Generating sequences of pseudorandom numbers is a prerequisite for many applications, such as Monte Carlo simulations. Since such applications are often executed on parallel computers, the parallel computation of pseudorandom numbers is also important. Furthermore, since kernels of parallel applications often run on graphics processing units (GPUs) these days, the parallel computation of pseudorandom numbers on GPUs is of relevance.
This paper proposes a pseudorandom number generator called the Mersenne twister for graphic processors (MTGP), which generates sequences whose period is a Mersenne prime (a prime of form 2p-1). The design of this generator is highly optimized for execution on GPUs. A notable feature of MTGP is that it works in parallel to compute multiple solutions of the generating recursion and thus traverses a single state space. This results in a long period and high-dimensional equidistribution. Benchmarks show that MTGP competes in performance with the fastest generators, using not only larger periods but also sometimes exhibiting better statistical properties.
MTGP depends on several parameters. The authors give parameter sets for three periods suitable for execution with 250, 512, and 1024 parallel threads. Moreover, they provide a dynamic parameter set generator, MTGP dynamic creator (MTGPDC). When MTGPDC is given a numerical identifier, it computes a parameter set of the desired period, such that the generated sequence is unique with high probability for that identifier. In this way, multiple independent sequences can be generated.
I found the paper to be well written. Apart from providing the mathematical background, it includes practical hints for the integration of the generator (which is available as open source) into concrete applications.
