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Handbook of Floating-Point Arithmetic

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  • © 2018
  • Latest edition

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Authors:
  1. Jean-Michel Muller

    1. CNRS - LIP, Lyon, France

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  2. Nicolas Brunie

    1. Kalray, Grenoble, France

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  3. Florent de Dinechin

    1. INSA-Lyon - CITI, Villeurbanne, France

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  4. Claude-Pierre Jeannerod

    1. Inria - LIP, Lyon, France

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  5. Mioara Joldes

    1. CNRS - LAAS, Toulouse, France

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  6. Vincent Lefèvre

    1. Inria - LIP, Lyon, France

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  7. Guillaume Melquiond

    1. Inria - LRI, Orsay, France

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  8. Nathalie Revol

    1. Inria - LIP, Lyon, France

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  9. Serge Torres

    1. ENS-Lyon - LIP, Lyon, France

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  • Provides a complete overview of a topic that is widely used to implement real-number arithmetic on modern computers, yet is far from being fully exploited to its full potential
  • Techniques are illustrated, whenever possible, by a corresponding program, allowing the reader to put them directly into practice
  • Develops smart and nontrivial algorithms for implementation of floating-point arithmetic in software
  • For a broad audience of programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators; as well as students and researchers in numerical analysis

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About this book

This handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-point numbers, and understanding their various implementations will allow readers to develop programs specifically tailored for the standard’s technical features. Algorithms for floating-point arithmetic are presented throughout the book and illustrated where possible by example programs which show how these techniques appear in actual coding and design.


The volume itself breaks its core topic into four parts: the basic concepts and history of floating-point arithmetic; methods of analyzing floating-point algorithms and optimizing them; implementations of IEEE 754-2008 in hardware and software; and useful extensions to the standard floating-point system, such as interval arithmetic, double- and triple-word arithmetic, operations on complex numbers, and formal verification of floating-point algorithms. This new edition updates chapters to reflect recent changes to programming languages and compilers and the new prevalence of GPUs in recent years. The revisions also add material on fused multiply-add instruction, and methods of extending the floating-point precision. 


As supercomputing becomes more common, more numerical engineers will need to use number representation to account for trade-offs between various parameters, such as speed, accuracy, and energy consumption. The Handbook of Floating-Point Arithmetic is designed for students and researchers in numerical analysis, programmers of numerical algorithms, compiler designers, and designers of arithmetic operators. 





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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xxv
    Download chapter PDF

  2. Introduction, Basic Definitions, and Standards

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Introduction

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 3-14

    3. Definitions and Basic Notions

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 15-45

    4. Floating-Point Formats and Environment

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 47-93

  3. Cleverly Using Floating-Point Arithmetic

    1. Front Matter

      Pages 95-95
      Download chapter PDF

    2. Basic Properties and Algorithms

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 97-162

    3. Enhanced Floating-Point Sums, Dot Products, and Polynomial Values

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 163-192

    4. Languages and Compilers

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 193-230

  4. Implementing Floating-Point Operators

    1. Front Matter

      Pages 231-231
      Download chapter PDF

    2. Algorithms for the Basic Operations

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 233-266

    3. Hardware Implementation of Floating-Point Arithmetic

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 267-320

    4. Software Implementation of Floating-Point Arithmetic

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 321-374

    5. Evaluating Floating-Point Elementary Functions

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 375-433

  5. Extensions

    1. Front Matter

      Pages 435-435
      Download chapter PDF

    2. Complex Numbers

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 437-452

    3. Interval Arithmetic

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 453-477

    4. Verifying Floating-Point Algorithms

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 479-511

    5. Extending the Precision

      • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 513-552

  6. Back Matter

    Pages 553-627
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Reviews

“The new edition of this book updates chapters to reflect recent changes to programming languages and compilers and the new prevalence of Graphic Processing Units in recent years. … In the Appendix, the reader will find an introduction to relevant number theory tools … . This book is designed for programmers of numerical applications … and more generally students and researchers in numerical analysis who wish to more accurately understand a tool that they manipulate on an everyday basis.” (T. C. Mohan, zbMATH 1394.65001, 2018)

Authors and Affiliations

  • CNRS - LIP, Lyon, France

    Jean-Michel Muller

  • Kalray, Grenoble, France

    Nicolas Brunie

  • INSA-Lyon - CITI, Villeurbanne, France

    Florent de Dinechin

  • Inria - LIP, Lyon, France

    Claude-Pierre Jeannerod, Vincent Lefèvre, Nathalie Revol

  • CNRS - LAAS, Toulouse, France

    Mioara Joldes

  • Inria - LRI, Orsay, France

    Guillaume Melquiond

  • ENS-Lyon - LIP, Lyon, France

    Serge Torres

About the authors

Jean-Michel Muller (coordinator), CNRS, Laboratoire LIP, AriC teamNicolas Brunie, Kalray
Florent de Dinechin, INSA Lyon, Laboratoire CITI, Socrate team
Claude-Pierre Jeannerod, Inria, Laboratoire LIP, AriC team
Mioara Joldes, CNRS, LAAS, MAC team
Vincent Lefèvre, Inria, Laboratoire LIP, AriC team
Guillaume Melquiond, Inria, Laboratoire LRI, Toccata team
Nathalie Revol, Inria, Laboratoire LIP, AriC team
Serge Torres, ENS de Lyon, Laboratoire LIP, AriC team

Bibliographic Information

  • Book Title: Handbook of Floating-Point Arithmetic

  • Authors: Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, … Serge Torres

  • DOI: https://doi.org/10.1007/978-3-319-76526-6

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Hardcover ISBN: 978-3-319-76525-9Published: 24 May 2018

  • Softcover ISBN: 978-3-030-09513-0Published: 03 January 2019

  • eBook ISBN: 978-3-319-76526-6Published: 02 May 2018

  • Edition Number: 2

  • Number of Pages: XXV, 627

  • Number of Illustrations: 59 b/w illustrations, 5 illustrations in colour

  • Topics: Computational Mathematics and Numerical Analysis, Algorithm Analysis and Problem Complexity, Algorithms, Math Applications in Computer Science, Mathematical and Computational Engineering, Programming Languages, Compilers, Interpreters

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