Hidden Errors in Simulations and the Quality of Pseudorandom Numbers

TL;DR

This paper investigates the quality of pseudorandom number generators used in physics simulations, revealing no evidence of bit-level correlations and emphasizing the need for thorough physical testing of these generators.

Contribution

The study provides comprehensive statistical and visual assessments of random number generators, challenging previous claims of correlations and underscoring the importance of rigorous testing.

Findings

No evidence of bit-level correlations in tested generators

Highlights the importance of physical tests over simple statistical tests

Questions previous claims of correlations in Monte Carlo simulations

Abstract

We have carried out extensive statistical, bit level and visual tests of several random number generators used in the applications of physics. Two of the generators tested were recently included in a paper by Ferrenberg {\it et al.} (Phys. Rev. Lett. {\bf 68}, 3382 (1992)) who reported correlations in their Monte Carlo simulations. As a possible explanation of this, they suggest bit level correlations in the random numbers. However, our tests find no evidence of such correlations, which highlights the importance of more careful physical tests of random number generators.