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FAST-PT calculates 1-loop corrections to the matter power spectrum in cosmology. The code utilizes Fourier methods combined with analytic expressions to reduce the computation time down to scale as N log N, where N is the number of grid point in the input linear power spectrum. FAST-PT is extremely fast, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation.
FFTLog-and-beyond takes the FFTLog algorithm for single-Bessel integrals and generalizes it for integrals containing a derivative of the Bessel function to solve the non-Limber integrals. The full non-Limber angular power spectrum integral is simplified by noting the small contribution from unequal-time nonlinear terms; this significantly reduces the computation and avoids the double-Bessel integral. The original FFTLog algorithm is also extended to compute integrals containing derivatives of Bessel functions, which can be used to efficiently compute angular power spectra including redshift-space distortions (RSD) and Doppler effects. C and Python versions of the code are available.