5 ms·

Xoshiro over PCG arguments: http://pcg.di.unimi.it/pcg.php http://pcg.di.unimi.it/pcg.php Response by the author: https://www.pcg-random.org/posts/on-vignas-pc

by celrod 6y ago

Xoshiro over PCG arguments: http://pcg.di.unimi.it/pcg.php http://pcg.di.unimi.it/pcg.php Response by the author: https://www.pcg-random.org/posts/on-vignas-pcg-critique.html https://www.pcg-random.org/posts/on-vignas-pcg-critique.html Personally, I use a SIMD Xoshiro256+ when I want a solid and fast RNG (although I mostly use Julia's default -- a MersenneTwister).

BlackFly 6y ago
Thanks for digging this up. I was curious about exactly this.
GolDDranks 6y ago
Why does Julia use Mersenne Twister as default? I gather that it's quite bad by modern standards?
- shele 6y ago
  It _has_ a cool name, tough...
  - logos01 6y ago
    And the pcg page has pretty colors
- versteegen 6y ago
  "quite bad" is quite an overstatement; its quality isn't a problem for many real use cases. It's quite slow compared to the likes of PCG though.
  - logos01 6y ago
    Julia uses dSFMT, which is as fast as xoshiro on vigna own benchmark page. I would not call that slow.
  - GolDDranks 6y ago
    Right, a bad phrasing from my part; I didn't actually mean the distribution, but more like... the bang for the buck. Why would you use slow generator as a default, if you don't even get good distribution?
    - logos01 6y ago
      You get a good distribution in 99.99% of the cases. There is no perfect rng. I am sure that pcg and xoroshiro also have deficiencies. The issue of good seedings is quite general.
      - rurban 6y ago
        Of course there are perfect RNG's. Some of them even quite fast. Good PRNG's eg. do have no seeding problem as most bad LCG's.
        aksskfngt 6y ago
        Some people are easy to satisfy I guess
  - rurban 6y ago
    It is very bad. It's is huge, 10x slower than good LCG's, and fails statistical tests, esp. it's lower bits, most wellknown by the Ferrenberg affair. https://arxiv.org/pdf/1910.06437.pdf https://arxiv.org/pdf/1910.06437.pdf PCG is also not that good. There do exist proper and fast PRNG's though. DSFMT has the same problems as MT. I'm just adding some of them to gsl and dieharder btw.
    - versteegen 6y ago
      Thank you for the reference. I stand corrected. I wasn't aware that its quality problems are that bad. What's the best argument against PCG?
      - rurban 6y ago
        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. Preliminary results at https://github.com/rurban/dieharder/blob/pcg/QUALITY.md 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
        aksskfngt 6y ago
        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. https://arxiv.org/pdf/1806.03558 https://arxiv.org/pdf/1806.03558
    - aksskfngt 6y ago
      If you read that paper you referenced, the Mersenne-Twister actually ended the Ferrenberg affair. And where does it say that lower bits of dSFMT are bad? Is there proof for this statement? Now I am not saying that dSFMT is the best RNG ever, far from it. It's just very decent, and quite fast. LCGs have an awkward habit of bad projections in 2D.
- Iwan-Zotow 6y ago
  no, it is pretty good rng, but quite slow, and world move on since 80s
- jakobnissen 6y ago
  I can't tell you why it was originally chosen, but there is a PR underway to have tasklocal RNG in Julia. That necessitates a smaller RNG, and we'll probably land on xoshiro256 Ref: https://github.com/JuliaLang/julia/pull/34852 https://github.com/JuliaLang/julia/pull/34852
JoachimS 6y ago
That response by O'Neill is amazing. Solid analysis and response. Staying away from name calling, and actually getting new results and knowledge out of it all. It even ends with a thank you to Sebastiano Vigna.
- celrod 6y ago
  Definitely. Once the AVX512-IFMA instruction set becomes more common (only available on Intel 10nm CPUs so far), I may try a PCG with 104 bits of state. Wanting SIMD rngs (separate generator per vector lane), PCG is hurt by 64-bit integer multiplication being on the slower side. AVX2 has to perform three 32 bit multiplications, while the AVX512 instruction has much lower throughput than the likes of a xor, shift, or floating point arithmetic. The new IFMA may change that. My use cases are Monte Carlo, where "passes statistical tests" is probably all that's needed for good results. Maybe I should just try an mcg.
logos01 6y ago
For a view less centered on the pcg vs xoshiro world: https://chasethedevil.github.io/post/war-of-the-random-number-generators/ https://chasethedevil.github.io/post/war-of-the-random-numbe...

by celrod 6y ago

BlackFly 6y ago

Thanks for digging this up. I was curious about exactly this.

GolDDranks 6y ago

Why does Julia use Mersenne Twister as default? I gather that it's quite bad by modern standards?

shele 6y ago
It _has_ a cool name, tough...
- logos01 6y ago
  And the pcg page has pretty colors
versteegen 6y ago
"quite bad" is quite an overstatement; its quality isn't a problem for many real use cases. It's quite slow compared to the likes of PCG though.
- logos01 6y ago
  Julia uses dSFMT, which is as fast as xoshiro on vigna own benchmark page. I would not call that slow.
- GolDDranks 6y ago
  Right, a bad phrasing from my part; I didn't actually mean the distribution, but more like... the bang for the buck. Why would you use slow generator as a default, if you don't even get good distribution?
  - logos01 6y ago
    You get a good distribution in 99.99% of the cases. There is no perfect rng. I am sure that pcg and xoroshiro also have deficiencies. The issue of good seedings is quite general.
    - rurban 6y ago
      Of course there are perfect RNG's. Some of them even quite fast. Good PRNG's eg. do have no seeding problem as most bad LCG's.
      - aksskfngt 6y ago
        Some people are easy to satisfy I guess
- rurban 6y ago
  It is very bad. It's is huge, 10x slower than good LCG's, and fails statistical tests, esp. it's lower bits, most wellknown by the Ferrenberg affair. https://arxiv.org/pdf/1910.06437.pdf https://arxiv.org/pdf/1910.06437.pdf PCG is also not that good. There do exist proper and fast PRNG's though. DSFMT has the same problems as MT. I'm just adding some of them to gsl and dieharder btw.
  - versteegen 6y ago
    Thank you for the reference. I stand corrected. I wasn't aware that its quality problems are that bad. What's the best argument against PCG?
    - rurban 6y ago
      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. Preliminary results at https://github.com/rurban/dieharder/blob/pcg/QUALITY.md 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
      - aksskfngt 6y ago
        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. https://arxiv.org/pdf/1806.03558 https://arxiv.org/pdf/1806.03558
  - aksskfngt 6y ago
    If you read that paper you referenced, the Mersenne-Twister actually ended the Ferrenberg affair. And where does it say that lower bits of dSFMT are bad? Is there proof for this statement? Now I am not saying that dSFMT is the best RNG ever, far from it. It's just very decent, and quite fast. LCGs have an awkward habit of bad projections in 2D.
Iwan-Zotow 6y ago
no, it is pretty good rng, but quite slow, and world move on since 80s
jakobnissen 6y ago
I can't tell you why it was originally chosen, but there is a PR underway to have tasklocal RNG in Julia. That necessitates a smaller RNG, and we'll probably land on xoshiro256 Ref: https://github.com/JuliaLang/julia/pull/34852 https://github.com/JuliaLang/julia/pull/34852

JoachimS 6y ago

That response by O'Neill is amazing. Solid analysis and response. Staying away from name calling, and actually getting new results and knowledge out of it all. It even ends with a thank you to Sebastiano Vigna.

celrod 6y ago
Definitely. Once the AVX512-IFMA instruction set becomes more common (only available on Intel 10nm CPUs so far), I may try a PCG with 104 bits of state. Wanting SIMD rngs (separate generator per vector lane), PCG is hurt by 64-bit integer multiplication being on the slower side. AVX2 has to perform three 32 bit multiplications, while the AVX512 instruction has much lower throughput than the likes of a xor, shift, or floating point arithmetic. The new IFMA may change that. My use cases are Monte Carlo, where "passes statistical tests" is probably all that's needed for good results. Maybe I should just try an mcg.

logos01 6y ago

For a view less centered on the pcg vs xoshiro world: https://chasethedevil.github.io/post/war-of-the-random-number-generators/ https://chasethedevil.github.io/post/war-of-the-random-numbe...