Give me a bit more time. I just added all the relevant modern RNG's to dieharder and am running all the tests. TestU01 later.
Actually MT looks good enough to me now.
Re PCG: statistical weaknesses compared to the good xoshiro's or wyrand, and much slower.
I'm still missing SFMT (2x faster, due to simd), and the 2 newer PCG's with a good and a fast mixer.
But given the current results, there are a few new PRNG's which are so much better and faster than everything else: wyrand, xoshiro128+, xoroshiro64, xoshito128++, xoroshiro64
This is interesting. By the way, it is noticeable that Ferrenberg himself did not find anything wrong with MT in one of his latest papers. He however mostly used MRG32k3a, and checked that MT gave similar numbers.
Preliminary results at https://github.com/rurban/dieharder/blob/pcg/QUALITY.md
Re PCG: statistical weaknesses compared to the good xoshiro's or wyrand, and much slower. I'm still missing SFMT (2x faster, due to simd), and the 2 newer PCG's with a good and a fast mixer.
But given the current results, there are a few new PRNG's which are so much better and faster than everything else: wyrand, xoshiro128+, xoroshiro64, xoshito128++, xoroshiro64