A Fast, High Quality, and Reproducible Parallel Lagged-fibonacci Pseudorandom Number Generator

We study the suitability of the additive lagged-Fibonacci pseudorandom number generator for parallel computation. This generator has relatively short period with respect to the size of its seed. However, the short period is more than made up for with the huge number of full-period cycles it contains. These diierent full-period cycles are called equivalence classes. We show how to enumerate the equivalence classes and how to compute seeds to select a given equivalence class. In addition, we present some theoretical measures of quality for this generator when used in parallel. Next, we conjecture on the size of these measures of quality for this generator. Extensive empirical evidence supports this conjecture. In addition , a probabilistic interpretation of these measures leads to another conjecture similarly supported by empirical evidence. Finally we give an explicit parallelization suitable for a fully reproducible asynchronous MIMD implementation.