devirgo style on phase 1

[hero78119]

optimisation type

• same memory consumption, + throughtput

Change Scope

• merge phase-1 two steps into single step and applied similar tricks to move parallism, refer to prev work phase-2
• some singer utility improvement: auto-implement phaseX_idxes_map and code clean up, few debug assertion and refactor.

benchmark results on evm add ¹

EVM add throughput improvement can be up to 20x

benchmark on instance > 2^13 will run out of 64GB memory. It's due to some existing design where cloning witness between nodes input/output. We can address this issue in later PR.

| #instance | master delay  | new design delay (s) | Improvement |
|-----------|---------------|----------------------|-------------|
| 2^10      | 0.317735725s  | 0.134839749s         | 2.36x       |
| 2^11      | 0.905547894s  | 0.203267641s         | 4.45x       |
| 2^12      | 3.063349368s  | 0.3163026s           | 9.48x       |
| 2^13      | 11.522649178s | 0.556362988s         | 20.71x      |

benchmark results on keccak 256 ¹

keccak throughput improve on low instances and remain the same on high instances

| #instance | speedup (with p < 0.05)      |
|-----------|------------------------------|
| 1         | -13.958% -13.331% -12.749% |
| 2         | -9.6296% -8.7916% -7.9326% |
| 4         | -7.7858% -7.3198% -6.8180% |
| 8         | -7.9653% -7.4081% -6.8336%  |
| 16        | -7.2831% -7.1579% -7.0342% |
| 32        | -5.6185% -5.3883% -5.1286% |
| 64        | -1.3313% -0.9198% -0.4998% |
| 128        | -3.5177% -2.2666% -0.9425% |
| 256        | -1.0312% -0.0618% +0.9341% |
| 512        | +0.8020% +1.4282% +2.1008% |

Footnotes

1. AMD EPYC 9R14 (16 phy cores) + 32GB memory ↩ ↩²

[hero78119]

TODO: use #[rustfmt::skip] to avoid format comment

[hero78119]

TODO: use #[rustfmt::skip] to avoid format comment

Done by disable wrap_comment in rustfmt.toml

[dreamATD]

Is this sigma = \sum_y( f1(y) * (\sum_j g1^{(j)}(y)))?

[hero78119]

more precisely, should be sigma = \sum_{t || y}(f1({t || y}) * (\sum_j g1^{(j)}({t || y})))
fixed in latest commit ad4a6d8