Optimize Coset::at

[andrewmilson]

Refactored Coset::at() since it accounted for 50% of steps for a verification. New approach reduces to 4%.

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This change is 

[andrewmilson]

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This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
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• Used before introduced bug #154
• Add more proofs for testing #141
• Optimize polynomial folding #138
• Implement batch_inverse on M31,CM31 #137
• Optimize Coset::at #135 👈
• Refactor FriVerifier::decommit_inner_layers #134
• Add README for cairo verifier #153
• Optimize decommiting last FRI layer using univariate FFT #133 : 1 other dependent PR (#152 )
• Add verifier #127
• Compute FRI quotients #118
• Add CanonicCoset #117
• Add unreduced field arithmetic #116
• Refactor FRI implementation #115
• Refactor Coset with CirclePointIndex #114
• Add formatting to scarb.toml #113
• Update to latest Cairo version #112
• main

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[ilyalesokhin-starkware]

stwo_cairo_verifier/src/pcs/quotients.cairo line 805 at r1 (raw file):

        let p0 = QM31_CIRCLE_GEN;
        let p1 = QM31_CIRCLE_GEN + QM31_CIRCLE_GEN;
        let p2 = QM31_CIRCLE_GEN + QM31_CIRCLE_GEN + QM31_CIRCLE_GEN;

Suggestion:

 let p2 = p2 + QM31_CIRCLE_GEN;

[ilyalesokhin-starkware]

stwo_cairo_verifier/src/pcs/quotients.cairo line 805 at r1 (raw file):

        let p0 = QM31_CIRCLE_GEN;
        let p1 = QM31_CIRCLE_GEN + QM31_CIRCLE_GEN;
        let p2 = QM31_CIRCLE_GEN + QM31_CIRCLE_GEN + QM31_CIRCLE_GEN;

sorry
let p2 = p1 + QM31_CIRCLE_GEN;

[andrewmilson]

Reviewable status: 0 of 6 files reviewed, 1 unresolved discussion (waiting on @Alon-Ti and @ilyalesokhin-starkware)

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stwo_cairo_verifier/src/pcs/quotients.cairo line 805 at r1 (raw file):

Previously, ilyalesokhin-starkware wrote…

sorry
let p2 = p1 + QM31_CIRCLE_GEN;

Done.