A Report of a Significant Error On a Frequently Used Pseudo Random Number Generator

TL;DR

This paper uncovers a significant systematic error in the widely used GNU C Library's pseudo-random number generator, revealing complex correlations that compromise the randomness quality in stochastic simulations.

Contribution

It demonstrates that the commonly used additive lagged Fibonacci generator in Glibc produces systematic errors, challenging its assumed safety for scientific applications.

Findings

Identified systematic errors in Glibc's PRNG using a Poisson process test

Revealed complex correlation relations among generated random numbers

Questioned the reliability of Glibc's PRNG for scientific simulations

Abstract

Emergence of stochastic simulations as an extensively used computational tool for scientific purposes intensified the need for more accurate ways of generating sufficiently long sequences of uncorrelated random numbers. Even though several different methods have been proposed for this end, deterministic algorithms known as pseudo-random number generators (PRNGs) emerged to be the most widely used tool as a replicable, portable and easy to use method to generate such random number sequences. Here, we introduce a simple Poisson process whose simulation gives systematic errors when the very commonly used random number generator of the GNU C Library (Glibc) is utilised. The PRNG of Glibc is an additive lagged Fibonacci generator, the family of such PRNGs are accepted as relatively safe among other PRNGs. The systematic errors indicate complex correlation relations among random numbers which requires a further explanation.