Handbook of Floating-Point Arithmetic

1. Auflage. 2009
ISBN: 978-0-8176-4704-9
Verlag: Birkhäuser

Buch, Englisch, 572 Seiten, Book, Format (B × H): 178 mm x 254 mm, Gewicht: 2750 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Muller, Jean-Michel

Brisebarre, Nicolas

de Dinechin, Florent

Jeannerod, Claude-Pierre

Lefèvre, Vincent

Melquiond, Guillaume

Revol, Nathalie

Stehlé, Damien

Torres, Serge

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Programmier- und Skriptsprachen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

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