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CONTENTS

Chapter 3¡¡Random Numbers¡¡1

3.1¡¡Introduction¡¡1

3.2¡¡Generating Uniform Random Numbers¡¡10

3.2.1¡¡The Linear Congruential Method¡¡10

3.2.1.1¡¡Choice of modulus¡¡12

3.2.1.2¡¡Choice of multiplier¡¡16

3.2.1.3¡¡Potency¡¡23

3.2.2¡¡Other Methods¡¡26

3.3¡¡Statistical Tests¡¡41

3.3.1¡¡General Test Procedures for Studying Random Data¡¡42

3.3.2¡¡Empirical Tests¡¡61

*3.3.3¡¡Theoretical Tests¡¡80

3.3.4¡¡The Spectral Test¡¡93

3.4¡¡Other Types of Random Quantities¡¡119

3.4.1¡¡Numerical Distributions¡¡119

3.4.2¡¡Random Sampling and Shuffling¡¡142

*3.5¡¡What Is a Random Sequence ¡¡149

3.6¡¡Summary¡¡184

Chapter 4¡¡Arithmetic¡¡194

4.1¡¡Positional Number Systems¡¡195

4.2¡¡Floating Point Arithmetic¡¡214

4.2.1¡¡Single-Precision Calculations¡¡214

4.2.2¡¡Accuracy of Floating Point Arithmetic¡¡229

*4.2.3¡¡Double-Precision Calculations¡¡246

4.2.4¡¡Distribution of Floating Point Numbers¡¡253

4.3¡¡Multiple Precision Arithmetic¡¡265

4.3.1¡¡The Classical Algorithms¡¡265

*4.3.2¡¡Modular Arithmetic¡¡284

*4.3.3¡¡How Fast Can We Multiply ¡¡294

4.4¡¡Radix Conversion¡¡319

4.5¡¡Rational Arithmetic¡¡330

4.5.1¡¡Fractions¡¡330

4.5.2¡¡The Greatest Common Divisor¡¡333

*4.5.3¡¡Analysis of Euclid's Algorithm¡¡356

4.5.4¡¡Factoring into Primes¡¡379

4.6¡¡Polynomial Arithmetic¡¡418

4.6.1¡¡Division of Polynomials¡¡420

*4.6.2¡¡Factorization of Polynomials¡¡439

4.6.3¡¡Evaluation of Powers¡¡461

4.6.4¡¡Evaluation of Polynomials¡¡485

*4.7¡¡Manipulation of Power Series¡¡525

Answers to Exercises¡¡538

Appendix A¡¡Tables of Numerical Quantities¡¡726

1. Fundamental Constants (decimal)¡¡726

2. Fundamental Constants (octal)¡¡727

3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers¡¡728

Appendix B¡¡Index to Notations¡¡730

Index and Glossary¡¡735