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

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

Published $\text {1969}$

### Contents

Preface
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