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ID 15032
本文ファイル
著者
Nishimura, Takuji
キーワード
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
数学
抄録(英)
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.
掲載誌名
ACM Transactions on Modeling and Computer Simulation
8巻
1号
開始ページ
3
終了ページ
30
出版年月日
1998-01
出版者
ACM
ISSN
1049-3301
NCID
出版者DOI
言語
英語
NII資源タイプ
学術雑誌論文
広大資料タイプ
学術雑誌論文
DCMIタイプ
text
フォーマット
application/pdf
著者版フラグ
author
権利情報
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
関連情報URL(IsVersionOf)
http://dx.doi.org/10.1145/272991.272995
部局名
理学研究科