## 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; GSL; TOMS659; MRG32k3a; AS 183; NIST Statistical Test Suite; sobol.cc; SPRNG; dieharder; RANLUX; RngSteam; SFMT; rnorrexp; Ziggurat; GRASP; OpenCL; TSPLIB Referenced in: 332 Publications
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### Referenced by 703 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 Silva, Ricardo Martins Abreu E. 5 Nishimura, Takuji 5 Ökten, Giray 5 Pardalos, Panos M. 4 Hirsch, Michael J. 4 Komori, Yoshio 4 Römisch, Werner 3 Burrage, Kevin 3 Daida, Jason M. 3 Deng, Lih-Yuan 3 Festa, Paola 3 Haramoto, Hiroshi 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 Bruno, Odemir Martinez 2 Catanzaro, Daniele 2 Couchot, Jean-François 2 Czibula, Oliver G. 2 Demchik, Vadim 2 Di Pietro, Roberto 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, Dmitry S. 2 Lu, Henry Horng-Shing 2 Machicao, Jeaneth 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 Wakaki, Hirofumi 2 Werneck, Renato F. 2 Xu, Linlin 2 Yamaguchi, Akihiro 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 Äkäslompolo, S. 1 Al-Refa’ei, Mahmoud H. 1 Alba, Vincenzo 1 Allsopp, Nicholas K. 1 Almaraz-Luengo, Elena 1 Almeida, Eliana S. 1 Almiron, Marcelo G. 1 Altman, Micah 1 Amigó, José María 1 Ammon, A. 1 Andrade, Tomás ...and 603 more Authors
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### Referenced in 155 Serials

 12 Journal of Computational Physics 11 Mathematics and Computers in Simulation 9 Journal of Computational and Applied Mathematics 8 Computer Physics Communications 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 SIAM Journal on Scientific Computing 5 Monte Carlo Methods and Applications 5 Optimization Letters 4 Annals of Operations Research 4 Journal of Global Optimization 4 Computational Statistics 4 Computational Statistics and Data Analysis 4 Chaos 4 Journal of Statistical Mechanics: Theory and Experiment 4 Journal of Theoretical Biology 3 Computer Methods in Applied Mechanics and Engineering 3 Chaos, Solitons and Fractals 3 Theoretical Computer Science 3 Theoretical Population Biology 3 Physica D 3 Computational Optimization and Applications 3 Journal of High Energy Physics 2 Computers and Fluids 2 Computers & Mathematics with Applications 2 Information Processing Letters 2 Physica A 2 Physics Letters. A 2 Molecular Simulation 2 The Annals of Statistics 2 Computing 2 Information Sciences 2 Journal of Multivariate Analysis 2 Programming and Computer Software 2 Insurance Mathematics & Economics 2 Computational Mechanics 2 Journal of Economic Dynamics & Control 2 Journal of Scientific Computing 2 Designs, Codes and Cryptography 2 Computational Mathematics and Mathematical Physics 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 Methodology and Computing in Applied Probability 2 RAIRO. Operations Research 2 Quantitative Finance 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Kinetic and Related Models 2 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 2 Algorithms 2 Wiley Series in Probability and Statistics 1 Advances in Applied Probability 1 Artificial Intelligence 1 International Journal for Numerical Methods in Fluids 1 International Journal of Solids and Structures 1 Mathematical Biosciences 1 Bulletin of Mathematical Biology 1 Theoretical and Computational Fluid Dynamics 1 Waves in Random Media 1 Annals of the Institute of Statistical Mathematics 1 Biometrics 1 BIT 1 Journal of Computer and System Sciences 1 Journal of the Operational Research Society 1 Journal of Statistical Planning and Inference 1 Kybernetika 1 Memoirs of the American Mathematical Society 1 Networks 1 Numerische Mathematik 1 Operations Research 1 SIAM Journal on Numerical Analysis 1 Studia Logica 1 Synthese 1 Journal of the Japan Statistical Society 1 Mathematical Social Sciences 1 Algorithmica 1 Computers & Operations Research 1 Mathematical and Computer Modelling 1 Neural Networks 1 Japan Journal of Industrial and Applied Mathematics 1 The Annals of Applied Probability 1 Discrete Event Dynamic Systems 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Communications in Statistics. Theory and Methods 1 Journal of Non-Newtonian Fluid Mechanics 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Systems Analysis, Modelling Simulation 1 Applicable Algebra in Engineering, Communication and Computing 1 Journal of Mathematical Imaging and Vision 1 Journal of Nonlinear Science 1 Cybernetics and Systems Analysis 1 Experimental Mathematics 1 Turkish Journal of Mathematics ...and 55 more Serials
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### Referenced in 38 Fields

 159 Numerical analysis (65-XX) 56 Operations research, mathematical programming (90-XX) 48 Statistics (62-XX) 43 Probability theory and stochastic processes (60-XX) 39 Computer science (68-XX) 27 Number theory (11-XX) 27 Statistical mechanics, structure of matter (82-XX) 25 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Biology and other natural sciences (92-XX) 19 Fluid mechanics (76-XX) 17 Information and communication theory, circuits (94-XX) 12 Partial differential equations (35-XX) 9 Combinatorics (05-XX) 9 Dynamical systems and ergodic theory (37-XX) 5 Mechanics of deformable solids (74-XX) 5 Quantum theory (81-XX) 4 Ordinary differential equations (34-XX) 3 Mathematical logic and foundations (03-XX) 3 Field theory and polynomials (12-XX) 2 General and overarching topics; collections (00-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX) 2 Convex and discrete geometry (52-XX) 2 Relativity and gravitational theory (83-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-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 Systems theory; control (93-XX) 1 Mathematics education (97-XX)