feat: add modular inverse for variable modulus

[ivokub]

Description

This PR implements ModInverse for testing some ideas for more efficient ModExp. The problem with the approach right now is though that there may not always be an inverse in which case the solver would fail.

@yelhousni - maybe we could work past it by setting the inverse to be something 0 or 1 etc in case it doesn't exist?

Meanwhile - do not merge. I think in most cases we don't want to expose methods which would allow for liveness failure.

Type of change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

How has this been tested?

• TestVariableInverse
• Test B

Checklist:

• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have added tests that prove my fix is effective or that my feature works
• I did not modify files generated from templates
• golangci-lint does not output errors locally
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[Copilot]

Pull Request Overview

This PR adds a new feature to compute the modular inverse with a variable modulus to support more efficient modular exponentiation. Key changes include:

• Updating computeInverseHint to take an additional modulus parameter.
• Modifying inverse and modular operations to use the variable modulus.
• Adding tests to validate both successful and failing modular inversions.

Reviewed Changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 1 comment.

File	Description
std/math/emulated/hints.go	Updated computeInverseHint to accept a variable modulus parameter.
std/math/emulated/field_ops.go	Adjusted inverse to pass the variable modulus to computeInverseHint.
std/math/emulated/custommod.go	Introduced ModInverse and standardized zero checks in modular operations.
std/math/emulated/custommod_test.go	Added tests to validate modular inversion for both existent and non-existent cases.

Comments suppressed due to low confidence (1)

std/math/emulated/hints.go:43

• Consider updating the function's documentation comment to mention the new modulus parameter and how it is used to form the hint inputs.

func (f *Field[T]) computeInverseHint(inLimbs []frontend.Variable, modulus *Element[T]) (inverseLimbs []frontend.Variable, err error) {