Scalable parallel multiple recursive generators of large order

To speed up the process of performing a large statistical simulation study, it is natural and common to divide the large-scale simulation task into several relatively independent sub-tasks in a way that these sub-tasks can be handled by individual processors in parallel. To obtain a good overall simulation result by synthesizing results from these sub-tasks, it is crucial that good parallel random number generators are used. Thus, designing suitable and independent uniform random number generators for the sub-tasks has become a very important issue in large-scale parallel simulations. Two commonly used uniform random number generators, linear congruential generator (LCG) and multiple recursive generator (MRG), have served as backbone generators for some parallel random number generators constructed in the past. We will discuss some general construction methods. A systematic leapfrog method to automatically choose different multipliers for LCGs to have the maximum-period and a method to construct many maximum-period MRGs from a single MRG are available in the literature. In this paper, we propose to combine both approaches to generate different MRGs randomly , quickly and automatically, while retaining the maximum-period property