feat: direct multivariate polynomial evaluation in non-native #1299
+582
−50
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Description
This PR adds direct multivariate polynomial evaluation using non-native arithmetic. It can be used to perform direct extension computation, used in pairing computation (BW6, BN254, BLS12-377).
The idea is very similar to the multiplication approach, but when we do the evaluation check then we can work with arbitrary multivariate polynomials. This is really beneficial as the most of the cost is in range checking the result and the quotient, so when we can amortize multiple operations.
Another PR using it in BW6 evaluation is incoming, but it saves more than 50% of constraints in the Miller loop computation.
NB! One thing which I haven't figure out is how to allow negative coefficients. For example for BW6 we need to multiply by the non residue -4 for which we currently use a non-native value. But this changes the carry computation and SZ check which still isn't fully functional. But I think I'll keep it for the future to get working.
Type of change
How has this been tested?
Checklist:
golangci-lint
does not output errors locally