Computer arithmetic and validity : theory, implementation, and applications / Ulrich Kulisch.

Format:

Book

Author/Creator:

Kulisch, Ulrich.

Series:

De Gruyter Studies in Mathematics

De Gruyter studies in mathematics, 0179-0986 ; 33

De Gruyter Studies in Mathematics ; 33

Language:

English

Subjects (All):

Computer arithmetic.

Computer arithmetic and logic units.

Floating-point arithmetic.

Physical Description:

1 online resource (434 p.)

Edition:

2nd ed.

Place of Publication:

Berlin : De Gruyter, 2013.

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Foreword to the second edition

Preface

Contents

Introduction

Part I. Theory of computer arithmetic

Chapter 1. First concepts

Chapter 2. Ringoids and vectoids

Chapter 3. Definition of computer arithmetic

Chapter 4. Interval arithmetic

Part II. Implementation of arithmetic on computers

Chapter 5. Floating-point arithmetic

Chapter 6. Implementation of floating-point arithmetic on a computer

Chapter 7. Hardware support for interval arithmetic

Chapter 8. Scalar products and complete arithmetic

Part III. Principles of verified computing

Chapter 9. Sample applications

Appendix A. Frequently used symbols

Appendix B. On homomorphism

Bibliography

List of figures

List of tables

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

3-11-030179-2

OCLC:

851970604