Handbook of Floating-Point Arithmetic

• Main Authors: Muller, Jean-Michel. (Author), Brisebarre, Nicolas. (Author), de Dinechin, Florent. (Author), Jeannerod, Claude-Pierre. (Author), Lefv̈re, Vincent. (Author), Melquiond, Guillaume. (Author), Revol, Nathalie. (Author), Stehl,̌ Damien. (Author), Torres, Serge. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston, 2010.
• Edition: 1.
• Subjects: Mathematics.; Computer science.; Computer software.; Computer science > Mathematics.; Algorithms.; Engineering mathematics.; Computational Mathematics and Numerical Analysis.; Algorithm Analysis and Problem Complexity.; Math Applications in Computer Science.; Appl.Mathematics/Computational Methods of Engineering.; Programming Languages, Compilers, Interpreters.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4705-6

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 difficu...

Table of Contents:

• List of Figures
• List of Tables
• Preface
• Part I. Introduction, Basic Definitions, and Standards. Introduction
• Definitions and Basic Notions
• Floating-Point Formats and Environment
• Part II. Cleverly Using Floating-Point Arithmetic. Basic Properties and Algorithms
• The Fused Multiply-Add Instructions
• Enhanced Floating-Point Sums, Dot Products, and Polynomial Values
• Languages and Compilers
• Part III. Implementing Floating-Point Operators. Algorithms for the Five Basic Operations
• Hardware Implementation of Floating-Point Arithmetic
• Software Implementation of Floating-Point Arithmetic
• Part IV. Elementary Functions. Evaluating Floating-Point Elementary Functions
• Solving the Table Maker's Dilemma
• Part V. Extensions. Formalisms for Certifying Floating-Point Algorithms
• Extending the Precision
• Part VI. Perspectives and Appendix. Conclusion and Perspectives
• Appendix: Number Theory Tools for Floating-Point Arithmetic
• Bibliography
• Index.