Improve QutientConstantsImpl::gen performance (mostly in naive impl)

[dancarmoz]

This change is 

[ilyalesokhin-starkware]

Can you move this to sharp7 and document?

[ilyalesokhin-starkware]

stwo_cairo_verifier/crates/verifier_core/src/pcs/quotients.cairo line 314 at r1 (raw file):

            let [a, b, c, d] = sample_batch.point.y.to_fixed_array();
            let re_py = CM31Trait::pack(a, b);
            let im_py_inv = CM31Trait::pack(c, d).inverse();

Was there an inverse here before?

Code quote:

 let im_py_inv = CM31Trait::pack(c, d).inverse();

[ilyalesokhin-starkware]

I guess we need to decide if we want it in the mvp

[ilyalesokhin-starkware]

stwo_cairo_verifier/crates/verifier_core/src/pcs/quotients.cairo line 216 at r1 (raw file):

        }

        let minus_quotient = minus_numerator.reduce().mul_cm31(denom_inv);

This shouldn't be included through this PR.

Code quote:

  let minus_quotient = minus_numerator.reduce().mul_cm31(denom_inv);

[dancarmoz]

Reviewable status: 0 of 3 files reviewed, 2 unresolved discussions (waiting on @ilyalesokhin-starkware)

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stwo_cairo_verifier/crates/verifier_core/src/pcs/quotients.cairo line 216 at r1 (raw file):

Previously, ilyalesokhin-starkware wrote…

This shouldn't be included through this PR.

I know, but without it I had to inroduce ::zero which was an unnecessary complication. The branch over sharp 7 ( #1332 ) has this previously introduced.

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stwo_cairo_verifier/crates/verifier_core/src/pcs/quotients.cairo line 314 at r1 (raw file):

Previously, ilyalesokhin-starkware wrote…

Was there an inverse here before?

No. Previously every iteration multiplied alpha by the constant neg_dbl_im_py, which was very wasteful.
Instead, in this version we initialize alpha to that value, so everything is inherently multiplied by it. (Theoretically this is is unnecessary, the constant can be taken out at the protocol level. But this would require a change in the prover as well.)
Because we have to return alpha, we must divided by the same term in the end. Also some of ther other terms need to be divided by it.
Possibly there is a more efficient way to do this without the divisions (depending on how much more expensive they are than a mul).
We can also probably batch these, although that would be somewhat annoying.

[ilyalesokhin-starkware]

@ilyalesokhin-starkware reviewed 2 of 3 files at r1, all commit messages.
Reviewable status: 2 of 3 files reviewed, all discussions resolved

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stwo_cairo_verifier/crates/verifier_core/src/pcs/quotients.cairo line 314 at r1 (raw file):

Previously, dancarmoz (Dan Carmon) wrote…

No. Previously every iteration multiplied alpha by the constant neg_dbl_im_py, which was very wasteful.
Instead, in this version we initialize alpha to that value, so everything is inherently multiplied by it. (Theoretically this is is unnecessary, the constant can be taken out at the protocol level. But this would require a change in the prover as well.)
Because we have to return alpha, we must divided by the same term in the end. Also some of ther other terms need to be divided by it.
Possibly there is a more efficient way to do this without the divisions (depending on how much more expensive they are than a mul).
We can also probably batch these, although that would be somewhat annoying.

I think we should make the prover change as well in that case, and do it on main