Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator

Matsumoto Makoto

Nishimura Takuji

ACM Transactions on Modeling and Computer Simulation

A new algorithm called Mersenne Twister (MT) is proposed for generating uniform pseudorandom numbers. For a particular choice of parameters, the algorithm provides a super astronomical period of 219937 - 1 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words. This is a new variant of the previously proposed generators, TGFSR, modified so as to admit a Mersenne-prime period. The characteristic polynomial has many terms. The distribution up to v bits accuracy for 1 ≤ v ≤ 32 is also shown to be good. An algorithm is also given that checks the primitivity of the characteristic polynomial of MT with computational complexity O(p2) where p is the degree of the polynomial. We implemented this generator in portable C-code. It passed several stringent statistical tests, including diehard. Its speed is comparable to other modern generators. Its merits are due to the efficient algorithms that are unique to polynomial calculations over the two-element field.

Finite fields

GFSR

Incomplete array

Inversive-decimation method

k-distribution

M-sequences

Mersenne Primes

Mersenne Twister

MT19937

Multiple-recursive matrix method

Primitive polynomials

Random number generation

Tempering

TGFSR

Mathematics [ 410 ]

eng

ACM

Copyright (c) 2006 ACM. This is the author version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Modeling and Computer Simulation, Vol.8 No.1 ; http://dx.doi.org/10.1145/272991.272995

[ISSN] 1049-3301

[DOI] 10.1145/272991.272995

[NCID] AA10779230

[DOI] http://dx.doi.org/10.1145/272991.272995 isVersionOf