MersenneTwister

Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. 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 2 19937 -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(p 2 ) 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. (Source: http://freecode.com/)


References in zbMATH (referenced in 361 articles , 2 standard articles )

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  1. Almaraz Luengo, Elena: A brief and understandable guide to pseudo-random number generators and specific models for security (2022)
  2. Chiodi, Robert; Desjardins, Olivier: General, robust, and efficient polyhedron intersection in the interface reconstruction library (2022)
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  10. Etemadidavan, Sheida; Collins, Andrew J.: An empirical distribution of the number of subsets in the core partitions of hedonic games (2021)
  11. Haramoto, Hiroshi: Study on upper limit of sample size for a two-level test in NIST SP800-22 (2021)
  12. Harase, Shin: A table of short-period Tausworthe generators for Markov chain quasi-Monte Carlo (2021)
  13. Ji, Zhe; Fu, Lin; Hu, Xiangyu; Adams, Nikolaus: A feature-aware SPH for isotropic unstructured mesh generation (2021)
  14. Karatzas, Efthymios N.; Rozza, Gianluigi: A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements (2021)
  15. Maaboudallah, Farouk; Atalla, Noureddine: An efficient numerical strategy to predict the dynamic instabilities of a rubbing system: application to an automobile disc brake system (2021)
  16. Machicao, Jeaneth; Ngo, Quynh Quang; Molchanov, Vladimir; Linsen, Lars; Bruno, Odemir: A visual analysis method of randomness for classifying and ranking pseudo-random number generators (2021)
  17. Park, Jangho; Stockbridge, Rebecca; Bayraksan, Güzin: Variance reduction for sequential sampling in stochastic programming (2021)
  18. Belov, A. A.; Kalitkin, N. N.; Tintul, M. A.: Unreliability of available pseudorandom number generators (2020)
  19. Ferone, Daniele; Festa, Paola; Guerriero, Francesca: An efficient exact approach for the constrained shortest path tour problem (2020)
  20. Gevorkyan, M. N.; Demidova, A. V.; Korol’kova, A. V.; Kulyabov, D. S.: A practical approach to testing random number generators in computer algebra systems (2020)

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