chore: remove some TODOs from codebase

[guorong009]

Description

• Take care of some TODOs throughout the repo

Related issues

Changes

• parallelize compute_inner_product utility
• use ColumnMid in QueryBack
• remove renaming in halo2_backend/plonk/permutation
• refactor the EvaluationDomain::extended_to_coeff function

[codecov-commenter]

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Codecov Report

Attention: Patch coverage is 96.25000% with 3 lines in your changes missing coverage. Please review.

Project coverage is 85.15%. Comparing base (f0a2ebd) to head (381eb3e).

Files with missing lines	Patch %	Lines
halo2_backend/src/plonk/evaluation.rs	96.42%	1 Missing ⚠️
halo2_backend/src/plonk/lookup/verifier.rs	80.00%	1 Missing ⚠️
halo2_backend/src/plonk/shuffle/verifier.rs	80.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #376      +/-   ##
==========================================
+ Coverage   85.13%   85.15%   +0.02%     
==========================================
  Files          85       85              
  Lines       18862    18889      +27     
==========================================
+ Hits        16058    16085      +27     
  Misses       2804     2804              

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[adria0]

Just for curiosity, I made a bench with two other options:

using par_iter

    a.into_par_iter().zip_eq(b.into_par_iter())
        .map(|(a, b)| *a * *b)
        .sum()

using fold_chunk

    let num_threads = multicore::current_num_threads();
    let chunk_size = (a.len() + num_threads - 1) / num_threads;

    a.into_par_iter().zip_eq(b.into_par_iter())
        .fold_chunks_with(chunk_size, F::ZERO, |acc, (a,b)| acc + *a * b)
        .sum()

Graph is in logaritmic scale.

It seems that till ~100k elements, chunking is better, after is map.sum() is more performant (does not checked memory, btw)

https://gist.github.com/adria0/80fa9f0e90ca9b83e26ed96db213e54b

[davidnevadoc]

I've checked the uses of the function to see what sizes are the most common. Turns out it is only used for IPA and in the PI commitment computation in the verifier side.
Since IPA will be removed we are only left with the last use case, which is in the tens of elements. I don't think we can parallelize much then. I would favor code simplicity here.

[adria0]

@guorong009 I see that this happens in 133cbbb.
Is this due serialization changes with ColumnMid?