Implementing 64-bit Maximally Equidistributed Mersenne Twisters

@article{Harase2015Implementing6M,
  title={Implementing 64-bit Maximally Equidistributed Mersenne Twisters},
  author={Shin Harase and Takamitsu Kimoto},
  journal={ArXiv},
  year={2015},
  volume={abs/1505.06582}
}
CPUs and operating systems are moving from 32 to 64 bits, and hence it is important to have good pseudorandom number generators designed to fully exploit these word lengths. However, existing 64-bit very long period generators based on linear recurrences modulo 2 are not completely optimized in terms of the equidistribution properties. Here we develop 64-bit maximally equidistributed pseudorandom number generators that are optimal in this respect and have speeds equivalent to 64-bit Mersenne… 
1 Citations
Conversion of Mersenne Twister to double-precision floating-point numbers
  • S. Harase
  • Computer Science, Mathematics
    Math. Comput. Simul.
  • 2019
TLDR
This paper reports that MT19937 with a specific lag set fails several statistical tests, such as the overlapping collision test, matrix rank test, and Hamming independence test, by investigating hidden F 2 -linear relations among the bits of high-dimensional outputs.

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