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Improved long-period generators based on linear recurrences modulo 2 Panneton, François Panneton François L'Ecuyer, Pierre L'Ecuyer Pierre Matsumoto, Makoto Matsumoto Makoto open access Copyright (c) 2006 ACM. This is the author version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Mathematical Software, Vol.32 No.1 ; http://dx.doi.org/10.1145/272991.272995 GFSR linear recurrence modulo 2 Linear feedback shift register Mersenne twister Random number generation 410 Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed via their equidistribution properties. The huge-period generators proposed so far are not quite optimal in this respect. In this article, we propose new generators of that form with better equidistribution and "bit-mixing" properties for equivalent period length and speed. The state of our new generators evolves in a more chaotic way than for the Mersenne twister. We illustrate how this can reduce the impact of persistent dependencies among successive output values, which can be observed in certain parts of the period of gigantic generators such as the Mersenne twister. ACM 2006 eng journal article AO https://hiroshima.repo.nii.ac.jp/records/2006121 10.1145/1132973.1132974 0098-3500 AA00502525 ACM Transactions on Mathematical Software 32 1 1 1 16 https://hiroshima.repo.nii.ac.jp/record/2006121/files/ACMTraMath_32_1.pdf 305.5 KB