Computer Arithmetic and Validity : Theory, Implementation, and Applications

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.

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]