fix: gkr add gate evaluate

[BeratOz01]

Description

This PR addresses a bug in the gkr package related to the Evaluate function of the AddGate. The existing logic within the AddGate evaluation function had an error that caused incorrect addition behavior under certain input scenarios. In addition to fixing the bug, this PR includes related tests as well.

gnark-crypto/ecc/bn254/fr/gkr/gkr.go

Lines 881 to 894 in d72fcb3

	func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
	switch len(x) {
	case 0:
	// set zero
	case 1:
	res.Set(&x[0])
	case 2:
	res.Add(&x[0], &x[1])
	for i := 2; i < len(x); i++ {
	res.Add(&res, &x[2])
	}
	}
	return
	}

Type of change

• Bug fix (non-breaking change which fixes an issue)

How has this been tested?

How has this been benchmarked?

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

[ivokub]

Good catch, thanks! However, it seems the same issue is for the MulGate (we multply always x[2] when more than two inputs). Can you also fix it?

Also, would it be possible to add regressions tests, i.e. tests where the AddGate takes three inputs and MulGate takes three inputs?

[ivokub]

Also, would it be possible to add regressions tests, i.e. tests where the AddGate takes three inputs and MulGate takes three inputs?

Hmm, looking at it, I'm not sure it is worth adding regression tests -- the prover and verifier use the same definition of the gates and it is difficult to test regression (without defining the correct AddGate for the verifier).

[ivokub]

I implemented fix for MulGate directly in your branch.

Thanks for the contribution, I'll merge it currently as is. Let us know if there is anything else you notice!