My code, when run as a 2048-point FFT, agrees with the MIT FFTW one to a max error margin of 6 parts per million.
This might be of interest: I've ported FFTW's arbitrary-precision FFT to boost::multiprecision
Awesome. I am a co-author of multiprecision and interested in your work. May I ask... Which FFTs did you concentrate on, dimensions, complex, etc.? What precisions did you use? Which multiprecision FP backend did you use? How was the performance? Where do you see the main application of your work in this area? How was your experience with multiprecision (critical suggestions are OK)?
Generally, I think it would be better if a boost::fft library would primarily be a wrapper around existing FFT libraries, with the C++ implementation only used as a fallback for multiprecision or licensing issues since it's unlikely a template implementation would catch up with the years of optimization work that went into single- and double-precision libraries like MKL and FFTW, especially FFTW's kernel generator and planner.
I completely agree. This identically mirrors the philosophy used in multiprecision.
But a reasonably fast (and open) multidimensional multiprecision FFT implementation doesn't seem to exist yet.
I know. You're preaching to the choir. Got to put FFT on the back burner. GSoC 2014? Sincerely, Chris.