Handbook of Floating-Point Arithmetic (original) (raw)

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Authors:

  1. Jean-Michel Muller
    1. CNRS, Labo. Informatique du Parallélisme (LIP), École Normale Supérieure de Lyon, Lyon CX 07, France
  2. Nicolas Brisebarre
    1. CNRS, Labo. Informatique du Parallélisme (LIP), École Normale Supérieure de Lyon, Lyon CX 07, France
  3. Florent de Dinechin
    1. CNRS UMR 5668, Labo. Informatique du Parallelisme (LIP), Ecole Normale Supérieure de Lyon, Lyon CX 07, France
  4. Claude-Pierre Jeannerod
    1. Labo. Informatique du Parallélisme (LIP), INRIA, Ecole Normale Supérieure de Lyon, Lyon CX 07, France
  5. Vincent Lefèvre
    1. Labo. Informatique du Parallélisme (LIP), INRIA, Ecole Normale Supérieure de Lyon, Lyon CX 07, France
  6. Guillaume Melquiond
    1. INRIA Saclay - Île-de-France, Orsay CX, France
  7. Nathalie Revol
    1. Labo. Informatique du Parallélisme (LIP), INRIA, Ecole Normale Supérieure de Lyon, Lyon CX 07, France
  8. Damien Stehlé
    1. University of Sydney, School of Mathematics and Statistics, CNRS, Macquarie University, and, Sydney, Australia
  9. Serge Torres
    1. CNRS UMR 5668, Labo. Informatique du Parallelisme (LIP), Ecole Normale Supérieure de Lyon, Lyon CX 07, France

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About this book

Floating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic reliable and portable, yet fast, is a very difficult task. From the 1960s to the early 1980s, many different arithmetics were developed, but their implementation varied widely from one machine to another, making it difficult for nonexperts to design, learn, and use the required algorithms. As a result, floating-point arithmetic is far from being exploited to its full potential.

This handbook aims to provide a complete overview of modern floating-point arithmetic, including a detailed treatment of the newly revised (IEEE 754-2008) standard for floating-point arithmetic. Presented throughout are algorithms for implementing floating-point arithmetic as well as algorithms that use floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program.

Key topics and features include:

* Presentation of the history and basic concepts of floating-point arithmetic and various aspects of the past and current standards

* Development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction, e.g., correctly rounded software division and square roots

* Implementation of floating-point arithmetic, either in software—on an integer processor—or hardware, and a discussion of issues related to compilers and languages

* Coverage of several recent advances related to elementary functions: correct rounding of these functions and computation of very accurate approximations under constraints

* Extensions of floating-point arithmetic such as certification, verification, and big precision

Handbook of Floating-Point Arithmetic is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.

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Table of contents (16 chapters)

  1. Introduction, Basic Definitions, and Standards

    1. Introduction

      • Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond et al.
        Pages 3-12

    2. Definitions and Basic Notions

      • Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond et al.
        Pages 13-53

  2. Cleverly Using Floating-Point Arithmetic

    1. Basic Properties and Algorithms

      • Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond et al.
        Pages 119-150

    2. The Fused Multiply-Add Instruction

      • Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond et al.
        Pages 151-179

    3. Languages and Compilers

      • Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond et al.
        Pages 205-235

  3. Implementing Floating-Point Operators

  4. Elementary Functions

    1. Solving the Table Maker’s Dilemma

      • Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond et al.
        Pages 405-459

  5. Extensions

    1. Extending the Precision

      • Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond et al.
        Pages 493-516

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Reviews

From the reviews:

“This handbook aims to provide a complete overview of modern floating-point arithmetic, including a detailed treatment of the newly revised IEEE 751-2008 standard for floating-point arithmetic. … This book is useful to programmers, compiler designers and students and researchers in numerical analysis.”­­­ (T. C. Mohan, Zentralblatt MATH, Vol. 1197, 2010)

Authors and Affiliations

Jean-Michel Muller, Nicolas Brisebarre

Florent de Dinechin, Serge Torres

Claude-Pierre Jeannerod, Vincent Lefèvre, Nathalie Revol

Guillaume Melquiond

Damien Stehlé

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