Elementary Functions : Algorithms and Implementation

Книга Elementary Functions: Algorithms and Implementation Elementary Functions: Algorithms and Implementation Книги Математика Автор: Jean-Michel Muller Год издания: 2005 Формат: pdf Издат.:Birkhäuser Boston Страниц: 266 Размер: 2,1 ISBN: 0817643729 Язык: Английский0 (голосов: 0) Оценка:"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 functionssine, cosine, tangent, exponentials, and logarithms. 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 for their specific computing environment.This 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 1997such as Matulas bipartite method, another table-based method due to Ercegovac, Lang, Tisserand, and Mulleras well as new chapters on multiple-precision arithmetic and examples of implementation 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. Graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find the book a useful reference and resource. "An important topic, which is on the boundary between numericalanalysis 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. TOC:Introduction * Computer Arithmetic * Part I. Algorithms Based on Polynomial Approximationand/or Table Lookup, Multiple-Precision Evaluation of Functions * Polynomial Approximations *Table-Based Methods * Multiple Precision * Part II: Shift-and-Add Algorithms * Shift-and-Add Algorithms * The CORDIC Algorithm * Other Shift-and-Add Algorithms * Range Reduction, Final Rounding and Exceptions * Range Reduction * Final Rounding * Miscellaneous

"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—sine, cosine, tangent, exponentials, and logarithms. 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 for their specific computing environment.

This 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 new chapters on multiple-precision arithmetic and examples of implementation 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. Graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find the book a useful reference and resource.

'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. "This book provides concepts and background necessary to understand and build algorithms for computing the elementary functions - sine, cosine, tangent, exponentials, and logarithms. 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 for their specific computing environment." "This 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 new chapters on multiple-precision arithmetic and examples of implementation 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. Graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find the book a useful reference and resource."--Jacket This work deals with Numerical Algorithms. This unique book provides concepts and background necessary to understand and build algorithms for computing the elementary functions - sine, cosine, tangent, exponentials, and logarithms. 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 for their speci "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. Graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find the book a useful reference and resource."--Résumé de l'éditeur Second Edition Of Successful, Well-reviewed Birkhauser Book, Which Sold 866 Copies In North America Provides An Up-to-date Presentation By Including New Results, Examples, And Problems Throughout The Text The Second Edition Adds A Chapter On Multiple-precision Arithmetic, And New Algorithms Invented Since 1997