Optimizing the computation of n-point correlations on large-scale astronomical data

The n-point correlation functions (npcf) are powerful statistics that are widely used for data analyses in astronomy and other fields. These statistics have played a crucial role in fundamental physical breakthroughs, including the discovery of dark energy. Unfortunately, directly computing the npcf at a single value requires O(N
ⁿ
) time for N points and values of n of 2, 3, 4, or even larger. Astronomical data sets can contain billions of points, and the next generation of surveys will generate terabytes of data per night. To meet these computational demands, we present a highly-tuned npcf computation code that show an order-of-magnitude speedup over current state-of-the-art. This enables a much larger 3-point correlation computation on the galaxy distribution than was previously possible. We show a detailed performance evaluation on many different architectures.