chore: Experimenting with stepwise ACVM solver [DO NOT MERGE]

[TomAFrench]

Description

Problem*

Resolves

Summary*

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.

[TomAFrench]

@kevaundray Heads up that the new SSA code is still generating opcodes out of order.

[TomAFrench]

I'm getting failures on the program

use dep::std;

fn main(x: Field, y: Field, salt: Field, out_x: Field, out_y: Field ) {
    // let res = std::hash::pedersen([x, y]);
    // assert(res[0] == out_x);
    // assert(res[1] == out_y);

    let raw_data = [x,y];
    let mut state = 0;
    for i in 0..2 {
        state = state * 8 + raw_data[i];
    }
    state += salt;
    let hash = std::hash::pedersen([state]);
    // assert(std::hash::pedersen([43])[0] == hash[0]);
}   

Which results in the ACIR (pre/post optimization)

Unoptimised ACIR for main:
current witness index : 8
public parameters indices : []
return value indices : []
EXPR [ (8, _1) (1, _2) (1, _3) (-1, _6) 0 ]
BLACKBOX::PEDERSEN [(_6, num_bits: 254)] [ _7, _8] domain_separator: 0

Compiled ACIR for main:
current witness index : 11
public parameters indices : []
return value indices : []
EXPR [ (1, _3) (-1, _6) (-1, _10) 0 ]
EXPR [ (8, _1) (1, _2) (1, _10) 0 ]
BLACKBOX::PEDERSEN [(_6, num_bits: 254)] [ _7, _8] domain_separator: 0

Looks like it's running into the issue of not knowing how to sort the arithmetic opcodes. I purposefully removed the existing sorting here as it results in the bad outcome as described in noir-lang/acvm#419 but it seems like the underlying logic can't handle all cases properly either (which makes sense as it has no information on which witness was the "output" of the original expression and so is now included in an expression with two unknowns.

[TomAFrench]

As a rough heuristic we should prefer to attach intermediate variables to the lowest value witnesses in the expression.

[kevaundray]

@TomAFrench Is this still a [DO NOT MERGE] PR or will this be used for introducing stepwise execution?

[TomAFrench]

I'll probably repurpose this PR but for now it's a scratch branch while I get dynamic arrays working.

[TomAFrench]

Closing in favour of #2051