Beyond the traditional line-of-sight approach of cosmological angular statistics

We present a new efficient method to compute the angular power spectra of largescale structure observables that circumvents the numerical integration over Bessel functions, expanding on a recently proposed algorithm based on FFT1og. This new approach has better convergence properties. The method is explicitly implemented in the CLASS code for the case of number count C-l's (including redshift-space distortions, weak lensing, and all other relativistic corrections) and cosmic shear C-l's. In both cases our approach speeds up the calculation of the exact C-l's (without the Limber approximation) by a factor of order 400 at a fixed precision target of 0.1%.