Improve sum check in general and preprocess for sum check in mlkzg multi_open

[han0110]

This PR does 2 changes:

• Improve sum check prover in general
  • Adopt the algorithm for sum check prover specified in Batch all #89 (comment).
  • Evaluate individual products at products.len() +1 points instead of always max_degree + 1 points, and extrapolate it to max_degree + 1 points later.
• Preprocess more on mlkzg multi_open to combine the polys opening at the same point, to reduce the workload of updating the table.

Comparison

Running cargo bench --bench hyperplonk-benches --features print-trace and extract the following trace components of bench_vanilla_plonk when num_vars = 20, the result is as follows:

Name	Trace Components	Before	After	Ratio (Before/After)
Gate ZeroCheck	ZeroCheck on f	345.313ms	268.233ms	1.287
Permutation ZeroCheck	zerocheck in product check	424.487ms	345.190ms	1.229
PCS SumCheck	compute tilde g for 22 points compute tilde eq for 22 points sum check prove of 20 variables	414.559ms 100.478ms 991.671ms	110.617ms 69.953ms 235.245ms	3.623

[CLAassistant]

All committers have signed the CLA.

[chancharles92]

Thanks @han0110 ! I'll review it early next week.

[chancharles92]

LGTM, good job!