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Properties of Combined LCGs

The period of this generator is , which can be of order for combining two 32-bit LCGs, which is adequate for current computers. A Gigaflop-year is flops.

Empirical tests show no d-tuple lattice structure or correlations in the sequence for the combined generator.

The period and randomness properties could be improved by using two 48-bit or 64-bit LCGs instead of 32-bit generators.

The authors of the Numerical Recipes books suggest that this generator, combined with a shuffling procedure to further reduce any possible correlations, has ``perfect'' randomness properties, with perfect defined as ``we will pay $1000 to anyone who convinces us otherwise (by finding a statistical test that [this generator] fails in a non-trivial way, excluding the ordinary limitations of a machine's floating point representation).''



Paul Coddington, Northeast Parallel Architectures Center at Syracuse University, paulc@npac.syr.edu