Elementary Functions (eBook)

Algorithms and Implementation

Jean-Michel Muller (Autor)

eBook Download: PDF

2006 | 2. Auflage
XXII, 273 Seiten
Birkhauser Boston (Verlag)
978-0-8176-4408-6 (ISBN)

Infos

An important topic, which is on the boundary between numerical analysis and computer science …. I found the book well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find. Moreover, there are very few books on these topics and they are not recent.' Numerical Algorithms (review of the first edition) This unique book provides concepts and background necessary to understand and build algorithms for computing the elementary functions. The author presents and structures the algorithms (hardware-oriented as well as software-oriented), and also discusses issues related to accurate floating-point implementation. The purpose is not to give 'cookbook recipes' that allow one to implement a given function, but rather to provide the reader with tools necessary to build, or adapt, algorithms to their specific computing environment. The expanded second edition contains a number of revisions and additions, which incorporate numerous new results obtained during the last few years. New algorithms invented since 1997 – such as Matula’s bipartite method, another table-based method due to Ercegovac, Lang, Tisserand, and Muller – as well as a new chapter on multiple-precision arithmetic have been added. In addition, the section on correct rounding of elementary functions has been fully reworked, also in the context of new results. Finally, the introductory presentation of floating-point arithmetic has been expanded, with more emphasis given to the use of the fused multiply-accumulate instruction. The book is an up-to-date presentation of information needed to understand and accurately use mathematical functions and algorithms in computational work and design. Graduates, professionals, and researchers in scientific computing, software engineering, and computer engineering will find the book a useful reference and resource.

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"e;An important topic, which is on the boundary between numerical analysis and computer science .... I found the book well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find. Moreover, there are very few books on these topics and they are not recent."e; Numerical Algorithms (review of the first edition)This unique book provides concepts and background necessary to understand and build algorithms for computing the elementary functions. The author presents and structures the algorithms (hardware-oriented as well as software-oriented), and also discusses issues related to accurate floating-point implementation. The purpose is not to give "e;cookbook recipes"e; that allow one to implement a given function, but rather to provide the reader with tools necessary to build, or adapt, algorithms to their specific computing environment.The expanded second edition contains a number of revisions and additions, which incorporate numerous new results obtained during the last few years. New algorithms invented since 1997 such as Matula s bipartite method, another table-based method due to Ercegovac, Lang, Tisserand, and Muller as well as a new chapter on multiple-precision arithmetic have been added. In addition, the section on correct rounding of elementary functions has been fully reworked, also in the context of new results. Finally, the introductory presentation of floating-point arithmetic has been expanded, with more emphasis given to the use of the fused multiply-accumulate instruction. The book is an up-to-date presentation of information needed to understand and accurately use mathematical functions and algorithms in computational work and design. Graduates, professionals, and researchers in scientific computing, software engineering, and computer engineering will find the book a useful reference and resource.

Inhalt

List of figures.- List of tables.- Preface to the second edition.- Preface to the first edition.- Introduction.- Some basic things about computer arithmetic.- Part I. Algorithms based on polynomial approximation and/or table lookup, multiple-precision evaluation of functions.- Polynomial or rational approximations.- Table-based methods.- Multiple-precision evaluation of functions.- Part II. Shift-and-add algorithms.- Introduction to shift-and-add algorithms.- The CORDIC algorithm.- Some other shift-and-add algorithms.- Part III. Range reduction, final rounding and exceptions.- Range reduction.- Final rounding.- Miscellaneous.- Examples of implementation.- Bibliography.- Index

Produkt-Details

• Erscheint lt. Verlag: 11.9.2006
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Schlagworte: algorithms • Computer • Computer Science • Hardware • ksa • Numerical analysis • Scientific Computing
• ISBN-10: 0-8176-4408-3 / 0817644083
• ISBN-13: 978-0-8176-4408-6 / 9780817644086