Refactor pi gate

[ChihChengLiang]

• Fix part of Force all gates to return [(Cell, F);25] as state output and recieve as input to copy states between gates #219, take and return [(Cell, F); 25] in assign region
• Achieve Pi using only copy constraints.
• Use layouter to assign a distinct region for it.

[CPerezz]

Please. Don't remove the OFFSET as it's required later for assembliyng the entire Keccak circuit.

[ChihChengLiang]

Sorry, I'll return them back.

[ChihChengLiang]

Oh, I realize it's part of the layouter refactor.

Currently the circuit looks like this

  state = {
                // Apply pi outside circuit
                let out_state = KeccakFArith::pi(&state_to_biguint(state));
                let out_state = state_bigint_to_pallas(out_state);
                // assignment
                self.pi_config
                    .assign_state(region, offset, state, out_state)?
            };

            offset += PiConfig::OFFSET;

With the new interface, we can do

  state = self.pi_config.assign_state(mut layouter, state, out_state)?;

No need to track the region and the offset. The layouter find a new region for it.
What do you think?

[CPerezz]

hmmm.

So the proposal is to have each gate/config application within a different region then?

[ChihChengLiang]

Yes, it makes sense to let layouter decide where to put the state row. Counting offsets is like doing the layouter's job.

[CPerezz]

Why are you removing the gate from Pi??
It does not apply any constraints now.

[ChihChengLiang]

I realized that using purely copy constraints can achieve pi gate. There's no need to add polys for the gate.
What do you think

[CPerezz]

Hmmm. But copy constraints can only enforce that the provided input is indeed the one that has to be used.

Not sure how you still enforce with constraints:

 let lane = meta.query_advice(
                        state[5 * ((x + 3 * y) % 5) + x],
                        Rotation::cur(),
                    );
                    let new_lane =
                        meta.query_advice(state[5 * x + y], Rotation::next());

                    q_enable.clone() * (new_lane - lane)

[ChihChengLiang]

IIU the halo2 code correctly, copy constraints are applicable as long as we know what cells to copy. We don't have to create custom gates for them.
I did realize I forgot to add enable equality in this case. Will add now.

[CPerezz]

Ohh I see! That sounds correct! Thanks!

[CPerezz]

LGTM!
Depending on the Layouter instead of Region + offset seems like a really nice idea!

[ChihChengLiang]

Close in favor of #234