Testing parallel random number generators

Monte Carlo computations are considered easy to parallelize. However, the results can be adversely affected by defects in the parallel pseudorandom number generator used. A parallel pseudorandom number generator must be tested for two types of correlations - (i) intra-stream correlation, as for any sequential generator, and (ii) inter-stream correlation for correlations between random number streams on different processes. Since bounds on these correlations are difficult to prove mathematically, large and thorough empirical tests are necessary. Many of the popular pseudorandom number generators in use today were tested when computational power was much lower, and hence they were evaluated with much smaller test sizes. This paper describes several tests of pseudorandom number generators, both statistical and application-based. We show defects in several popular generators. We describe the implementation of these tests in the SPRNG [ACM Trans. Math. Software 26 (2000) 436; SPRNG - scalable parallel random number generators. SPRNG 1.0 - http://www.ncsa.uiuc.edu/Apps/SPRNG; SPRNG 2.0 - http://sprng.cs.fsu.edu] test suite and also present results for the tests conducted on the SPRNG generators. These generators have passed some of the largest empirical random number tests.