Computer Arithmetic And Validity

Author : Ulrich Kulisch
Publisher : Walter de Gruyter
Page : 456 pages
File Size : 40,9 Mb
Release : 2013-04-30
Category : Mathematics
ISBN : 9783110301793

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Computer Arithmetic and Validity by Ulrich Kulisch Pdf

This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics.

Author : Ulrich W. Kulisch,Willard L. Miranker
Publisher : Academic Press
Page : 268 pages
File Size : 43,8 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483264738

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Computer Arithmetic in Theory and Practice by Ulrich W. Kulisch,Willard L. Miranker Pdf

Computer Arithmetic in Theory and Practice deals with computer arithmetic and the various implementations of the entire arithmetic package on diverse processors, including microprocessors. It illustrates the importance of theoretical development in the sound implementation of arithmetic on computers, and argues that such an implementation requires the establishment of various isomorphisms between different definitions of arithmetic operations. Comprised of seven chapters, this volume begins with an introduction to the theory of computer arithmetic by giving an axiomatic characterization of the essential properties of sets and subsets; complete lattices and complete subnets; screens and roundings; and arithmetic operations. The discussion then turns to the concepts of a ringoid and a vectoid as well as those of ordered or weakly ordered ringoids and vectoids; interval arithmetic; and floating-point arithmetic. The operations in interval spaces are defined by means of semimorphisms. The final chapter shows how to embed the five basic data types (integer, real, complex, real interval, and complex interval) together with the arithmetic operations that are defined for all of these types into existing higher programming languages. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.

Author : Jean-Michel Muller,Nicolas Brisebarre,Florent de Dinechin,Claude-Pierre Jeannerod,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Damien Stehlé,Serge Torres
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 50,9 Mb
Release : 2009-11-11
Category : Mathematics
ISBN : 0817647058

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Handbook of Floating-Point Arithmetic by Jean-Michel Muller,Nicolas Brisebarre,Florent de Dinechin,Claude-Pierre Jeannerod,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Damien Stehlé,Serge Torres Pdf

Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. 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. 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. The handbook 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.

Author : Earl E. Swartzlander
Publisher : Los Alamitos, CA : IEEE Computer Society Press
Page : 424 pages
File Size : 54,6 Mb
Release : 1990
Category : Computer arithmetic
ISBN : 0818689455

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Computer Arithmetic by Earl E. Swartzlander Pdf

Mathematics of Computing -- Numerical Analysis.

Author : R. Albrecht,G. Alefeld,H.J. Stetter
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783709169186

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Validation Numerics by R. Albrecht,G. Alefeld,H.J. Stetter Pdf

The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.

Author : Christian Ullrich
Publisher : Academic Press
Page : 316 pages
File Size : 54,7 Mb
Release : 2014-05-10
Category : Computers
ISBN : 9781483267814

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Computer Arithmetic and Self-Validating Numerical Methods by Christian Ullrich Pdf

Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods, held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.

Author : Richard P. Brent,Paul Zimmermann
Publisher : Cambridge University Press
Page : 238 pages
File Size : 49,8 Mb
Release : 2010-11-25
Category : Computers
ISBN : 9781139492287

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Modern Computer Arithmetic by Richard P. Brent,Paul Zimmermann Pdf

Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors.

Author : Frank Honywill George
Publisher : Pergamon
Page : 0 pages
File Size : 42,6 Mb
Release : 1966-05
Category : Arithmetic
ISBN : 0080114636

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Computer Arithmetic by Frank Honywill George Pdf

Author : Israel Koren
Publisher : CRC Press
Page : 298 pages
File Size : 40,6 Mb
Release : 2018-10-08
Category : Computers
ISBN : 9781439863718

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Computer Arithmetic Algorithms by Israel Koren Pdf

This text explains the fundamental principles of algorithms available for performing arithmetic operations on digital computers. These include basic arithmetic operations like addition, subtraction, multiplication, and division in fixed-point and floating-point number systems as well as more complex operations such as square root extraction and evaluation of exponential, logarithmic, and trigonometric functions. The algorithms described are independent of the particular technology employed for their implementation.

Author : Earl E Swartzlander
Publisher : World Scientific
Page : 486 pages
File Size : 55,8 Mb
Release : 2015-03-17
Category : Mathematics
ISBN : 9789814641487

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Computer Arithmetic by Earl E Swartzlander Pdf

This is the new edition of the classic book Computer Arithmetic in three volumes published originally in 1990 by IEEE Computer Society Press. As in the original, the book contains many classic papers treating advanced concepts in computer arithmetic, which is very suitable as stand-alone textbooks or complementary materials to textbooks on computer arithmetic for graduate students and research professionals interested in the field. Told in the words of the initial developers, this book conveys the excitement of the creators, and the implementations provide insight into the details necessary to realize real chips. This second volume presents topics on error tolerant arithmetic, digit on-line arithmetic, number systems, and now in this new edition, a topic on implementations of arithmetic operations, all wrapped with an updated overview and a new introduction for each chapter. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:Error Tolerant ArithmeticOn-Line ArithmeticVLSI Adder ImplementationsVLSI Multiplier ImplementationsFloating-Point VLSI ChipsNumber RepresentationImplementations Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers advanced arithmetic operationsIt does this in the words of the original creatorsKeywords:Computer Arithmetic;Fault Tolerant;Arithmetic;On-Line Arithmetic;Adder Implementations;Multiplier Implementations;Floating Point Chips;Number Representation;Implementations

Author : Earl E Swartzlander,Carl E Lemonds
Publisher : World Scientific
Page : 474 pages
File Size : 42,9 Mb
Release : 2015-02-12
Category : Mathematics
ISBN : 9789814651158

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Computer Arithmetic by Earl E Swartzlander,Carl E Lemonds Pdf

Computer Arithmetic Volume III is a compilation of key papers in computer arithmetic on floating-point arithmetic and design. The intent is to show progress, evolution, and novelty in the area of floating-point arithmetic. This field has made extraordinary progress since the initial software routines on mainframe computers have evolved into hardware implementations in processors spanning a wide range of performance. Nevertheless, these papers pave the way to the understanding of modern day processors design where computer arithmetic are supported by floating-point units. The goal of Volume III is to collect the defining document for floating-point arithmetic and many of the key papers on the implementation of both binary and decimal floating-point arithmetic into a single volume. Although fewer than forty papers are included, their reference lists will direct the interested reader to other excellent work that could not be included here. Volume III is specifically oriented to the needs of designers and users of both general-purpose computers and special-purpose digital processors. The book should also be useful to systems engineers, computer architects, and logic designers. It is also intended to serve as a primary text for a course on floating-point arithmetic, as well as a supplementary text for courses in digital arithmetic and high-speed signal processing. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:OverviewFloating-Point AdditionFloating-Point MultiplicationRoundingFused Multiply AddFloating-Point DivisionElementary FunctionsDecimal Floating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:The papers that are included cover the key concepts needed to develop efficient (fast, small and low-power) floating-point processing unitsThe papers include presentations by the initial developers in their own words to better explain the basic techniquesIncludes five papers on decimal floating-point arithmetic, which has been added to the IEEE standardKeywords:Floating-Point Addition;Floating-Point Multiplication;Floating-Point Division;Decimal Floating-Point Arithmetic

Author : Earl E Swartzlander
Publisher : World Scientific
Page : 398 pages
File Size : 49,8 Mb
Release : 2015-03-17
Category : Mathematics
ISBN : 9789814651585

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Computer Arithmetic by Earl E Swartzlander Pdf

The book provides many of the basic papers in computer arithmetic. These papers describe the concepts and basic operations (in the words of the original developers) that would be useful to the designers of computers and embedded systems. Although the main focus is on the basic operations of addition, multiplication and division, advanced concepts such as logarithmic arithmetic and the calculations of elementary functions are also covered. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:OverviewAdditionParallel Prefix AdditionMulti-Operand AdditionMultiplicationDivisionLogarithmsElementary FunctionsFloating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers the basic arithmetic operationsIt does this in the words of the creatorsKeywords:Computer Arithmetic;Adders;Parallel Prefix Adders;Multi-operand Adders;Multipliers;Dividers;Logarithmic Arithmetic;Elementary Function Evaluation

Author : Ulrich Kulisch
Publisher : ISSN
Page : 0 pages
File Size : 42,8 Mb
Release : 2013
Category : Computer arithmetic
ISBN : 3110301733

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Computer Arithmetic and Validity by Ulrich Kulisch Pdf

This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic capability of the computer can be enhanced. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties.

Author : F. H. George
Publisher : Elsevier
Page : 293 pages
File Size : 50,6 Mb
Release : 2014-05-09
Category : Mathematics
ISBN : 9781483180915

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Computer Arithmetic by F. H. George Pdf

Computer Arithmetic provides information pertinent to the fundamental aspects of a digital computer. This book discusses how the control unit uses the arithmetic unit to produce, under commands, the answers asked by the user. Organized into four chapters, this book begins with an overview of the binary code and provides a preview of the use of other arithmetic codes outside the computer. This text then explains in detail the codes employed in the representation of numbers inside the computer. Other chapters consider the number systems as well as other related matters to be able to understand computer arithmetic. This book discusses as well the signed numbers and their conversations, as well as the problems of scaling. The final chapter deals with the methods of fixed- and floating-point arithmetic, rounding off, and overflow. This book is a valuable resource for sixth form as well as university students who are interested in arithmetic codes.

Author : Otto Spaniol
Publisher : John Wiley & Sons
Page : 288 pages
File Size : 43,7 Mb
Release : 1981
Category : Mathematics
ISBN : UOM:39015002903386

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Computer Arithmetic by Otto Spaniol Pdf

Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.