perf: add a function for handling hints more efficiently

[aybehrouz]

This PR provides a possible solution for issue #653.

[aybehrouz]

Tests are failing here, but on my local machine they look fine. By using NewStateLessHint when ToBinary is called on a constant, it only creates one constraint, while I've not handled the constant path in the function at all.

[aybehrouz]

@ivokub @gbotrel @Tabaie

Hi,
What do you think about this PR, guys? It is the implementation of this idea: #653 (comment)

[gbotrel]

hey sorry we had a lot going on forgot about that one, thanks for the nudge.

• I prefer to see hints (all of them) as stateless functions. but we have several examples where circuit-developers used them as ... a way to introduce new wires and/or put a "hook" in the solver.
  --> so far the contract was "using a solver hint, you are introducing new wires and putting a placeholder for the solver to resolve these wires at solve time".

• not sure we do need the "hint inputs are constants, let's optimized it out" a lot. If it's isolated in one or two places (like ToBinary) might be simpler to target the issue there for now. it is more conservative but maybe a couple of extra constraints on some edge cases is better than introducing subtle behavior / doubling APIs for hints (note that for the stateless one; the compiler has no way to actually check that the function is indeed stateless).

will sync with @ivokub & @Tabaie 👍

[aybehrouz]

I see. So, If you don't like the idea of a generic solution, For now I'd recommend handling constant inputs in ToBinary explicitly. There are some practical examples that shows ToBinary may be called with a constant input, while the programmer cannot notice it. (the call is done inside another function) The current Implementation of ToBinary creates around 250 constraints for a constant input, while no constraints are needed.