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Parallel linear congruential generators with prime moduli

By Michael Mascagni


Abstract. Linear congruential generators (LCGs) remain the most popular method of pseudorandom number generation on digital computers. Ease of implementation has favored implementing LCGs with power-of-two moduli. However, prime modulus LCGs are superior in quality to power-of-two modulus LCGs, and the use of a Mersenne prime minimizes the computational cost of generation. When implemented for parallel computation, quality becomes an even more compelling issue. We use a full-period exponential sum as the measure of stream independence and present a method for producing provably independent streams of LCGs in parallel by utilizing an explicit parameterization of all of the primitive elements modulo a given prime. The minimization of this measure of independence further motivates an algorithm required in the explicit parameterization. We describe and analyze this algorithm and describe its use in a parallel LCG package. 1. Introduction. Perhaps the oldest generator still in use for the generation of uniformly distributed integers is the linear congruential generator (LCG). This generator is sometime

Year: 1998
DOI identifier: 10.1016/s0167-8191(98)00010-6
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
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