⚡️ Optimize ffs

[adhusson]

Description

Cheaper FFS using a de Bruijn-like sequence for the first 3 bits of the lsb position.

Works using a sequence where substrings don't appear only once (like in a de Bruijn sequence) but only appear in one given 32-bit block. So (sequence * isolated_bit)[0:5] identifies the first 3 bits of the isolated bit position. Details here.

Also replaced b with x.

Checklist

Ensure you completed all of the steps below before submitting your pull request:

• Ran forge fmt?
• Ran forge snapshot?
• Ran forge test?

Pull requests with an incomplete checklist will be thrown out.

[Vectorized]

This is hands down the most impressive PR to Solady I have ever seen.

[atarpara]

Very impressive PR. Great work.

[Vectorized]

z3 to hunt for the two constants if anyone is interested:

from z3 import *
import math

def lookup(j, l, q):
    j = j & 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
    t = (l * j) & 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
    t = (t >> 250) 
    t = (t << 2) 
    t = (q << t) & 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
    t = (t >> 252) 
    return t

l = BitVec('l', 512) 
q = BitVec('q', 512)

solve(*[
    lookup(1 << i, l, q) == ((int(math.log2(1 << i)) >> 5) & 0b111)
    for i in range(256)
], lookup(1 << 256, l, q) == 0b1000, l >> 256 == 0, q >> 256 == 0)