Re: [eigen] FFT for Eigen

[Mark Borgerding <mark@xxxxxxxxxxxxxx>]

Ricard Marxer Piñón wrote:
> I have been using fftw as well [1], and by doing so I also end up
> copying the data, which is a pity, so I would also very much
> appreciate such a module.
>
> There are several tricky points I have been bumping into:
>
> 1- If I recall correctly, when creating a plan, you pass it two
> pointers (or optionally when done inplace, only one) that have been
> allocated by fftw.  This way fftw assures they are aligned, etc.
> Maybe there is lower level API fftw which might let you apply plans to
> pointers you have allocated on your own, otherwise, I don't know how a
> copy could be avoided.
>   
You can reuse the FFTW plan on other buffers rather than those the plan 
was created for, e.g. via the fftw_execute_dft_r2c
There are a few things that need to be the same as in the planning 
buffers, such as 16 bit alignment (for SIMD) ,and the choice of in-place 
vs out-of-place FFTs.


> 2- The complex type matrices in Eigen are still somewhat basic.  I
> think they are just a Matrix with data type std::complex (real and
> imaginary components are interleaved).  Which for some use cases is
> not great.  For example if I am going to do a lot of vector operations
> with the real and imaginary part separately, these operations cannot
> be easily vectorized (correct me if I'm wrong).  On the other hand it
> is true that this storage might be the one used by most external
> libraries.
> It has been already a long time since I told Benoit I would write a
> wiki page for this discussion, but still haven't.  Sorry for that.
>   
This seems like a worthwhile discussion, but one that is orthogonal (no 
pun intended) to the subject of FFTs. I will say that most (all?) modern 
FFT routines work with interleaved real,imag  components. I agree it 
would be easier to vectorize some operations if real, imag were stored 
separately.   It is still quite possible to vectorize interleaved 
complex.  Starting with SSE3 , intel introduced SIMD instructions aimed 
at complex math.  The Intel Performance Primitives make good use of 
these to create some really good complex-by-complex vector math 
routines. I'm sure AMD has similar stuff in ACML.

-- Mark

P.S. The question of "why not just use FFTW?" has come up in this 
discussion.  FFTW is GPL, not LGPL. It is incompatible with the Eigen 
dual license.