Bit Level Correlations in Some Pseudorandom Number Generators

TL;DR

This paper evaluates the bit-level correlations in pseudorandom number generators used in physics, introducing a new cluster test based on the Ising model, revealing correlations in some generators but not in those with recent systematic errors.

Contribution

The paper introduces a novel cluster test for detecting bit correlations in pseudorandom generators, enhancing analysis methods in the field.

Findings

Some generators show clear bit-level correlations.

The new cluster test effectively detects periodic correlations.

Generators with recent systematic errors show no discernible correlations.

Abstract

We present results of extensive bit level tests on some pseudorandom number generators which are commonly used in physics applications. The generators have first been tested with an extended version of the $d$-tuple test. Second, we have developed a novel {\it cluster test} where a physical analogy of the binary numbers with the two dimensional Ising model has been utilized. We demonstrate that the new test is rather powerful in finding periodic correlations on bit level. Results of both test methods are presented for each bit of the output of the generators. Some generators exhibit clear bit level correlations but we find no evidence of discernible correlations for generators, which have recently produced systematic errors in Monte Carlo simulations.