Random Number Generation for Petascale Quantum Monte Carlo

The quality of random number generators can affect the results of Monte Carlo computations, especially when a large number of random numbers are consumed. Furthermore, correlations present between different random number streams in a parallel computation can further affect the results. The SPRNG software, which the author had developed earlier, has pseudo-random number generators (PRNGs) capable of producing large numbers of streams with large periods. However, they had been empirically tested on only thousand streams earlier. In the work summarized here, we tested the SPRNG generators with over a hundred thousand streams, involving over 10^14 random numbers per test, on some tests. We also tested the popular Mersenne Twister. We believe that these are the largest tests of PRNGs, both in terms of the numbers of streams tested and the number of random numbers tested. We observed defects in some of these generators, including the Mersenne Twister, while a few generators appeared to perform well. We also corrected an error in the implementation of one of the SPRNG generators