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Implementing complex numbers and FFT with just datatypes (2023)
Implementing complex numbers and FFT with just datatypes (no floats) - implementing_fft.md
The program above implements addition by repeated increment, and is the simplest numerical example where fusion makes a big difference, being exponential on Haskell and linear on HVM. Our ultimate goal is to come up with an implementation of Complex that can be used on FFT, and that is based purely on ADTs, i.e., no native floats, in such a way that is simple and direct enough to possibly fuse. Just to think of the complexity of floats (which include sign, mantissa, exponent, NaNs...), Dedekind Cuts, Cauchy Sequences and the like would give us the feeling we'll never find a representation of real numbers that is as nice and uniform as the Int type above.
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