Bad subsequences of well-known linear congruential pseudorandom number generators

Entacher, Karl

doi:10.1145/272991.273009

Cited by 41 publications

(17 citation statements)

References 29 publications

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“…One way to become sure against such pitfalls is employing the spectral test [40 -43]. Several LCGs have been proposed due to their good spectral test results in different dimensions [41,44], others have been revealed to exhibit low quality substreams due to their bad spectral test results [45].…”

Section: Leaping Lcgsmentioning

confidence: 99%

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Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique

Entacher

Schell

Schmid

et al. 2003

Parallel Algorithms and Applications

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Currently, the most efficient numerical techniques for evaluating high-dimensional integrals are based on Monte Carlo and quasi-Monte Carlo techniques. These tasks require a significant amount of computation and are therefore often executed on parallel computer systems. In order to keep the communication amount within a parallel system to a minimum, each processing element (PE) requires its own source of integration nodes. Therefore, techniques for using separately initialized and disjoint portions of a given point set on a single PE are classically employed. Using the so-called substreams may lead to dramatic errors in the results under certain circumstances. In this work, we compare the possible defects employing leaped quasi-Monte Carlo and Monte Carlo substreams. Apart from comparing the magnitude of the observed integration errors we give an overview under which circumstances (i.e. parallel programming models) such errors can occur.

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Section: Leaping Lcgsmentioning

confidence: 99%

“…See Ref. [45] for more examples of this kind. Such streams are likely to occur in practice since the leap factor will often be chosen equal to the number of PEs which are available in order to obtain one substream per PE.…”

Section: Leaping Lcgsmentioning

confidence: 99%

Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique

Entacher

Schell

Schmid

et al. 2003

Parallel Algorithms and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…A Pseudorandom Number Generators (PRNG) are well-known techniques with broad applications in such areas as cryptography (Tusnoo et al, 2003;Ozturk et al, 2004;Panneton et al, 2006), simulation of stochastic processes (Entacher, 1998), comprehensive testing of technical systems (Leeb and Wegenkittl, 1997;Park and Miller, 1998), medical (Menyaev and Zharov, 2006a;2006b;Menyaev and Zharova, 2006;2013;2016;Sarimollaoglu et al, 2014;Cai et al, 2016a;2016b) and biological research (Wiese et al, 2005;Leonard and Jackson, 2015;Juratly et al, 2015;2016) and others (Rababbah 2004;2007;Politano et al, 2014;2016;Riguzzi, 2016). In these publications, the concept of uniform random numbers in PRNG actively uses the operations of bit logic.…”

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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“…Such claims may later be falsified when a particular weakness in a generator is discovered. For example, Linear congruential generators which have been widely used in commercial software were found after many years to have serious defects (Entacher, 1998). The popular and often recommended Mersenne Twister has the flaw that it can produce long sequences with more 0's than 1's if it comes into a state where the state buffer contains mostly 0's.…”

Section: How Much Can Be Proven?mentioning

confidence: 99%

Pseudo-Random Number Generators for Vector Processors and Multicore Processors

Fog

2015

J. Mod. App. Stat. Meth.

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Large scale Monte Carlo applications need a good pseudo-random number generator capable of utilizing both the vector processing capabilities and multiprocessing capabilities of modern computers in order to get the maximum performance. The requirements for such a generator are discussed. New ways of avoiding overlapping subsequences by combining two generators are proposed. Some fundamental philosophical problems in proving independence of random streams are discussed. Remedies for hitherto ignored quantization errors are offered. An open source C++ implementation is provided for a generator that meets these needs.

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Bad subsequences of well-known linear congruential pseudorandom number generators

Cited by 41 publications

References 29 publications

Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique

Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique

Parametrical Tuning of Twisting Generators

Pseudo-Random Number Generators for Vector Processors and Multicore Processors

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