Handbook of Floating-Point Arithmetic

Authors: Muller, J.-M., Brisebarre, N., de Dinechin, F., Jeannerod, C.-P., Lefèvre, V., Melquiond, G., Revol, N., Stehlé, D., Torres, S.

  • First comprehensive treatment of floating-point arithmetic
  • 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

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.
 

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)

Table of contents (16 chapters)

  • Introduction

    Muller, Jean-Michel (et al.)

    Pages 3-12

  • Definitions and Basic Notions

    Muller, Jean-Michel (et al.)

    Pages 13-53

  • Floating-Point Formats and Environment

    Muller, Jean-Michel (et al.)

    Pages 55-116

  • Basic Properties and Algorithms

    Muller, Jean-Michel (et al.)

    Pages 119-150

  • The Fused Multiply-Add Instruction

    Muller, Jean-Michel (et al.)

    Pages 151-179

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-0-8176-4705-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-0-8176-4704-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Handbook of Floating-Point Arithmetic
Authors
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4705-6
DOI
10.1007/978-0-8176-4705-6
Hardcover ISBN
978-0-8176-4704-9
Edition Number
1
Number of Pages
XXIV, 572
Topics