Computer Arithmetic and Validity PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Computer Arithmetic and Validity PDF full book. Access full book title Computer Arithmetic and Validity by Ulrich Kulisch. Download full books in PDF and EPUB format.
Author: Ulrich Kulisch
Publisher: Walter de Gruyter
ISBN: 3110301792
Category : Mathematics
Languages : en
Pages : 456
Get Book Here
Book Description
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 Kulisch
Publisher: Walter de Gruyter
ISBN: 3110301792
Category : Mathematics
Languages : en
Pages : 456
Get Book Here
Book Description
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 Kulisch
Publisher: ISSN
ISBN: 9783110301731
Category : Computer arithmetic
Languages : en
Pages : 0
Get Book Here
Book Description
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: Annie A.M. Cuyt
Publisher: Springer Science & Business Media
ISBN: 3642015905
Category : Computers
Languages : en
Pages : 272
Get Book Here
Book Description
The major emphasis of the Dagstuhl Seminar on “Numerical Validation in C- rent Hardware Architectures” lay on numerical validation in current hardware architecturesand softwareenvironments. The generalidea wasto bring together experts who are concerned with computer arithmetic in systems with actual processor architectures and scientists who develop, use, and need techniques from veri?ed computation in their applications. Topics of the seminar therefore included: – The ongoing revision of the IEEE 754/854 standard for ?oating-point ari- metic – Feasible ways to implement multiple precision (multiword) arithmetic and to compute the actual precision at run-time according to the needs of input data – The achievement of a similar behavior of ?xed-point, ?oating-point and - terval arithmetic across language compliant implementations – The design of robust and e?cient numerical programsportable from diverse computers to those that adhere to the IEEE standard – The development and propagation of validated special-purpose software in di?erent application areas – Error analysis in several contexts – Certi?cation of numerical programs, veri?cation and validation assessment Computer arithmetic plays an important role at the hardware and software level, when microprocessors, embedded systems, or grids are designed. The re- ability of numerical softwarestrongly depends on the compliance with the cor- sponding ?oating-point norms. Standard CISC processors follow the 1985 IEEE norm 754, which is currently under revision, but the new highly performing CELL processor is not fully IEEE compliant.
Author: Jean-Michel Muller
Publisher: Birkhäuser
ISBN: 3319765264
Category : Mathematics
Languages : en
Pages : 640
Get Book Here
Book Description
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: Olga Kosheleva
Publisher: Springer Nature
ISBN: 3030310418
Category : Computers
Languages : en
Pages : 638
Get Book Here
Book Description
Data processing has become essential to modern civilization. The original data for this processing comes from measurements or from experts, and both sources are subject to uncertainty. Traditionally, probabilistic methods have been used to process uncertainty. However, in many practical situations, we do not know the corresponding probabilities: in measurements, we often only know the upper bound on the measurement errors; this is known as interval uncertainty. In turn, expert estimates often include imprecise (fuzzy) words from natural language such as "small"; this is known as fuzzy uncertainty. In this book, leading specialists on interval, fuzzy, probabilistic uncertainty and their combination describe state-of-the-art developments in their research areas. Accordingly, the book offers a valuable guide for researchers and practitioners interested in data processing under uncertainty, and an introduction to the latest trends and techniques in this area, suitable for graduate students.
Author: Richard P. Brent
Publisher: Cambridge University Press
ISBN: 9780521194693
Category : Computers
Languages : en
Pages : 236
Get Book Here
Book Description
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 favorite 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 are available from the authors.
Author: Johannes Blömer
Publisher: Springer
ISBN: 3319724533
Category : Computers
Languages : en
Pages : 466
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017, held in Vienna, Austria, in November 2017. The 28 revised papers and 8 short papers presented were carefully reviewed and selected from 67 submissions. The papers are organized in the following topical sections: foundation of algorithms in mathematics, engineering and scientific computation; combinatorics and codes in computer science; data modeling and analysis; and mathematical aspects of information security and cryptography.
Author: Roman Wyrzykowski
Publisher: Springer
ISBN: 3319321528
Category : Computers
Languages : en
Pages : 631
Get Book Here
Book Description
This two-volume-set (LNCS 9573 and 9574) constitutes the refereed proceedings of the 11th International Conference of Parallel Processing and Applied Mathematics, PPAM 2015, held in Krakow, Poland, in September 2015. The 111 revised full papers presented in both volumes were carefully reviewed and selected from 196 submissions. The focus of PPAM 2015 was on models, algorithms, and software toolswhich facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications, including big data problems.
Author: Earl E Swartzlander
Publisher: World Scientific
ISBN: 981465115X
Category : Mathematics
Languages : en
Pages : 474
Get Book Here
Book Description
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: Roman Wyrzykowski
Publisher: Springer
ISBN: 3642315003
Category : Computers
Languages : en
Pages : 687
Get Book Here
Book Description
This two-volume-set (LNCS 7203 and 7204) constitutes the refereed proceedings of the 9th International Conference on Parallel Processing and Applied Mathematics, PPAM 2011, held in Torun, Poland, in September 2011. The 130 revised full papers presented in both volumes were carefully reviewed and selected from numerous submissions. The papers address issues such as parallel/distributed architectures and mobile computing; numerical algorithms and parallel numerics; parallel non-numerical algorithms; tools and environments for parallel/distributed/grid computing; applications of parallel/distributed computing; applied mathematics, neural networks and evolutionary computing; history of computing.
