chore(ssa refactor): array eq ACIR gen

[joss-aztec]

Description

Problem*

Resolves GH-1625

Summary*

WIP

Documentation

• This PR requires documentation updates when merged.

  • I will submit a noir-lang/docs PR.
  • I will request for and support Dev Rel's help in documenting this PR.

Additional Context

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[jfecher]

Is there a reason this was implemented in acir-gen? I think it'd be better if this were implemented in SSA-gen. That way we may not need to implement it separately for brillig.

[joss-aztec]

That way we may not need to implement it separately for brillig.

I think the brillig solution is intended to take advantage of control flow for this

[jfecher]

I think we can leverage the same in SSA by inserting a loop:
For arrays v0 and v1 of length v2:

  v0 = [ ... ]
  v1 = [ ... ]
  v2 = length of v0 and v1
  jmp b1(Field 0)
b1(v3: Field):  // v3 will be the index
  v4 = lt v3, v2
  jmpif v4, then: b2, else: end_true
b2(): // loop body
  v5 = array_get v0, index v3
  v6 = array_get v1, index v3
  v7 = eq v5, v6
  jmpif v7, then: b4, else: end_false
b4():
  v8 = add v3, Field 1
  jmp b1(v8)
end_false():
  jmp end(u1 0)
end_true():
  jmp end(u1 1)
end(v9: u1) // result of the eq in v9
  ...

A bit long but there's a few ways you can encode it.

Another advantage of having it in SSA (versus ACIR) is that it can be optimized out for any array elements that are known.

[joss-aztec]

Closed in favour of #1704