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There has been quite a lot of research on developing algorithms for parallel random number generators, but very little work has been done on developing and applying methods for testing such generators. Not many rigorous mathematical results are known about the properties of parallel random number generators, so stringent and varied empirical tests are vital.
The many standard statistical tests for checking the randomness properties of sequential generators can be applied to parallel generators, by testing the random number streams on each processor, and from all processors combined. This is the usual approach in testing parallel generators. However, new techniques are necessary to test algorithms for generating random numbers on parallel computers, for example to look for correlations between random number streams on different processors [25, 26]. Thus far, very little work has been done in this area.
A good empirical test of parallel random number generators is to use them with parallel implementations of the Monte Carlo algorithms used for simulating the two dimensional Ising model, which have proven to be very effective at testing sequential generators. Such tests have been done for a number of parallel generators [23, 24].
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