Modern Computer Arithmetic

Contains all state-of-the-art algorithms dealing with multiple-precision integers or floating-point numbers in a ready-to-implement format.

Richard P. Brent (Author), Paul Zimmermann (Author)

9780521194693, Cambridge University Press

Hardback, published 25 November 2010

236 pages, 15 b/w illus. 190 exercises
23.5 x 15.6 x 1.7 cm, 0.47 kg

'Very few books do justice to material that is suitable for both professional software engineers and graduate students. This book does just that, without losing its focus or stressing one audience over the other. As the authors make clear, this book is about algorithms for arithmetic (and not hardware considerations and implementations); this focus allows them to cover integer arithmetic, modular arithmetic, and floating-point arithmetic broadly and in detail. the notes and references at the end of each chapter guide readers to more details, and provide a historical backdrop for each major topic.' Marlin Thomas, Reviews.com

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.

Preface
Acknowledgements
Notation
1. Integer arithmetic
2. Modular arithmetic and the FFT
3. Floating-point arithmetic
4. Newton's method and function evaluation
Appendix. Implementations and pointers
Bibliography
Index.

Subject Areas: Mathematical theory of computation [UYA], Numerical analysis [PBKS]