In fairly comprehensive comparisons of PRNGs (MT, MTSMT, basic LGC, PGC and Xoroshiro256+) for genering random numbers for Monte Carlo sampling for pathtracing and simulation, generating both unit length float32s and shuffle indices, I found Xoroshiro256+ as good as the rest from a statistical sample distribution point-of-view (in terms of not being biased and providing excellent sample distribution in terms of converging to a ground-truth in many different simulations) and the fastest.

I don't dispute that at the bit level using something like PractRand it has issues and there are better "quality" ones, but at a practical sense in generating excellent 0.0f -> 1.0f float32 numbers and uint32_t indices I couldn't actually notice any quality issues with what it generated for very long running Monto Carlo simulations using billions of random numbers, even though it should have been causing issues with the integer numbers due to the weaker lower bits (although in practice, most of the indices were < 16 bits in size, so that might have explained it).

I wasn't aware of SHISHUA though, I'll check it out.

Wasn't xoshiro256+ mostly weak in the lower bits, and recommended to use to generate floating point numbers?

I suppose that this is probably indicative of a more fundamental weakness, but for reference the upper bits should be way higher quality that the Messene Twister (As that one fails PractRand while the upper bits of xoshiro256+ don't IIRC)

Yes, but it is also weak in terms of seed correlation, which makes xoshiro256+x8 weak in many more bits.

That said, there are certainly use-cases for it! I just like the idea that we can have our cake and eat it too: something closer to the Pareto frontier, that doesn’t have those caveats, and yet is faster.