Random number generator (included)

Random number generator (included) is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

State the type of random number generator algorithm used in a languages built-in random number generator, or omit the language if no random number generator is given as part of the language or its immediate libraries.
If possible, a link to a wider explanation of the algorithm used should be given.

Note: the task is not to create an RNG, but to report on the languages in-built RNG that would be the most likely RNG used.

Java

Java's Random class uses a Linear congruential formula, as described in its documentation.

PHP

PHP has two random number generators: rand, which uses the underlying C library's rand function; and mt_rand, which uses the Mersenne twister algorithm.

Python

Python uses the Mersenne twister algorithm accessed via the built-in random module.

Ruby

Ruby's rand function currently uses the Mersenne twister algorithm, as described in its documentation.

Tcl

Tcl uses a linear congruential generator in it's built-in rand() function. This is seeded by default from the system time, and kept per-interpreter so different security contexts and different threads can't affect each other's generators (avoiding key deployment issues with the rand function from C's math library).

Citations (from Tcl source code):

• S.K. Park & K.W. Miller, “Random number generators: good ones are hard to find,” Comm ACM 31(10):1192-1201, Oct 1988
• W.H. Press & S.A. Teukolsky, “Portable random number generators,” Computers in Physics 6(5):522-524, Sep/Oct 1992.