  This paper proposes a type of pseudorandom number generator, Mersenne Twister
for Graphic Processor (MTGP), for efficient generation on graphic processessing
units (GPUs). MTGP supports large state sizes such as 11213 bits, and uses the
high parallelism of GPUs in computing many steps of the recursion in parallel.
The second proposal is a parameter-set generator for MTGP, named MTGP Dynamic
Creator (MTGPDC). MT- GPDC creates up to 2^32 distinct parameter sets which
generate sequences with high-dimensional uniformity. This facility is suitable
for a large grid of GPUs where each GPU requires separate random number
streams. MTGP is based on linear recursion over the two-element field, and has
better high-dimensional equidistribution than the Mersenne Twister pseudorandom
number generator.
