Corrfunc --- A Suite of Blazing Fast Correlation Functions on the CPU (1911.03545v1)

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.

• The paper introduces a highly optimized suite that significantly speeds up the calculation of galaxy clustering 2-point correlation functions.
• It leverages domain partitioning, custom SIMD kernels, and OpenMP parallelism to reduce computational time on modern CPUs.
• Robust benchmarking demonstrates its superior performance over traditional methods, making it essential for next-generation galaxy surveys.

Corrfunc: A Suite of Highly Optimized Correlation Function Calculations on the CPU

The paper presents "Corrfunc," a suite of highly optimized algorithms designed to calculate two-dimensional and three-dimensional correlation functions efficiently on modern CPUs. The computation of correlation functions, specifically the two-point correlation function (2PCF), is fundamental in astrophysics for analyzing the spatial distribution of galaxies, which in turn informs our understanding of galaxy formation and cosmology. However, the calculation of these functions is computationally intensive, especially with the vast datasets generated by next-generation galaxy surveys.

The 2PCF provides insights into the cosmology and structure formation by quantifying galaxy clustering. Calculating these functions involves determining pairwise separations among galaxies, a process that scales quadratically with the number of galaxies involved. The traditional approach of brute-force computations becomes untenable for modern surveys poised to observe millions of galaxies.

Core Contributions of Corrfunc

Corrfunc addresses these computational challenges through several algorithmic and software optimizations:

1. Domain Partitioning: The space is divided into a 3D grid of cells, minimizing the number of pairs that need distance computations by focusing on neighboring cells. This approach leverages the geometric property that points within a maximum separation distance must lie within adjacent cells.
2. Performance and Architecture-Awareness: Corrfunc utilizes efficient algorithms complemented by a software design that exploits the architecture of modern CPUs. This includes cache-efficient memory access patterns and explicit vectorized implementations using SIMD (Single Instruction Multiple Data) intrinsics.
3. Parallelism through OpenMP: The use of OpenMP enables Corrfunc to scale across multiple CPU cores, facilitating significant speedups in computations. This multithreading support is critical given the increased core counts in modern processors.
4. Custom SIMD Kernels: Corrfunc eschews compiler-generated vectorization in favor of custom SIMD implementations that dramatically enhance computation speeds by processing multiple pairwise operations simultaneously.
5. Reusable and Extensible Codebase: Besides performance improvements, Corrfunc is engineered for flexibility and correctness. Every clustering statistic function is rigorously tested against correct outputs to ensure computational accuracy, and the codebase supports extensions beyond the 2PCF to other clustering statistics.

Empirical Evaluation

The paper includes robust benchmarking against other correlation function codes, demonstrating significant performance advantages of Corrfunc across scenarios due to its extensive optimization strategies. These benchmarks substantiate the efficacy of its design choices in delivering superior performance across several metrics and conditions — including particle numbers, radius range, and multi-threading capabilities.

Implications and Future Directions

Corrfunc substantially reduces a major computational bottleneck in the analysis of galaxy surveys, facilitating more detailed and numerous analyses within feasible timeframes. The framework's ability to handle increasing datasets with scalable performance portends well for its application in upcoming astronomical surveys, which will demand fast and accurate computations over unprecedentedly large datasets.

The paper suggests future directions that include further optimizations, such as loop-blocking strategies for enhancing data reuse and the use of GPU computing. Additionally, the authors acknowledge the importance of continual improvements in code maintainability and user experience to ensure the software remains a valuable tool for the astrophysical community.

Overall, Corrfunc stands as a critical advancement in computational astrophysics, bridging the gap between theoretical astrophysical inquiries and the computational capabilities required to process burgeoning data volumes effectively.