(WIP) Refactor row major matrix

[mcalancea]

No description provided.

[hero78119]

This is a great effort! As some moment I am also curious what would be the impact if we remove MaybeUint feature and use raw vector as we only have one implementation.

I just do a very quick tried on this branch against master branch on riscv_add benchmark with command on remote ceno benchmark machine, with command

### on master branch
cargo bench --bench riscv_add --package ceno_zkvm -- --save-baseline baseline

### on this branch
cargo bench --bench riscv_add --package ceno_zkvm -- --baseline baseline

and the result turns out to be ~+6% slower on e2e latency.

## master branch
add_op_20/prove_add/prove_add_log2_20
                        time:   [1.5172 s 1.5615 s 1.6110 s]

### this branch
add_op_20/prove_add/prove_add_log2_20
                        time:   [1.6454 s 1.6695 s 1.6898 s]
                        change: [+4.1692% +6.3642% +8.4701%] (p = 0.00 < 0.05)

I believed with fibonacchi example it might be even much slower. So it's still nessesary to this feature for keeping high performance.

[hero78119]

If we just talked about capture this unssignment error, I think we can achieve it from different path: in unittest we support init vector into 2 different default value with same execution trance, and then compare 2 witnesses which should be identical. An unequality indicate there are some unassigment bug. And with that, we can capture the unassignment error in early stage.

[mcalancea]

@hero78119

Thank you! This is still work in progress; I'm examining some ways to make it faster while keeping it clean/safe. My bench results are a bit better for some reason:

add_op_20/prove_add/prove_add_log2_20
                        time:   [4.7420 s 4.7740 s 4.8031 s]
                        change: [+1.3563% +2.2286% +3.0911%] (p = 0.00 < 0.05)
                        Performance has regressed.
add_op_21/prove_add/prove_add_log2_21
                        time:   [9.9516 s 10.189 s 10.450 s]
                        change: [-1.7437% +0.5352% +2.8403%] (p = 0.70 > 0.05)
                        No change in performance detected.

What regression % (evaluated at yours) would you consider acceptable?

[naure]

Looking nice so far 👍

[naure]

Confusing name. Maybe total_len, num_cells, …?

[naure]

What if empty?

There was a special case if steps.is_empty() somewhere:

                InstancePaddingStrategy::RepeatLast if steps.is_empty() => {
                    tracing::debug!("No {} steps to repeat, using zero padding", Self::name());
                    vec![MaybeUninit::new(E::BaseField::ZERO); num_witin]
                }

although that was not completely correct either; better than crashing.