utils: faster add_multilinears

[tcoratger]

Benchmarks when compared to before (on small dimensions, the very small degradation is noise, I tested various run and the results are kind of different each time but on large dimensions this is always big win).

add_multilinears_fn/optimized/10
                        time:   [50.002 µs 50.549 µs 51.090 µs]
                        thrpt:  [20.043 Melem/s 20.258 Melem/s 20.479 Melem/s]
                 change:
                        time:   [+1.2641% +3.4338% +5.7785%] (p = 0.00 < 0.05)
                        thrpt:  [−5.4629% −3.3198% −1.2483%]
                        Performance has regressed.
Found 1 outliers among 100 measurements (1.00%)
  1 (1.00%) high mild
add_multilinears_fn/optimized/14
                        time:   [76.380 µs 77.374 µs 78.297 µs]
                        thrpt:  [209.25 Melem/s 211.75 Melem/s 214.51 Melem/s]
                 change:
                        time:   [+1.7252% +3.9230% +6.2144%] (p = 0.00 < 0.05)
                        thrpt:  [−5.8508% −3.7749% −1.6960%]
                        Performance has regressed.
Found 1 outliers among 100 measurements (1.00%)
  1 (1.00%) high mild
add_multilinears_fn/optimized/18
                        time:   [112.78 µs 117.96 µs 125.47 µs]
                        thrpt:  [2.0893 Gelem/s 2.2223 Gelem/s 2.3244 Gelem/s]
                 change:
                        time:   [−18.608% −16.871% −14.746%] (p = 0.00 < 0.05)
                        thrpt:  [+17.297% +20.294% +22.862%]
                        Performance has improved.
Found 9 outliers among 100 measurements (9.00%)
  1 (1.00%) low mild
  4 (4.00%) high mild
  4 (4.00%) high severe
add_multilinears_fn/optimized/20
                        time:   [315.30 µs 320.84 µs 329.73 µs]
                        thrpt:  [3.1801 Gelem/s 3.2682 Gelem/s 3.3257 Gelem/s]
                 change:
                        time:   [−52.253% −50.004% −47.859%] (p = 0.00 < 0.05)
                        thrpt:  [+91.787% +100.02% +109.44%]
                        Performance has improved.
Found 6 outliers among 100 measurements (6.00%)
  3 (3.00%) high mild
  3 (3.00%) high severe

add_multilinears_sparse/optimized/10
                        time:   [88.945 µs 90.308 µs 91.541 µs]
                        thrpt:  [715.92 Melem/s 725.70 Melem/s 736.81 Melem/s]
                 change:
                        time:   [−2.9823% +0.0009% +2.8453%] (p = 1.00 > 0.05)
                        thrpt:  [−2.7666% −0.0009% +3.0740%]
                        No change in performance detected.
Found 11 outliers among 100 measurements (11.00%)
  7 (7.00%) low mild
  3 (3.00%) high mild
  1 (1.00%) high severe
add_multilinears_sparse/optimized/50
                        time:   [88.014 µs 88.741 µs 89.512 µs]
                        thrpt:  [732.15 Melem/s 738.51 Melem/s 744.61 Melem/s]
                 change:
                        time:   [−9.0176% −7.0711% −5.2000%] (p = 0.00 < 0.05)
                        thrpt:  [+5.4853% +7.6092% +9.9113%]
                        Performance has improved.
Found 9 outliers among 100 measurements (9.00%)
  4 (4.00%) low mild
  2 (2.00%) high mild
  3 (3.00%) high severe
add_multilinears_sparse/optimized/90
                        time:   [86.818 µs 89.123 µs 92.157 µs]
                        thrpt:  [711.13 Melem/s 735.34 Melem/s 754.87 Melem/s]
                 change:
                        time:   [−6.2371% −4.5692% −2.7610%] (p = 0.00 < 0.05)
                        thrpt:  [+2.8394% +4.7879% +6.6520%]
                        Performance has improved.
Found 6 outliers among 100 measurements (6.00%)
  2 (2.00%) low mild
  1 (1.00%) high mild
  3 (3.00%) high severe
add_multilinears_sparse/optimized/100
                        time:   [85.672 µs 86.673 µs 87.685 µs]
                        thrpt:  [747.40 Melem/s 756.13 Melem/s 764.96 Melem/s]
                 change:
                        time:   [−3.8784% −1.3785% +0.8765%] (p = 0.27 > 0.05)
                        thrpt:  [−0.8689% +1.3978% +4.0349%]
                        No change in performance detected.
Found 5 outliers among 100 measurements (5.00%)
  3 (3.00%) high mild
  2 (2.00%) high severe

When doing this

let batched_column_mixed = add_multilinears(
        &column_up(&batched_column),
        &scale_poly(&column_down(&batched_column), alpha),
    );

In order to avoid double allocations:

• One vec is allocated as a result of column_up(&batched_column)
• One vec is allocated as a result of add_multilinears,

You could do in place operations:

let mut col_up = column_up(&batched_column);
let batched_column_mixed = add_multilinears_inplace(
        &col_up
        &scale_poly(&column_down(&batched_column), alpha),
    );

with

pub fn add_multilinears_inplace<F: Field>(dst: &mut [F], src: &[F]) {
    assert_eq!(dst.len(), src.len());

    dst.par_iter_mut()
        .zip(src.par_iter())
        .filter(|(_, b)| !b.is_zero())
        .for_each(|(a, b)| *a += *b);
}

should be much more efficient.

[TomWambsgans]

I am not sure of the:

           if a.is_zero() {
                *b
            } else if b.is_zero() {
                *a
            }  else {...}

Because this assumes the polynomial is sparse, which in some case we know for sure it's not the case, so I would suggest to remove the case disjonction (assuming not sparse) or alternatively 2 separate functions ?

also, add_multilinears_inplace seems a good idea to me

[tcoratger]

pub fn add_multilinears_inplace<F: Field>(dst: &mut [F], src: &[F]) {
    assert_eq!(dst.len(), src.len());

    dst.par_iter_mut()
        .zip(src.par_iter())
        .filter(|(_, b)| !b.is_zero())
        .for_each(|(a, b)| *a += *b);
}

Just replaced by in place version so that this removes all the problems