计算机程序设计艺术(卷2)半数值算法(英文版 第3版)

CONTENTS

Chapter 3　Random Numbers　1

3.1　Introduction　1

3.2　Generating Uniform Random Numbers　10

3.2.1　The Linear Congruential Method　10

3.2.1.1　Choice of modulus　12

3.2.1.2　Choice of multiplier　16

3.2.1.3　Potency　23

3.2.2　Other Methods　26

3.3　Statistical Tests　41

3.3.1　General Test Procedures for Studying Random Data　42

3.3.2　Empirical Tests　61

*3.3.3　Theoretical Tests　80

3.3.4　The Spectral Test　93

3.4　Other Types of Random Quantities　119

3.4.1　Numerical Distributions　119

3.4.2　Random Sampling and Shuffling　142

*3.5　What Is a Random Sequence 　149

3.6　Summary　184

Chapter 4　Arithmetic　194

4.1　Positional Number Systems　195

4.2　Floating Point Arithmetic　214

4.2.1　Single-Precision Calculations　214

4.2.2　Accuracy of Floating Point Arithmetic　229

*4.2.3　Double-Precision Calculations　246

4.2.4　Distribution of Floating Point Numbers　253

4.3　Multiple Precision Arithmetic　265

4.3.1　The Classical Algorithms　265

*4.3.2　Modular Arithmetic　284

*4.3.3　How Fast Can We Multiply 　294

4.4　Radix Conversion　319

4.5　Rational Arithmetic　330

4.5.1　Fractions　330

4.5.2　The Greatest Common Divisor　333

*4.5.3　Analysis of Euclid's Algorithm　356

4.5.4　Factoring into Primes　379

4.6　Polynomial Arithmetic　418

4.6.1　Division of Polynomials　420

*4.6.2　Factorization of Polynomials　439

4.6.3　Evaluation of Powers　461

4.6.4　Evaluation of Polynomials　485

*4.7　Manipulation of Power Series　525

Answers to Exercises　538

Appendix A　Tables of Numerical Quantities　726

1. Fundamental Constants (decimal)　726

2. Fundamental Constants (octal)　727

3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers　728

Appendix B　Index to Notations　730

Index and Glossary　735