Improved CMB (de-)lensing using general spherical harmonic transforms

We propose a novel way of performing CMB lensing and adjoint lensing by using non-uniform-discrete-Fourier-transforms and find many orders increase in accuracy, at least one order of magnitude faster computation time, and strongly reduced memory consumption with this new approach. With this, CMB lensing analyses on a typical stage-4 like experiment can be done within a few seconds. We provide a fully tested Python package, lenspyx\url{https://github.com/carronj/lenspyx} for the CMB lensing related tasks, and the low level implementations of the C++ core-functions DUCC \url{https://pypi.org/project/ducc0/} which comes with a handy Python wrapper.