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. Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus: On the quasi-Monte Carlo method with halton points for elliptic PDEs with log-normal diffusion (2017)
  2. Blaser, Rico; Fryzlewicz, Piotr: Random rotation ensembles (2016)
  3. Heitsch, H.; Leövey, H.; Römisch, W.: Are quasi-Monte Carlo algorithms efficient for two-stage stochastic programs? (2016)
  4. Lista, Luca: Statistical methods for data analysis in particle physics (2016)
  5. Murphy, James T.; Johnson, Mark P.; Viard, Frédérique: A modelling approach to explore the critical environmental parameters influencing the growth and establishment of the invasive seaweed \itUndaria pinnatifida in Europe (2016)
  6. Naudé, Kevin A.: Refined pivot selection for maximal clique enumeration in graphs (2016)
  7. Niederreiter, Harald: A survey of some applications of finite fields (2016)
  8. Portal, Gabriel M.; Ritt, Marcus; Borba, Leonardo M.; Buriol, Luciana S.: Simulated annealing for the machine reassignment problem (2016)
  9. Ramirez-Nafarrate, Adrian; Muñoz, David F.: Performance evaluation of output analysis methods in steady-state simulations (2016)
  10. Self, Julian; Mackey, Michael C.: Random numbers from a delay equation (2016)
  11. Bianchi, Reinaldo A. C.; Celiberto, Luiz A. jun.; Santos, Paulo E.; Matsuura, Jackson P.; Lopez de Mantaras, Ramon: Transferring knowledge as heuristics in reinforcement learning: a case-based approach (2015)
  12. Guo, Gang; Bittig, Arne; Uhrmacher, Adelinde: Lattice Monte Carlo simulation of Galilei variant anomalous diffusion (2015)
  13. Hiller, Benjamin; Hayn, Christine; Heitsch, Holger; Henrion, René; Leövey, Hernan; Möller, Andris; Römisch, Werner: Methods for verifying booked capacities (2015)
  14. Koch, Thorsten (ed.); Hiller, Benjamin (ed.); Pfetsch, Marc (ed.); Schewe, Lars (ed.): Evaluating gas network capacities (2015)
  15. Leövey, H.; Römisch, W.: Quasi-Monte Carlo methods for linear two-stage stochastic programming problems (2015)
  16. Luu, Thomas: Efficient and accurate parallel inversion of the gamma distribution (2015)
  17. Silva, R.M.A.; Resende, M.G.C.; Pardalos, P.M.: A Python/C++ library for bound-constrained global optimization using a biased random-key genetic algorithm (2015)
  18. Spiliopoulos, Konstantinos: Rare event simulation for multiscale diffusions in random environments (2015)
  19. Ünlü, Ali; Schrepp, Martin: Untangling comparison bias in inductive item tree analysis based on representative random quasi-orders (2015)
  20. Wood, Simon N.: Core statistics (2015)

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