Combining the Mersenne Twister and the Xorgens Designs

10/10/2020

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by   Marcel Van de Vel, et al.

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We combine the design of two random number generators, Mersenne Twister and Xorgens, to obtain a new class of generators with heavy-weight characteristic polynomials (exceeded only by the well generators) and high speed (comparable with the originals). Tables with parameter combinations are included for state sizes ranging from 521 to 44497 bits and each of the word lengths 32, 64, 128. These generators passed all tests of the TestU01-package for each 32-bit integer part and each 64-bit derived real part of the output. We determine dimension gaps for 32-bit words, neglecting the non-linear tempering, and compare with an alternative experimental linear tempering.