Random Number Generation

Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.

John Von Neumann (1951)

Here is information on pseudo and quasi random number generation with implementations in several languages. An a tutorial on how to generate nonuniformly distributed random numbers.

Forth Dimensions (1994, XVI Nos 1 & 2) review article on random numbers (tar.Z or tar.gz formats). Contains R250 and quasi in (F-PC) Forth.

A Reference list of papers.

Note on generating Gaussian/Normal Random Numbers (or other nonuniform distributions).

A Monte Carlo method Reference list.

A Bestiary of Random Distributions.

Pseudo-Random number generation using R250 (Kirkpatrick and Stoll, 1981).

Ada implementation.

Cimplementation ( shell archive, tar archive).

C++implementation( shell archive, Gnu compressed tar archive).

ANS Forth implementation.

FORTRAN implementation

Java implementation.

Note: R250 is an example of a shift register generator. This one has a register length of 250 which results in a period of 2^249. The code provide here can easily be modifed for other register lengths. The following two papers describe the parameters that are needed for lengths from 1 to 1000:

Zierler, N. and J. Brillhart,1968; On primitive trinomials (mod 2), Information and Control, Vol 13 No 6 (Dec), pp. 541 - 554
Zierler, N. and J. Brillhart,1969; On primitive trinomials (mod 2) II, Information and Control, Vol 14 No 6 (Jun), pp. 566 - 569

Warning: R250 requires the use of a separate random number generator in order to intialize itself. It can fail spectacularly if the initialization is poorly done. I have had reliable results using the Park and Miller "minimal standard" generator for the initializer. The above implementations use this initializer (which is included in the source code).

The RANLUX portable pseudorandom generator original paper and implementation report.

A Site with ISAAC and related generators plus analyses and tests.

Quasi-Random number generation (Press and Teukolsky, 1989).

Ada implementation.

C implementation ( shell archive, tar archive).

C++ implementation ( shell archive, tar archive).

ANS Forth implementation.

George Marsaliga's Mother of all Pseudo-Random-Number-Generators. (Warning: this is a slow PRNG, R250 is much faster).

Whats all the fuss about ? Why can't I just use the PRNG that came with my compiler ?