On the fast generation of long-period pseudorandom number sequences

Abstract

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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1024</sup> 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.