Benchmark of the Unrolling of Pseudorandom Numbers Generators

Research software involving stochastic behaviour often requires an enormous quantity of random numbers. In addition to the quality of the pseudorandom number generator (PRNG), the speed of the algorithm and the ease of its implementation are common practical aspects. In this work we will discuss how to optimize the access speed to random numbers independently from the generation algorithm using a lookup table. This idea was exploited in the late fifties, when the Rand Corporation started to propose sets of ready to use pseudo-random numbers (PRNs). The need of larger and larger sets of PRNs cancelled the possibility of storing those sets into the memory of our past computers, even supercomputers were not able to store tables with hundreds of millions of PRNs. In this paper we propose an implementation technique in order to speedup any kind of PRNG taking into account the capacities of current computers and microcomputers. The speed of our solution stems from the classical unrolling optimization technique, it is named the URNG technique (Unrolled Random Number Generator). Random numbers are first generated in source code, then precompiled and stored inside the RAM of inexpensive computers at the executable loading time. With this technique random numbers need to be computed only once. The UNRG technique is compliant with parallel computing. Limits and effects on speed and sensitivity are explored over 4 computer generations with a simple Monte Carlo simulation. Every research field using stochastic computation can be concerned by this software optimization technique.