The Resource Elementary Functions : Algorithms and Implementation, by JeanMichel Muller, (electronic resource)
Elementary Functions : Algorithms and Implementation, by JeanMichel Muller, (electronic resource)
Resource Information
The item Elementary Functions : Algorithms and Implementation, by JeanMichel Muller, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Elementary Functions : Algorithms and Implementation, by JeanMichel Muller, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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 softwareoriented algorithms are included, along with issues related to accurate floatingpoint 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 floatingpoint 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 tablebased methods; the final chapter in this section deals with basic principles of multipleprecision arithmetic. Part II is devoted to a presentation of “shiftandadd” algorithms (hardwareoriented 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 indepth overview of the IEEE7542008 standard for floatingpoint arithmetic; a section on using double and tripleword numbers; a presentation of new tools for designing accurate function software; and a section on the ToomCook 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).
 Language
 eng
 Edition
 3rd ed. 2016.
 Extent
 1 online resource (XXV, 283 pages)
 Contents

 Introduction
 Introduction to Computer Arithmetic
 Part I: Algorithms Based on Polynomial Approximation and/or Table Lookup, MultiplePrecision Evaluation of Functions
 The Classical Theory of Polynomial or Rational Approximations
 Polynomial Approximations with Special Constraints
 Polynomial Evaluation
 TableBased Methods
 MultiplePrecision Evaluation of Functions
 Part II: ShiftandAdd Algorithms
 Introduction to ShiftandAdd Algorithms
 The CORDIC Algorithm
 Some Other ShiftandAdd Algorithms
 Part III: Range Reduction, Final Rounding, and Exceptions
 Range Reduction
 Final Rounding
 Miscellaneous
 Examples of Implementation
 References
 Index
 Isbn
 9781489979834
 Label
 Elementary Functions : Algorithms and Implementation
 Title
 Elementary Functions
 Title remainder
 Algorithms and Implementation
 Statement of responsibility
 by JeanMichel Muller
 Language
 eng
 Summary
 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 softwareoriented algorithms are included, along with issues related to accurate floatingpoint 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 floatingpoint 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 tablebased methods; the final chapter in this section deals with basic principles of multipleprecision arithmetic. Part II is devoted to a presentation of “shiftandadd” algorithms (hardwareoriented 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 indepth overview of the IEEE7542008 standard for floatingpoint arithmetic; a section on using double and tripleword numbers; a presentation of new tools for designing accurate function software; and a section on the ToomCook 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).
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Muller, JeanMichel
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Springer eBooks
 http://library.link/vocab/subjectName

 Mathematics
 Numerical analysis
 Applied mathematics
 Engineering mathematics
 Algorithms
 Computer mathematics
 Label
 Elementary Functions : Algorithms and Implementation, by JeanMichel Muller, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Introduction to Computer Arithmetic  Part I: Algorithms Based on Polynomial Approximation and/or Table Lookup, MultiplePrecision Evaluation of Functions  The Classical Theory of Polynomial or Rational Approximations  Polynomial Approximations with Special Constraints  Polynomial Evaluation  TableBased Methods  MultiplePrecision Evaluation of Functions  Part II: ShiftandAdd Algorithms  Introduction to ShiftandAdd Algorithms  The CORDIC Algorithm  Some Other ShiftandAdd Algorithms  Part III: Range Reduction, Final Rounding, and Exceptions  Range Reduction  Final Rounding  Miscellaneous  Examples of Implementation  References  Index
 Control code
 9781489979834
 Dimensions
 unknown
 Edition
 3rd ed. 2016.
 Extent
 1 online resource (XXV, 283 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781489979834
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781489979834
 Other physical details
 40 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)964631030
 Label
 Elementary Functions : Algorithms and Implementation, by JeanMichel Muller, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Introduction to Computer Arithmetic  Part I: Algorithms Based on Polynomial Approximation and/or Table Lookup, MultiplePrecision Evaluation of Functions  The Classical Theory of Polynomial or Rational Approximations  Polynomial Approximations with Special Constraints  Polynomial Evaluation  TableBased Methods  MultiplePrecision Evaluation of Functions  Part II: ShiftandAdd Algorithms  Introduction to ShiftandAdd Algorithms  The CORDIC Algorithm  Some Other ShiftandAdd Algorithms  Part III: Range Reduction, Final Rounding, and Exceptions  Range Reduction  Final Rounding  Miscellaneous  Examples of Implementation  References  Index
 Control code
 9781489979834
 Dimensions
 unknown
 Edition
 3rd ed. 2016.
 Extent
 1 online resource (XXV, 283 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781489979834
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781489979834
 Other physical details
 40 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)964631030
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/ElementaryFunctionsAlgorithmsand/5m_lEksuYE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/ElementaryFunctionsAlgorithmsand/5m_lEksuYE/">Elementary Functions : Algorithms and Implementation, by JeanMichel Muller, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>