An implementation of the lattice and spectral tests for multiple recursive linear random number generators

We discuss the implementation of theoretical tests to assess the structural properties of simple or combined linear congruential and multiple recursive random number generators. In particular, we describe a package implementing the so-called spectral and lattice tests for such generators. Our programs analyze the lattices generated by vectors of successive or non-successive values produced by the generator, analyze the behavior of generators in high dimensions, and deal with moduli of practically unlimited sizes. We give numerical illustrations. We also explain how to build lattice bases in several different cases, e.g., for vectors of far-apart nonsuccessive values, or for sublattices generated by the set of periodic states or by a subcycle of a generator, and, for all these cases, how to increase the dimension of a (perhaps partially reduced) basis.