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Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator Matsumoto, Makoto Matsumoto Makoto Nishimura, Takuji Nishimura Takuji open access 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 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 410 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. ACM 1998-01 eng journal article AO https://hiroshima.repo.nii.ac.jp/records/2006125 10.1145/272991.272995 http://dx.doi.org/10.1145/272991.272995 1049-3301 AA10779230 ACM Transactions on Modeling and Computer Simulation ACM Transactions on Modeling and Computer Simulation 8 1 3 3 30 https://hiroshima.repo.nii.ac.jp/record/2006125/files/ACMTraModel_8_3.pdf 401.5 KB