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Fast Fourier transforms are widely used for applications in engineering, music, science, and mathematics.The current fft implementation was introduced two years ago(#11885, #11888 ), which is not the best implementation as far as I know, The drawbacks includes:
- Don't supports single precision transforms.
- Don't support for multi-D transforms.
- Don't make use of vector instructions for FFTs, The main reason that It's performance is not good enough(At least better than fftpack).
Although the author published the C++ based pypocketfft later, which has overcame these shortcomings, but It's was not compatible with C based numpy, I found out that there has several backend projects that worth considering.
| project | worth introducing? |
|---|---|
| fftw3 | Most popular FFT library, which nowadays is the "gold standard" for FFT implementations. It's also the default fft algorithm of matlab, there has a python wrapper pyfftw, can't integrated due to it's GPL Licence. |
| Intel MKL/IPP | Significantly faster than FFTW with intel processors, already integrated as a third party lib. |
| KFR | Claims to be faster than FFTW, can't integrated due to it's commecial Licence. |
| FFTS | reported to be faster than FFTW because the use of SIMD instructions, at least in some cases. worth considering. |
| FFTE | reported to be faster than FFTW, but the source code is Fortran-based. |
| Ooura FFT | provide C and Fortran version implementation, but It hasn't been updated in a long time. |
| muFFT/pffft/PGFFT | have performance comparable to FFTW.depends strongly on the SIMD instructions. but with limited features. |
| KissFFT/PocketFFT | The simplest but also the slowest one here, which is the current solution. |
Now we have two options:
- choose a new backend system such as FFTS, which is painful because of the trival adaptation process.
- optimize the current algorithm based on universal intrinsics, which is more practical and operable.
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