#### The Mathematical-Function Computation Handbook

**Book Description**

This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision.

Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built

C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions.

This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw

are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.

Table of Contents

Chapter 1 Introduction

Chapter 2 Iterative Solutions And Other Tools

Chapter 3 Polynomial Approximations

Chapter 4 Implementation Issues

Chapter 5 The Floating-Point Environment

Chapter 6 Converting Floating-Point Values To Integers

Chapter 7 Random Numbers

Chapter 8 Roots

Chapter 9 Argument Reduction

Chapter 10 Exponential And Logarithm

Chapter 11 Trigonometric Functions

Chapter 12 Hyperbolic Functions

Chapter 13 Pair-Precision Arithmetic

Chapter 14 Power Function

Chapter 15 Complex Arithmetic Primitives

Chapter 16 Quadratic Equations

Chapter 17 Elementary Functions In Complex Arithmetic

Chapter 18 The Greek Functions: Gamma, Psi, And Zeta

Chapter 19 Error And Probability Functions

Chapter 20 Elliptic Integral Functions

Chapter 21 Bessel Functions

Chapter 22 Testing The Library

Chapter 23 Pair-Precision Elementary Functions

Chapter 24 Accuracy Of The Cody/Waite Algorithms

Chapter 25 Improving Upon The Cody/Waite Algorithms

Chapter 26 Floating-Point Output

Chapter 27 Floating-Point Input

Appendix A Ada Interface

Appendix B C# Interface

Appendix C C++ Interface

Appendix D decimal Arithmetic

Appendix E Errata In The Cody/Waite Book

Appendix F Fortran Interface

Appendix H historical Floating-Point Architectures

Appendix I Integer Arithmetic

Appendix J Java Interface

Appendix L Letter Notation

Appendix P Pascal Interface