So, Rule30RND was ok as a fun experiment, but not a PRNG that someone could take seriously.

I kept tinkering, as if I was playing a game: change this and that, run the tests, check my score.

Side note: after I published the last post, I realized that my test scripts had fundamental flaws, like adding text headers in the randomly generated bytes.

Radius-2

No matter how hard I tried, it was obvious that a Rule 30-based algorithm would not pass BigCrush unless I changed it so much that would become something else with a sprinkle of CA.

Now, Rule 30 works like this: If C is our bit, L is the one on its left and R the one on its right:
new_bit = L XOR (C OR R)

That’s a "radius-1 CA". What if I tried with a radius-2 CA, that uses two bits on the left and two on the right?

Unfortunately, there is much less literature for radius-2 than radius-1 CAs. After some search that did not return a documented good candidate for what I wanted to build, and a few failed experiments, I decided to extend Rule 30 in a “symmetric” way.

new_bit = (L2 XOR L1) XOR (C OR (R1 OR R2))

This gave significantly better results.

Not exceptional. The new algorithm failed 5/15 SmallCrush tests (Gap, SimpPoker, CouponCollector, WeightDistrib, HammingIndep).

But these are the tests I might be able to fix with a diffusion function.

Searching for a diffusion fucntion

I wanted a diffusion function, so I let Claude test 7 different functions, run the tests, collect the results, and let me know when it was done.

The winner was the “Hybrid” approach that combines rotation, multiplication by the golden ratio, and shift-XOR:

func mix(x uint64) uint64 {
    x ^= bits.RotateLeft64(x, 13)
    x *= 0x9e3779b97f4a7c15  // Golden ratio constant
    x ^= x >> 27
    return x
}

SmallCrush is the first step, but I needed it to pass BigCrush.

And, YES! My rule-30-radius-2-diffused algo scored 160/160 on BigCrush for the first time!

Staying true

Now, this worked, but it was also cheating: I applied mix() to every state evolution: s1, s2=mix(rule30(s1)), s3=mix(rule30(s2)), ..., so this was no longer a CA algorithm.

What if I applied mix() only to the output? I.e. keep a pure Rule 30, radius-2 algorithm that generates states s1, s2, ..., but return mix(s1), mix(s2), .... Would this work?

IT WORKED! IT WORKED!

And it was also 6% faster.

I present you “R30R2”

Along the way, I fixed some annoying Makefile issues, optimized how Read() reads data from the state, and tweaked a few things here and there.

I was ready to release it, but when “Rule 30” is mentioned in literature, it means a radius-1 CA.

I decided to rename the project, the documentation, the function names, etc. And it's name is... R30R2.

R30R2 is a radius-2 Rule 30-based PRNG with a diffusion function applied on output. It scores 160/160 on BigCrush, and is 2× faster than math/rand/v2.

You can find it at https://github.com/vrypan/r30r2/

🎉🍾🍻