Synopses & Reviews
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.
Review
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)
Synopsis
This handbook aims to provide a complete overview of modern floating-point arithmetic. This includes a detailed treatment of the current (IEEE-754) and next (preliminarily called IEEE-754R) standards for floating-point arithmetic.
Synopsis
Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. 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. 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.
The handbook 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.
Table of Contents
List of Figures
List of Tables
Preface
I. Introduction, Basic Definitions, and Standards
1. Introduction
2. Definitions and Basic Notions
3. Floating-Point Formats and Environment
II. Cleverly Using Floating-Point Arithmetic
4. Basic Properties and Algorithms
5. The Fused Multiply-Add Instructions
6. Enhanced Floating-Point Sums, Dot Products, and Polynomial Values
7. Languages and Compilers
III. Implementing Floating-Point Operators
8. Algorithms for the Five Basic Operations
9. Hardware Implementation of Floating-Point Arithmetic
10. Software Implementation of Floating-Point Arithmetic
IV. Elementary Functions
11. Evaluating Floating-Point Elementary Functions
12. Solving the Table Maker's Dilemma
V. Extensions
13. Formalisms for Certifying Floating-Point Algorithms
14. Extending the Precision
VI. Perspectives and Appendix
15. Conclusion and Perspectives
16. Appendix: Number Theory Tools for Floating-Point Arithmetic
Bibliography
Index