Elementary Functions : Algorithms & implementation (2^nd Ed.)

This book gives the concepts and background necessary to understand and build algorithms for computing elementary functions, presenting and structuring the algorithms (hardware- oriented as well as software-oriented), and discusses issues related to the accurate floating-point implementation. The purpose is not to give "cookbook recipes" that allow one to implement some given function, but to provide the reader with the knowledge that is necessary to build, or adapt, algorithms to their specific computing environment. Topics and Features : background material reviewed in Chapter 2, Computer Arithmetic. Polynomial and rational approximations. Table based methods. Shift-and-add algorithms thoroughly covered in Part Two. CORDIC algorithm. Range reduction and accuracy covered in Part Three. Web site for the book containing additional resources and selected code. The book provides an up-to-date presentation of the information needed to understand and accurately use mathematical functions and algorithms in computational work and design. Graduates, professionals and researchers in scientific computing, software engineering, and computer engineering will find the book a useful reference and resource.

List of figures.- List of tables.- Preface to the second edition.- Preface to the first edition.- Introduction.- Some basic things about computer arithmetic.- Part I. Algorithms based on polynomial approximation and/or table lookup, multiple-precision evaluation of functions.- Polynomial or rational approximations.- Table-based methods.- Multiple-precision evaluation of functions.- Part II. Shift-and-add algorithms.- Introduction to shift-and-add algorithms.- The CORDIC algorithm.- Some other shift-and-add algorithms.- Part III. Range reduction, final rounding and exceptions.- Range reduction.- Final rounding.- Miscellaneous.- Examples of implementation.- Bibliography.- Index