One time I needed a random number generator. It was for the PIC10, which has something like a few dozen bytes of RAM. I didn't need security, just speed and reasonably long periods sizes.
After much testing, I came up with one that passes most statistical tests. Emphasis on "most". It's not a very good RNG, but a few people seem to be using it, so I figured I'd better migrate it here.
It has an undefined period size. It's state loops back to the start at different times depending on what the start is. So far I don't think there's been any issues, but there could be.
Are there very short cycles? Maybe! likely not too short though, as there is a fixed counter that is guaranteed not to loop for 256 bytes, and IIRC the testing I did with randomly chosen seeds usually had periods in the hundreds of millions.
This thing is pure trial and error. There's no logic to it, and I wouldn't even begin to understand how to formally analyze it. If you need good fast numbers, use XORShift, or maybe blake2b hash a counter or something if you need even better.
If you need four bytes of state and very few operations, all single 8 byte instructions, and you don't care if there's a chance that it loops endlessly in a very short cycles, and you don't need security, maybe you need XABC! It's named for the 4 bytes of state it carries, in 4 separate variables.
Just don't ask me how it works. I have no clue. It's blazing fast though!
uint8_t randRNG8() // Originally unsigned char randomize().
x++; //x is incremented every round and is not affected by any other variable
a = (a^c^x); //note the mix of addition and XOR
b = (b+a); //And the use of very few instructions
c = ((c+(b>>1))^a); //the right shift is to ensure that high-order bits from b can affect
return(c); //low order bits of other variables
There you have it! You can spend 5+ years on a FOSS automation framework, and a week on a terrible RNG, and find the terrible RNG is actually more useful to more people than most of your more professional projects!