Authors:
- 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
- Includes supplementary material: sn.pub/extras
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (16 chapters)
-
Front Matter
-
Introduction, Basic Definitions, and Standards
-
Front Matter
-
-
Cleverly Using Floating-Point Arithmetic
-
Front Matter
-
-
Implementing Floating-Point Operators
-
Front Matter
-
-
Elementary Functions
-
Front Matter
-
-
Extensions
-
Front Matter
-
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)Authors and Affiliations
-
CNRS, Labo. Informatique du Parallélisme (LIP), École Normale Supérieure de Lyon, Lyon CX 07, France
Jean-Michel Muller, Nicolas Brisebarre
-
CNRS UMR 5668, Labo. Informatique du Parallelisme (LIP), Ecole Normale Supérieure de Lyon, Lyon CX 07, France
Florent de Dinechin, Serge Torres
-
Labo. Informatique du Parallélisme (LIP), INRIA, Ecole Normale Supérieure de Lyon, Lyon CX 07, France
Claude-Pierre Jeannerod, Vincent Lefèvre, Nathalie Revol
-
INRIA Saclay - Île-de-France, Orsay CX, France
Guillaume Melquiond
-
University of Sydney, School of Mathematics and Statistics, CNRS, Macquarie University, and, Sydney, Australia
Damien Stehlé
Bibliographic Information
Book Title: Handbook of Floating-Point Arithmetic
Authors: Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Damien Stehlé, … Serge Torres
DOI: https://doi.org/10.1007/978-0-8176-4705-6
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkh�user Boston 2010
eBook ISBN: 978-0-8176-4705-6Published: 11 November 2009
Edition Number: 1
Number of Pages: XXIV, 572
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