Pseudorandom Numbers

Algorithms for generating numbers according to a particular probability distribution. For example, the two most common problems are generating integers uniformly between 1 and n, and generating real numbers uniformly between 0 and 1. Other common distributions include Gaussian and Poisson. Because most random-number-generation algorithms have no influence from the outside environment, they are inherently pseudorandom: predictable, and following a pattern, also ideally not an apparent one. Thus the quote:

"Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." - John von Neumann (1951)

A classic reference on this topic, and a good starting point, is Donald Knuth's Art of Computer Programming.

"Random number generators should not be chosen at random." - Donald Knuth (1986)

Another good reference, for nonuniform random number generation in particular, is Luc Devroye's Non-Uniform Random Variate Generation (Springer-Verlag); see also his page in this category. There are also some approaches that claim to be "truly random," based on outside data like radioactive decay and white noise from deep space. However, randomness is inherently a theoretical notion, and is difficult to exhibit perfectly in real life, unless perhaps we fully master quantum mechanics.

Sub-Categories:

Hardware

Random Number Generation, Taygeta Scientific Inc. - Information and articles on random number generation.
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The pLab Project - A server on the theory and practice of random number generation.
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Pseudo Random Number Generators - Algorithms for good random number generators with theoretical discussion and software examples.
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Mersenne Twister: A Random Number Generator - Fast generator of fixed high period implemented in various languages. Includes a paper about the mathematical foundations.
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NIST: Random Number Generation and Testing - Project to develop a battery of statistical tests to detect nonrandomness in binary sequences, to produce documentation and a software implementation of these tests, and to provide guidance in the use of these tests.
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Luc Devroye: Random Number Generation - Links to downloadable papers, related journals, and links to software.
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Segobit Software: Random Number Generator Pro - Windows application to generate several random numbers in a given range, subject to constraints like excluding certain digits.
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WWW Virtual Library: Random numbers and Monte Carlo Methods - Links to related conferences, papers, software, webpages, people.
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Try to Find Where the Ball Is Hidden - A small test to see how well humans can generate random numbers compared to computer predictions.
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Netlib: Random Number Generators - Source code for various random number generators in C and Fortran, including the well-known RANLIB library supporting many continuous and discrete probability distributions.
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Pseudo-random Numbers - A guide to the literature.
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HENKOS Pseudorandom Number Generator - Presents and evaluates this generator, intended for use as a key generator for a one-time pad cipher.
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Random Bots - Generators for random number samples, random selection and random check number audits. Windows software for on-line purchase.
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Random Number Generator - A small, simple open-source shareware program by Scott Donato Saccenti [Win95].
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frandom - Fast RNG for the Linux kernel. A sourceforge project.
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ENT - A pseudorandom number sequence test program. Free download of C++ source code and MS-DOS executable.
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The NHSE Guide to Random Number Generators - Random number generators and pointers to software at the National HPCC Software Exchange for generating and testing pseudo-random numbers on high-performance computers.
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Random Number Generator Algorithms - Documentation of algorithms in the GNU Scientific Library Reference Manual.
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Random Number Generators - An etext by the Computational Science Education Project.
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RANDPOLY - A REDUCE package based on a port of the Maple random polynomial generator together with some support facilities for the generation of random numbers and anonymous procedures. By Francis J. Wright.
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RngPack - A pseudorandom number generator package for Java. Source code free under BSD licence.
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UNURAN - Universal Non-Uniform RANdom number generators: a GPL library of C functions to generate nonuniform random numbers, by Josef Leydold and Wolfgang Hoermann of the University of Economics, Vienna.
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