Possibility to support many customized gates in Libra/Virgo

[weikengchen]

One thing special in Libra/Virgo is that it supports many customized gates, particularly:

1. a gate that sums 2^L values together.
2. an expsum gate that computes the bit composition of 2^L values.

These gates have the potential to reduce the amount of computation---adding 2^L values together with the 2-input, 1-output addition gates would take about 2^{L}-1 gates and L layers.

Reducing the number of layers would have multiple benefits: (1) cut the rounds, so fewer sumchecks, fewer poly-commits and (2) in general fewer gates, so smaller FFT (in Virgo).

[tsunrise]

sorry I haven't revisited this repo for a long time. For now, this repo only contains native code for multivariate sumcheck. (I plan to refactor some of the code after ark-bcs becomes public)

I'm not familiar with Libra/Virgo, but are we supposed to implement those gates in r1cs-std?