Book:Donald E. Knuth/The Art of Computer Programming: Volume 2: Seminumerical Algorithms
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Donald E. Knuth: The Art of Computer Programming: Volume 2: Seminumerical Algorithms
Published $\text {1969}$
Subject Matter
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
- 3.2.1. The Linear Congruential Method
- 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