Right, I know, but what's the advantage of gpu vs cpu for fft, considering cpu-s support some vectorization and you need to format the data and send it to the gpu and back.

As far as I understand that's not a very meaningful question b/c it depends on what CPU and what GPU. So it's a bit apples to oranges and depends on the user's configuration. There is a benchmark at the very bottom: https://openbenchmarking.org/test/pts/vkfft

Also, maybe a bit obvious.. but that even if there is no huge benefit - sending compute to the GPU frees up your CPU/application to do other things .. like keeping your application responsive :)

The FFT is rarely the only thing you're doing, so at the very least you get to keep the data local if it was already on gpu.

FFT is memory bound (it’s N log N flops for N bytes, so little arithmetic). GPU HBM is much faster than DRAM, so generally it’s much faster on GPU.

Nvidia has something they call cuFFTW. Its basically a drop-in replacement for FFTW.

That's the kind of stuff Nvidia has offered for the last decade while AMD did god knows what.

https://docs.nvidia.com/cuda/cufft/index.html