feat: let multiplicity depend on payload size

[akonring]

closes: #663

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[ggutoski]

Status as of https://github.com/EspressoSystems/jellyfish/pull/667/commits/17d55fba72b2cb4739fb417525c57ac41e9523e0 :

The new test max_multiplicity fails with

thread 'advz::test::max_multiplicity' panicked at vid/src/advz.rs:882:13:
assertion `left == right` failed
  left: 4096
 right: 4

Here's the code: https://github.com/EspressoSystems/jellyfish/blob/17d55fba72b2cb4739fb417525c57ac41e9523e0/vid/src/advz.rs#L876-L883

The problem is that we're still calling FFT with the original self.eval_domain, which auto-magically resizes the polynomial degree to the size of self.eval_domain, which was originally set in the Advz constructor according to max_multiplicity. In the above test failure a small payload of size 4 field elements is resized to a large payload of size 4096.

Any fix for this issue must also address the above problem. But that's a bigger task. We now need the eval domain to change size at disperse-time to accommodate a small payload.

Options

1. Construct small domains on-the-fly as needed at disperse-time: if at disperse-time we find that self.eval_domain is too big then construct a new small domain, otherwise use self.eval_domain.
   • It would be nice of arkworks EvaluationDomain has a convenient way to construct a subdomain from a given domain. But I don't see such a method. Fortunately the code to construct a new domain is not difficult.
2. Perhaps we should delete the field eval_domain from struct Advz. Instead, we always construct this domain on-the-fly with the correct size at disperse-time. But that's a nontrivial change so I prefer to discuss with others.

[EDIT: I think it's cleaner to do option 2. That's what I'm currently doing.]

[ggutoski]

closing so that I can open a new PR for this branch so as to better facilitate review from others.