  The Mersenne Twister (MT) is a pseudo-random number generator (PRNG) widely
used in High Performance Computing for parallel stochastic simulations. We aim
to assess the quality of common parallelization techniques used to generate
large streams of MT pseudo-random numbers. We compare three techniques:
sequence splitting, random spacing and MT indexed sequence. The TestU01 Big
Crush battery is used to evaluate the quality of 4096 streams for each
technique on three different hardware configurations. Surprisingly, all
techniques exhibited almost 30% of defects with no technique showing better
quality than the others. While all 106 Big Crush tests showed failures, the
failure rate was limited to a small number of tests (maximum of 6 tests failed
per stream, resulting in over 94% success rate). Thanks to 33 CPU years,
high-quality streams identified are given. They can be used for sensitive
parallel simulations such as nuclear medicine and precise high-energy physics
applications.
