Parallel Streams of Nonlinear Congruential Pseudorandom Numbers

AbstractThis paper deals with the general nonlinear congruential method for generating uniform pseudorandom numbers, in which permutation polynomials over finite prime fields play an important role. It is known that these pseudorandom numbers exhibit an attractive equidistribution and statistical independence behavior. In the context of parallelized simulation methods, a large number of parallel streams of pseudorandom numbers with strong mutual statistical independence properties are required. In the present paper, such properties of parallelized nonlinear congruential generators are studied based on the discrepancy of certain point sets. Upper and lower bounds for the discrepancy both over the full period and over (sufficiently large) parts of the period are established. The method of proof rests on the classical Weil bound for exponential sums

The Vortex Filament Equation as a Pseudorandom Generator

In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel point of view: that of an evolution equation which yields a very good generator of pseudorandom numbers in a completely natural way. This essential randomness of VFE is in agreement with the randomness of the physical phenomena upon which it is based

Parallel random number generation

We present a library of 19 pseudo-random number generators, implemented for graphical processing units. The library is implemented in the OpenCL framework and empirically evaluated using the TestU01 library. Most of the presented generators pass the tests. The generators' performance is evaluated on five different devices. The Tyche-i generator is the best choice overall, while on some specific devices other generators are better