# Book:Donald E. Knuth/The Art of Computer Programming: Volume 2: Seminumerical Algorithms/Third Edition

## Donald Ervin Knuth: The Art of Computer Programming: Volume 2: Seminumerical Algorithms (3rd Edition)

Published $\text {1998}$, Addison-Wesley

ISBN 0-201-89684-2.

### Contents

Preface
Preface to the Third Edition (Stanford, California, July 1997)
Notes on the Exercises

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 ls a Random Sequence?
3.6 Summary
Chapter 4 - Arithmetic
4.1. Positional Number Systems
4.2. Floating Point Arithmetic
4.2.1. Single-Precision Calculations
4.2.2. Accuracy of Floating Point Arithmetic
*4.2.3. Double-Precision Calculations
4.2.4. Distribution of Floating Point Numbers
4.3. Multiple Precision Arithmetic
4.3.1. The Classical Algorithms
*4.3.2. Modular Arithmetic
*4.3.3. How Fast Can We Multiply?
4.5. Rational Arithmetic
4.5.1. Fractions
4.5.2. The Greatest Common Divisor
*4.5.3. Analysis of Euclid's Algorithm
4.5.4. Factoring into Primes
4.6. Polynomial Arithmetic
4.6.1. Division of Polynomials
*4.6.2. Factorisation of Polynomials
4.6.3. Evaluation of Powers
4.6.4. Evaluation of Polynomials
*4.7. Manipulation of Power Series
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

## Source Work Progress

Starting on Section $4.3$ with Next: