高德纳(Donald E. Knuth)著名计算机科学家,算法与程序设计技术的先驱者、斯坦福大学计算机系荣休教授、计算机排版系统TEX和METAFONT字体系统的发明人,因诸多成就以及大量富于创造力和具有深远影响的著作(19部书,160篇论文)而誉满全球。近些年,他将精力全部投入到《计算机程序设计艺术》七卷集的史诗般创作中。
目錄:
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