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

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. Front Matter ....Pages i-xxxvi Introduction (Nelson H. F. Beebe)....Pages 1-6 Iterative solutions and other tools (Nelson H. F. Beebe)....Pages 7-22 Polynomial approximations (Nelson H. F. Beebe)....Pages 23-60 Implementation issues (Nelson H. F. Beebe)....Pages 61-104 The floating-point environment (Nelson H. F. Beebe)....Pages 105-128 Converting floating-point values to integers (Nelson H. F. Beebe)....Pages 129-156 Random numbers (Nelson H. F. Beebe)....Pages 157-214 Roots (Nelson H. F. Beebe)....Pages 215-242 Argument reduction (Nelson H. F. Beebe)....Pages 243-266 Exponential and logarithm (Nelson H. F. Beebe)....Pages 267-298 Trigonometric functions (Nelson H. F. Beebe)....Pages 299-340 Hyperbolic functions (Nelson H. F. Beebe)....Pages 341-352 Pair-precision arithmetic (Nelson H. F. Beebe)....Pages 353-410 Power function (Nelson H. F. Beebe)....Pages 411-440 Complex arithmetic primitives (Nelson H. F. Beebe)....Pages 441-464 Quadratic equations (Nelson H. F. Beebe)....Pages 465-474 Elementary functions in complex arithmetic (Nelson H. F. Beebe)....Pages 475-520 The Greek functions: gamma, psi, and zeta (Nelson H. F. Beebe)....Pages 521-592 Error and probability functions (Nelson H. F. Beebe)....Pages 593-618 Elliptic integral functions (Nelson H. F. Beebe)....Pages 619-692 Bessel functions (Nelson H. F. Beebe)....Pages 693-762 Testing the library (Nelson H. F. Beebe)....Pages 763-776 Pair-precision elementary functions (Nelson H. F. Beebe)....Pages 777-810 Accuracy of the Cody/Waite algorithms (Nelson H. F. Beebe)....Pages 811-822 Improving upon the Cody/Waite algorithms (Nelson H. F. Beebe)....Pages 823-828 Floating-point output (Nelson H. F. Beebe)....Pages 829-878 Floating-point input (Nelson H. F. Beebe)....Pages 879-910 Back Matter ....Pages 911-1115