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ID 15032
file
creator
Nishimura, Takuji
subject
Finite fields
GFSR
Incomplete array
Inversive-decimation method
k-distribution
M-sequences
Mersenne Primes
Mersenne Twister
MT19937
Multiple-recursive matrix method
Primitive polynomials
Random number generation
Tempering
TGFSR
NDC
Mathematics
abstract
A new algorithm called Mersenne Twister (MT) is proposed for generating uniform pseudorandom numbers. For a particular choice of parameters, the algorithm provides a super astronomical period of 219937 - 1 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words. This is a new variant of the previously proposed generators, TGFSR, modified so as to admit a Mersenne-prime period. The characteristic polynomial has many terms. The distribution up to v bits accuracy for 1 ≤ v ≤ 32 is also shown to be good. An algorithm is also given that checks the primitivity of the characteristic polynomial of MT with computational complexity O(p2) where p is the degree of the polynomial. We implemented this generator in portable C-code. It passed several stringent statistical tests, including diehard. Its speed is comparable to other modern generators. Its merits are due to the efficient algorithms that are unique to polynomial calculations over the two-element field.
journal title
ACM Transactions on Modeling and Computer Simulation
volume
Volume 8
issue
Issue 1
start page
3
end page
30
date of issued
1998-01
publisher
ACM
issn
1049-3301
ncid
publisher doi
language
eng
nii type
Journal Article
HU type
Journal Articles
DCMI type
text
format
application/pdf
text version
author
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 Modeling and Computer Simulation, Vol.8 No.1 ; http://dx.doi.org/10.1145/272991.272995
relation is version of URL
http://dx.doi.org/10.1145/272991.272995
department
Graduate School of Science



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