Engineering Nonlinear Pseudorandom Number Generators

In the era of multi and many-core processors, computer simulations increasingly require parallel, small and fast pseudorandom number generation. Although linear generators lend themselves to a simpler evaluation that ensures favorable properties like guaranteed period, they may adversely affect the result of simulations or be quite large. Conversely, nonlinear generators may provide apparently random sequences, but are either very slow or difficult to analyze regarding their period. This is the case of our previous functions, Tyche and Tyche-i. Despite being among the fastest in their class and having average periods of 2, they may contain smaller cycles of arbitrary size. To overcome this limitation, in this paper we explore different forms of counters impacting either the state or the speed of the generator. We also introduce two number-theoretic generators that use 2 × 127 bits for periods of 2 and 2 and low to moderate computational costs. We experimentally demonstrate the efficiency of our new generators and observe that they exchange speed for period guarantees in a tradeoff that seems widespread in state-of-the-art random number generators.