feat: Batch inversion in quotient_evaluator

[hatemosphere]

What ❔

Optimize quotient evaluator with batch field inversions:

• Collects all values to invert (4 per row) into a single batch
• Performs one batch inversion operation instead of 4 individual inversions
• Properly distributes inverted values back to their respective divisor computations

Why ❔

Tackling the TODO.
~5x average speedup for field inversion operations

Is this a breaking change?

• Yes
• No

Checklist

• PR title corresponds to the body of PR (we generate changelog entries from PRs).
• Tests for the changes have been added / updated.
• Documentation comments have been added / updated.
• Code has been formatted.

[0xVolosnikov]

Generally LGTM.

But please also get a review from @mm-zk or @shamatar since I'm not very deeply in the context here (e.g. I don't know if it affects peak RAM or smth).

[shamatar]

I look at the code and have a hard time to understand what it did before and why this way. Divisors are in the form of (X^N - 1)/(X - 1), but we only divide by them, so batch inversions are not even needed in that form - (X^N - 1) is constant, and instead it's easy to compute just (X - 1)/(X^N - 1) and multiply by them later. I'll check properly when back from vacation

[hatemosphere]

I look at the code and have a hard time to understand what it did before and why this way. Divisors are in the form of (X^N - 1)/(X - 1), but we only divide by them, so batch inversions are not even needed in that form - (X^N - 1) is constant, and instead it's easy to compute just (X - 1)/(X^N - 1) and multiply by them later. I'll check properly when back from vacation

can't really comment on that, since i was just trying to blindly follow up on simplest TODO i've found, to get the grasp of the code base, also having very crappy math background.

looks like:

• for 0-1 divisors we are fine already with no inversion due to (x - omega^i)/(x^N - 1)
• i've tried to implement inversion for 2-5. if i understand you correctly, the suggestion is to do (x^N - 1)/(x - omega^i) which still requires (to some degree expensive)division. possible better option - getting rid of inversions by completely changing the quotient evaluation logic, which is definitely beyond what i tried to do :D

ps. i still naively believe this change brings some perf improvements as is