Re: [eigen] A complex FFT for Eigen

[Tim Molteno <tim@xxxxxxxxxxxxxxxxxxx>]

Benoit Jacob wrote:
> - your code doesn't leverage Eigen as much as it could to enable high
> performance. For example, in apply(), replacing the for loop by single
> operations on vectors would let Eigen handle loop unrolling and
> vectorization. Well, except that Eigen doesn't vectorize std::complex
> currently, so I wonder if your code should be adapted to that or if
> this means that we should consider vectorizing std::complex. (So far
> we haven't seen many uses for std::complex anyway so we didn't
> optimize it as much as we maybe could).
>   
I'd love to vectorize this better. I'll look into this, but ran into the 
issue of addressing sub-vectors in-place. I could not work out how to do 
it in Eigen. How do I carry out operations like

data[1:N] += data[N+1:2N]

In other words, can I create a vector object that refers into part of 
another vector object?

I tried using MatrixBlock objects, but could not get it to work? Using 
pointers into the arrays loses bounds checking, and makes assumptions 
about how arrays are stored.

> - the factorize() function here is not vectorizable at all because it
> doesn't do any contiguous access. Aren't there other, more
> hardware-friendly algorithms?
>   
I think that FFT's are inherently non-local operations. There might be 
better ways of doing this, but as it stands this code is pretty fast for 
an FFT and extremely small and lightweight, so I'd rather vectorize the 
apply function first as this is where most of the computation is happening.

Cheers

Tim

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