The Mathematical-Function Computation Handbook

Programming Using the MathCW Portable Software Library
1. Auflage 2017
ISBN: 978-3-319-64109-6
Verlag: Springer International Publishing

Buch, Englisch, 1115 Seiten, Format (B × H): 215 mm x 285 mm, Gewicht: 2994 g

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Beebe, Nelson H. F.

Fachgebiete

• Naturwissenschaften Chemie Chemie Allgemein Chemometrik, Chemoinformatik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

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

Über Autor(innen)

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.