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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. And 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 1: 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).

Warning 2: R250 is not crypotographically secure (it easily cloned from its output). This is not an issue when doing physics modelling but it certainly is if your random numbers are part of a cryptographic application.

Other generators:

The RANLUX portable pseudorandom generator original paper and implementation report.

George Marsaliga's Mother of all Pseudo-Random-Number-Generators

much

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

The popular Mersenne Twister pseudorandom generator. This generator is reasonably fast, has a very long period (2^19937-1), and the built in generator for many languages (Python, Ruby, PHP, R and Exel, for example). However it is not crypotographically secure, like R250 its internal state can be deduced from its output allowing it to be cloned. ANS Forth 32 bit implementation.

Blum Blum Shub pseudorandom generator. This generator is designed to be crypotographically secure without the need for internal cryptographic functions. It can easily be implemented for any word size.

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.

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