Reconfigurable Arithmetic Using Redundant Complex Number Systems
crossref: Lang:1997:ISC
pages: 200--207
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Aoki.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Takafumi Aoki and Hiroaki Amada and Tatsuo Higuchi
rawtitle: Real\slash Complex Reconfigurable Arithmetic Using Redundant Complex Number Systems
entry:
@InProceedings{Aoki:1997:RCR,
  author =       "Takafumi Aoki and Hiroaki Amada and Tatsuo Higuchi",
  title =        "Real\slash Complex Reconfigurable Arithmetic Using
                 Redundant Complex Number Systems",
  crossref =     "Lang:1997:ISC",
  pages =        "200--207",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Aoki.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:1997:ACT
author: Mark G. Arnold and Thomas A. Bailey and John R. Cowles and Mark D. Winkel
title: Arithmetic Co-Transformations in the Real and Complex Logarithmic Number Systems
crossref: Lang:1997:ISC
pages: 190--199
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Arnold.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Mark G. Arnold and Thomas A. Bailey and John R. Cowles and Mark D. Winkel
rawtitle: Arithmetic Co-Transformations in the Real and Complex Logarithmic Number Systems
entry:
@InProceedings{Arnold:1997:ACT,
  author =       "Mark G. Arnold and Thomas A. Bailey and John R. Cowles
                 and Mark D. Winkel",
  title =        "Arithmetic Co-Transformations in the Real and Complex
                 Logarithmic Number Systems",
  crossref =     "Lang:1997:ISC",
  pages =        "190--199",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Arnold.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Atkinson-Barr:1997:LEP
author: Martin Atkinson-Barr
title: Letter to the Editor: Pentium II Math Bug
journal: j-DDJ
volume: 22
number: 10
pages: 10--10
month: oct
monthnumber: 10
year: 1997
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Thu Nov 8 14:50:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:37 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Martin Atkinson-Barr
rawtitle: Letter to the {Editor}: {Pentium II} Math Bug
note:
Identifies himself as the ``Mr. X'' cited in cite Collins:1997:IPI, and provides more the background on the discovery of the Pentium FIST (floating-point to integer store) instruction.

rawnote:
Identifies himself as the ``Mr. X'' cited in \cite{Collins:1997:IPI}, and provides more the background on the discovery of the Pentium FIST (floating-point to integer store) instruction.

entry:
@Article{Atkinson-Barr:1997:LEP,
  author =       "Martin Atkinson-Barr",
  title =        "Letter to the {Editor}: {Pentium II} Math Bug",
  journal =      j-DDJ,
  volume =       "22",
  number =       "10",
  pages =        "10--10",
  month =        oct,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Identifies himself as the ``Mr. X'' cited in
                 \cite{Collins:1997:IPI}, and provides more the
                 background on the discovery of the Pentium FIST
                 (floating-point to integer store) instruction.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Avnaim:1997:ESD
title: Evaluating Signs of Determinants Using Single-Precision Arithmetic
journal: j-ALGORITHMICA
volume: 17
number: 2
pages: 111--132
month: feb
monthnumber: 2
year: 1997
CODEN: ALGOEJ
ISSN: 0178-4617 (print), 1432-0541 (electronic) OR 01784617 (print), 14320541 (electronic)
ISSNL: 0178-4617 OR 01784617
MRclass: 65Y25 (65F99 68U05)
MRnumber: MR1425729 (97k:65311)
MRreviewer: Luiz Henrique de Figueiredo
bibdate: Fri Jan 6 11:38:07 MST 2006
bibtimestamp: 2006.01.06 11:38:07 MST
fjournal: Algorithmica. An International Journal in Computer Science
keywords: exact arithmetic; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/453
rawtitle: Evaluating Signs of Determinants Using Single-Precision Arithmetic
author:
Francis Avnaim and Jean-Daniel Boissonnat and Olivier Devillers and Franco P. Preparata and Mariette Yvinec

bibsource:
dblp-journals-algorithmica.bib; http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica17.html#AvnaimBDPY97; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0178-4617&volume=17&issue=2; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica; MathSciNet database

URL:
http://www.springerlink.com/link.asp?id=nlr883hde9w2av31; http://www.springerlink.com/openurl.asp?genre=article&eissn=1432-0541&volume=17&issue=2&spage=111; http://www.springerlink.com/openurl.asp?genre=article&issn=0178-4617&volume=17&issue=2&spage=111

abstract:
We propose a method to evaluate signs of $ 2 times 2 $ and $ 3 times 3 $ determinants with $b$-bit integer entries using only $b$ and $ (b + 1) $-bit arithmetic respectively. This algorithm has numerous applications in geometric computation and provides a general and practical approach to robustness. The algorithm has been implemented and experimental results show that it slows down the computing time by only a small factor with respect to floating-point calculation.

rawabstract:
We propose a method to evaluate signs of $ 2 \times 2 $ and $ 3 \times 3 $ determinants with $b$-bit integer entries using only $b$ and $ (b + 1) $-bit arithmetic respectively. This algorithm has numerous applications in geometric computation and provides a general and practical approach to robustness. The algorithm has been implemented and experimental results show that it slows down the computing time by only a small factor with respect to floating-point calculation.

rawauthor:
Francis Avnaim and Jean-Daniel Boissonnat and Olivier Devillers and Franco P. Preparata and Mariette Yvinec

entry:
@Article{Avnaim:1997:ESD,
  author =       "Francis Avnaim and Jean-Daniel Boissonnat and Olivier
                 Devillers and Franco P. Preparata and Mariette Yvinec",
  title =        "Evaluating Signs of Determinants Using
                 Single-Precision Arithmetic",
  journal =      j-ALGORITHMICA,
  volume =       "17",
  number =       "2",
  pages =        "111--132",
  month =        feb,
  year =         "1997",
  CODEN =        "ALGOEJ",
  ISSN =         "0178-4617 (print), 1432-0541 (electronic)",
  ISSN-L =       "0178-4617",
  MRclass =      "65Y25 (65F99 68U05)",
  MRnumber =     "MR1425729 (97k:65311)",
  MRreviewer =   "Luiz Henrique de Figueiredo",
  bibdate =      "Fri Jan 6 11:38:07 MST 2006",
  bibsource =    "dblp-journals-algorithmica.bib;
                 http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica17.html#AvnaimBDPY97;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0178-4617&volume=17&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica;
                 MathSciNet database",
  URL =          "http://www.springerlink.com/link.asp?id=nlr883hde9w2av31;
                 http://www.springerlink.com/openurl.asp?genre=article&eissn=1432-0541&volume=17&issue=2&spage=111;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0178-4617&volume=17&issue=2&spage=111",
  abstract =     "We propose a method to evaluate signs of $ 2 \times 2
                 $ and $ 3 \times 3 $ determinants with $b$-bit integer
                 entries using only $b$ and $ (b + 1) $-bit arithmetic
                 respectively. This algorithm has numerous applications
                 in geometric computation and provides a general and
                 practical approach to robustness. The algorithm has
                 been implemented and experimental results show that it
                 slows down the computing time by only a small factor
                 with respect to floating-point calculation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Algorithmica. An International Journal in Computer
                 Science",
  journal-URL =  "http://link.springer.com/journal/453",
  keywords =     "exact arithmetic; floating-point arithmetic",
  oldlabel =     "AvnaimBDPY97",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/algorithmica/AvnaimBDPY97",
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bibtype: inproceedings
filename: fparith.bib
label: Bajard:1997:RMM
author: Jean-Claude Bajard and Laurent-Stephane Didier and Peter Kornerup
title: An RNS Montgomery Modular Multiplication Algorithm
crossref: Lang:1997:ISC
pages: 234--239
year: 1997
bibdate: Wed Nov 14 18:54:27 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:54:27 ???
note: A revised version published in IEEE Transactions on Computers, Vol.46(7), July 1998
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Bajard.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Jean-Claude Bajard and Laurent-St{\'e}phane Didier and Peter Kornerup
rawnote: A revised version published in IEEE Transactions on Computers, Vol.46(7), July 1998
rawtitle: An {RNS Montgomery} Modular Multiplication Algorithm
entry:
@InProceedings{Bajard:1997:RMM,
  author =       "Jean-Claude Bajard and Laurent-St{\'e}phane Didier and
                 Peter Kornerup",
  title =        "An {RNS Montgomery} Modular Multiplication Algorithm",
  crossref =     "Lang:1997:ISC",
  pages =        "234--239",
  year =         "1997",
  bibdate =      "Wed Nov 14 18:54:27 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A revised version published in IEEE Transactions on
                 Computers, Vol.46(7), July 1998",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Bajard.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Baker:1997:LEP
author: Louis Baker
title: Letter to the Editor: Pentium II Math Bug
journal: j-DDJ
volume: 22
number: 10
pages: 10--10
month: oct
monthnumber: 10
year: 1997
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Thu Nov 8 14:50:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:37 ???
note: Comments on the Ariane 5 missile failure mentioned in cite Collins:1997:IPI.
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Louis Baker
rawnote: Comments on the Ariane 5 missile failure mentioned in \cite{Collins:1997:IPI}.
rawtitle: Letter to the {Editor}: {Pentium II} Math Bug
entry:
@Article{Baker:1997:LEP,
  author =       "Louis Baker",
  title =        "Letter to the {Editor}: {Pentium II} Math Bug",
  journal =      j-DDJ,
  volume =       "22",
  number =       "10",
  pages =        "10--10",
  month =        oct,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Comments on the Ariane 5 missile failure mentioned in
                 \cite{Collins:1997:IPI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: inproceedings
filename: fparith.bib
label: Beaumont-Smith:1997:GBA
author: Andrew Beaumont-Smith and Neil Burgess
title: A GaAs 32-Bit Adder
crossref: Lang:1997:ISC
pages: 10--17
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Beaumont_Smith.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Andrew Beaumont-Smith and Neil Burgess
rawtitle: A {GaAs} 32-Bit Adder
entry:
@InProceedings{Beaumont-Smith:1997:GBA,
  author =       "Andrew Beaumont-Smith and Neil Burgess",
  title =        "A {GaAs} 32-Bit Adder",
  crossref =     "Lang:1997:ISC",
  pages =        "10--17",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Beaumont_Smith.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Blackford:1997:PEN
title: Practical Experience in the Numerical Dangers of Heterogeneous Computing
journal: j-TOMS
volume: 23
number: 2
pages: 133--147
month: jun
monthnumber: 6
year: 1997
CODEN: ACMSCU
DOI: https://doi.org/10.1145/264029.264030
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Nov 8 14:50:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:37 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p133-blackford/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawtitle: Practical Experience in the Numerical Dangers of Heterogeneous Computing
author:
L. S. Blackford and A. Cleary and A. Petitet and R. C. Whaley and J. Demmel and I. Dhillon and H. Ren and K. Stanley and J. Dongarra and S. Hammarling

abstract:
Special challenges exist in writing reliable numerical library software for heterogeneous computing environments. Although a lot of software for distributed-memory parallel computers has been written, porting this software to a network of workstations requires careful consideration. The symptoms of heterogeneous computing failures can range from erroneous results without warning to deadlock. Some of the problems are straightforward to solve, but for others the solutions are not so obvious, or incur an unacceptable overhead. Making software robust on heterogeneous systems often requires additional communication. We describe and illustrate the problems encountered during the development of ScaLAPACK and the NAG Numerical PVM Library. Where possible, we suggest ways to avoid potential pitfalls, or if that is not possible, we recommend that the software not be used on heterogeneous networks.

keywords:
distributed-memory systems, floating-point arithmetic, heterogeneous processor networks, message passing, numerical software, reliability

subject:
bf D.1.3 Software, PROGRAMMING TECHNIQUES, Concurrent Programming, Distributed programming. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms.

rawabstract:
Special challenges exist in writing reliable numerical library software for heterogeneous computing environments. Although a lot of software for distributed-memory parallel computers has been written, porting this software to a network of workstations requires careful consideration. The symptoms of heterogeneous computing failures can range from erroneous results without warning to deadlock. Some of the problems are straightforward to solve, but for others the solutions are not so obvious, or incur an unacceptable overhead. Making software robust on heterogeneous systems often requires additional communication. We describe and illustrate the problems encountered during the development of ScaLAPACK and the NAG Numerical PVM Library. Where possible, we suggest ways to avoid potential pitfalls, or if that is not possible, we recommend that the software not be used on heterogeneous networks.

rawauthor:
L. S. Blackford and A. Cleary and A. Petitet and R. C. Whaley and J. Demmel and I. Dhillon and H. Ren and K. Stanley and J. Dongarra and S. Hammarling

entry:
@Article{Blackford:1997:PEN,
  author =       "L. S. Blackford and A. Cleary and A. Petitet and R. C.
                 Whaley and J. Demmel and I. Dhillon and H. Ren and K.
                 Stanley and J. Dongarra and S. Hammarling",
  title =        "Practical Experience in the Numerical Dangers of
                 Heterogeneous Computing",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "133--147",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264030",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p133-blackford/",
  abstract =     "Special challenges exist in writing reliable numerical
                 library software for heterogeneous computing
                 environments. Although a lot of software for
                 distributed-memory parallel computers has been written,
                 porting this software to a network of workstations
                 requires careful consideration. The symptoms of
                 heterogeneous computing failures can range from
                 erroneous results without warning to deadlock. Some of
                 the problems are straightforward to solve, but for
                 others the solutions are not so obvious, or incur an
                 unacceptable overhead. Making software robust on
                 heterogeneous systems often requires additional
                 communication. We describe and illustrate the problems
                 encountered during the development of ScaLAPACK and the
                 NAG Numerical PVM Library. Where possible, we suggest
                 ways to avoid potential pitfalls, or if that is not
                 possible, we recommend that the software not be used on
                 heterogeneous networks.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "distributed-memory systems, floating-point arithmetic,
                 heterogeneous processor networks, message passing,
                 numerical software, reliability",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming, Distributed programming. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic. {\bf G.1.0} Mathematics
                 of Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms.",
}


bibtype: article
filename: fparith.bib
label: Blinn:1997:JBC
author: James F. Blinn
title: Jim Blinn's Corner: Floating-Point Tricks
journal: j-IEEE-CGA
volume: 17
number: 4
pages: 80--84
month: jul
monthnumber: 7
year: 1997
CODEN: ICGADZ
DOI: https://doi.org/10.1109/38.595279
ISSN: 0272-1716 (print), 1558-1756 (electronic) OR 02721716 (print), 15581756 (electronic)
ISSNL: 0272-1716 OR 02721716
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Computer Graphics and Applications
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/portal/web/csdl/magazines/cga
rawauthor: James F. Blinn
rawtitle: {Jim Blinn}'s Corner: Floating-Point Tricks
note:
Discusses use of IEEE 754 single-precision floating-point bit patterns as integers for implementations of fast, but low-accuracy, functions useful in computer graphics.

rawnote:
Discusses use of IEEE 754 single-precision floating-point bit patterns as integers for implementations of fast, but low-accuracy, functions useful in computer graphics.

entry:
@Article{Blinn:1997:JBC,
  author =       "James F. Blinn",
  title =        "{Jim Blinn}'s Corner: Floating-Point Tricks",
  journal =      j-IEEE-CGA,
  volume =       "17",
  number =       "4",
  pages =        "80--84",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/38.595279",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Discusses use of IEEE 754 single-precision
                 floating-point bit patterns as integers for
                 implementations of fast, but low-accuracy, functions
                 useful in computer graphics.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
  summary =      "The author discusses IEEE floating point
                 representation that stores numbers in what amounts to
                 scientific notation. He considers the sign bit, the
                 logarithm function, function approximations, errors and
                 refinements \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Bomar:1997:RNA
author: B. W. Bomar and L. M. Smith and R. D. Joseph
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 44
number: 11
pages: 952--955
month: nov
monthnumber: 11
year: 1997
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.644048
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
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 Circuits and Systems. 2, Analog and Digital Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: B. W. Bomar and L. M. Smith and R. D. Joseph
title:
Roundoff noise analysis of state-space digital filters implemented on floating-point digital signal processors

rawtitle:
Roundoff noise analysis of state-space digital filters implemented on floating-point digital signal processors

entry:
@Article{Bomar:1997:RNA,
  author =       "B. W. Bomar and L. M. Smith and R. D. Joseph",
  title =        "Roundoff noise analysis of state-space digital filters
                 implemented on floating-point digital signal
                 processors",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "44",
  number =       "11",
  pages =        "952--955",
  month =        nov,
  year =         "1997",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.644048",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  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 Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "An expression is obtained for the output
                 floating-point roundoff noise variance of a general
                 Nth-order state-space digital filter with zero-mean
                 white noise input signal. This expression is then
                 simplified for the case there the filter is implemented
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Bshouty:1997:TBA
author: Nader H. Bshouty and Yishay Mansour and Baruch Schieber and Prasoon Tiwari
title: A tight bound for approximating the square root
journal: j-INFO-PROC-LETT
volume: 63
number: 4
pages: 211--213
day: 10
month: sep
monthnumber: 9
year: 1997
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68Q25 (65B15 68Q40)
MRnumber: 1 477 306
bibdate: Sat Nov 7 17:55:54 MST 1998
bibtimestamp: 1998.11.07 17:55:54 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Nader H. Bshouty and Yishay Mansour and Baruch Schieber and Prasoon Tiwari
rawtitle: A tight bound for approximating the square root
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Bshouty:1997:TBA,
  author =       "Nader H. Bshouty and Yishay Mansour and Baruch
                 Schieber and Prasoon Tiwari",
  title =        "A tight bound for approximating the square root",
  journal =      j-INFO-PROC-LETT,
  volume =       "63",
  number =       "4",
  pages =        "211--213",
  day =          "10",
  month =        sep,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68Q25 (65B15 68Q40)",
  MRnumber =     "1 477 306",
  bibdate =      "Sat Nov 7 17:55:54 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: inproceedings
filename: fparith.bib
label: Burgess:1997:SUR
author: Neil Burgess
title: Scaled and unscaled residue number system to binary conversion techniques using the core function
crossref: Lang:1997:ISC
pages: 250--257
year: 1997
DOI: https://doi.org/10.1109/ARITH.1997.614902
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Burgess.pdf
keywords: ARITH-13; residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Neil Burgess
rawtitle: Scaled and unscaled residue number system to binary conversion techniques using the core function
entry:
@InProceedings{Burgess:1997:SUR,
  author =       "Neil Burgess",
  title =        "Scaled and unscaled residue number system to binary
                 conversion techniques using the core function",
  crossref =     "Lang:1997:ISC",
  pages =        "250--257",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ARITH.1997.614902",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Burgess.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13; residue arithmetic; residue number system",
  summary =      "The paper presents related techniques for converting a
                 residue number system (RNS) number to binary, with and
                 without scaling, that use the core function. The
                 techniques remove the difficulties associated with
                 conversion procedures based on the \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Callaway:1997:PDC
author: Thomas K. Callaway and Earl E. Swartzlander, Jr.
title: Power-Delay Characteristics of CMOS Multipliers
crossref: Lang:1997:ISC
pages: 26--33
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Callaway.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Thomas K. Callaway and Earl E. {Swartzlander, Jr.}
rawtitle: Power-Delay Characteristics of {CMOS} Multipliers
entry:
@InProceedings{Callaway:1997:PDC,
  author =       "Thomas K. Callaway and Earl E. {Swartzlander, Jr.}",
  title =        "Power-Delay Characteristics of {CMOS} Multipliers",
  crossref =     "Lang:1997:ISC",
  pages =        "26--33",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Callaway.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Cao:1997:HPH
author: Jun Cao and Belle W. Y. Wei
title: High-Performance Hardware for Function Generation
crossref: Lang:1997:ISC
pages: 184--189
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cao.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Jun Cao and Belle W. Y. Wei
rawtitle: High-Performance Hardware for Function Generation
entry:
@InProceedings{Cao:1997:HPH,
  author =       "Jun Cao and Belle W. Y. Wei",
  title =        "High-Performance Hardware for Function Generation",
  crossref =     "Lang:1997:ISC",
  pages =        "184--189",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cao.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Cena:1997:QCA
author: Gianluca Cena and Paolo Montuschi and Luigi Ciminiera and Andrea Sanna
title: A Q-Coder Algorithm with Carry Free Addition
crossref: Lang:1997:ISC
pages: 282
year: 1997
bibdate: Sat Nov 17 12:22:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:22:42 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cena.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Gianluca Cena and Paolo Montuschi and Luigi Ciminiera and Andrea Sanna
rawtitle: A {Q}-Coder Algorithm with Carry Free Addition
entry:
@InProceedings{Cena:1997:QCA,
  author =       "Gianluca Cena and Paolo Montuschi and Luigi Ciminiera
                 and Andrea Sanna",
  title =        "A {Q}-Coder Algorithm with Carry Free Addition",
  crossref =     "Lang:1997:ISC",
  pages =        "282",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cena.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: techreport
filename: fparith.bib
label: Chen:1997:PEG
author: Yirng-An Chen and Randal E. Bryant
title: PBHD: an efficient graph representation for floating point circuit verification
type: Report
number: CMU-CS-97-134
institution: Department of Computer Science, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 282
year: 1997
bibdate: Thu May 09 08:39:56 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:39:56 ???
acknowledgement: ack-nhfb
rawauthor: Yirng-An Chen and Randal E. Bryant
rawtitle: {PBHD}: an efficient graph representation for floating point circuit verification
entry:
@TechReport{Chen:1997:PEG,
  author =       "Yirng-An Chen and Randal E. Bryant",
  title =        "{PBHD}: an efficient graph representation for floating
                 point circuit verification",
  type =         "Report",
  number =       "CMU-CS-97-134",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  year =         "1997",
  bibdate =      "Thu May 09 08:39:56 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Collins:1997:IPI
author: Robert C. Collins
title: Inside the Pentium II Math Bug
journal: j-DDJ
volume: 22
number: 8
pages: 52, 55--57
month: aug
monthnumber: 8
year: 1997
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Sat Mar 07 08:27:48 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.07 08:27:48 ???
note: See letters cite Atkinson-Barr:1997:LEP,Baker:1997:LEP.
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Robert C. Collins
rawnote: See letters \cite{Atkinson-Barr:1997:LEP,Baker:1997:LEP}.
rawtitle: Inside the {Pentium II} Math Bug
abstract:
Two days before Intel's biggest processor announcement in years, a math bug in the Pentium Pro and Pentium II came to light. Robert takes you inside the Dan-0411 flag erratum,' and tells how the story unfolded.

rawabstract:
Two days before Intel's biggest processor announcement in years, a math bug in the Pentium Pro and Pentium II came to light. Robert takes you inside the Dan-0411 flag erratum,' and tells how the story unfolded.

entry:
@Article{Collins:1997:IPI,
  author =       "Robert C. Collins",
  title =        "Inside the {Pentium II} Math Bug",
  journal =      j-DDJ,
  volume =       "22",
  number =       "8",
  pages =        "52, 55--57",
  month =        aug,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Sat Mar 07 08:27:48 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letters
                 \cite{Atkinson-Barr:1997:LEP,Baker:1997:LEP}.",
  abstract =     "Two days before Intel's biggest processor announcement
                 in years, a math bug in the Pentium Pro and Pentium II
                 came to light. Robert takes you inside the Dan-0411
                 flag erratum,' and tells how the story unfolded.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: fparith.bib
label: Compagner:1997:RER
author: A. Compagner and A. S. Berdnikov and S. B. Turtia and A. Larionov
title: Rounding errors in random number generators
journal: j-COMP-PHYS-COMM
volume: 106
number: 3
pages: 207--218
month: nov
monthnumber: 11
year: 1997
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(97)00070-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Dec 29 21:19:40 MST 2011
bibtimestamp: 2011.12.29 21:19:40 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465597000702
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. Compagner and A. S. Berdnikov and S. B. Turtia and A. Larionov
rawtitle: Rounding errors in random number generators
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib

abstract:
The deviations of the cumulative distribution function from the uniform one for the pseudorandom floating point values produced by integer arithmetics are discussed. It is shown that the conversion from fixed point values into floating point values introduces specific artefacts even when the integer arithmetics guarantees ideal uniformity. Two type of defects are considered: the appearance of the value 1.0 among pseudorandom values, and the sharp jumps of uniformity at the level of discreteness which corresponds to the computer representation of the floating point values. The non-uniformity at small level of discreteness can be neglected in most cases, but the appearance of the parasitic value 1.0 where nobody expects it can be very dangerous if special precautions are not taken by the user. Both defects are demonstrated using the random number generator from the system library of the Microsoft Power Station Fortran 1.0.

rawabstract:
The deviations of the cumulative distribution function from the uniform one for the pseudorandom floating point values produced by integer arithmetics are discussed. It is shown that the conversion from fixed point values into floating point values introduces specific artefacts even when the integer arithmetics guarantees ideal uniformity. Two type of defects are considered: the appearance of the value 1.0 among pseudorandom values, and the sharp jumps of uniformity at the level of discreteness which corresponds to the computer representation of the floating point values. The non-uniformity at small level of discreteness can be neglected in most cases, but the appearance of the parasitic value 1.0 where nobody expects it can be very dangerous if special precautions are not taken by the user. Both defects are demonstrated using the random number generator from the system library of the Microsoft Power Station Fortran 1.0.

entry:
@Article{Compagner:1997:RER,
  author =       "A. Compagner and A. S. Berdnikov and S. B. Turtia and
                 A. Larionov",
  title =        "Rounding errors in random number generators",
  journal =      j-COMP-PHYS-COMM,
  volume =       "106",
  number =       "3",
  pages =        "207--218",
  month =        nov,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00070-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 29 21:19:40 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465597000702",
  abstract =     "The deviations of the cumulative distribution function
                 from the uniform one for the pseudorandom floating
                 point values produced by integer arithmetics are
                 discussed. It is shown that the conversion from fixed
                 point values into floating point values introduces
                 specific artefacts even when the integer arithmetics
                 guarantees ideal uniformity. Two type of defects are
                 considered: the appearance of the value 1.0 among
                 pseudorandom values, and the sharp jumps of uniformity
                 at the level of discreteness which corresponds to the
                 computer representation of the floating point values.
                 The non-uniformity at small level of discreteness can
                 be neglected in most cases, but the appearance of the
                 parasitic value 1.0 where nobody expects it can be very
                 dangerous if special precautions are not taken by the
                 user. Both defects are demonstrated using the random
                 number generator from the system library of the
                 Microsoft Power Station Fortran 1.0.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: fparith.bib
label: Cuyt:1997:FPV
author: A. Cuyt
title: Floating-point versus Symbolic Computations in the QD-algorithm
journal: j-J-SYMBOLIC-COMP
volume: 24
number: 6
pages: 695--703
month: dec
monthnumber: 12
year: 1997
CODEN: JSYCEH
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
fjournal: Journal of Symbolic Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/07477171
rawauthor: A. Cuyt
rawtitle: Floating-point versus Symbolic Computations in the {QD}-algorithm
entry:
@Article{Cuyt:1997:FPV,
  author =       "A. Cuyt",
  title =        "Floating-point versus Symbolic Computations in the
                 {QD}-algorithm",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "24",
  number =       "6",
  pages =        "695--703",
  month =        dec,
  year =         "1997",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  pagecount =    "9",
}


bibtype: techreport
filename: fparith.bib
label: Daumas:1997:RPC
author: Marc Daumas and D. W. Matula
title: Recoders for partial compression and rounding
type: Technical Report
number: 97-01
institution: Laboratoire de l'Informatique du Parallelisme
address: Lyon, France
pages: 695--703
year: 1997
bibdate: Thu Nov 13 10:48:03 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.11.13 10:48:03 ???
acknowledgement: ack-nhfb
rawauthor: Marc Daumas and D. W. Matula
rawtitle: Recoders for partial compression and rounding
entry:
@TechReport{Daumas:1997:RPC,
  author =       "Marc Daumas and D. W. Matula",
  title =        "Recoders for partial compression and rounding",
  type =         "Technical Report",
  number =       "97-01",
  institution =  "Laboratoire de l'Informatique du Parall{\`e}lisme",
  address =      "Lyon, France",
  year =         "1997",
  bibdate =      "Thu Nov 13 10:48:03 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Daumas:1997:VRD
author: Marc Daumas and D. W. Matula
title: Validated roundings of dot products by sticky accumulation
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 5
pages: 623--629
month: may
monthnumber: 5
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.589241
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:23 MDT 2011
bibtimestamp: 2011.07.06 10:06:23 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589241
fjournal: IEEE Transactions on Computers
keywords: floating-point arithmetic
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Marc Daumas and D. W. Matula
rawtitle: Validated roundings of dot products by sticky accumulation
abstract:
The dot product operation is very prevalent in scientific computation and has therefore been incorporated as a primitive operation in some languages. The implementation of the dot product operation by a sequence of IEEE standard multiplications and additions does not prevent a substantial accumulation of the round-off errors or warn the user about a catastrophic cancellation. We present the design of a double precision dot product operation employing sticky accumulation, where the final rounded result is validated by raising a new exception flag if the result incurred catastrophic cancellation. Sticky accumulation can be implemented in a pipeline or parallel environment to sustain double precision with an extended control of the error. Our design allows that, in the absence of catastrophic cancellation, one ulp accuracy is guaranteed

rawabstract:
The dot product operation is very prevalent in scientific computation and has therefore been incorporated as a primitive operation in some languages. The implementation of the dot product operation by a sequence of IEEE standard multiplications and additions does not prevent a substantial accumulation of the round-off errors or warn the user about a catastrophic cancellation. We present the design of a double precision dot product operation employing sticky accumulation, where the final rounded result is validated by raising a new exception flag if the result incurred catastrophic cancellation. Sticky accumulation can be implemented in a pipeline or parallel environment to sustain double precision with an extended control of the error. Our design allows that, in the absence of catastrophic cancellation, one ulp accuracy is guaranteed

entry:
@Article{Daumas:1997:VRD,
  author =       "Marc Daumas and D. W. Matula",
  title =        "Validated roundings of dot products by sticky
                 accumulation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "5",
  pages =        "623--629",
  month =        may,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.589241",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589241",
  abstract =     "The dot product operation is very prevalent in
                 scientific computation and has therefore been
                 incorporated as a primitive operation in some
                 languages. The implementation of the dot product
                 operation by a sequence of IEEE standard
                 multiplications and additions does not prevent a
                 substantial accumulation of the round-off errors or
                 warn the user about a catastrophic cancellation. We
                 present the design of a double precision dot product
                 operation employing sticky accumulation, where the
                 final rounded result is validated by raising a new
                 exception flag if the result incurred catastrophic
                 cancellation. Sticky accumulation can be implemented in
                 a pipeline or parallel environment to sustain double
                 precision with an extended control of the error. Our
                 design allows that, in the absence of catastrophic
                 cancellation, one ulp accuracy is guaranteed",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1997:AME
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
title: Algorithms for Multi-Exponentiation Based on Complex Arithmetic
crossref: Lang:1997:ISC
pages: 208--217
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_algorithms.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawtitle: Algorithms for Multi-Exponentiation Based on Complex Arithmetic
entry:
@InProceedings{Dimitrov:1997:AME,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "Algorithms for Multi-Exponentiation Based on Complex
                 Arithmetic",
  crossref =     "Lang:1997:ISC",
  pages =        "208--217",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_algorithms.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1997:ERN
author: V. Dimitrov and G. A. Jullien and W. C. Miller
booktitle: Proceedings of the 40th Midwest Symposium on Circuits and Systems, 1997
title: Eisenstein residue number system with applications to DSP
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 675--678
year: 1997
DOI: https://doi.org/10.1109/MWSCAS.1997.662165
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: V. Dimitrov and G. A. Jullien and W. C. Miller
rawbooktitle: Proceedings of the 40th Midwest Symposium on Circuits and Systems, 1997
rawtitle: {Eisenstein} residue number system with applications to {DSP}
entry:
@InProceedings{Dimitrov:1997:ERN,
  author =       "V. Dimitrov and G. A. Jullien and W. C. Miller",
  booktitle =    "Proceedings of the 40th Midwest Symposium on Circuits
                 and Systems, 1997",
  title =        "{Eisenstein} residue number system with applications
                 to {DSP}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "675--678",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1997.662165",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new approach for processing complex numbers has been
                 proposed, Basically, it is aimed at the implementation
                 of radix-3 FFTs, but it can be used in any situation
                 where the requirement to process Eisenstein integers
                 arises, The comparison between \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1997:TAD
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
title: Theory and Applications for a Double-Base Number System
crossref: Lang:1997:ISC
pages: 44--53
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_theory.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawtitle: Theory and Applications for a Double-Base Number System
entry:
@InProceedings{Dimitrov:1997:TAD,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "Theory and Applications for a Double-Base Number
                 System",
  crossref =     "Lang:1997:ISC",
  pages =        "44--53",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_theory.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Doring:1997:DAL
author: Andreas Doring and Wolfgang J. Paul
title: Decimal adjustment of long numbers in constant time
journal: j-INFO-PROC-LETT
volume: 62
number: 3
pages: 161--163
day: 4
month: jun
monthnumber: 6
year: 1997
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68M07 (68M20)
MRnumber: 1 453 700
bibdate: Sat Nov 7 17:55:52 MST 1998
bibtimestamp: 1998.11.07 17:55:52 MST
fjournal: Information Processing Letters
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Andreas D{\"o}ring and Wolfgang J. Paul
rawtitle: Decimal adjustment of long numbers in constant time
entry:
@Article{Doring:1997:DAL,
  author =       "Andreas D{\"o}ring and Wolfgang J. Paul",
  title =        "Decimal adjustment of long numbers in constant time",
  journal =      j-INFO-PROC-LETT,
  volume =       "62",
  number =       "3",
  pages =        "161--163",
  day =          "4",
  month =        jun,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07 (68M20)",
  MRnumber =     "1 453 700",
  bibdate =      "Sat Nov 7 17:55:52 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Drmac:1997:IJR
author: Zlatko Drmac
journal: j-SIAM-J-SCI-COMP
volume: 18
number: 4
pages: 1200--1222
month: jul
monthnumber: 7
year: 1997
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827594265095
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
MRclass: 65F15 (65G10)
MRnumber: 98e:65027; 1 453 565
MRreviewer: Ljiljana Petkovi{\'c}
bibdate: Fri Dec 4 14:47:53 MST 1998
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SISC/18/4; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.12.04 14:47:53 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/26509
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
rawauthor: Zlatko Drma{\v{c}}
title:
Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic

rawtitle:
Implementation of {Jacobi} Rotations for Accurate Singular Value Computation in Floating Point Arithmetic

entry:
@Article{Drmac:1997:IJR,
  author =       "Zlatko Drma{\v{c}}",
  title =        "Implementation of {Jacobi} Rotations for Accurate
                 Singular Value Computation in Floating Point
                 Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "18",
  number =       "4",
  pages =        "1200--1222",
  month =        jul,
  year =         "1997",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827594265095",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F15 (65G10)",
  MRnumber =     "98e:65027; 1 453 565",
  MRreviewer =   "Ljiljana Petkovi{\'c}",
  bibdate =      "Fri Dec 4 14:47:53 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/18/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/26509",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}


bibtype: inproceedings
filename: fparith.bib
label: Drolshagen:1997:PES
author: A. Drolshagen and H. Henkelmann and W. Anheier
title: Processor elements for the standard cell implementation of residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 116--123
year: 1997
DOI: https://doi.org/10.1109/ASAP.1997.606818
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Drolshagen and H. Henkelmann and W. Anheier
rawtitle: Processor elements for the standard cell implementation of residue number systems
booktitle:
IEEE International Conference on Application-Specific Systems, Architectures and Processors, Proceedings, 14--16 July 1997

rawbooktitle:
{IEEE} International Conference on Application-Specific Systems, Architectures and Processors, Proceedings, 14--16 July 1997

entry:
@InProceedings{Drolshagen:1997:PES,
  author =       "A. Drolshagen and H. Henkelmann and W. Anheier",
  booktitle =    "{IEEE} International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, Proceedings, 14--16 July 1997",
  title =        "Processor elements for the standard cell
                 implementation of residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "116--123",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.1997.606818",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this article processor elements for the effective
                 implementation of standard cell circuits based on
                 residue number systems (RNS) are presented. Two new
                 processors are proposed helping to reduce the hardware
                 requirements of the implementations. \ldots{}",
}


bibtype: manual
filename: fparith.bib
label: EC:1997:IER
author: European Commission
title: The Introduction of the Euro and the Rounding of Currency Amounts
organization: European Commission Directorate General II Economic and Financial Affairs
address: Brussels, Belgium
pages: 29
year: 1997
bibdate: Fri Nov 28 11:18:05 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:18:05 ???
acknowledgement: ack-nhfb
rawauthor: {European Commission}
rawtitle: The Introduction of the Euro and the Rounding of Currency Amounts
entry:
@Manual{EC:1997:IER,
  author =       "{European Commission}",
  title =        "The Introduction of the Euro and the Rounding of
                 Currency Amounts",
  organization = "European Commission Directorate General II Economic
                 and Financial Affairs",
  address =      "Brussels, Belgium",
  pages =        "29",
  year =         "1997",
  bibdate =      "Fri Nov 28 11:18:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Edelman:1997:MPD
author: Alan Edelman
title: The Mathematics of the Pentium Division Bug
journal: j-SIAM-REVIEW
volume: 39
number: 1
pages: 54--67
month: mar
monthnumber: 3
year: 1997
CODEN: SIREAD
DOI: https://doi.org/10.1137/S0036144595293959
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 68M07
MRnumber: 1 439 485
bibdate: Sat Mar 29 09:55:47 MDT 2014
bibtimestamp: 2014.03.29 09:55:47 MDT
fjournal: SIAM Review
keywords: Intel Pentium divide flaw; Thomas R. Nicely
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1997
rawauthor: Alan Edelman
rawtitle: The Mathematics of the {Pentium} Division Bug
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIREV/39/1; http://epubs.siam.org/toc/siread/39/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

URL:
http://epubs.siam.org/sam-bin/dbq/article/29395; http://www-math.mit.edu/~edelman/homepage/papers/pentiumbug.pdf; http://www.siam.org/journals/sirev/sirev391.htm

abstract:
Despite all of the publicity surrounding the Pentium bug of 1994, the mathematical details of the bug are poorly understood. We discuss these details and supply a new proof of the Coe--Tang result that the at-risk divisors have six consecutive ones in positions 5 through 10. Also, we prove that the worst-case absolute error for arguments in $ [1, 2) $ is on the order of 1e-5.

rawabstract:
Despite all of the publicity surrounding the Pentium bug of 1994, the mathematical details of the bug are poorly understood. We discuss these details and supply a new proof of the Coe--Tang result that the at-risk divisors have six consecutive ones in positions 5 through 10. Also, we prove that the worst-case absolute error for arguments in $ [1, 2) $ is on the order of 1e-5.

entry:
@Article{Edelman:1997:MPD,
  author =       "Alan Edelman",
  title =        "The Mathematics of the {Pentium} Division Bug",
  journal =      j-SIAM-REVIEW,
  volume =       "39",
  number =       "1",
  pages =        "54--67",
  month =        mar,
  year =         "1997",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144595293959",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "68M07",
  MRnumber =     "1 439 485",
  bibdate =      "Sat Mar 29 09:55:47 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/39/1;
                 http://epubs.siam.org/toc/siread/39/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/29395;
                 http://www-math.mit.edu/~edelman/homepage/papers/pentiumbug.pdf;
                 http://www.siam.org/journals/sirev/sirev391.htm",
  abstract =     "Despite all of the publicity surrounding the Pentium
                 bug of 1994, the mathematical details of the bug are
                 poorly understood. We discuss these details and supply
                 a new proof of the Coe--Tang result that the at-risk
                 divisors have six consecutive ones in positions 5
                 through 10. Also, we prove that the worst-case absolute
                 error for arguments in $ [1, 2) $ is on the order of
                 1e-5.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "Intel Pentium divide flaw; Thomas R. Nicely",
  onlinedate =   "January 1997",
}


bibtype: inproceedings
filename: fparith.bib
label: Even:1997:DIC
author: Guy Even and Wolfgang Paul
title: On the Design of IEEE Compliant Floating Point Units
crossref: Lang:1997:ISC
pages: 54--63
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Even.pdf
keywords: ARITH-13
remark: Cited in cite Mueller:2000:CAC.
acknowledgement: ack-nhfb
rawauthor: Guy Even and Wolfgang Paul
rawtitle: On the Design of {IEEE} Compliant Floating Point Units
entry:
@InProceedings{Even:1997:DIC,
  author =       "Guy Even and Wolfgang Paul",
  title =        "On the Design of {IEEE} Compliant Floating Point
                 Units",
  crossref =     "Lang:1997:ISC",
  pages =        "54--63",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Even.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}


bibtype: article
filename: fparith.bib
label: Fitzpatrick:1997:EBE
author: P. Fitzpatrick
title: Extending backward error assertions to tolerance of large errors in floating point computations
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 4
pages: 505--510
month: apr
monthnumber: 4
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.588072
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:22 MDT 2011
bibtimestamp: 2011.07.06 10:06:22 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588072
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Fitzpatrick
rawtitle: Extending backward error assertions to tolerance of large errors in floating point computations
entry:
@Article{Fitzpatrick:1997:EBE,
  author =       "P. Fitzpatrick",
  title =        "Extending backward error assertions to tolerance of
                 large errors in floating point computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "505--510",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588072",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588072",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The use of backward error assertions combined with
                 iterative refinement has been suggested for the
                 correction of small fault induced errors in the
                 floating point solution of linear systems. We extend
                 this to the correction of large errors, typically
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Frougny:1997:FAS
author: Christiane Frougny
title: On-the-Fly Algorithms and Sequential Machines
crossref: Lang:1997:ISC
pages: 260--265
year: 1997
bibdate: Wed Nov 14 18:57:13 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:57:13 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Frougny.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Christiane Frougny
rawtitle: On-the-Fly Algorithms and Sequential Machines
entry:
@InProceedings{Frougny:1997:FAS,
  author =       "Christiane Frougny",
  title =        "On-the-Fly Algorithms and Sequential Machines",
  crossref =     "Lang:1997:ISC",
  pages =        "260--265",
  year =         "1997",
  bibdate =      "Wed Nov 14 18:57:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Frougny.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Garber:1997:NBB
author: Lee Garber
journal: j-COMPUTER
volume: 30
number: 4
pages: 25--27
month: apr
monthnumber: 4
year: 1997
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Tue May 06 16:51:53 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.06 16:51:53 ???
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: Lee Garber
title:
News Briefs: Binary Version Could Bring VRML into the Mainstream. FCC Jumps Into Internet Fray. Java and Floating-Point Math. Intel to Design NDRAM. Battle over Net Telephony. Vendors Seek Fast Modems. US Permits Export of Strong Encryption. E-commerce Nears $1 Billion. Chasing the Blue Light. Personal E-mail Use Will Soar

rawtitle:
News Briefs: Binary Version Could Bring {VRML} into the Mainstream. {FCC} Jumps Into {Internet} Fray. {Java} and Floating-Point Math. {Intel} to Design {NDRAM}. Battle over Net Telephony. Vendors Seek Fast Modems. {US} Permits Export of Strong Encryption. {E}-commerce Nears \$1 Billion. Chasing the Blue Light. Personal {E}-mail Use Will Soar

entry:
@Article{Garber:1997:NBB,
  author =       "Lee Garber",
  title =        "News Briefs: Binary Version Could Bring {VRML} into
                 the Mainstream. {FCC} Jumps Into {Internet} Fray.
                 {Java} and Floating-Point Math. {Intel} to Design
                 {NDRAM}. Battle over Net Telephony. Vendors Seek Fast
                 Modems. {US} Permits Export of Strong Encryption.
                 {E}-commerce Nears \$1 Billion. Chasing the Blue Light.
                 Personal {E}-mail Use Will Soar",
  journal =      j-COMPUTER,
  volume =       "30",
  number =       "4",
  pages =        "25--27",
  month =        apr,
  year =         "1997",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Tue May 06 16:51:53 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: inproceedings
filename: fparith.bib
label: Garjanov:1997:CRE
author: A. E. Garjanov
booktitle: Proceedings of the 1st International Conference on Control of Oscillations and Chaos, 1997
title: Controlled round-off error oscillations for initial value problem numerical solution
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 333--334
year: 1997
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: A. E. Garjanov
rawbooktitle: Proceedings of the 1st International Conference on Control of Oscillations and Chaos, 1997
rawtitle: Controlled round-off error oscillations for initial value problem numerical solution
entry:
@InProceedings{Garjanov:1997:CRE,
  author =       "A. E. Garjanov",
  booktitle =    "Proceedings of the 1st International Conference on
                 Control of Oscillations and Chaos, 1997",
  title =        "Controlled round-off error oscillations for initial
                 value problem numerical solution",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "333--334",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A new methodology of a computer simulation is desired
                 for the accumulated round-off error elimination to be
                 possible. It is well known that the propagation of
                 round-off error in the numerical integration of
                 differential equations may be crucial \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Giachetti:1997:PRF
author: Ronald E. Giachetti and Robert E. Young
title: A Parametric Representation of Fuzzy Numbers and Their Arithmetic Operators
journal: j-FUZZY-SETS-SYSTEMS
volume: 92
number: 2
pages: ??--??
day: 1
month: sep
monthnumber: 9
year: 1997
CODEN: FSSYD8
ISSN: 0165-0114 (print), 1872-6801 (electronic) OR 01650114 (print), 18726801 (electronic)
ISSNL: 0165-0114 OR 01650114
bibdate: Tue Nov 05 15:22:41 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.11.05 15:22:41 ???
fjournal: Fuzzy Sets and Systems
keywords: arithmetic approximations; Fuzzy arithmetic; membership functions; triangular fuzzy numbers
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01650114
rawauthor: Ronald E. Giachetti and Robert E. Young
rawtitle: A Parametric Representation of Fuzzy Numbers and Their Arithmetic Operators
URL:
https://www.nist.gov/publications/parametric-representation-fuzzy-numbers-and-their-arithmetic-operators

abstract:
Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation of the extended operators can be performed on the parameters defining the fuzzy numbers, thus making the calculations trivial. Unfortunately the TFN shape is not closed under multiplication and division. The result of these operators is a polynomial membership function and the triangular shape only approximates the actual result.The linear approximation can be quite poor and may lead to incorrect results when used in engineering applications. We analyze this problem and propose six parameters which define parameterized fuzzy numbers (PFN), of which TFNs are a special case. We provide the methods for performing fuzzy arithmetic and show that the PFN representation is closed under the arithmetic operations. The new representation in conjunction with the arithmetic operators obeys many of the same arithmetic properties as TFNs. The new method has better accuracy and similar computational speed to using TFNs and appears to have benefits when used in engineering applications.

rawabstract:
Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation of the extended operators can be performed on the parameters defining the fuzzy numbers, thus making the calculations trivial. Unfortunately the TFN shape is not closed under multiplication and division. The result of these operators is a polynomial membership function and the triangular shape only approximates the actual result.The linear approximation can be quite poor and may lead to incorrect results when used in engineering applications. We analyze this problem and propose six parameters which define parameterized fuzzy numbers (PFN), of which TFNs are a special case. We provide the methods for performing fuzzy arithmetic and show that the PFN representation is closed under the arithmetic operations. The new representation in conjunction with the arithmetic operators obeys many of the same arithmetic properties as TFNs. The new method has better accuracy and similar computational speed to using TFNs and appears to have benefits when used in engineering applications.

entry:
@Article{Giachetti:1997:PRF,
  author =       "Ronald E. Giachetti and Robert E. Young",
  title =        "A Parametric Representation of Fuzzy Numbers and Their
                 Arithmetic Operators",
  journal =      j-FUZZY-SETS-SYSTEMS,
  volume =       "92",
  number =       "2",
  pages =        "??--??",
  day =          "1",
  month =        sep,
  year =         "1997",
  CODEN =        "FSSYD8",
  ISSN =         "0165-0114 (print), 1872-6801 (electronic)",
  ISSN-L =       "0165-0114",
  bibdate =      "Tue Nov 05 15:22:41 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nist.gov/publications/parametric-representation-fuzzy-numbers-and-their-arithmetic-operators",
  abstract =     "Direct implementation of extended arithmetic operators
                 on fuzzy numbers is computationally complex.
                 Implementation of the extension principle is equivalent
                 to solving a nonlinear programming problem. To overcome
                 this difficulty many applications limit the membership
                 functions to certain shapes, usually either triangular
                 fuzzy numbers (TFN) or trapezoidal fuzzy numbers
                 (TrFN). Then calculation of the extended operators can
                 be performed on the parameters defining the fuzzy
                 numbers, thus making the calculations trivial.
                 Unfortunately the TFN shape is not closed under
                 multiplication and division. The result of these
                 operators is a polynomial membership function and the
                 triangular shape only approximates the actual
                 result.The linear approximation can be quite poor and
                 may lead to incorrect results when used in engineering
                 applications. We analyze this problem and propose six
                 parameters which define parameterized fuzzy numbers
                 (PFN), of which TFNs are a special case. We provide the
                 methods for performing fuzzy arithmetic and show that
                 the PFN representation is closed under the arithmetic
                 operations. The new representation in conjunction with
                 the arithmetic operators obeys many of the same
                 arithmetic properties as TFNs. The new method has
                 better accuracy and similar computational speed to
                 using TFNs and appears to have benefits when used in
                 engineering applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Fuzzy Sets and Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01650114",
  keywords =     "arithmetic approximations; Fuzzy arithmetic;
                 membership functions; triangular fuzzy numbers",
}


bibtype: misc
filename: fparith.bib
label: Gosling:1997:ENC
author: James A. Gosling
title: The Evolution of Numerical Computing in Java
pages: ??--??
year: 1997
bibdate: Mon May 06 17:11:19 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 17:11:19 ???
URL: http://java.sun.com/people/jag/FP.html
acknowledgement: ack-nhfb
howpublished: World Wide Web document.
rawauthor: James A. Gosling
rawtitle: The Evolution of Numerical Computing in {Java}
entry:
@Misc{Gosling:1997:ENC,
  author =       "James A. Gosling",
  title =        "The Evolution of Numerical Computing in {Java}",
  howpublished = "World Wide Web document.",
  year =         "1997",
  bibdate =      "Mon May 06 17:11:19 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://java.sun.com/people/jag/FP.html",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Grosse:1997:RI
author: Eric Grosse
title: Real Inferno
crossref: Boisvert:1997:QNS
pages: 270--279
year: 1997
bibdate: Tue Jul 21 11:18:48 1998
bibtimestamp: 1998.07.21 11:18:48 ???
URL: ftp://cm.bell-labs.com/inferno/real.ps
acknowledgement: ack-nhfb
rawauthor: Eric Grosse
rawtitle: Real {Inferno}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
From cite Steele:2004:RHP: ``the language Limbo adopted accurate base conversion as one of its improvements over C (p. 271 of this article)''.

entry:
@InProceedings{Grosse:1997:RI,
  author =       "Eric Grosse",
  title =        "Real {Inferno}",
  crossref =     "Boisvert:1997:QNS",
  pages =        "270--279",
  year =         "1997",
  bibdate =      "Tue Jul 21 11:18:48 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://cm.bell-labs.com/inferno/real.ps",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``the language Limbo
                 adopted accurate base conversion as one of its
                 improvements over C (p. 271 of this article)''.",
}


bibtype: book
filename: fparith.bib
label: Guedj:1997:NUL
author: Denis Guedj
title: Numbers: The Universal Language
publisher: Harry N. Abrams, Inc.
address: New York, NY, USA
pages: 175
year: 1997
ISBN: 0-8109-2845-0 OR 0810928450
ISBN13: 978-0-8109-2845-9 OR 9780810928459
LCCN: QA141.G8413 1997
bibdate: Fri Nov 28 17:05:12 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 17:05:12 ???
note: Translated from the French edition cite Guedj:1996:EN by Lory Frankel.
acknowledgement: ack-mfc
rawauthor: Denis Guedj
rawnote: Translated from the French edition \cite{Guedj:1996:EN} by Lory Frankel.
rawtitle: Numbers: The Universal Language
entry:
@Book{Guedj:1997:NUL,
  author =       "Denis Guedj",
  title =        "Numbers: The Universal Language",
  publisher =    "Harry N. Abrams, Inc.",
  address =      "New York, NY, USA",
  pages =        "175",
  year =         "1997",
  ISBN =         "0-8109-2845-0",
  ISBN-13 =      "978-0-8109-2845-9",
  LCCN =         "QA141.G8413 1997",
  bibdate =      "Fri Nov 28 17:05:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from the French edition
                 \cite{Guedj:1996:EN} by Lory Frankel.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Hagihara:1997:FPD
author: Y. Hagihara and S. Inui and F. Okamoto and M. Nishida and T. Nakamura and H. Yamada
title: Floating-point datapaths with online built-in self speed test
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 32
number: 3
pages: 444--449
month: mar
monthnumber: 3
year: 1997
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: Y. Hagihara and S. Inui and F. Okamoto and M. Nishida and T. Nakamura and H. Yamada
rawtitle: Floating-point datapaths with online built-in self speed test
entry:
@Article{Hagihara:1997:FPD,
  author =       "Y. Hagihara and S. Inui and F. Okamoto and M. Nishida
                 and T. Nakamura and H. Yamada",
  title =        "Floating-point datapaths with online built-in self
                 speed test",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "32",
  number =       "3",
  pages =        "444--449",
  month =        mar,
  year =         "1997",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  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 Journal of Solid-State Circuits",
  summary =      "This paper describes floating-point (FP) datapaths
                 developed for graphics and simulation applications. The
                 datapaths are fabricated using 0.35 $\mu$m CMOS
                 technology and embedded in a 125 MHz, 291 MFLOPS vector
                 pipelined processor for use in supercomputers
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Haller:1997:HIS
author: B. Haller and M. Streiff and U. Fleisch and R. Zimmermann
booktitle: 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing
title: Hardware implementation of a systolic antenna array signal processor based on CORDIC arithmetic
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 4141--4144 (vol. 5)
year: 1997
DOI: https://doi.org/10.1109/ICASSP.1997.604858
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: B. Haller and M. Streiff and U. Fleisch and R. Zimmermann
rawbooktitle: {1997 IEEE International Conference on Acoustics, Speech, and Signal Processing}
rawtitle: Hardware implementation of a systolic antenna array signal processor based on {CORDIC} arithmetic
keywords:
Adaptive arrays; Antenna arrays; Application specific integrated circuits; Hardware; Minimization; Radar antennas; Real time systems; Signal processing algorithms; Sonar; Systolic arrays

entry:
@InProceedings{Haller:1997:HIS,
  author =       "B. Haller and M. Streiff and U. Fleisch and R.
                 Zimmermann",
  booktitle =    "{1997 IEEE International Conference on Acoustics,
                 Speech, and Signal Processing}",
  title =        "Hardware implementation of a systolic antenna array
                 signal processor based on {CORDIC} arithmetic",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4141--4144 (vol. 5)",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ICASSP.1997.604858",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adaptive arrays; Antenna arrays; Application specific
                 integrated circuits; Hardware; Minimization; Radar
                 antennas; Real time systems; Signal processing
                 algorithms; Sonar; Systolic arrays",
}


bibtype: book
filename: fparith.bib
label: Hanson:1997:CII
author: David R. Hanson
title: C Interfaces and Implementations: Techniques for Creating Reusable Software
publisher: pub-AW
address: pub-AW:adr
pages: xvii + 519
year: 1997
ISBN: 0-201-49841-3 OR 0201498413
ISBN13: 978-0-201-49841-7 OR 9780201498417
LCCN: QA76.73.C15H37 1997
bibdate: Fri Feb 27 16:08:11 1998
bibtimestamp: 1998.02.27 16:08:11 ???
series: Addison-Wesley Professional Computing Series
URL: http://www.cs.princeton.edu/software/cii/
subject: C (Computer program language); Computer software; Reusability; Literate Programming
acknowledgement: ack-nhfb
rawauthor: David R. Hanson
rawtitle: {C} Interfaces and Implementations: Techniques for Creating Reusable Software
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/litprog.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

TOC:
1. Introduction 2. Interfaces and Implementations 3. Atoms 4. Exceptions and Assertions 5. Memory Management 6. More Memory Management 7. Lists 8. Tables 9. Sets 10. Dynamic Arrays 11. Sequences 12. Rings 13. Bit Vectors 14. Formatting 15. Low-Level Strings 16. High-Level Strings 17. Extended-Precision Arithmetic 18. Arbitrary-Precision Arithmetic 19. Multiple-Precision Arithmetic 20. Threads

rawTOC:
1. Introduction \\ 2. Interfaces and Implementations \\ 3. Atoms \\ 4. Exceptions and Assertions \\ 5. Memory Management \\ 6. More Memory Management \\ 7. Lists \\ 8. Tables \\ 9. Sets \\ 10. Dynamic Arrays \\ 11. Sequences \\ 12. Rings \\ 13. Bit Vectors \\ 14. Formatting \\ 15. Low-Level Strings \\ 16. High-Level Strings \\ 17. Extended-Precision Arithmetic \\ 18. Arbitrary-Precision Arithmetic \\ 19. Multiple-Precision Arithmetic \\ 20. Threads

entry:
@Book{Hanson:1997:CII,
  author =       "David R. Hanson",
  title =        "{C} Interfaces and Implementations: Techniques for
                 Creating Reusable Software",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xvii + 519",
  year =         "1997",
  ISBN =         "0-201-49841-3",
  ISBN-13 =      "978-0-201-49841-7",
  LCCN =         "QA76.73.C15H37 1997",
  bibdate =      "Fri Feb 27 16:08:11 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/litprog.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "Addison-Wesley Professional Computing Series",
  URL =          "http://www.cs.princeton.edu/software/cii/",
  acknowledgement = ack-nhfb,
  subject =      "C (Computer program language); Computer software;
                 Reusability; Literate Programming",
  tableofcontents = "1. Introduction \\
                 2. Interfaces and Implementations \\
                 3. Atoms \\
                 4. Exceptions and Assertions \\
                 5. Memory Management \\
                 6. More Memory Management \\
                 7. Lists \\
                 8. Tables \\
                 9. Sets \\
                 10. Dynamic Arrays \\
                 11. Sequences \\
                 12. Rings \\
                 13. Bit Vectors \\
                 14. Formatting \\
                 15. Low-Level Strings \\
                 16. High-Level Strings \\
                 17. Extended-Precision Arithmetic \\
                 18. Arbitrary-Precision Arithmetic \\
                 19. Multiple-Precision Arithmetic \\
                 20. Threads",
}


bibtype: techreport
filename: fparith.bib
label: Hanson:1997:ECR
author: Kenton L. Hanson
title: Economical Correctly Rounded Binary Decimal Conversion
type: Report
pages: xvii + 519
day: 19
month: dec
monthnumber: 12
year: 1997
bibdate: Sat May 07 09:46:31 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.05.07 09:46:31 ???
acknowledgement: ack-nhfb
rawauthor: Kenton L. Hanson
rawtitle: Economical Correctly Rounded Binary Decimal Conversion
note:
Cited in cite [p. 134, reference 4]Hack:2004:IPR, and reported there to be now inaccessible. Further queries in May 2022 to four search engines fail to find this document, or its institution and address.

rawnote:
Cited in \cite[p. 134, reference 4]{Hack:2004:IPR}, and reported there to be now inaccessible. Further queries in May 2022 to four search engines fail to find this document, or its institution and address.

entry:
@TechReport{Hanson:1997:ECR,
  author =       "Kenton L. Hanson",
  title =        "Economical Correctly Rounded Binary Decimal
                 Conversion",
  type =         "Report",
  number =       "??",
  institution =  "????",
  address =      "????",
  day =          "19",
  month =        dec,
  year =         "1997",
  bibdate =      "Sat May 07 09:46:31 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in \cite[p. 134, reference 4]{Hack:2004:IPR},
                 and reported there to be now inaccessible. Further
                 queries in May 2022 to four search engines fail to find
                 this document, or its institution and address.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Hanson:1997:MAD
author: Kenton L. Hanson
pages: xvii + 519
day: 29
month: jul
monthnumber: 7
year: 1997
bibdate: Thu Oct 14 14:54:45 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.14 14:54:45 ???
URL: http://www.patentgenius.com/patent/5652862.html
remark: Patent held by Apple Computer, Inc., Cupertino, CA, USA.
acknowledgement: ack-nhfb
howpublished: US Patent 5652862
rawauthor: Kenton L. Hanson
title:
Method and apparatus for determining a precision of an intermediate arithmetic for converting values between a first numeric format and a second numeric format

abstract:
A method and apparatus for efficient allocation of temporary storage for performing accurate and correct numeric base conversions on a computer system is provided. Numeric base conversions are common because computers operate in binary whereas the values that are input into computers are based on a decimal system. A common source of error occurs when converted values are rounded. The intermediate arithmetic used to perform the conversion requires greater precision than the target floating point format. It is known that to always insure correctly rounded results, an extremely high precision intermediate arithmetic may be used. However, in many case this is a waste of system memory. To efficiently allocate system memory to this task, the most difficult rounding case is determined. The precision needed to correctly round the most difficult case is then derived. This information is then stored and subsequently used to allocate an efficient amount of storage whenever a numeric base conversion is to take place.

rawabstract:
A method and apparatus for efficient allocation of temporary storage for performing accurate and correct numeric base conversions on a computer system is provided. Numeric base conversions are common because computers operate in binary whereas the values that are input into computers are based on a decimal system. A common source of error occurs when converted values are rounded. The intermediate arithmetic used to perform the conversion requires greater precision than the target floating point format. It is known that to always insure correctly rounded results, an extremely high precision intermediate arithmetic may be used. However, in many case this is a waste of system memory. To efficiently allocate system memory to this task, the most difficult rounding case is determined. The precision needed to correctly round the most difficult case is then derived. This information is then stored and subsequently used to allocate an efficient amount of storage whenever a numeric base conversion is to take place.

rawtitle:
Method and apparatus for determining a precision of an intermediate arithmetic for converting values between a first numeric format and a second numeric format

entry:
@Misc{Hanson:1997:MAD,
  author =       "Kenton L. Hanson",
  title =        "Method and apparatus for determining a precision of an
                 intermediate arithmetic for converting values between a
                 first numeric format and a second numeric format",
  howpublished = "US Patent 5652862",
  day =          "29",
  month =        jul,
  year =         "1997",
  bibdate =      "Thu Oct 14 14:54:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentgenius.com/patent/5652862.html",
  abstract =     "A method and apparatus for efficient allocation of
                 temporary storage for performing accurate and correct
                 numeric base conversions on a computer system is
                 provided. Numeric base conversions are common because
                 computers operate in binary whereas the values that are
                 input into computers are based on a decimal system. A
                 common source of error occurs when converted values are
                 rounded. The intermediate arithmetic used to perform
                 the conversion requires greater precision than the
                 target floating point format. It is known that to
                 always insure correctly rounded results, an extremely
                 high precision intermediate arithmetic may be used.
                 However, in many case this is a waste of system memory.
                 To efficiently allocate system memory to this task, the
                 most difficult rounding case is determined. The
                 precision needed to correctly round the most difficult
                 case is then derived. This information is then stored
                 and subsequently used to allocate an efficient amount
                 of storage whenever a numeric base conversion is to
                 take place.",
  acknowledgement = ack-nhfb,
  remark =       "Patent held by Apple Computer, Inc., Cupertino, CA,
                 USA.",
}


bibtype: inproceedings
filename: fparith.bib
label: Harris:1997:SDA
author: David L. Harris and Stuart F. Oberman and Mark A. Horowitz
title: SRT Division Architectures and Implementations
crossref: Lang:1997:ISC
pages: 18--25
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: David L. Harris and Stuart F. Oberman and Mark A. Horowitz
rawtitle: {SRT} Division Architectures and Implementations
URL:
ftp://arith.stanford.edu/tr/srtcircuits.ps.Z; http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Harris.pdf

entry:
@InProceedings{Harris:1997:SDA,
  author =       "David L. Harris and Stuart F. Oberman and Mark A.
                 Horowitz",
  title =        "{SRT} Division Architectures and Implementations",
  crossref =     "Lang:1997:ISC",
  pages =        "18--25",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/srtcircuits.ps.Z;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Harris.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: techreport
filename: fparith.bib
label: Harrison:1997:FPV
author: John Robert Harrison
title: Floating point verification in HOL Light: the exponential function
type: Technical Report
number: 428
institution: University of Cambridge Computer Laboratory
address: Cambridge, UK
pages: ii + 110
month: jun
monthnumber: 6
year: 1997
LCCN: QA76.9.A96 H367 1997
bibdate: Thu Oct 24 14:30:40 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 14:30:40 ???
URL: http://www.cl.cam.ac.uk/users/jrh/papers/tang.ps.gz
keywords: automatic theorem proving; floating-point arithmetic; proof theory
acknowledgement: ack-nhfb
rawauthor: John Robert Harrison
rawtitle: Floating point verification in {HOL Light}: the exponential function
entry:
@TechReport{Harrison:1997:FPV,
  author =       "John Robert Harrison",
  title =        "Floating point verification in {HOL Light}: the
                 exponential function",
  type =         "Technical Report",
  number =       "428",
  institution =  "University of Cambridge Computer Laboratory",
  address =      "Cambridge, UK",
  pages =        "ii + 110",
  month =        jun,
  year =         "1997",
  LCCN =         "QA76.9.A96 H367 1997",
  bibdate =      "Thu Oct 24 14:30:40 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cl.cam.ac.uk/users/jrh/papers/tang.ps.gz",
  acknowledgement = ack-nhfb,
  keywords =     "automatic theorem proving; floating-point arithmetic;
                 proof theory",
}


bibtype: inproceedings
filename: fparith.bib
label: Harrison:1997:VAP
author: John Harrison
editor: Elsa L. Gunter and Amy Felty
title: Verifying the accuracy of polynomial approximations in HOL
publisher: pub-SV
address: pub-SV:adr
pages: 137--152
year: 1997
DOI: https://doi.org/10.1007/BFb0028391
ISBN: 3-540-63379-0 (print), 3-540-69526-5 (electronic) OR 3540633790 (print), 3540695265 (electronic)
LCCN: QA76.9.A96 I577 1997
bibdate: Tue May 07 16:45:16 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2024.05.07 16:45:16 ???
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/BFb0028381
rawauthor: John Harrison
raweditor: Elsa L. Gunter and Amy Felty
rawtitle: Verifying the accuracy of polynomial approximations in {HOL}
booktitle:
Theorem Proving in Higher Order Logics: 10th International Conference, TPHOLs'97, Murray Hill, NJ, USA, August 19--22, 1997, Proceedings

ISBN13:
978-3-540-63379-2 (print), 978-3-540-69526-4 (electronic) OR 9783540633792 (print), 9783540695264 (electronic)

rawbooktitle:
Theorem Proving in Higher Order Logics: {10th International Conference, TPHOLs'97, Murray Hill, NJ, USA, August 19--22, 1997, Proceedings}

entry:
@InProceedings{Harrison:1997:VAP,
  author =       "John Harrison",
  editor =       "Elsa L. Gunter and Amy Felty",
  booktitle =    "Theorem Proving in Higher Order Logics: {10th
                 International Conference, TPHOLs'97, Murray Hill, NJ,
                 USA, August 19--22, 1997, Proceedings}",
  title =        "Verifying the accuracy of polynomial approximations in
                 {HOL}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "137--152",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/BFb0028391",
  ISBN =         "3-540-63379-0 (print), 3-540-69526-5 (electronic)",
  ISBN-13 =      "978-3-540-63379-2 (print), 978-3-540-69526-4
                 (electronic)",
  LCCN =         "QA76.9.A96 I577 1997",
  bibdate =      "Tue May 07 16:45:16 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0028381",
}


bibtype: article
filename: fparith.bib
label: Hasan:1997:DA
author: M. A. Hasan
title: Division-and-accumulation over $ mathrm GF(2^m) $
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 6
pages: 705--708
month: jun
monthnumber: 6
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.600829
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:23 MDT 2011
bibtimestamp: 2011.07.06 10:06:23 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=600829
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. A. Hasan
rawtitle: Division-and-accumulation over {$ \mathrm {GF}(2^m) $}
entry:
@Article{Hasan:1997:DA,
  author =       "M. A. Hasan",
  title =        "Division-and-accumulation over {$ \mathrm {GF}(2^m)
                 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "6",
  pages =        "705--708",
  month =        jun,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.600829",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=600829",
  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: Hekstra:1997:FRL
author: Gerber J. Hekstra and Ed F. A. Deprettere
title: Fast Rotations: Low-Cost Arithmetic Methods for Orthonormal Rotation
crossref: Lang:1997:ISC
pages: 116--125
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hekstra.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Gerber J. Hekstra and Ed F. A. Deprettere
rawtitle: Fast Rotations: Low-Cost Arithmetic Methods for Orthonormal Rotation
entry:
@InProceedings{Hekstra:1997:FRL,
  author =       "Gerber J. Hekstra and Ed F. A. Deprettere",
  title =        "Fast Rotations: Low-Cost Arithmetic Methods for
                 Orthonormal Rotation",
  crossref =     "Lang:1997:ISC",
  pages =        "116--125",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hekstra.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Hiasat:1997:DIR
author: Ahmad A. Hiasat and Hoda S. Abdel-Aty-Zohdy
title: Design and Implementation of an RNS Division Algorithm
crossref: Lang:1997:ISC
pages: 240--249
year: 1997
bibdate: Wed Nov 14 18:57:54 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 18:57:54 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hiasat.pdf
keywords: ARITH-13; residue number system
acknowledgement: ack-nhfb
rawauthor: Ahmad A. Hiasat and Hoda S. Abdel-Aty-Zohdy
rawtitle: Design and Implementation of an {RNS} Division Algorithm
entry:
@InProceedings{Hiasat:1997:DIR,
  author =       "Ahmad A. Hiasat and Hoda S. Abdel-Aty-Zohdy",
  title =        "Design and Implementation of an {RNS} Division
                 Algorithm",
  crossref =     "Lang:1997:ISC",
  pages =        "240--249",
  year =         "1997",
  bibdate =      "Wed Nov 14 18:57:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hiasat.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13; residue number system",
}


bibtype: mastersthesis
filename: fparith.bib
label: Hix:1997:CTV
author: Robert W. Hix
title: A comparison of two VHDL design environments for FPGA-based computer arithmetic
type: Thesis (M.S.)
school: Tennessee Technological University
address: Cookeville, TN, USA
pages: x + 301
year: 1997
bibdate: Mon Mar 05 14:38:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.05 14:38:08 ???
acknowledgement: ack-nhfb
rawauthor: Robert W. Hix
rawtitle: A comparison of two {VHDL} design environments for {FPGA}-based computer arithmetic
entry:
@MastersThesis{Hix:1997:CTV,
  author =       "Robert W. Hix",
  title =        "A comparison of two {VHDL} design environments for
                 {FPGA}-based computer arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Tennessee Technological University",
  address =      "Cookeville, TN, USA",
  pages =        "x + 301",
  year =         "1997",
  bibdate =      "Mon Mar 05 14:38:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Holmes:1997:CAP
author: W. Neville Holmes
title: Composite Arithmetic: Proposal for a New Standard
journal: j-COMPUTER
volume: 30
number: 3
pages: 65--73
month: mar
monthnumber: 3
year: 1997
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Fri May 9 17:30:55 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.09 17:30:55 MDT
fjournal: Computer
acknowledgement: ack-nhfb
corpsource: Department of Comput., Tasmania University, Launceston, Tas., Australia
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
treatment: P Practical
rawauthor: W. Neville Holmes
rawtitle: Composite Arithmetic: Proposal for a New Standard
URL:
ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsdf.ps; ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsrf.ps; ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dssf.ps

keywords:
composite arithmetic; digital arithmetic; exact numbers; extended arithmetic; floating point arithmetic; formatting scheme; general computation; general-purpose arithmetic standard; inexact numbers; number display; number format; number storage; reliability; stability; standards

entry:
@Article{Holmes:1997:CAP,
  author =       "W. Neville Holmes",
  title =        "Composite Arithmetic: Proposal for a New Standard",
  journal =      j-COMPUTER,
  volume =       "30",
  number =       "3",
  pages =        "65--73",
  month =        mar,
  year =         "1997",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri May 9 17:30:55 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsdf.ps;
                 ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsrf.ps;
                 ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dssf.ps",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Comput., Tasmania University,
                 Launceston, Tas., Australia",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "composite arithmetic; digital arithmetic; exact
                 numbers; extended arithmetic; floating point
                 arithmetic; formatting scheme; general computation;
                 general-purpose arithmetic standard; inexact numbers;
                 number display; number format; number storage;
                 reliability; stability; standards",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Irmay:1997:RBZ
author: Shragga Irmay
title: The relationship between Zipf's law and the distribution of first digits
journal: j-J-APPL-STAT
volume: 24
number: 4
pages: 383--393
day: 1
month: aug
monthnumber: 8
year: 1997
ISSN: 0266-4763 (print), 1360-0532 (electronic) OR 02664763 (print), 13600532 (electronic)
ISSNL: 0266-4763 OR 02664763
MRclass: 62E15
MRnumber: 98h:62015
bibdate: Sat Apr 13 11:27:31 MDT 2002
bibtimestamp: 2002.04.13 11:27:31 MDT
fjournal: Journal of Applied Statistics
keywords: Benford's Law; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/cjas20
rawauthor: Shragga Irmay
rawtitle: The relationship between {Zipf}'s law and the distribution of first digits
bibsource:
http://www.catchword.co.uk/titles/carfax/02664763/; http://www.tandf.co.uk/journals/routledge/02664763.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.catchword.co.uk/cgi-bin/cgi?ini=carfax&body=linker&reqidx=/catchword/carfax/13600532/v24n4/s2/p383

entry:
@Article{Irmay:1997:RBZ,
  author =       "Shragga Irmay",
  title =        "The relationship between {Zipf}'s law and the
                 distribution of first digits",
  journal =      j-J-APPL-STAT,
  volume =       "24",
  number =       "4",
  pages =        "383--393",
  day =          "1",
  month =        aug,
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  MRclass =      "62E15",
  MRnumber =     "98h:62015",
  bibdate =      "Sat Apr 13 11:27:31 MDT 2002",
  bibsource =    "http://www.catchword.co.uk/titles/carfax/02664763/;
                 http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.catchword.co.uk/cgi-bin/cgi?ini=carfax&body=linker&reqidx=/catchword/carfax/13600532/v24n4/s2/p383",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  keywords =     "Benford's Law; Zipf's Law",
  xxpages =      "383--394",
}


bibtype: article
filename: fparith.bib
label: Ito:1997:EIA
author: M. Ito and N. Takagi and S. Yajima
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 4
pages: 495--498
month: apr
monthnumber: 4
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.588066
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:22 MDT 2011
bibtimestamp: 2011.07.06 10:06:22 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Ito and N. Takagi and S. Yajima
title:
Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification

rawtitle:
Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification

entry:
@Article{Ito:1997:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  title =        "Efficient initial approximation for multiplicative
                 division and square root by a multiplication with
                 operand modification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "495--498",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588066",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An efficient initial approximation method for
                 multiplicative division and square root is proposed. It
                 is a modification of the piecewise linear
                 approximation. The multiplication and the addition
                 required for the linear approximation are replaced by
                 \ldots{}",
}


bibtype: misc
filename: fparith.bib
label: Kahan:1997:JNL
author: W. Kahan
title: The John von Neumann lecture at the SIAM 45th annual meeting
pages: 495--498
year: 1997
bibdate: Sat Apr 28 18:52:17 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 18:52:17 ???
URL: http://www.cs.berkeley.edu/~wkahan/SIAMjvnl.ps
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: W. Kahan
rawtitle: The {John von Neumann} lecture at the {SIAM} 45th annual meeting
entry:
@Misc{Kahan:1997:JNL,
  author =       "W. Kahan",
  title =        "The {John von Neumann} lecture at the {SIAM} 45th
                 annual meeting",
  howpublished = "World-Wide Web document.",
  year =         "1997",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SIAMjvnl.ps",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Kahan:1997:LNS
author: W. Kahan
title: Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic
pages: 30
day: 1
month: oct
monthnumber: 10
year: 1997
bibdate: Mon Apr 25 17:54:35 2005
bibtimestamp: 2005.04.25 17:54:35 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: W. Kahan
rawtitle: Lecture Notes on the Status of {IEEE Standard 754 for Binary Floating-Point Arithmetic}
entry:
@Misc{Kahan:1997:LNS,
  author =       "W. Kahan",
  title =        "Lecture Notes on the Status of {IEEE Standard 754 for
                 Binary Floating-Point Arithmetic}",
  howpublished = "World-Wide Web document",
  pages =        "30",
  day =          "1",
  month =        oct,
  year =         "1997",
  bibdate =      "Mon Apr 25 17:54:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1997:RDI
author: W. Kahan and Melody Y. Ivory
title: Roundoff Degrades an Idealized Cantilever
type: Technical report
address: Berkeley, CA, USA
pages: 11
day: 3
month: jul
monthnumber: 7
year: 1997
bibdate: Fri May 03 12:15:09 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.03 12:15:09 ???
URL: http://www.cs.berkeley.edu/~wkahan/Cantilever.pdf; http://www.cs.berkeley.edu/~wkahan/Cantilever.ps
acknowledgement: ack-nhfb
rawauthor: W. Kahan and Melody Y. Ivory
rawtitle: Roundoff Degrades an Idealized Cantilever
institution:
Department of Mathematics and Department of Electrical Engineering and Computer Science, University of California, Berkeley

entry:
@TechReport{Kahan:1997:RDI,
  author =       "W. Kahan and Melody Y. Ivory",
  title =        "Roundoff Degrades an Idealized Cantilever",
  type =         "Technical report",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "11",
  day =          "3",
  month =        jul,
  year =         "1997",
  bibdate =      "Fri May 03 12:15:09 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Cantilever.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Cantilever.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kako:1997:PEF
author: Fujio Kako and Tateaki Sasaki
title: Proposal of ``Effective Floating-Point Number'' for Approximate Algebraic Computation
journal: j-SIGSAM
volume: 31
number: 3
pages: 31--31
month: sep
monthnumber: 9
year: 1997
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Wed Dec 17 07:49:58 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.12.17 07:49:58 ???
note: Poster abstract only. Discusses fuzzy and interval floating-point arithmetic.
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
rawauthor: Fujio Kako and Tateaki Sasaki
rawnote: Poster abstract only. Discusses fuzzy and interval floating-point arithmetic.
rawtitle: Proposal of {``Effective} Floating-Point Number'' for Approximate Algebraic Computation
entry:
@Article{Kako:1997:PEF,
  author =       "Fujio Kako and Tateaki Sasaki",
  title =        "Proposal of {``Effective} Floating-Point Number'' for
                 Approximate Algebraic Computation",
  journal =      j-SIGSAM,
  volume =       "31",
  number =       "3",
  pages =        "31--31",
  month =        sep,
  year =         "1997",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Dec 17 07:49:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Poster abstract only. Discusses fuzzy and interval
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: article
filename: fparith.bib
label: Kapur:1997:MVA
author: Deepak Kapur and M. Subramaniam
title: Mechanizing Verification of Arithmetic Circuits: SRT Division
journal: j-LECT-NOTES-COMP-SCI
volume: 1346
pages: 103--??
year: 1997
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:51:29 MST 2002
bibtimestamp: 2002.02.05 11:51:29 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Deepak Kapur and M. Subramaniam
rawtitle: Mechanizing Verification of Arithmetic Circuits: {SRT} Division
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1346.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1346/13460103.htm; http://link.springer-ny.com/link/service/series/0558/papers/1346/13460103.pdf

entry:
@Article{Kapur:1997:MVA,
  author =       "Deepak Kapur and M. Subramaniam",
  title =        "Mechanizing Verification of Arithmetic Circuits: {SRT}
                 Division",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1346",
  pages =        "103--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:29 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1346.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1346/13460103.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1346/13460103.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Karp:1997:HPD
author: Alan H. Karp and Peter Markstein
title: High-Precision Division and Square Root
journal: j-TOMS
volume: 23
number: 4
pages: 561--589
month: dec
monthnumber: 12
year: 1997
CODEN: ACMSCU
DOI: https://doi.org/10.1145/279232.279237
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Nov 8 14:50:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:37 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms, performance, division, quad precision, square root.
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Alan H. Karp and Peter Markstein
rawtitle: High-Precision Division and Square Root
URL:
http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/

abstract:
We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.

subject:
G.1.0 [Numerical Analysis]: General -- computer arithmetic. G.4 [Mathematics of Computing]: Mathematical Software.

rawabstract:
We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.

entry:
@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
  abstract =     "We present division and square root algorithms for
                 calculation with more bits than are handled by the
                 floating-point hardware. These algorithms avoid the
                 need to multiply two high-precision numbers, speeding
                 up the last iteration by as much as a factor of 10. We
                 also show how to produce the floating-point number
                 closest to the exact result with relatively few
                 additional operations.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, division, quad precision,
                 square root.",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic. G.4 [Mathematics of Computing]:
                 Mathematical Software.",
}


bibtype: book
filename: fparith.bib
label: Khinchin:1997:CF
author: Aleksandr Iakovlevich Khinchin
title: Continued fractions
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xi + 95
year: 1997
ISBN: 0-486-69630-8 (paperback) OR 0486696308 (paperback)
ISBN13: 978-0-486-69630-0 (paperback) OR 9780486696300 (paperback)
LCCN: QA295 .K513 1997
bibdate: Fri Nov 30 06:55:53 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.11.30 06:55:53 MST
acknowledgement: ack-nhfb
authordates: 1894--1959
rawauthor: Aleksandr Iakovlevich Khinchin
rawtitle: Continued fractions
URL:
http://www.loc.gov/catdir/description/dover032/97008056.html; http://www.loc.gov/catdir/toc/dover031/97008056.html

remark:
Translated from the Russian by Scripta Technica, Inc. Originally published: Chicago : University of Chicago Press, 1964. Edited by Herbert Eagle.

entry:
@Book{Khinchin:1997:CF,
  author =       "Aleksandr Iakovlevich Khinchin",
  title =        "Continued fractions",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 95",
  year =         "1997",
  ISBN =         "0-486-69630-8 (paperback)",
  ISBN-13 =      "978-0-486-69630-0 (paperback)",
  LCCN =         "QA295 .K513 1997",
  bibdate =      "Fri Nov 30 06:55:53 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/97008056.html;
                 http://www.loc.gov/catdir/toc/dover031/97008056.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1959",
  remark =       "Translated from the Russian by Scripta Technica, Inc.
                 Originally published: Chicago : University of Chicago
                 Press, 1964. Edited by Herbert Eagle.",
}


bibtype: inproceedings
filename: fparith.bib
label: King:1997:DDT
author: E. J. King and E. E. Swartzlander, Jr.
title: Data-Dependent Truncation Scheme for Parallel Multipliers
crossref: Fargues:1997:CRT
pages: 1178--1182
year: 1997
bibdate: Fri Jun 24 20:50:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:50:14 ???
acknowledgement: ack-nhfb
rawauthor: E. J. King and E. E. {Swartzlander, Jr.}
rawtitle: Data-Dependent Truncation Scheme for Parallel Multipliers
entry:
@InProceedings{King:1997:DDT,
  author =       "E. J. King and E. E. {Swartzlander, Jr.}",
  title =        "Data-Dependent Truncation Scheme for Parallel
                 Multipliers",
  crossref =     "Fargues:1997:CRT",
  pages =        "1178--1182",
  year =         "1997",
  bibdate =      "Fri Jun 24 20:50:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kinoshita:1997:RAE
author: Eisuke Kinoshita and Ki-Ja Lee
title: A Residue Arithmetic Extension for Reliable Scientific Computation
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 2
pages: 129--138
month: feb
monthnumber: 2
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.565587
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65G10 (65Y99)
MRnumber: MR1434396 (97j:65080)
bibdate: Wed Jul 6 10:06:20 MDT 2011
bibtimestamp: 2011.07.06 10:06:20 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565587
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Eisuke Kinoshita and Ki-Ja Lee
rawtitle: A Residue Arithmetic Extension for Reliable Scientific Computation
entry:
@Article{Kinoshita:1997:RAE,
  author =       "Eisuke Kinoshita and Ki-Ja Lee",
  title =        "A Residue Arithmetic Extension for Reliable Scientific
                 Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "129--138",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.565587",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G10 (65Y99)",
  MRnumber =     "MR1434396 (97j:65080)",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565587",
  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: Koc:1997:FSE
author: C. K. Koc and T. Acar
title: Fast Software Exponentiation in $ mathrm GF(2^k) $
crossref: Lang:1997:ISC
pages: 225--231
year: 1997
bibdate: Sat Nov 17 12:22:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:22:42 ???
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Koc.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: {\c{C}}. K. Ko{\c{c}} and T. Acar
rawtitle: Fast Software Exponentiation in {$ \mathrm {GF}(2^k) $}
entry:
@InProceedings{Koc:1997:FSE,
  author =       "{\c{C}}. K. Ko{\c{c}} and T. Acar",
  title =        "Fast Software Exponentiation in {$ \mathrm {GF}(2^k)
                 $}",
  crossref =     "Lang:1997:ISC",
  pages =        "225--231",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Koc.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Kramer:1997:PWC
author: Walter Kramer
title: A Priori Worst-Case Error Bounds for Floating-Point Computations
crossref: Lang:1997:ISC
pages: 64--73
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Kramer.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
authordates: 1952--2014
rawauthor: Walter Kr{\"a}mer
rawtitle: A Priori Worst-Case Error Bounds for Floating-Point Computations
entry:
@InProceedings{Kramer:1997:PWC,
  author =       "Walter Kr{\"a}mer",
  title =        "A Priori Worst-Case Error Bounds for Floating-Point
                 Computations",
  crossref =     "Lang:1997:ISC",
  pages =        "64--73",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Kramer.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014",
  keywords =     "ARITH-13",
}


bibtype: article
filename: fparith.bib
label: Kravchenko:1997:AEP
author: Yu. P. Kravchenko and M. A. Liberman
title: On the Application of Extended Precision Arithmetic to Quantum Mechanical Calculations
journal: j-IJQC
volume: 62
number: 6
pages: 593--601
year: 1997
CODEN: IJQCB2
DOI: https://doi.org/10.1002/(SICI)1097-461X(1997)62:6<593::AID-QUA3>3.0.CO;2-R
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Tue Oct 4 06:59:08 MDT 2011
bibtimestamp: 2011.10.04 06:59:08 MDT
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Int. J. Quantum Chem.
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
journalabr: Int J Quant Chem
onlinedate: 6 Dec 1998
rawauthor: Yu. P. Kravchenko and M. A. Liberman
rawtitle: On the Application of Extended Precision Arithmetic to Quantum Mechanical Calculations
bibsource:
Compendex database; http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42544; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42544&PLACEBO=IE.pdf

entry:
@Article{Kravchenko:1997:AEP,
  author =       "Yu. P. Kravchenko and M. A. Liberman",
  title =        "On the Application of Extended Precision Arithmetic to
                 Quantum Mechanical Calculations",
  journal =      j-IJQC,
  volume =       "62",
  number =       "6",
  pages =        "593--601",
  month =        "????",
  year =         "1997",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1997)62:6<593::AID-QUA3>3.0.CO;2-R",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:08 MDT 2011",
  bibsource =    "Compendex database;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42544;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42544&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  journalabr =   "Int J Quant Chem",
  onlinedate =   "6 Dec 1998",
}


bibtype: inproceedings
filename: fparith.bib
label: Lang:1997:CVA
author: Tomas Lang and Elisardo Antelo
title: CORDIC Vectoring with Arbitrary Target Value
crossref: Lang:1997:ISC
pages: 108--115
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lang.pdf
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Elisardo Antelo
rawtitle: {CORDIC} Vectoring with Arbitrary Target Value
bibsource:
https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database

entry:
@InProceedings{Lang:1997:CVA,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "{CORDIC} Vectoring with Arbitrary Target Value",
  crossref =     "Lang:1997:ISC",
  pages =        "108--115",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Lang:1997:FIS
author: Tomas Lang and Jean-Michel Muller and Naofumi Takagi
title: Foreword: 13th IEEE Symposium on Computer Arithmetic, July 6--9, 1997, Asilomar, California, USA
crossref: Lang:1997:ISC
pages: viii--viii
year: 1997
bibdate: Sat Nov 17 12:22:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:22:42 ???
keywords: ARITH-13
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Jean-Michel Muller and Naofumi Takagi
rawtitle: Foreword: {13th IEEE Symposium on Computer Arithmetic, July 6--9, 1997, Asilomar, California, USA}
URL:
http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_contents.pdf; http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_foreword.pdf; http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_preface.pdf

entry:
@InProceedings{Lang:1997:FIS,
  author =       "Tom{\'a}s Lang and Jean-Michel Muller and Naofumi
                 Takagi",
  title =        "Foreword: {13th IEEE Symposium on Computer Arithmetic,
                 July 6--9, 1997, Asilomar, California, USA}",
  crossref =     "Lang:1997:ISC",
  pages =        "viii--viii",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}


bibtype: inproceedings
filename: fparith.bib
label: Lee:1997:SSA
author: Choong Ho Lee and M. Kawamata and T. Higuchi
title: State-space approach to roundoff error analysis of fractal image coding
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1341--1344
year: 1997
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: Choong Ho Lee and M. Kawamata and T. Higuchi
rawtitle: State-space approach to roundoff error analysis of fractal image coding
booktitle:
Proceedings of 1997 IEEE International Symposium on Circuits and Systems: ISCAS '97, 9--12 June 1997

rawbooktitle:
Proceedings of 1997 {IEEE} International Symposium on Circuits and Systems: {ISCAS '97}, 9--12 June 1997

entry:
@InProceedings{Lee:1997:SSA,
  author =       "Choong Ho Lee and M. Kawamata and T. Higuchi",
  booktitle =    "Proceedings of 1997 {IEEE} International Symposium on
                 Circuits and Systems: {ISCAS '97}, 9--12 June 1997",
  title =        "State-space approach to roundoff error analysis of
                 fractal image coding",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1341--1344",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Roundoff error due to iterative computation with
                 finite wordlength degrades the quality of decoded
                 images in fractal image coding that employs a
                 deterministic iterated function system. This paper
                 presents a state-space approach to roundoff error
                 \ldots{}",
}


