Refactor Polyeval{Instance, Witness}

[huitseeker]

After #305 (which it includes, so go review there plz)

Refactors Polynomial evaluation instances / witnesses to express the specialized functions in terms of the general ones.

For review: the refactoring of PolyEvalInstance::batch_diff_size, which is strict about the size of its arguments and inspects it ,to be the implementation of PolyEvalInstance::batch, has revealed the later call sites are not rigorous about the size of their arguments, nor do they inspect them.

I've patched call-sites to be compliant with the rigor of batch_diff_size, but there's another "looser" variant of this PR that would eliminate x from the PolyEvalInstance.

[storojs72]

Now with generic PolyEvalInstance we can derive various implementations of it, right? Do we use that already (or have plans to create and use) and if so where concretely (more exactly - do we have / need alternative implementation which is different comparing to the previous reference one implemented at Solidity side of things)?

[huitseeker]

PolyEvalInstance has been generic since the beginning, and the type itself has not changed:
https://github.com/microsoft/Nova/blob/37871d04ba04771bf19c51e5b336e45fdb86c7f7/src/spartan/mod.rs#L117-L121
I'm not sure I understand the question?

The idea here is that batch_diff_size is a more general function that performs a re-scaling in case the passed-in arguments have a different # of variables. When the # of variables is the same for every argument, batch and batch_diff_size produce exactly the same output, which allows implementing one in terms of the other.

[storojs72]

Right, the question is actually - does new PolyEvalInstanse preserve compatibility with older one and where alt_batch is planning to be used (since as far as I see it is absent in upstream)

[huitseeker]

alt_batch isn't new, it's the moved, old implementation of batch. it is here in a tests module, gated by #[cfg(test)] and is not planned to be used anywhere. It is here specifically to ensure (through fuzzing unit tests) that PolyEval{Instance, Witness}::batch remains backward-compatible.