國立虎尾科技大學 |

Elementary Functions = Algorithms and Implementation /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Elementary Functions/ by Jean-Michel Muller.
其他題名:	Algorithms and Implementation /
作者:	Muller, Jean-Michel.
面頁冊數:	XXV, 283 p. 40 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Computer mathematics. -
電子資源:	https://doi.org/10.1007/978-1-4899-7983-4
ISBN:	9781489979834

Elementary Functions = Algorithms and Implementation /
Muller, Jean-Michel.

Elementary FunctionsAlgorithms and Implementation /[electronic resource] :by Jean-Michel Muller. - 3rd ed. 2016. - XXV, 283 p. 40 illus.online resource.

Introduction -- Introduction to Computer Arithmetic -- Part I: Algorithms Based on Polynomial Approximation and/or Table Lookup, Multiple-Precision Evaluation of Functions -- The Classical Theory of Polynomial or Rational Approximations -- Polynomial Approximations with Special Constraints -- Polynomial Evaluation -- 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 -- References -- Index.

This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding, as well as some examples of implementation are explored in Part III. Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. New to this edition are an in-depth overview of the IEEE-754-2008 standard for floating-point arithmetic; a section on using double- and triple-word numbers; a presentation of new tools for designing accurate function software; and a section on the Toom-Cook family of multiplication algorithms. The techniques presented in this book will be of interest to implementers of elementary function libraries or circuits and programmers of numerical applications. Additionally, graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find this a useful reference and resource. PRAISE FOR PREVIOUS EDITIONS “[T]his book seems like an essential reference for the experts (which I'm not). More importantly, this is an interesting book for the curious (which I am). In this case, you'll probably learn many interesting things from this book. If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class." — MAA Reviews (Review of Second Edition) "The rich content of ideas sketched or presented in some detail in this book is supplemented by a list of over three hundred references, most of them of 1980 or more recent. The book also contains some relevant typical programs." — Zentralblatt MATH (Review of Second Edition) “I think that the book will be very valuable to students both in numerical analysis and in computer science. I found [it to be] well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find." — Numerical Algorithms (Review of First Edition).

ISBN: 9781489979834

Standard No.: 10.1007/978-1-4899-7983-4doiSubjects--Topical Terms:

1199796
Computer mathematics.

LC Class. No.: QA71-90

Dewey Class. No.: 004

Elementary Functions = Algorithms and Implementation /
LDR:05139nam a22003855i 4500 001 978195
003 DE-He213
005 20200630053533.0
007 cr nn 008mamaa
008 201211s2016 xxu| s |||| 0|eng d
020 $a 9781489979834 $9 978-1-4899-7983-4
024 7 $a 10.1007/978-1-4899-7983-4 $2 doi
035 $a 978-1-4899-7983-4
050 4 $a QA71-90
072 7 $a PDE $2 bicssc
072 7 $a COM014000 $2 bisacsh
072 7 $a PDE $2 thema
082 0 4 $a 004 $2 23
100 1 $a Muller, Jean-Michel. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1115790
245 1 0 $a Elementary Functions $h [electronic resource] : $b Algorithms and Implementation / $c by Jean-Michel Muller.
250 $a 3rd ed. 2016.
264 1 $a Boston, MA : $b Birkhäuser Boston : $b Imprint: Birkhäuser, $c 2016.
300 $a XXV, 283 p. 40 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a Introduction -- Introduction to Computer Arithmetic -- Part I: Algorithms Based on Polynomial Approximation and/or Table Lookup, Multiple-Precision Evaluation of Functions -- The Classical Theory of Polynomial or Rational Approximations -- Polynomial Approximations with Special Constraints -- Polynomial Evaluation -- 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 -- References -- Index.
520 $a This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding, as well as some examples of implementation are explored in Part III. Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. New to this edition are an in-depth overview of the IEEE-754-2008 standard for floating-point arithmetic; a section on using double- and triple-word numbers; a presentation of new tools for designing accurate function software; and a section on the Toom-Cook family of multiplication algorithms. The techniques presented in this book will be of interest to implementers of elementary function libraries or circuits and programmers of numerical applications. Additionally, graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find this a useful reference and resource. PRAISE FOR PREVIOUS EDITIONS “[T]his book seems like an essential reference for the experts (which I'm not). More importantly, this is an interesting book for the curious (which I am). In this case, you'll probably learn many interesting things from this book. If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class." — MAA Reviews (Review of Second Edition) "The rich content of ideas sketched or presented in some detail in this book is supplemented by a list of over three hundred references, most of them of 1980 or more recent. The book also contains some relevant typical programs." — Zentralblatt MATH (Review of Second Edition) “I think that the book will be very valuable to students both in numerical analysis and in computer science. I found [it to be] well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find." — Numerical Algorithms (Review of First Edition).
650 0 $a Computer mathematics. $3 1199796
650 0 $a Algorithms. $3 527865
650 0 $a Numerical analysis. $3 527939
650 0 $a Applied mathematics. $3 1069907
650 0 $a Engineering mathematics. $3 562757
650 1 4 $a Computational Science and Engineering. $3 670319
650 2 4 $a Numeric Computing. $3 669943
650 2 4 $a Applications of Mathematics. $3 669175
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9781489979810
776 0 8 $i Printed edition: $z 9781489979827
856 4 0 $u https://doi.org/10.1007/978-1-4899-7983-4
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)