  We present a novel algorithm, FAST-PT, for performing convolution or
mode-coupling integrals that appear in nonlinear cosmological perturbation
theory. The algorithm uses several properties of gravitational structure
formation -- the locality of the dark matter equations and the scale invariance
of the problem -- as well as Fast Fourier Transforms to describe the input
power spectrum as a superposition of power laws. This yields extremely fast
performance, enabling mode-coupling integral computations fast enough to embed
in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and
demonstrate its application to calculating nonlinear corrections to the matter
power spectrum, including one-loop standard perturbation theory and the
renormalization group approach. We also describe our public code (in Python) to
implement this algorithm, including the applications described here.
