For more details on how pcg works so good, why hash functions beat PRNGs (sometimes even in their own field), and more goodies, I totally recommend this GDC talk on the topic https://www.youtube.com/wat...

I'd like to add mine 5 cents here. In addition to “PRNG form” it is usually needed to provide a code, that initializes random generator. Such code can be found at pcg-random.org, and if being simplified will look like following: prng_state = 0; rand_pcg(); prng_state += seed; rand_pcg(); The uint seed is the value to initialize random number generator.

As is, the pcg_hash function fails PractRand (stdin32 -te 0 -tf 2 -tlmin 10) at 2^22 bytes. Replacing the "LCG part" with XQO primitive

uint32_t xqo_hash(uint32_t input)
{
uint32_t state = (input | 1u) ^ (input * input);
uint32_t word = ((state >> ((state >> 28u) + 4u)) ^ state) * 277803737u;
return (word >> 22u) ^ word;
}

raises that to 2^29 bytes (it nearly fails at 2^28). Not sure about BigCrush.
On x86, the perf seems to suffer slightly ( https://godbolt.org/z/fY9Mv... ), not sure about the GPUs.
Same as pcg_hash, it only requires 32-bit arithmetic (and only 32x32->32 multiplication).
The function is a permutation (same as pcg_hash), so it obviously fails the birthday test (which is a bug/feature depending on the requirements).

If you change rand_pcg to set "state" from the _new_ value of rng_state rather than the old, then you can initialize just by setting rand_pcg to the required seed (otherwise you need to run rand_pcg at least once to mix things up properly).