计算机程序设计艺术

Chapter 3-- Random Numbers

3.1. Introduction

3.2. Generating Uniform Random Numbers

3.2.1. The Linear Congruential Method

3.2.1.1. Choice of modulus

3.2.1.2. Choice of multiplier

3.2.1.3. Potency

3.2.2. Other Methods

3.3. Statistical Tests

3.3.1. General Test Procedures for Studying Random Data

3.3.2. Empirical Tests

3.3.3. Theoretical Tests

3.3.4. The Spectral Test

3.4. Other Types of Random Quantities

3.4.1. Numerical Distributions

3.4.2. Random Sampling and Shuffling

3.5. What Is a Random Sequence?

Chapter 4- Arithmetic

4.1. Poitional Number Systems

4.2. Floating Point Arithmetic

4.2.1. Singl-Precision Calculations

4.2.2. Accuracy of Floating Point Arithnletic

4.2.3. Double -Preision Calculations

4.2.4. Distribution of Floating Point Numbers

4.3. Multiple Preision Arithmetic

4.3.1. The Classical Algorithms

4.3.3. How Fast Can We Multiply?

4.5. Rational Arithmetic

4.5.1. Fractinns

4.5.2. The Greatest Common Divisor

4.5.3. Analysis of Euclids Algorithm

4.5.4. Factoring into Primes3.6. Summary

4.6. Polynomial Arithmetic

4.6.1. Division of Polynomials

4.6.2. Factorization of Polynomials

4.6.3. Evaluation of Powers

4.6.4. Evaluation of Polynomials

4.7. Manipulation of Power Series

Answers to Exercises

Appendix A - Tables of Numerical Quantities

1.Fundamental Constants (decimal)

2.Fundamental Constants (octal)

3.Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers

Appendix B--index to Notations

Index and Glossary

关于算法分析的这多卷论著已经长期被公认为经典计算机科学的定义性描述。迄今已出版的完整的三卷已经组成了程序设计理论和实践的惟一的珍贵资源，无数读者都赞扬Knuth的著作对个人的深远影响，科学家们为他的分析的美丽和优雅所惊叹，而从事实践的程序员已经成功地将他的“ 菜谱式”的解应用到日常问题上，所有人都由于Knuth在书中表现出的博学、清晰、精确和高度幽默而对他无比敬仰。
第2卷为半数值算法，分“随机数”和“算术”两章。本卷总结了主要算法范例及这些算法的基本理论，广泛剖析了计算机程序设计与数值分析间的相互联系。