GitHub (MIT): https://github.com/danielcota/LoopMix128
Highlights:
* ~0.37 ns/value (GCC 11.4, -O3 -march=native), 98% faster than xoroshiro128++ and PCG64.
* Passes TestU01 BigCrush & PractRand (32TB).
* Guaranteed 2^128 period.
* Proven injective (192-bit state) via Z3 SMT solver; allows parallel streams.
* Core requires only stdint.h.
Seeking feedback on design, use cases, or further testing.
Curious to learn more about the circumstance :)
Wondering how this PRNG compares to PCG PRNGs that also claim to be "simple fast space-efficient statistically good algorithms" and "hard to predict" [0].
In any case, it's good to see the excellent work being accomplished in this space.
A purely random function can lead to clumping and aliasing.
The state update function is effectively "a = rotate(a, constant) + b; b = rotate(b, constant) + constant;" and the output derivation is "output = (a + b) * constant".
That update function is _barely_ nonlinear, and the output derivation is linear. The output would probably be slightly better as "(a ^ b) * constant".
The slow_loop thing to guarantee 2^128 period is probably not needed - anyone with an application that cares about a period that high is probably going to choose a more robust generator (a few rounds of hardware-accelerated AES in counter mode is your best bet there)
The use of the Z3 prover is neat and I should read up on that more.
For example, if f(0) = 1 and f(1) = 0, even if the rest of f's domain is injective the period of f is still only 2 when the initial value is 0 or 1.
When iterating I first tried to make fast_loop as random as possible by trying all possible rotational values and then having each option tested in PractRand 1000 times from 256M to 8GB. There was a wide range of performance by rotation. 47 was the best (for the GR constant) and resulted in the most tests being passed. The goal was a stronger than normal core for the PRNG that could feed actively into mix.
I found the multiplication to be necessary for passing PractRand and BigCrush with the state mixing as posted.
I had a variant which assigned mix as rotate(mix,constant) + (mix^fast_mix). That would pass cleanly with mix directly outputted (with no multiplication) - but I couldn’t get Z3 prover to show injectivity so I decided to go with the posted route.
Basically any generator with a 192 bit state can pass BigCrush/PranctRand- even known terrible ones like middle square!
Here are corresponding results for LCGs, interestingly there's a clear affine relationship between state size and log(bytes to practrand failure).
https://www.pcg-random.org/posts/does-it-beat-the-minimal-st...
I did have to alter the output to be "(GR * mix) + fast_loop" and change the rotation constants to be 12 and 5.
The main thing this knowledge is worth when designing RNGs is that it tells you how reasonable it is to 'lose' N bits. Eg. if you're 2 bits worse than PCG, you're about twice as much worse than ideal.
LoopMix128 ns/call: 0.380 ns
xoroshiro128++ ns/call: 0.757 ns
wyrand ns/call: 0.379 ns
PCG64 ns/call: 0.757 ns
RomuQuad ns/call: 0.575 ns
RomuDuoJr ns/call: 0.416 ns
See https://www.pcg-random.org/posts/does-it-beat-the-minimal-st... for examples and constants
- your test codes are not reproducible: running twice generates different sets of numbers because they have unknown seeds. As a result, if you change (a) compilers or compiler switches, (b) operating system versions, (c) host processors or (d) architectures, the question arises: what is wrong? What is different? This is known as a regression test.
- try shishua as another speedy PRNG. See https://espadrine.github.io/blog/posts/shishua-the-fastest-p...
- You only test a few times? I think one hundred BigCrush tests, using a set of 100 seeds, would be suitable. Takes a few days on an RPI 4 (with cooler). Run the same 100 tests on a Ryzen and Xeon, just to be sure. They should be bit-for-bit identical.
- 100 BigCrush tests should show only a handful (4 or fewer) duplicate test failures.
- your seeds are almost great: too many people think "42" is random in a space of 0 through 2^64. But 0xdeadbeef is so 1990s...
- you don't need different seeds per PRNG; you can generate reproducible ones (2x to 4x 64bit) from a single good 64-bit seed and your favourite PRNG. Your test code should read a seed or set from the command line (see first item).
- warmups? Really?
- Remember that BigCrush and other tests are created by mathematical people not practical people. Do they test for equal numbers of odd and even results? Hmmmm....
- try Collatz, see https://news.ycombinator.com/item?id=39733685
- the tests are very cache-friendly; nobody does this. It's true that everybody compares against this unrealistic scenario, however.
- if you've spent a month in twisty little PRNG passages, all alike, you are on the first steps of your journey. Take a towel.
J
And you are so right about being just one month in. Every time I think I'm starting to understand what's going on here, I realize the maze just keeps getting deeper.
zX41ZdbW•5mo ago
the_othernet•5mo ago