Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator

@article{Matsumoto1998MersenneTA,
  title={Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator},
  author={Makoto Matsumoto and Takuji Nishimura},
  journal={ACM Trans. Model. Comput. Simul.},
  year={1998},
  volume={8},
  pages={3-30}
}
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<supscrpt>19937</supscrpt> −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… 
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Assessment of non-random bit patterns in dimensions that are higher than the dimension of equidistribution with v -bit accuracy, which focuses on the relationship between points in the Couture-L'Ecuyer dual lattices and F 2 -linear relations on the most significant v bits of output sequences.
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This paper surveys the results for the non-specialist, providing new, simple, understandable examples, and it is intended as a guide for the final user, or for language implementors, so that they can take an informed decision about whether to use the Mersenne Twister or not.
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A system of multiple recursive generators of modulus p and order k where all nonzero coefficients of the recurrence are equal is proposed, so the generator would run faster than the general case.
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