An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1
SIAM Journal on Scientific and Statistical Computing
A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Testing random number generators
WSC '92 Proceedings of the 24th conference on Winter simulation
Some portable very-long-period random number generators
Computers in Physics
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
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Two or more multiplicative congruential random-number generators with prime modulus combined by means of a method proposed by Wichmann and Hill (1982) yield a random-number generator equivalent to a multiplicative congruential random-number generator with modulus equal to the product of the moduli of the component multiplicative congruential generators. The period of a random-number sequence obtained by the Wichmann-Hill method is equal to the least common multiple of the periods of the combined sequences. One of the two purposes of this paper is to present a necessary and sufficient set of efficiently verifiable conditions for the period to be equal to its maximum, which is the maximum of the least common multiple. Each of the conditions is always satisfied or is more easily verifiable when the modulus of each of the component generators is a safe prime. The other purpose of this paper is to derive an efficiently evaluatable formula for serial correlations of the maximum-period sequences by the Wichmann-Hill method. The authors recommend (i) to make the modulus of each of the component generators a safe prime, and (ii) to chose the multipliers of the components so as to (a) maximize the period and (b) make the serial correlations small in absolute value.