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MersenneTwister

swMATH ID: 5367
Software Authors: Matsumoto, Makoto; Nishimura, Takuji
Description: 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.
Homepage: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
Programming Languages: C++
Keywords: random number generation; finite fields; incomplete array; inversive-decimation method; \(k\)-distribution; Mersenne primes; multiple-recursive matrix method; primitive polynomials; algorithm; Mersenne twister; computational complexity; statistical tests
Related Software: TestU01; R; Diehard; CUDA; MRG32k3a; GSL; TOMS659; AS 183; NIST Statistical Test Suite; SPRNG; sobol.cc; RngSteam; Ziggurat; rnorrexp; SFMT; dieharder; RANLUX; RngStreams; GRASP; CPLEX
Cited in: 351 Documents
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Cited by 742 Authors

13 Resende, Mauricio G. C.
11 Matsumoto, Makoto
7 Harase, Shin
6 Balakrishnan, Narayanaswamy
6 Koibuchi, Hiroshi
6 L’Ecuyer, Pierre
6 Leovey, Hernan
6 Nagatsuka, Hideki
6 Ökten, Giray
6 Silva, Ricardo Martins Abreu E.
5 Nishimura, Takuji
5 Pardalos, Panos M.
4 Hirsch, Michael J.
4 Komori, Yoshio
4 Römisch, Werner
3 Bruno, Odemir Martinez
3 Burrage, Kevin
3 Daida, Jason M.
3 Deng, Lih-Yuan
3 Festa, Paola
3 Haramoto, Hiroshi
3 Machicao, Jeaneth
3 Mateus, Geraldo Robson
3 Noronha, Thiago F.
3 Panneton, François
3 Saito, Mutsuo
2 Bai, Fengshan
2 Bayraksan, Güzin
2 Benson, Hande Y.
2 Bhattacharjee, Kamalika
2 Catanzaro, Daniele
2 Choi, Jeong-Ok
2 Collins, Andrew J.
2 Couchot, Jean-François
2 Czibula, Oliver G.
2 Das, Sukanta
2 Demchik, Vadim
2 Di Pietro, Roberto
2 Etemadidavan, Sheida
2 Fernández de Bustos, I.
2 Gevorkyan, Migran N.
2 Gonçalves, José Fernando
2 Griewank, Andreas
2 Gu, Hanyu
2 Guyeux, Christophe
2 Haiman, George
2 Heitsch, Holger
2 Hellekalek, Peter
2 Henderson, Nélio
2 Hiller, Benjamin
2 Hilss, Adam M.
2 Kallemov, Bakytzhan
2 Kolonko, Michael
2 Korn, Elke
2 Korn, Ralf
2 Korolkova, Anna V.
2 Koscholke, Jakob
2 Kulyabov, Dmitriĭ Sergeevich
2 Lu, Henry Horng-Shing
2 Miller, Gregory Hale
2 Nguyen, Nguyet Thanh
2 Preda, Cristian
2 Prieto, Juan Luis
2 Ribeiro, Celso Carneiro
2 Sacco, Wagner F.
2 Saito, Asaki
2 Sanders, Peter
2 Savvidy, George K.
2 Savvidy, Konstantin G.
2 Shanno, David F.
2 Skanderova, Lenka
2 Stanhope, Stephen A.
2 Sulak, Fatih
2 Vvedensky, Dimitri D.
2 Wakaki, Hirofumi
2 Werneck, Renato F.
2 Xu, Linlin
2 Yamaguchi, Akihiro
2 Yu, Unjong
2 Zelinka, Ivan
2 Zinder, Yakov
1 Abasolo, M.
1 Abdul-Rahman, Houssam M.
1 Abdullah, Rosni
1 Abramov, Rafail V.
1 Abrams, Cameron F.
1 Abreu Júnior, João Carlos
1 Aceves-Sánchez, Pedro
1 Ackermann, Jörg
1 Adams, Nikolaus A.
1 Adler, Michael C.
1 Agarwal, Ravi P.
1 Agirrebeitia, Josu
1 Aihara, Kazuyuki
1 Ajuria, Goizalde
1 Akahori, Jirô
1 Akashi, Ryosuke
1 Äkäslompolo, S.
1 Akasobe, Shigenori
1 Al-Refa’ei, Mahmoud H.
...and 642 more Authors
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Cited in 160 Serials

12 Journal of Computational Physics
11 Mathematics and Computers in Simulation
9 Computer Physics Communications
9 Journal of Computational and Applied Mathematics
7 European Journal of Operational Research
6 ACM Transactions on Mathematical Software
6 Journal of Statistical Computation and Simulation
6 ACM Transactions on Modeling and Computer Simulation
5 Journal of Statistical Physics
5 Mathematics of Computation
5 Applied Mathematics and Computation
5 Annals of Operations Research
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5 Optimization Letters
4 Chaos, Solitons and Fractals
4 Journal of Global Optimization
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4 Journal of Statistical Mechanics: Theory and Experiment
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3 Computer Methods in Applied Mechanics and Engineering
3 Physica A
3 Theoretical Computer Science
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3 Communications in Statistics. Simulation and Computation
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3 Journal of High Energy Physics
2 The American Statistician
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2 Programming and Computer Software
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2 Applied Mathematical Modelling
2 Mathematical Programming. Series A. Series B
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 International Transactions in Operational Research
2 Journal of Combinatorial Optimization
2 Communications in Nonlinear Science and Numerical Simulation
2 Methodology and Computing in Applied Probability
2 RAIRO. Operations Research
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2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
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2 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
2 Algorithms
2 Computer Science Review
2 Wiley Series in Probability and Statistics
1 Advances in Applied Probability
1 Artificial Intelligence
1 European Journal of Physics
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1 Mathematical Biosciences
1 Bulletin of Mathematical Biology
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1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
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1 SIAM Review
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Cited in 38 Fields

163 Numerical analysis (65-XX)
58 Operations research, mathematical programming (90-XX)
57 Statistics (62-XX)
44 Probability theory and stochastic processes (60-XX)
41 Computer science (68-XX)
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9 Combinatorics (05-XX)
6 Mechanics of deformable solids (74-XX)
6 Quantum theory (81-XX)
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