feat: MSM sorting

[ledwards2225]

Implements logic for reducing MSM inputs by first summing points which share a scalar. See description in sorted_msm.hpp for details of the approach. This is useful when the scalars input for an MSM contains many repeated values because point addition is much cheaper than scalar multiplication. For example, when using the structured trace, the permutation grand product polynomial is non-zero but constant over 'dead' regions between blocks.

Note: For now this work is not integrated into the proving systems. That will be done in a follow on. At that time, considerations will be made for memory consumption (e.g. perhaps memory allocated in pippenger_runtime_state can be repurposed for the MSM sorting logic etc.)

[Rumata888]

Could you add a comment what this test is testing?

[ledwards2225]

done, thanks, not sure why I missed this

[Rumata888]

Same here, please describe what the test is for

[ledwards2225]

done

[Rumata888]

Probably would be good to parallelise both for larger ranges. For sort you can do similar to

aztec-packages/barretenberg/cpp/src/barretenberg/honk/proof_system/permutation_library.hpp

Lines 188 to 192 in 59b92ca

	#ifdef NO_TBB
	std::sort(extra_denominator_uint.begin(), extra_denominator_uint.end());
	#else
	std::sort(std::execution::par_unseq, extra_denominator_uint.begin(), extra_denominator.end());
	#endif

[ledwards2225]

Good call thanks. BTW is there a typo in the code you linked? Seems like in else it should be extra_denominator_uint.end() instead of extra_denominator.end()

[porco-rosso-j]

@Rumata888 I got the following error when running ./bootstrap.sh in cpp ( on v0.46.1 ).

.../honk/proof_system/permutation_library.hpp:191:74: fatal error: use of undeclared identifier 'extra_denominator'; did you mean 'extra_denominator_uint'?
  191 |     std::sort(std::execution::par_unseq, extra_denominator_uint.begin(), extra_denominator.end());
      |                                                                          ^~~~~~~~~~~~~~~~~
      |                                                                          extra_denominator_uint

[Rumata888]

Is it the same error on latest master?

[Rumata888]

Since we call this all the time in one loop it would be helpful to inline it, I think

[ledwards2225]

Thanks, done

[Rumata888]

It's a very clean PR with lots of docs (thank you) and everything looks good, The only issue I see is that the whole algorithm is single-threaded which will probably impede it quite a lot if we use it in a multi threaded environment

[ledwards2225]

@Rumata888 Thanks for the helpful review, as always. As part of the follow where this work will be integrated, I'll ensure things are multithreaded and proven out in benchmarks that demonstrate when (if!) this is advantageous.