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

Subject Matter

• Number Theory
• Discrete Mathematics
• Computer Science

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?

4.4. Radix Conversion

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

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

Further Editions

• 1969: Donald E. Knuth: The Art of Computer Programming: Volume 2: Seminumerical Algorithms

Source Work Progress

Starting on Section $4.3$ with Next:

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