Orbits and lattices for linear random number generators with composite moduli

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.