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.
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.