Tables Of Linear Congruential Generators Of Different Sizes And Good Lattice Structure (1999)
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@MISC{L'Ecuyer99tablesof,
author = {Pierre L'Ecuyer},
title = {Tables Of Linear Congruential Generators Of Different Sizes And Good Lattice Structure},
year = {1999}
}
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Abstract
. We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ` = 8; 9; : : : ; 64; 127; 128, we take as a modulus m the largest prime smaller than 2 ` , and provide a list of multipliers a such that the MLCG with modulus m and multiplier a has a good lattice structure in dimensions 2 to 32. We provide similar lists for power-of-two moduli m = 2 ` , for multiplicative and non-multiplicative LCGs. 1. Introduction A multiplicative linear congruential generator (MLCG) is defined by a recurrence of the form xn = axn\Gamma1 mod m (1) where m and a are integers called the modulus and the multiplier , respectively, and xn 2 Zm = f0; : : : ; m \Gamma 1g is the state at step n. To obtain a sequence of "random numbers" in the interval [0; 1), one can define the output at step n as un = xn=m: (2) We use the expression "the MLCG (m; a)" to denote a sequence that obeys (1) and (2). Th...
