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© 2018

Handbook of Floating-Point Arithmetic

Book

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Introduction, Basic Definitions, and Standards

    1. Front Matter
      Pages 1-1
    2. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 3-14
    3. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 15-45
    4. 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
    2. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 97-162
    3. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 163-192
    4. 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
    2. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 233-266
    3. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 267-320
    4. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 321-374
    5. 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
    2. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 437-452
    3. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 453-477
    4. Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre et al.
      Pages 479-511
    5. 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

About this book

Introduction

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. 

 

Keywords

Floating-Point Arithmetic IEEE 754-2008 Standard Fused Multiply-Add Instruction Floating-Point Operators Elementary Functions Fast2Sum and 2Sum Algorithms

Authors and affiliations

  1. 1.CNRS - LIPLyonFrance
  2. 2.KalrayGrenobleFrance
  3. 3.INSA-Lyon - CITIVilleurbanneFrance
  4. 4.Inria - LIPLyonFrance
  5. 5.CNRS - LAASToulouseFrance
  6. 6.Inria - LIPLyonFrance
  7. 7.Inria - LRIOrsayFrance
  8. 8.Inria - LIPLyonFrance
  9. 9.ENS-Lyon - LIPLyonFrance

About the authors

Jean-Michel Muller (coordinator), CNRS, Laboratoire LIP, AriC team
Nicolas 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

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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)