Finite Precision Number Systems and Arithmetic: 133 (Encyclopedia of Mathematics and its Applications, Series Number 133)
Cambridge University Press
Edition: Illustrated, 9/30/2010
EAN 9780521761352, ISBN10: 0521761352
Hardcover, 716 pages, 24.1 x 16.3 x 4.1 cm
Language: English
Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.
Preface
1. Radix polynomial representations
2. Base and digit set conversion
3. Addition
4. Multiplication
5. Division
6. Square root
7. Floating point number systems
8. Modular arithmetic and residue number systems
9. Rational arithmetic
Author index
Index.