Sumcheck loop ordering

[lucasxia01]

Brought up in a discussion with Zac over potential slowdowns in Sumcheck.

Currently we iterate over each polynomial and for each one, we call add_scaled, which loops over the same batched_poly_unshifted and batched_poly_to_be_shifted memory over and over again. Instead, we should consider switching the order of the loops so that we iterate over the polynomial indices in the outer loop and over the polynomials in the inner loop.

[ledwards2225]

@lucasxia01 Is this still relevant? If so, can you clarify what part of the code this refers to?

[lucasxia01]

I don't remember exactly what this is referring to. Should've attached it to a line in the code. Maybe @zac-williamson would know.

[ledwards2225]

I assume this is referring to the actual polynomial folding in PG. Zac has this PR which could be picked up if we want to handle this.

[lucasxia01]

No, its related to sumcheck going row by row instead of column by column.

[ledwards2225]

I cant make any sense of how sumcheck could be executed column by column :)