A Fast Hardware Pseudorandom Number Generator Based on xoroshiro128

The Graphcore Intelligent Processing Unit contains an original pseudorandom number generator (PRNG) called xoroshiro128aox, based on the F2-linear generator xoroshiro128. It is designed to be cheap to implement in hardware and provide high-quality statistical randomness. In this paper, we present a rigorous assessment of the generator's quality using standard statistical test suites and compare the results with the fast contemporary PRNGs xoroshiro128+, pcg64 and philox4x32-10. We show that xoroshiro128aox mitigates the known weakness in the lower order bits of xoroshiro128+ with a new 'AOX' output function by passing the BigCrush and PractRand suites, but we note that the function is not provably uniform. We focus our testing with specific tests for linear artefacts to highlight the weaknesses of both xoroshiro128 PRNGs, but conclude that they are hard to detect, and xoroshiro128aox otherwise provides an excellent trade off between statistical quality and hardware implementation cost.