Twisted GFSR generators

Matsumoto, Makoto; Kurita, Yoshiharu

doi:10.1145/146382.146383

Cited by 145 publications

(110 citation statements)

References 8 publications

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“…In these publications, the concept of uniform random numbers in PRNG actively uses the operations of bit logic. Great success has been found in directions such as linear congruential generators (Niederreiter, 1995;Entacher, 1999) and in twisting algorithm generators where Mersenne numbers are usually used (Matsumoto and Kurita, 1992;1994;Matsumoto and Nishimura, 1998;Nishimura, 2000). Important results were received in the use of approaches such as Fibonacci numbers (Makino, 1994;Aluru, 1997), Blum-Blum-Shub algorithm (Blum et al, 1986) and others.…”

Section: Related Workmentioning

confidence: 99%

Parametrical Tuning of Twisting Generators

Deon¹,

Menyaev²

2016

Journal of Computer Science

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Generators of uniformly distributed random numbers are broadly applied in simulations of stochastic processes that rely on normal and other distributions. In a point of fact, the uniform random numbers are actively used for applications that range from, modeling different phenomena such as theoretical mathematics and technical designing, to evidence-based medicine. This paper proposes a novel approach which consists of a combination of global twister with circular technique and initial congruential generation with complete stochastic sequences. It has been experimentally confirmed that for complete sequences this type of generation provides uniformity in distribution of random numbers. The offered program codes include the tuning methods for the generation technique where random numbers may take any bit length. Moreover, the automatic switching of generator parameters such as initial congruential constants depending on intervals for generated numbers is considered as well. Demonstrated results of testing confirm the uniformity of distribution without any repeated or skipped generated elements.

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Section: Related Workmentioning

confidence: 99%

Parametrical Tuning of Twisting Generators

Deon¹,

Menyaev²

2016

Journal of Computer Science

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“…For more than thirty years, GFSRs [11] based on three-term relations are known to suffer from statistical nonsymmetricity between 0 and 1, and to be rejected by χ 2 -test on the goodness-of-fit to the binomial distribution [12][6] [3][18] [16].…”

Section: Necessity Of a Theoretical Test On Weightmentioning

confidence: 99%

“…In the case of the weight discrepancy test, the corresponding empirical test is a classical test sometimes called the weight distribution test (c.f. [16]), which we shall briefly recall.…”

Section: Weight Distribution Test and Random Walkmentioning

confidence: 99%

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A Nonempirical Test on the Weight of Pseudorandom Number Generators

Matsumoto

Nishimura

2002

Monte Carlo and Quasi-Monte Carlo Methods 2000

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Abstract. We introduce a theoretical test, named weight discrepancy test, on pseudorandom number generators. This test measures the χ 2 -discrepancy between the distribution of the number of ones in some specified bits in the generated sequence and the binomial distribution, under the assumption that the initial value is randomly selected.This test can be performed for most generators based on a linear recursion over the two-element field 2, and predicts with high precision for which sample size the generator will be rejected by a classical statistical test called the weight distribution test.This test may be considered as a theoretical version of a one-dimensional random walk test. Differently from the empirical tests which can reject only very bad generators, this test assigns a ranking to generators. Thus it is useful to select good generators, similarly to the spectral tests and the k-distribution tests. This test rejects practically all generators linear over 2 that are known to fail in some physical tests although they pass k-distribution tests.

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“…Some results of the latter paper will also be useful in the present work. These pseudorandom number generators include various interesting generators as special cases, for instance the classical GFSR generators and the twisted GFSR generators recently introduced by Matsumoto and Kurita [10].…”

Section: H=0mentioning

confidence: 99%

Pseudorandom Vector Generation by the Multiple-Recursive Matrix Method

Niederreiter¹

1995

Mathematics of Computation

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Abstract.Pseudorandom vectors are of importance for parallelized simulation methods. In this paper we carry out an in-depth analysis of the multiplerecursive matrix method for the generation of uniform pseudorandom vectors which was introduced in an earlier paper of the author. We study, in particular, the periodicity properties, the lattice structure, and the behavior under the serial test for sequences of pseudorandom vectors generated by this method.

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Twisted GFSR generators

Cited by 145 publications

References 8 publications

Parametrical Tuning of Twisting Generators

Parametrical Tuning of Twisting Generators

A Nonempirical Test on the Weight of Pseudorandom Number Generators

Pseudorandom Vector Generation by the Multiple-Recursive Matrix Method

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