Computer Arithmetic and Validity: Theory, Implementation, and Applications

Ulrich Kulisch

Published by De Gruyter 2012

Computer Arithmetic and Validity

Theory, Implementation, and Applications

Ulrich Kulisch

Volume 33 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110301793

Overview
Contents

About this book

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 / Editor information

Ulrich Kulisch, University Karlsruhe, Germany.

Reviews

Review for the first edition:

"The book deals with the theory of computer arithmetic, the implementation of arithmetic on computers, and principles of verified computing. These items are at the same time the titles of the three main parts in which the very informative and highly interesting monograph of 400 pages is divided. [...] an important book which should be read by everyone who does not merely apply a computer uncritically as a black box, but wants to know how it, works, and is interested in how it could work better.

[Günter Mayer (Rostock) in ZenralblattMath]

Supplementary Materials

Contents

Topics

Frontmatter Publicly Available Download PDF	i
Foreword to the second edition Requires Authentication Unlicensed Licensed Download PDF	vii
Preface Requires Authentication Unlicensed Licensed Download PDF	ix
Contents Publicly Available Download PDF	xix
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Part I. Theory of computer arithmetic
Chapter 1. First concepts Requires Authentication Unlicensed Licensed Download PDF	13
Chapter 2. Ringoids and vectoids Requires Authentication Unlicensed Licensed Download PDF	43
Chapter 3. Definition of computer arithmetic Requires Authentication Unlicensed Licensed Download PDF	62
Chapter 4. Interval arithmetic Requires Authentication Unlicensed Licensed Download PDF	87
Part II. Implementation of arithmetic on computers
Chapter 5. Floating-point arithmetic Requires Authentication Unlicensed Licensed Download PDF	157
Chapter 6. Implementation of floating-point arithmetic on a computer Requires Authentication Unlicensed Licensed Download PDF	191
Chapter 7. Hardware support for interval arithmetic Requires Authentication Unlicensed Licensed Download PDF	236
Chapter 8. Scalar products and complete arithmetic Requires Authentication Unlicensed Licensed Download PDF	249
Part III. Principles of verified computing
Chapter 9. Sample applications Requires Authentication Unlicensed Licensed Download PDF	307
Appendix A. Frequently used symbols Requires Authentication Unlicensed Licensed Download PDF	367
Appendix B. On homomorphism Requires Authentication Unlicensed Licensed Download PDF	369
Bibliography Requires Authentication Unlicensed Licensed Download PDF	371
List of figures Requires Authentication Unlicensed Licensed Download PDF	421
List of tables Requires Authentication Unlicensed Licensed Download PDF	425
Index Requires Authentication Unlicensed Licensed Download PDF	427

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Students of Mathematics and Computer Sciences, Researchers; Academic Libraries.
Pages
- Front matter: 22
- Main content: 434
Illustrations
- Illustrations: 101
- Tables: 34
Keywords: Computer Arithmetic; Interval calculation; Numerical Analysis

eBook

Published: April 30, 2013
ISBN: 9783110301793

Hardcover

Published: April 17, 2013
ISBN: 9783110301731