On the fast generation of long-period pseudorandom number sequences

Monte Carlo simulations and other scientific applications that depend on random numbers are increasingly implemented in parallel configurations in programmable hardware. High-quality pseudo-random number generators (PRNGs), such as the Mersenne Twister, are based on binary linear recurrence equations. They have extremely long periods (more than 2
¹⁰²⁴
numbers generated before the entire sequence repeats) and well-proven statistical properties. Many software implementations of such dasialong-periodpsila PRNGs exist, but hardware implementations are rare. We develop optimized, resource-efficient parallel architectures for long-period PRNGs that generate multiple independent streams by exploiting the underlying algorithm as well as hardware-specific architectural features.