Refactor MSM instances in the IPA

[huitseeker]

What's in this PR

This experiments with re-structuring the IPA to:

• avoid implicit or needless CommitmentKey clones (I've had to import some changes from Remove superfluous instances of derive(Clone) (easy) #287),
• avoid depending on calling the MSM in impl CommitmentKeyExtTrait for pedersen::CommitmentKey, instead relying on an already-available implementation of Mul<E::Scalar, Output = E> for E::Affine.

That experiement is largely unsuccessful, since MSM implementation (which resolves to cpu_best_msm since the scalar length is 2) is about 5% faster¹. We tactically revert to the MSM in that particular line.

Benchmarks

I ran the pcs benchmarks (click to unfold)

group                                                                                                                                      dev                                unmsm_ipa
PCS-Proving 10/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/10                                              1.00     32.2±0.18ms    1.00     32.1±0.28ms
PCS-Proving 12/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/12                                              1.00     86.3±0.35ms    1.00     86.7±0.22ms
PCS-Proving 14/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/14                                              1.00    295.3±1.40ms    1.00    294.1±1.19ms
PCS-Proving 16/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/16                                              1.00   1115.9±5.35ms    1.00   1114.3±5.28ms
PCS-Proving 18/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/18                                              1.00       4.4±0.04s    1.00       4.4±0.03s
PCS-Proving 20/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/20                                              1.00      17.5±0.07s    1.00      17.5±0.05s
PCS-Verifying 10/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/10                                            1.04      3.4±0.05ms    1.00      3.3±0.04ms
PCS-Verifying 12/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/12                                            1.04      5.8±0.10ms    1.00      5.6±0.17ms
PCS-Verifying 14/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/14                                            1.00     13.9±0.37ms    1.01     14.0±0.43ms
PCS-Verifying 16/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/16                                            1.01     35.9±0.79ms    1.00     35.6±0.26ms
PCS-Verifying 18/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/18                                            1.00    124.9±0.95ms    1.00    124.8±0.84ms
PCS-Verifying 20/arecibo::provider::ipa_pc::EvaluationEngine<arecibo::provider::Bn256Engine>/20                                            1.00   506.0±30.68ms    1.01   508.9±21.72ms

Note

Companion PR at lurk-lab/lurk-beta#1088

Footnotes

1. note the scale function moving away from the MSM doesn't seem to have nearly the same perf. impact, ↩