Corrfunc --- A Suite of Blazing Fast Correlation Functions on the CPU

Abstract

The two-point correlation function (2PCF) is the most widely used tool for quantifying the spatial distribution of galaxies. Since the distribution of galaxies is determined by galaxy formation physics as well as the underlying cosmology, fitting an observed correlation function yields valuable insights into both. The calculation for a 2PCF involves computing pair-wise separations and consequently, the computing time scales quadratically with the number of galaxies. The next-generation galaxy surveys are slated to observe many millions of galaxies, and computing the 2PCF for such surveys would be prohibitively time-consuming. Additionally, modern modelling techniques require the 2PCF to be calculated thousands of times on simulated galaxy catalogues of {\em at least} equal size to the data and would be completely unfeasible for the next generation surveys. Thus, calculating the 2PCF forms a substantial bottleneck in improving our understanding of the fundamental physics of the universe, and we need high-performance software to compute the correlation function. In this paper, we present Corrfunc --- a suite of highly optimised, OpenMP parallel clustering codes. The improved performance of Corrfunc arises from both efficient algorithms as well as software design that suits the underlying hardware of modern CPUs. Corrfunc can compute a wide range of 2-D and 3-D correlation functions in either simulation (Cartesian) space or on-sky coordinates. Corrfunc runs efficiently in both single- and multi-threaded modes and can compute a typical 2-point projected correlation function ($w_p(r_p)$) for ~1 million galaxies within a few seconds on a single thread. Corrfunc is designed to be both user-friendly and fast and is publicly available at https://github.com/manodeep/Corrfunc.