feat: add compress to compiler

[vlopes11]

This commit introduces Compiler::compress and Compiler::decompress, two functions that will create a compressed representation of a circuit that can be used to generate prover and verifier keys.

The compression strategy takes advantage of the fact that circuit representations are sparse; meaning, most of the scalars are zeroes. We also have a higher incidence of 1 and -1, so any value that is equivalent to a i8 is compressed into a single byte, instead of the regular 32 bytes of a bls12-381.

This will result in expressive gains in terms of storage. For instance, a 2^12 circuit can be compressed into roughly 100Kb.

[codecov]

Codecov Report

Merging #752 (4c24a8e) into master (0487cc4) will decrease coverage by 0.26%.
The diff coverage is 85.91%.

❗ Current head 4c24a8e differs from pull request most recent head c4fda09. Consider uploading reports for the commit c4fda09 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #752      +/-   ##
==========================================
- Coverage   85.33%   85.07%   -0.26%     
==========================================
  Files          54       56       +2     
  Lines        4166     4343     +177     
==========================================
+ Hits         3555     3695     +140     
- Misses        611      648      +37     

Impacted Files	Coverage Δ
src/composer.rs	91.05% <ø> (ø)
src/composer/verifier.rs	89.47% <ø> (+3.26%)	⬆️
src/constraint_system/witness.rs	66.66% <ø> (ø)
src/error.rs	0.00% <ø> (ø)
tests/common/mod.rs	76.47% <ø> (ø)
src/constraint_system/constraint.rs	60.25% <33.33%> (ø)
src/composer/compiler/compress/hades.rs	80.95% <80.95%> (ø)
src/composer/compiler.rs	97.95% <85.71%> (-0.62%)	⬇️
src/composer/compiler/compress.rs	87.89% <87.89%> (ø)
src/composer/prover.rs	95.75% <100.00%> (-2.79%)	⬇️
... and 1 more

... and 8 files with indirect coverage changes

---

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[moCello]

Overall it lgtm, just some requests for comments here and there.
The PR still needs an issue though

[moCello]

Imo it would be nice to have 'compressor' somewhere in the module path. Maybe add a compressor module with scalar and witness in it?

[moCello]

I am missing tests for compressing and decompressing scalars that are bigger than i8.

[vlopes11]

These tests are here:

plonk/src/composer/compiler/scalar.rs

Lines 1049 to 1073 in 0862d97

	#[test]
	fn compress_decompress_works() {
	let compressor = ScalarCompressor::default();
	let mut buffer: Vec<u8> = vec![];
	// check negatives
	for v in 0..=u8::MAX {
	buffer.clear();
	let x = BlsScalar::zero() - BlsScalar::from(v as u64);
	let n = compressor.compress(&x, &mut buffer);
	let (p, y) = ScalarCompressor::decompress(&buffer[..n]);
	assert_eq!(n, p);
	assert_eq!(x, y);
	}
	// check positives
	for v in 0..=u8::MAX {
	buffer.clear();
	let x = BlsScalar::from(v as u64);
	let n = compressor.compress(&x, &mut buffer);
	let (p, y) = ScalarCompressor::decompress(&buffer[..n]);
	assert_eq!(n, p);
	assert_eq!(x, y);
	}
	}

[moCello]

And for scalars bigger than u8?

[moCello]

LGTM