Improved long-period generators based on linear recurrences modulo 2

Panneton François

L'Ecuyer Pierre

Matsumoto Makoto

ACM Transactions on Mathematical Software

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.

GFSR linear recurrence modulo 2

Linear feedback shift register

Mersenne twister

Random number generation

Mathematics [ 410 ]

eng

ACM

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

[ISSN] 0098-3500

[DOI] 10.1145/1132973.1132974

[NCID] AA00502525

[DOI] http://dx.doi.org/10.1145/1132973.1132974 isVersionOf