Optimize Msm

[ashWhiteHat]

Msm Optimization

Hi there.
I optimized the best_multiexp algorithm and replaced it with a more efficient rayon method.

What I did

Task Size

• Before
  Current implementation divides task into coeffs length / thread number parts.
  The more PC has process skill, the smaller the task size of each thread process.
  It causes task size to be too heavy for small-core PCs and too small for large-core PCs.

• After
  Flatten task size to addition and sum of bucket for each segment.

Parallelization Scope

• Before
  The current implementation performs final sum with a non-parallel process.

• After
  Include the final sum to parallel scope.

Rayon Method

• Before
  According to official documentation, speed relation is as follows.
  $join =< par_iter =< scope$

• After
  Replace best_multiexp scope with par_iter

Other

Refactoring Bucket and get_at.

Benchmark

I ran best_multiexp benchmark twiceafter -> before and before -> after in order to make machine condition same.

First

k	After	Before	Changes
8	2.0513 ms 2.1645 ms 2.3813 ms	3.2626 ms 3.3768 ms 3.4963 ms	+56.013%
9	4.3738 ms 4.8203 ms 5.3524 ms	5.4233 ms 5.8586 ms 6.2619 ms	+29.595%
10	6.3364 ms 6.7132 ms 7.1306 ms	8.5226 ms 9.1460 ms 9.9017 ms	+45.833%
11	10.845 ms 11.595 ms 12.519 ms	15.413 ms 16.760 ms 18.197 ms	+54.984%
12	19.057 ms 21.092 ms 22.951 ms	26.509 ms 28.703 ms 31.225 ms	+43.060%
13	32.293 ms 33.667 ms 35.468 ms	39.831 ms 40.534 ms 41.308 ms	+20.397%
14	56.018 ms 57.386 ms 58.956 ms	67.785 ms 70.827 ms 74.546 ms	+23.423%

Second

k	Before	After	Changes
8	3.3917 ms 3.5141 ms 3.6436 ms	2.1795 ms 2.2404 ms 2.3090 ms	-36.243%
9	5.8065 ms 6.2340 ms 6.6611 ms	3.8219 ms 4.2643 ms 4.7574 ms	-34.941%
10	9.2216 ms 9.8577 ms 10.495 ms	6.2926 ms 6.6160 ms 6.9694 ms	-36.077%
11	13.582 ms 14.203 ms 15.074 ms	10.587 ms 11.265 ms 11.983 ms	-24.557%
12	24.982 ms 27.123 ms 29.894 ms	17.488 ms 17.926 ms 18.550 ms	-32.419%
13	48.558 ms 52.740 ms 57.494 ms	33.177 ms 34.301 ms 35.544 ms	-34.961%
14	71.452 ms 74.974 ms 78.797 ms	58.742 ms 61.173 ms 63.892 ms	-18.408%

I would appreciate it if you could confirm.
Thank you.