Perf: special squaring for sparse elements in the pairing algorithm #772
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PR #763 triggered some unnecessary additions by 0 in pairing circuits (for 2-chains). It also happens for emulated pairings but it's hidden by how field emulation works. @ivokub tracked these occurrences and suggested to handle them in the pairing algorithm. These happen at the second iteration of the Miller loop. In fact, at this point, for a single pairing, the accumulator is a sparse element in Fpk (it's actually just the assigned line). So in this PR instead of calling the plain
Square
function we implement a specialSquare034
that takes into account this sparsity. The benefit is not huge but still, e.g.:PLONK bench of emulated BN254 pairing in a BN254 circuit: