Add ChunkedPippenger to variable-base MSM

[huyuncong]

Description

ChunkedPippenger is a core algorithm for streaming MSM.
We could add streaming MSM on top of it after the stream utils are imported.
The test of this algorithm is added into tests macros in test-templates.

---

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[weikengchen]

Interesting: internal compiler error: unexpected panic
This is often due to the nightly being unstable.

The other bug: https://github.com/arkworks-rs/algebra/runs/4478158408?check_suite_focus=true
This could be fixed by using the full name of the struct.

[Pratyush]

I would move this into variable_base, since it's a variable-base MSM

[huyuncong]

This is the core internal algorithm of streaming MSM. But we do have another streaming MSM function for public use that has not been imported yet because it relies on streaming utilities. The plan is to first decide which repo to put streaming utilities and then import streaming MSM into variable-base MSM.

[weikengchen]

Pratyush, I think here involves a decision, that is where to put this newer stream variable-base MSM---it clearly belongs to variable base. Does it replace the original variable base algorithm? If not, how should we name then?

[Pratyush]

I mean that we add this algorithm as another file in the variable_base module, instead of making it a top-level member of the msm module.

[Pratyush]

A micro-optimization that you might want to consider is to build up a buffer of results, and then sum that buffer up in parallel.

[huyuncong]

Interesting: internal compiler error: unexpected panic This is often due to the nightly being unstable.

It seems the compiler error is not caused by the imported code. Any idea on fixing that?

[weikengchen]

We can either wait for one more day or ignore that. Sometimes, nightly is just unstable.

[mmaker]

A micro-optimization that you might want to consider is to build up a buffer of results, and then sum that buffer up in parallel.

We can't. The chunk size max_msm_buffer is a constant and, if we want to keep log space, we can't store N/max_msm_buffer elements. We can, however, build them up in chunks again, but that seems.. overkill? After all it's just group addition. What would you expect from this?

As another note: when/if you merge, can you please credit me as co-author of the commitment? This code comes from mmaker/gemini. I can push an empty commitment here if this makes it easier for you.

[Pratyush]

You can build up a max_msm_buffer-sized buffer of results, and then sum that. This would at most double your memory consumption. However that might still be out of your memory budget, and the time savings might not be sufficient to warrant it...

Re: the authorship, we'll merge it via squash-ing the PR, so if you add an empty commit then you should be automatically credited with co-authorship in the squash commit.

[mmaker]

Yah, that's what I meant; I'd stick with this "naïve" version for now.
Added a marker, thanks!

[weikengchen]

It seems that pub mod variable_base; can be changed back to mod variable_base;. So I changed that.

[weikengchen]

I will wait for Pratyush to do a final pass.