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 219 articles , 2 standard articles )

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  1. Adler, Michael C.; Gonzalez, David R.; Stack, Cory M.; Gaitonde, Datta V.: Synthetic generation of equilibrium boundary layer turbulence from modeled statistics (2018)
  2. Bakiri, Mohammed; Guyeux, Christophe; Couchot, Jean-François; Oudjida, Abdelkrim Kamel: Survey on hardware implementation of random number generators on FPGA: theory and experimental analyses (2018)
  3. de Andrade, Bernardo B.; Souza, Geraldo S.: Likelihood computation in the normal-gamma stochastic frontier model (2018)
  4. Fernández de Bustos, I.; García-Marina, V.; Urkullu, G.; Abasolo, M.: An efficient LDU algorithm for the minimal least squares solution of linear systems (2018)
  5. Henderson, Nélio; de Sá R^ego, Marroni; Imbiriba, Janaína; de Sá R^ego, Márlison; Sacco, Wagner F.: Testing the topographical global initialization strategy in the framework of an unconstrained optimization method (2018)
  6. Howard, C. Douglas: It’s puzzling (2018)
  7. Ito, Daisuke; Ueta, Tetsushi; Aihara, Kazuyuki: Bifurcation analysis of eight coupled degenerate optical parametric oscillators (2018)
  8. Kneusel, Ronald T.: Random numbers and computers (2018)
  9. Lin, Y.; Wang, F.; Liu, B.: Random number generators for large-scale parallel Monte Carlo simulations on FPGA (2018)
  10. Rose, Gregory G.: KISS: a bit too simple (2018)
  11. Savvidy, George; Savvidy, Konstantin: Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers (2018)
  12. Segredo, Eduardo; Paechter, Ben; Segura, Carlos; González-Vila, Carlos I.: On the comparison of initialisation strategies in differential evolution for large scale optimisation (2018)
  13. Yianni, Panayioti C.; Neves, Luis C.; Rama, Dovile; Andrews, John D.: Accelerating Petri-net simulations using NVIDIA graphics processing units (2018)
  14. Beebe, Nelson H. F.: The mathematical-function computation handbook. Programming using the MathCW portable software library (2017)
  15. Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal: Chaotic traversal (CHAT): very large graphs traversal using chaotic dynamics (2017)
  16. Contassot-Vivier, Sylvain; Couchot, Jean-François; Guyeux, Christophe; Heam, Pierre-Cyrille: Random walk in a $\mathsf N$-cube without Hamiltonian cycle to chaotic pseudorandom number generation: theoretical and practical considerations (2017)
  17. Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus: On the quasi-Monte Carlo method with halton points for elliptic PDEs with log-normal diffusion (2017)
  18. Komori, Yoshio; Cohen, David; Burrage, Kevin: Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations (2017)
  19. LeFloch, Philippe G.; Mercier, Jean-Marc: A new method for solving Kolmogorov equations in mathematical finance (2017)
  20. Machicao, Jeaneth; Bruno, Odemir M.: Improving the pseudo-randomness properties of chaotic maps using deep-zoom (2017)

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