perf: improve poseidon2 time by 2 times

[alxiong]

closes: #738

This PR:

• Unroll .pow(5) to significantly cut down permutation cost

Flamegraph

Download this: cargo 2025-01-14 16.20 profile.json

Go to https://profiler.firefox.com and load this file (which you can hover around to see the percentage clearly). Alternatively, see the below screenshot:

Right now, the new dominant cost leader is MulAssign which I don't think we can cut further, but I still didn't quite achieve the same performance than the paper reported, still a (7.2-6.5) gap for bls12, with t=2.

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[alxiong]

🥂 We are on-par with the expected speed:

Poseidon2 over (Bls12_381::Fr, t=2)/1k iter
                        time:   [5.3735 ms 5.3750 ms 5.3771 ms]
Poseidon2 over (Bls12_381::Fr, t=2)/100k iter
                        time:   [545.90 ms 557.12 ms 568.68 ms]

Poseidon2 over (Bls12_381::Fr, t=3)/1k iter
                        time:   [6.2261 ms 6.2424 ms 6.2607 ms]
Poseidon2 over (Bls12_381::Fr, t=3)/100k iter
                        time:   [623.22 ms 624.88 ms 626.58 ms]

Poseidon2 over (Bn254::Fr, t=3)/1k iter
                        time:   [6.1864 ms 6.2344 ms 6.2721 ms]
Poseidon2 over (Bn254::Fr, t=3)/100k iter
                        time:   [614.75 ms 617.18 ms 619.94 ms]

for comparison, the old one:

Poseidon2 over (Bls12_381::Fr, t=2)/1k iter
                        time:   [12.217 ms 12.254 ms 12.324 ms]
Poseidon2 over (Bls12_381::Fr, t=2)/100k iter
                        time:   [1.2291 s 1.2487 s 1.2811 s]

Poseidon2 over (Bls12_381::Fr, t=3)/1k iter
                        time:   [14.579 ms 14.650 ms 14.713 ms]
Poseidon2 over (Bls12_381::Fr, t=3)/100k iter
                        time:   [1.4549 s 1.4633 s 1.4767 s]

Poseidon2 over (Bn254::Fr, t=3)/1k iter
                        time:   [14.828 ms 14.891 ms 15.010 ms]
Poseidon2 over (Bn254::Fr, t=3)/100k iter
                        time:   [1.4809 s 1.4891 s 1.5012 s]

[mrain]

Could we also post the previous bench result here?

[alxiong]

yes i have included the previous benchmark above @mrain