A Comparative Study of Some Pseudorandom Number Generators

TL;DR

This paper evaluates various pseudorandom number generators used in physics and Monte Carlo simulations through extensive statistical, bit-level, and visual tests, assessing their quality and efficiency.

Contribution

It provides a comprehensive comparison of common pseudorandom generators and highlights the need for more refined physical tests to detect hidden correlations.

Findings

Different generators vary significantly in statistical properties.

Some generators exhibit correlations not detected by standard tests.

The study emphasizes the importance of physical noise-based generators.

Abstract

We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs, manufacturer installed routines and a random number sequence produced from physical noise. We start by traditional statistical tests, followed by detailed bit level and visual tests. The computational speed of various algorithms is also scrutinized. Our results allow direct comparisons between the properties of different generators, as well as an assessment of the efficiency of the various test methods. This information provides the best available criterion to choose the best possible generator for a given problem. However, in light of recent problems reported with some of these generators, we also discuss the importance of developing more refined physical tests to find possible correlations not revealed by the present test methods.