  Cosmological perturbation theory is a powerful tool to predict the statistics
of large-scale structure in the weakly non-linear regime, but even at 1-loop
order it results in computationally expensive mode-coupling integrals. Here we
present a fast algorithm for computing 1-loop power spectra of quantities that
depend on the observer's orientation, thereby generalizing the FAST-PT
framework (McEwen et al., 2016) that was originally developed for scalars such
as the matter density. This algorithm works for an arbitrary input power
spectrum and substantially reduces the time required for numerical evaluation.
We apply the algorithm to four examples: intrinsic alignments of galaxies in
the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB
polarization due to baryon flows; and the 1-loop matter power spectrum in
redshift space. Code implementing this algorithm and these applications is
publicly available at https://github.com/JoeMcEwen/FAST-PT .
