feat(fft): fft/fftInv now works on abitrary cosets #58
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ThomasPiellard
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The FFT package now allows to execute the fft (and fft inv) on shifted subgroup/dual basis (ex if u is a primitive n-th root of 1, and v a primitive m-th root of 1 with n|m, then we can evaluate a polynomial of degree n-1 on (1,u,..,u^n-1), on (v,vu,..vu^n-1), etc, up to v^(m/n) ). It will come handy for fast polynomial division while avoiding vanishing set of the quotient polynomial, for polynomials of arbitrary degree.
Breaking changes
NewDomain(m uint64)-->NewDomain(m, nbCosets uint64)(the greater nbCosets, the more memory is needed)FFT(a []fr.Element, decimation Decimation)-->FFT(a []fr.Element, decimation Decimation, coset uint64)FFTInverse(a []fr.Element, decimation Decimation)-->FFTInverse(a []fr.Element, decimation Decimation, coset uint64)Domainnow has a fieldNbCosets, which affects the serialization (so several parts of the coded are impacted, notably the Groth&6 setup has been re run for solidity integration test and in gnarkd)