Improved long-period generators based on linear recurrences modulo 2

ACM Transactions on Mathematical Software Volume 32 Issue 1 Page 1-16 published_at 2006
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Title ( eng )
Improved long-period generators based on linear recurrences modulo 2
Creator
Panneton François
L'Ecuyer Pierre
Source Title
ACM Transactions on Mathematical Software
Volume 32
Issue 1
Start Page 1
End Page 16
Abstract
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.
Keywords
GFSR linear recurrence modulo 2
Linear feedback shift register
Mersenne twister
Random number generation
NDC
Mathematics [ 410 ]
Language
eng
Resource Type journal article
Publisher
ACM
Date of Issued 2006
Rights
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
Publish Type Author’s Original
Access Rights open access
Source Identifier
[ISSN] 0098-3500
[DOI] 10.1145/1132973.1132974
[NCID] AA00502525
[DOI] http://dx.doi.org/10.1145/1132973.1132974 isVersionOf