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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Orbits and Lattices
for Linear Random Number Generators
with Composite Moduli


Authors: Raymond Couture and Pierre L’Ecuyer
Journal: Math. Comp. 65 (1996), 189-201
MSC (1991): Primary 65C10
MathSciNet review: 1322887
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Abstract: In order to analyze certain types of combinations of multiple recursive linear congruential generators (MRGs), we introduce a generalized spectral test. We show how to apply the test in large dimensions by a recursive procedure based on the fact that such combinations are subgenerators of other MRGs with composite moduli. We illustrate this with the well-known RANMAR generator. We also design an algorithm generalizing the procedure to arbitrary random number generators.


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Additional Information

Raymond Couture
Affiliation: Département d’Informatique, et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada
Email: couture@iro.umontreal.ca

Pierre L’Ecuyer
Affiliation: Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada
Email: lecuyer@iro.umontreal.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00673-4
PII: S 0025-5718(96)00673-4
Keywords: Random number generation, lattice structure, combined generators
Received by editor(s): April 6, 1994
Received by editor(s) in revised form: November 29, 1994
Additional Notes: This work has been supported by NSERC-Canada grant # OGP0110050 and FCAR-Québec grant # 93ER1654 to the second author.
Article copyright: © Copyright 1996 American Mathematical Society