Handbook of Floating-Point Arithmetic (eBook)

Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Serge Torres (Autoren)

eBook Download: PDF

2018 | 2nd ed. 2018
XXV, 627 Seiten
Springer International Publishing (Verlag)
978-3-319-76526-6 (ISBN)

Infos

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.

Jean-Michel Muller (coordinator), CNRS, Laboratoire LIP, AriC team

Nicolas Brunie, Kalray

Florent de Dinechin, INSA Lyon, Laboratoire CITI, Socrate team

Claude-Pierre Jeannerod, Inria, Laboratoire LIP, AriC team

Mioara Joldes, CNRS, LAAS, MAC team

Vincent Lefèvre, Inria, Laboratoire LIP, AriC team

Guillaume Melquiond, Inria, Laboratoire LRI, Toccata team

Nathalie Revol, Inria, Laboratoire LIP, AriC team

Serge Torres, ENS de Lyon, Laboratoire LIP, AriC team

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 2.5.2018
• Zusatzinfo: XXV, 627 p. 64 illus., 5 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Programmiersprachen / -werkzeuge
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: Algorithm analysis and problem complexity • elementary functions • Fast2Sum and 2Sum Algorithms • Floating-point arithmetic • Floating-Point Operators • Fused Multiply-Add Instruction • IEEE 754-2008 Standard
• ISBN-10: 3-319-76526-4 / 3319765264
• ISBN-13: 978-3-319-76526-6 / 9783319765266