Table of Contents

1 Introduction

2 Quick Start

3 Characteristics of Random Number Sequences

3.1 Distribution

3.2 Range

3.3 Type

3.4 Period

3.5 Coverage

3.6 Runs

3.7 Serial Correlation

3.8 Permutations

3.9 Spectral Characteristics

4 Choosing a Random Number Generator

4.1 Instant Gratification

4.2 A little bit of work

4.3 Willing to work for it

5 The Class Interfaces

5.1 The RandomGenerator Interface

5.2 The rand() Interface

5.3 The Function Object Interface

5.3.1 RNGFuncAdaptor

5.3.2 RNGFuncAdaptorFloat

5.3.3 RNGFuncAdaptorLimit

5.3.4 RNGFuncAdaptorPercentLikely

5.3.5 RNGFuncAdaptorRange

6 Abstract Classes

6.1 RandomGenerator

6.2 CongruentialRandGen

6.3 TableRandGen

6.4 TextTableRandGen

6.5 ByteTableRandGen

6.6 CombineRandGen

6.7 AdaptorRandGen

6.8 SHARandGen

7 Concrete Classes

7.1 LinConRandGen

7.2 LinConModRandGen

7.3 MultConRandGen

7.4 MultConModRandGen

7.5 SecConRandGen

7.6 SecConModRandGen

7.7 InvConModRandGen

7.8 InvConRandGen

7.9 QuadConRandGen

7.10 NumberTableRandGen

7.11 BinaryTableRandGen

7.12 DecimalTableRandGen

7.13 HexTableRandGen

7.14 DifferenceRandGen

7.15 ShuffledMRandGen

7.16 A15BitRandGen

7.17 LaggedFibonacciRandGen

7.18 LaggedFibonacciModRandGen

7.19 LinMultWCarryRandGen

8 Generator Instantiations

8.1 BorlandRandGen

8.2 StdCRandGen

8.3 BoroshNiederreiterRandGen

8.4 WatermanRandGen

8.5 MarsagliaMCRandGen

8.6 LavauxJanssensRandGen

8.7 Knuth28RandGen

8.8 Knuth22RandGen

8.9 Knuth27RandGen

8.10 MitchellMooreRandGen

9 Special Generators

9.1 DwyerRandGen

9.2 CompilerRandGen

9.3 SHACtrRandGen

9.4 SHARngRandGen

10 Bad Pseudo-Random Number Generators

10.1 ConstantRandGen

10.2 CounterRandGen

10.3 SawtoothRandGen

10.4 SquareRandGen

10.5 RANDURandGen

10.6 FibonacciRandGen

11 Testing a Generator

12 Utility Functions and Classes

12.1 The Secure Hash Algorithm

12.2 The Modulus Arithmetic Functions

12.3 The RingBuffer class

13 Defining New Generators

13.1 General Design Considerations

13.2 Instantiating a new concrete generator

13.3 The RNGFuncAdaptorRange Function Object

13.4 Minor Modifications to a generator

13.5 Deriving the Quadratic Congruential generator

13.6 Creating a generator from scratch

Bibliography

1. James O. Coplien. Advanced C++: Programming Styles and Idioms. Addison-Wesley, Reading, MA, USA, 1992.
2. Jerry Dwyer. Quick and portable random number generators. C/C++ Users Journal, pages 33--44, June 1995.
3. Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides. Design Patterns. Addison-Wesley Professional Computing Series. Addison-Wesley, Reading, MA, USA, 1995.
4. Donald E. Knuth. Seminumerical Algorithms, volume 2 of The Art of Computer Programming. Addison-Wesley, Reading, MA, USA, second edition, 10 January 1981.
5. David R. Musser and Atul Saini. STL Tutorial and Reference Guide. Addison-Wesley, Reading, MA, USA, 1996.
6. Random chapter. http://csep1.phy.ornl.gov/rn/rn.html, December 1994.
7. Herbert Schildt. The Annotated ANSI C Standard. Osborne McGraw-Hill, Berkeley, CA, 94710, USA, 1990. Contains the entire ANSI/ISO 9899-1990 Standards document.
8. Bruce Schneier. Applied Cryptography. John Wiley & Sons, Inc., New York, NY 10158-0012, USA, second edition, 1996.
9. Specification for a secure hash standard (shs). Federal Information Processing Standards Publication, January 1992.
10. Andreas Weingartener. Nonlinear congruential pseudorandom number generators. Master's thesis, Universität Salzburg, June 1994.

© 1997 G. Wade Johnson. All rights reserved.
http://www.anomaly.org/ThinAir/random.html