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Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator

Authors:

Makoto Matsumoto and

Takuji NishimuraAuthors Info & Claims

ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 8, Issue 1

Pages 3 - 30

https://doi.org/10.1145/272991.272995

Published: 01 January 1998 Publication History

Abstract

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.

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Index Terms

Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
1. Mathematics of computing

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Published In

cover image ACM Transactions on Modeling and Computer Simulation

ACM Transactions on Modeling and Computer Simulation Volume 8, Issue 1

Special issue on uniform random number generation

Jan. 1998

102 pages

ISSN:1049-3301

EISSN:1558-1195

DOI:10.1145/272991

Editors:
Philip Heidelberger
IBM, Norktown Heights, NY
,
Raymond Coutre
Univ. de Montreal, Montreal, P.Q., Canada
,
Pierre L'Ecuyer
Univ. de Montreal, Montreal, P.Q., Canada

Issue’s Table of Contents

Copyright © 1998 ACM.

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Association for Computing Machinery

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Publication History

Published: 01 January 1998

Published in TOMACS Volume 8, Issue 1

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