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; NIST Statistical Test Suite; MRG32k3a; GSL; TOMS659; AS 183; SPRNG; dieharder; SFMT; sobol.cc; RngSteam; rnorrexp; Ziggurat; RANLUX; RngStreams; GRASP; GitHub Cited in: 379 Documents Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Variants of Mersenne Twister suitable for graphic processors. Zbl 1295.65005Saito, Mutsuo; Matsumoto, Makoto 2013 Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. Zbl 0917.65005Matsumoto, Makoto; Nishimura, Takuji 1998 all top 5 Cited by 797 Authors 13 Resende, Mauricio G. C. 11 Matsumoto, Makoto 8 Harase, Shin 7 L’Ecuyer, Pierre 6 Balakrishnan, Narayanaswamy 6 Koibuchi, Hiroshi 6 Leovey, Hernan 6 Nagatsuka, Hideki 6 Ökten, Giray 6 Silva, Ricardo Martins Abreu E. 5 Komori, Yoshio 5 Nishimura, Takuji 5 Pardalos, Panos M. 4 Burrage, Kevin 4 Deng, Lih-Yuan 4 Hirsch, Michael J. 4 Panneton, François 4 Römisch, Werner 3 Bhattacharjee, Kamalika 3 Bruno, Odemir Martinez 3 Daida, Jason M. 3 Festa, Paola 3 Haramoto, Hiroshi 3 Lu, Henry Horng-Shing 3 Machicao, Jeaneth 3 Mateus, Geraldo Robson 3 Noronha, Thiago F. 3 Saito, Mutsuo 3 Sanders, Peter 3 Zelinka, Ivan 2 Bai, Fengshan 2 Barash, Lev Yur’evich 2 Bayraksan, Güzin 2 Benson, Hande Y. 2 Bock, Stefan 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 Hübschle-Schneider, Lorenz 2 Kallemov, Bakytzhan 2 Kolonko, Michael 2 Korn, Elke 2 Korn, Ralf 2 Korolkova, Anna V. 2 Koscholke, Jakob 2 Kulyabov, Dmitriĭ Sergeevich 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 Savvidy, George K. 2 Savvidy, Konstantin G. 2 Shanno, David F. 2 Shchur, Lev Nikolaevich 2 Shiau, Jyh-Jen Horng 2 Skanderova, Lenka 2 Stanhope, Stephen A. 2 Sulak, Fatih 2 Urkullu, Gorka 2 Vigna, Sebastiano 2 Voß, Stefan 2 Vvedensky, Dimitri D. 2 Wakaki, Hirofumi 2 Werneck, Renato F. 2 Xu, Linlin 2 Yamaguchi, Akihiro 2 Yu, Unjong 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 Adamatzky, Andrew I. 1 Adams, Nikolaus A. 1 Adler, Michael C. ...and 697 more Authors all top 5 Cited in 164 Serials 12 Journal of Computational Physics 11 Mathematics and Computers in Simulation 10 ACM Transactions on Mathematical Software 10 Journal of Computational and Applied Mathematics 10 ACM Transactions on Modeling and Computer Simulation 9 Computer Physics Communications 8 European Journal of Operational Research 6 Journal of Statistical Computation and Simulation 6 Chaos 5 Journal of Statistical Physics 5 Mathematics of Computation 5 Applied Mathematics and Computation 5 Annals of Operations Research 5 Communications in Statistics. 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Probabilités et Statistiques ...and 64 more Serials all top 5 Cited in 39 Fields 176 Numerical analysis (65-XX) 64 Operations research, mathematical programming (90-XX) 60 Statistics (62-XX) 49 Probability theory and stochastic processes (60-XX) 49 Computer science (68-XX) 31 Number theory (11-XX) 31 Statistical mechanics, structure of matter (82-XX) 26 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Biology and other natural sciences (92-XX) 22 Information and communication theory, circuits (94-XX) 20 Fluid mechanics (76-XX) 13 Partial differential equations (35-XX) 11 Combinatorics (05-XX) 10 Dynamical systems and ergodic theory (37-XX) 7 Quantum theory (81-XX) 5 Mechanics of deformable solids (74-XX) 4 Ordinary differential equations (34-XX) 3 Mathematical logic and foundations (03-XX) 3 Field theory and polynomials (12-XX) 3 Algebraic geometry (14-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 General and overarching topics; collections (00-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 2 Convex and discrete geometry (52-XX) 2 Relativity and gravitational theory (83-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX) Citations by Year