Introduce Assembly

[ashWhiteHat]

Abstract

I implemented assembly arithmetic #2 so I am going to introduce to field arithmetic to this repo.

What I did

1. Described simple field arithmetic test
2. Introduce github actions test
3. Bench add, sub, double and mul, square arithmetic
4. Update tool chain
5. Introduce add, sub and double, mul, neg assembly method
6. Replace Fq ~ Fq12 and Fr arithmetic with assembly if features = ["asm"]

Progress

Optimizing instruction according to here

Performance

Environment: Github Actions
Number of operations: 1000000

Result is here

fq

Arithmetic	Default	Assembly	Reduction Rate
addition	364.510ms	280.245ms	23.12 %
subtraction	236.869ms	180.653ms	23.73%
doubling	136.012ms	111.777ms	17.82%
multiplication	591.789ms	464.390ms	21.53%
squaring	201.071ms	158.661ms	21.09%
negation	129.898ms	108.840ms	16.21%
expansion	633.768ms	507.126ms	19.98%
inversion	24.067s	18.858s	21.64%

fr

Arithmetic	Default	Assembly	Reduction Rate
addition	380.275ms	285.533ms	24.91%
subtraction	235.534ms	188.833ms	19.83%
doubling	135.003ms	114.632ms	15.09%
multiplication	603.598ms	453.916ms	24.80%
squaring	189.001ms	173.377ms	8.27%
negation	124.072ms	118.184ms	4.75%
expansion	605.518ms	507.126ms	16.25%
inversion	20.368s	18.858s	7.41%

fq12

Arithmetic	Default	Assembly	Reduction Rate
addition	4.609s	3.919s	14.97%
subtraction	4.609s	2.356s	48.88%
doubling	1.595s	1.269s	20.44%
multiplication	28.062s	22.235s	20.76%
squaring	8.342s	6.668s	20.07%
negation	1.565s	1.247s	20.32%
expansion	25.480s	20.214s	20.67%
inversion	36.619s	29.090s	20.56%