Jean-Michel Muller, Nicolas Brisebarre, Florent De Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Damien Stehlé, Serge Torres

Handbook of Floating-Point Arithmetic (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 572
• Erscheinungstermin: 11. November 2009
• Englisch
• ISBN-13: 9780817647056
• Artikelnr.: 37347441

Autorenporträt

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

Inhaltsangabe

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.

Rezensionen

"The new edition of this book updates chapters to reflect recent changes to programming languages and compilers and the new prevalence of Graphic Processing Units in recent years. ... In the Appendix, the reader will find an introduction to relevant number theory tools ... . This book is designed for programmers of numerical applications ... and more generally students and researchers in numerical analysis who wish to more accurately understand a tool that they manipulate on an everyday basis." (T. C. Mohan, zbMATH 1394.65001, 2018)