  A fast and exact algorithm is developed for the spin +-2 spherical harmonics
transforms on equi-angular pixelizations on the sphere. It is based on the
Driscoll and Healy fast scalar spherical harmonics transform. The theoretical
exactness of the transform relies on a sampling theorem. The associated
asymptotic complexity is of order O(L^2 log^2_2(L)), where 2L stands for the
square-root of the number of sampling points on the sphere, also setting a band
limit L for the spin +-2 functions considered. The algorithm is presented as an
alternative to existing fast algorithms with an asymptotic complexity of order
O(L^3) on other pixelizations. We also illustrate these generic developments
through their application in cosmology, for the analysis of the cosmic
microwave background (CMB) polarization data.
