Strong deviations from randomness in
            <i>m</i>
            -sequences based on trinomials

Matsumoto, Makoto; Kurita, Yoshiharu

doi:10.1145/232807.232815

Cited by 25 publications

(17 citation statements)

References 9 publications

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“…GFSR rejected in an Ising-Model simulation [Ferrenberg, A.M. et al 1992], and a slight modication of trinomials [Fushimi 1990] rejected in [Matsumoto and Kurita 1994]). For these defects, see [Lindholm 1968] [Fredricsson 1975] [Compagner 1991] [Matsumoto and Kurita 1992] [Matsumoto and Kurita 1994] [Matsumoto and Kurita 1996].…”

Section: Number Of Terms In Characteristic Polynomialmentioning

confidence: 99%

Mersenne twister

Matsumoto

Nishimura

1998

ACM Trans. Model. Comput. Simul.

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4,690

1,930

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In this paper, a new algorithm named Mersenne Twister (MT) for generating uniform pseudorandom numbers is proposed. For a particular choice of parameters, the algorithm provides a super astronomical period of 2 19937 0 1 and 623-dimensional equidistribution up to 32 bits accuracy, while consuming a working area of only 624 words. This is a new variant of the previously proposed generators TGFSR, modied 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.Also, an algorithm to check the primitivity of the characteristic polynomial of MT with computational complexity O(p 2 ) is given, where p is the degree of the polynomial.We implemented this generator as a portable C-code. It passed several stringent statistical tests, including diehard. The speed is comparable to other modern generators.These merits are a consequence of the ecient algorithms unique to polynomial calculations over the two-element eld.

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Section: Number Of Terms In Characteristic Polynomialmentioning

confidence: 99%

Mersenne twister

Matsumoto

Nishimura

1998

ACM Trans. Model. Comput. Simul.

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4,690

1,930

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“…In particular, generators for which P (z) is a trinomial or a pentanomial, which have been widely used in the past, do not satisfy this condition and have been shown to fail rather simple statistical tests [Lindholm 1968;Matsumoto and Kurita 1996]. So, as a secondary quality criterion we look at the number of nonzero coefficients in P (z), which we denote by N 1 .…”

Section: Equidistribution and Measures Of Qualitymentioning

confidence: 99%

Improved long-period generators based on linear recurrences modulo 2

Panneton

L’Ecuyer

Matsumoto

2006

ACM Trans. Math. Softw.

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222

175

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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.

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“…However Lindholm (1968) and Matsumoto and Kurita (1996) have shown that this leads to poor statistical behavior, and argued that there should be near 50% nonzero coefficients in the characteristic polynomial. The MT generators do not satisfy this, but the WELL do.…”

Section: Linear Recurrences Modulo a Large Primementioning

confidence: 99%

History of uniform random number generation

L’Ecuyer¹

2017

2017 Winter Simulation Conference (WSC)

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Random number generators were invented before there were symbols for writing numbers, and long before mechanical and electronic computers. All major civilizations through the ages found the urge to make random selections, for various reasons. Today, random number generators, particularly on computers, are an important (although often hidden) ingredient in human activity. In this article, we give a historical account on the design, implementation, and testing of uniform random number generators used for simulation.

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Strong deviations from randomness in m -sequences based on trinomials

Abstract: The fixed vector of any m-sequence based on a trinomial is explicitly obtained. Local nonrandomness around the fixed vector is analyzed through model-construction and experiments. We conclude that the initial vector near the fixed vector should be avoided.

Cited by 25 publications

References 9 publications

Mersenne twister

Mersenne twister

Improved long-period generators based on linear recurrences modulo 2

History of uniform random number generation

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