Handbook of Floating-Point Arithmetic

• Main Authors: Muller, Jean-Michel (Author, http://id.loc.gov/vocabulary/relators/aut), Brunie, Nicolas (http://id.loc.gov/vocabulary/relators/aut), de Dinechin, Florent (http://id.loc.gov/vocabulary/relators/aut), Jeannerod, Claude-Pierre (http://id.loc.gov/vocabulary/relators/aut), Joldes, Mioara (http://id.loc.gov/vocabulary/relators/aut), Lefèvre, Vincent (http://id.loc.gov/vocabulary/relators/aut), Melquiond, Guillaume (http://id.loc.gov/vocabulary/relators/aut), Revol, Nathalie (http://id.loc.gov/vocabulary/relators/aut), Torres, Serge (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 2nd ed. 2018.
• Subjects: Computer mathematics.; Algorithms.; Computer science-Mathematics.; Applied mathematics.; Engineering mathematics.; Programming languages (Electronic computers).; Computational Mathematics and Numerical Analysis.; Algorithm Analysis and Problem Complexity.; Math Applications in Computer Science.; Mathematical and Computational Engineering.; Programming Languages, Compilers, Interpreters.

This handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-...

Table of Contents:

• Part I: Introduction, Basic Definitions, and Standards
• Introduction
• Definitions and Basic Notations
• Floating-Point Formats and Environment
• Part II: Cleverly Using Floating-Point Arithmetic
• Basic Properties and Algorithms
• Enhanced FP Sums, Dot Products, and Polynomial Values
• Languages and Compilers
• Part III: Implementing Floating-Point Operators
• Algorithms for the Basic Operations
• Hardware Implementation of Floating-Point Arithmetic
• Software Implementation of Floating-Point Arithmetic
• Evaluating Floating-Point Elementary Functions
• Part IV: Extensions
• Complex Numbers
• Interval Arithmetic
• Verifying Floating-Point Arithmetic
• Extending the Precision
• Appendix A: Number Theory Tools
• Appendix B: Previous Standards
• References
• Index.