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:

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  1. Ferone, Daniele; Festa, Paola; Guerriero, Francesca: An efficient exact approach for the constrained shortest path tour problem (2020)
  2. 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)
  3. Leövey, H.; Römisch, W.: Randomized QMC methods for mixed-integer two-stage stochastic programs with application to electricity optimization (2020)
  4. Bhattacharjee, Kamalika; Das, Sukanta: Random number generation using decimal cellular automata (2019)
  5. Dos Reis, Daniel Morais; Goulart, Natã; Noronha, Thiago F.; De Souza, Sérgio Ricardo: On the problem of minimizing the cost with optical devices in wavelength division multiplexing optical networks: complexity analysis, mathematical formulation and improved heuristics (2019)
  6. Hagebring, Fredrik; Lennartson, Bengt: Time-optimal control of large-scale systems of systems using compositional optimization (2019)
  7. Harase, Shin: Comparison of Sobol’ sequences in financial applications (2019)
  8. Kuschel, Torben; Bock, Stefan: Solving the weighted capacitated planned maintenance problem and its variants (2019)
  9. Terenin, Alexander; Dong, Shawfeng; Draper, David: GPU-accelerated Gibbs sampling: a case study of the horseshoe probit model (2019)
  10. Yaegashi, Yuta; Yoshioka, Hidekazu; Tsugihashi, Kentaro; Fujihara, Masayuki: Analysis and computation of probability density functions for a 1-D impulsively controlled diffusion process (2019)
  11. Adler, Michael C.; Gonzalez, David R.; Stack, Cory M.; Gaitonde, Datta V.: Synthetic generation of equilibrium boundary layer turbulence from modeled statistics (2018)
  12. Atanassov, E.; Gurov, T.; Ivanovska, S.; Karaivanova, A.; Simchev, T.: On the parallel implementation of quasi-Monte Carlo algorithms (2018)
  13. 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)
  14. Czibula, Oliver G.; Gu, Hanyu; Zinder, Yakov: Lagrangian relaxation versus genetic algorithm based metaheuristic for a large partitioning problem (2018)
  15. de Andrade, Bernardo B.; Souza, Geraldo S.: Likelihood computation in the normal-gamma stochastic frontier model (2018)
  16. Fatih Nar, Osman Erman Okman, Atilla Özgür, Müjdat Çetin: RmSAT-CFAR: Fast and accurate target detection in radar images (2018) not zbMATH
  17. 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)
  18. Gori, Giacomo; Viti, Jacopo: Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance (2018)
  19. Henderson, Nélio; de Sá Rêgo, Marroni; Imbiriba, Janaína; de Sá Rêgo, Márlison; Sacco, Wagner F.: Testing the topographical global initialization strategy in the framework of an unconstrained optimization method (2018)
  20. Howard, C. Douglas: It’s puzzling (2018)

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