Gaussian Random Number Generation

Abstract

Some excellent surveys of the Gaussian random number generators (GRNGs) from the algorithmic perspective exist in the published literature to date (e.g., Thomas et al. [2007]). In the last decade, however, advancements in digital hardware have resulted in an ever-decreasing hardware cost and increased design flexibility. Additionally, recent advances in applications like gaming, weather forecasting, and simulations in physics and astronomy require faster, cheaper, and statistically accurate GRNGs. These two trends have contributed toward the development of a number of novel GRNG architectures optimized for hardware design. A detailed comparative study of these hardware architectures has been somewhat missing in the published literature. This work provides the potential user a capsulization of the published hardware GRNG architectures. We have provided the method and theory, pros and cons, and a comparative summary of the speed, statistical accuracy, and hardware resource utilization of these architectures. Finally, we have complemented this work by describing two novel hardware GRNG architectures, namely, the CLT-inversion and the multihat algorithm, respectively. These new architectures provide high tail accuracy ( 6σ and 8σ , respectively) at a low hardware cost.