A study of 128-bit multipliers for congruential pseudorandom number generators
type: Item
instance of: scholarly article
title: A study of 128-bit multipliers for congruential pseudorandom number generators
zbMATH Open document ID: 0980.65008
DOI: 10.1016/S0010-4655(99)00467-1
author: Iosif G. Dyadkin
author: Kenneth G. Hamilton
published in: Computer Physics Communications
publication date: 2002-02-25T00:00:00Z
review text: For the multiplicative congruential pseudorandom number generator \[ X_{n+1}=AX_n\text{ mod }2^{128}, \] the authors search for good multipliers of the form \(A=5^K\text{ mod }2^{128}\) with a prime number \(K\leq 2^{31}-1\). The paper is the continuation of the authors' paper [ibid. 103, No.~2-3, 103-130 (1997; reviewed above)]. For these generators with a period of \(2^{126}\), the naturally underlying lattice structure of pairs, triplets etc. is so fine that one cannot observe it. By using of parallel computing technique and mixing several flows of random numbers, this effect will even be amplified. The arbitrary postulate \(K>100000\) and five rather rigorously working number-theoretical tests, mainly from the literature (bitmap, crosstalk, lattice, lacunary and others) lead to a reduction of 2155 ``good'' primes \(K\). They remained unnamed and can be taken from a CPC library. The used software and its origin is mentioned in detail. It follow statistical tests as frequency, Kolmogorov-Smirnov, gap, birthday spacing and others. The test results are presented graphically and well correspond to what expected. Difficulties in computational converting are discussed in detail.
Mathematics Subject Classification ID: 65C10
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1437224
zbMATH Keywords: random numbers
zbMATH Keywords: pseudorandom number generators
zbMATH Keywords: congruential methods
zbMATH Keywords: multipliers
zbMATH Keywords: parallel computation
zbMATH Keywords: Monte-Carlo method
zbMATH Keywords: numerical examples
describes a project that uses: Algorithm 693
describes a project that uses: Algorithm 719
MaRDI profile type: Publication
full work available at URL: s0010-4655(99)00467-1
OpenAlex ID: W2041086511
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description: scientific article; zbMATH DE number 1437224