The Mathematical-Function Computation Handbook: Programming Using the Mathcw Portable Software Library

ISBN-13: 9783319641096 / Angielski / Twarda / 2017 / 1115 str.

Nelson H. F. Beebe

Opis

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.

Spis treści

Introduction

Iterative Solutions and Other Tools

Polynomial Approximations

Implementation Issues

The Floating-Point Environment

Converting Floating-Point Values to Integers

Random Numbers

Roots

Argument Reduction

Exponential and Logarithm

Trigonometric Functions

Hyperbolic Functions

Pair-Precision Arithmetic

Power Function

Complex Arithmetic Primitives

Quadratic Equations

Elementary Functions in Complex Arithmetic

The Greek Functions: Gamma, Psi, and Zeta

Error and Probability Functions

Elliptic Integral Functions

Bessel Functions

Testing the Library

Pair-Precision Elementary Functions

Accuracy of the Cody/Waite Algorithms

Improving Upon the Cody/Waite Algorithms

Floating-Point Output

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

O autorze

​Dr. Nelson H.F. Beebe is a Research Professor and Software Specialist in the Department of Mathematics at the University of Utah, USA. He has a diverse background in chemistry, physics, mathematics, computer science, systems management, and typography, having studied, worked, and taught in three countries. He has written extensive software projects in numerous programming-language, operating-system, and hardware environments. His bibliographic database work has exposed him to a wide range of journals on current research.

Blurb

All major computer programming languages—as well as the disciplines of science and engineering more broadly—require computation of elementary and special functions of mathematics. The MathCW Software Library emphasizes portability, precisely because the code needs to capable of use on a wide variety of platforms.

This highly comprehensive handbook provides a substantial advance in such computation, 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 hardware 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.