Some Methods of Parallel Pseudorandom Number Generation

Abstract

We detail several methods used in the production of pseudorandom numbers for scalable systems. We will focus on methods based on parameterization, meaning that we will not consider splitting methods. We describe parameterized versions of the following pseudorandom number generation: 1. linear congruential generators 2. linear matrix generators 3. shift-register generators 4. lagged-Fibonacci generators 5. inversive congruential generators We brieey describe the methods, detail some advantages and disadvantages of each method and recount results from number theory that impact our understanding of their quality in parallel applications. Several of these methods are currently part of scalable library for pseudorandom number generation, called the SPRNG package available at the URL: www.ncsa.uiuc.edu/Apps/CMP/RNG.