[SciPy-Dev] Accuracy of single-precision FFT

Charles R Harris charlesr.harris@gmail....
Thu Jun 24 12:55:15 CDT 2010

On Thu, Jun 24, 2010 at 11:41 AM, Anne Archibald <aarchiba@physics.mcgill.ca
> wrote:

> I'm not sure exactly what you're listing here, but I wrote a test
> program to compare single- and double-precision FFTs using FFTW; the
> root-mean-squared fractional errors are:
> 1 1.10991e-09
> 17 9.26845e-08
> 37 1.16509e-07
> 97 1.20773e-07
> 313 1.33648e-07
> 701 1.55432e-07
> 1447 1.75132e-07
> 2011 1.80602e-07
> 3469 1.93587e-07
> We can't use FFTW, unfortunately, but it's clear that prime-size FFTs
> can do much better than we are. (Though what exactly is the definition
> of the errors, below?) FFTW does this, IIRC, by not actually doing
> prime-size FFTs; they have some scheme by which the prime-size FFT is
> viewed as a convolution, then padded and computed with a
> nicely-divisible-size FFT.
Yeah, there is a longstanding ticket open to implement that. There are two
possibilities, Rader's or Winograd's algorithm. I don't know which FFTW
uses, but I'd like to see the Winograd algorithm since it can be used for
other things, like chirp transforms.  In any case, I think the single
precision results for FFTPACK should be better than they are, if not as good
as those that could be obtained using a better algorithm. Something isn't
quite right in there.

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