  Deep cosmic microwave background polarization experiments allow a very
precise internal reconstruction of the gravitational lensing signal in
pricinple. For this aim, likelihood-based or Bayesian methods are typically
necessary, where very large numbers of lensing and delensing remappings on the
sphere are sometimes required before satisfactory convergence. We discuss here
an optimized piece of numerical code in some detail that is able to efficiently
perform both the lensing operation and its adjoint (closely related to
delensing) to arbitrary accuracy, using nonuniform fast Fourier transform
technology. Where applicable, we find that the code outperforms current
widespread software by a very wide margin. It is able to produce
high-resolution maps that are accurate enough for next-generation cosmic
microwave background experiments on the timescale of seconds on a modern
laptop. The adjoint operation performs similarly well and removes the need for
the computation of inverse deflection fields. This publicly available code
enables de facto efficient spherical harmonic transforms on completely
arbitrary grids, and it might be applied in other areas as well.
