Corrfunc: Blazing fast correlation functions with AVX512F SIMD Intrinsics (1911.08275v1)

Abstract: Correlation functions are widely used in extra-galactic astrophysics to extract insights into how galaxies occupy dark matter halos and in cosmology to place stringent constraints on cosmological parameters. A correlation function fundamentally requires computing pair-wise separations between two sets of points and then computing a histogram of the separations. Corrfunc is an existing open-source, high-performance software package for efficiently computing a multitude of correlation functions. In this paper, we will discuss the SIMD AVX512F kernels within Corrfunc, capable of processing 16 floats or 8 doubles at a time. The latest manually implemented Corrfunc AVX512F kernels show a speedup of up to $\sim 4\times$ relative to compiler-generated code for double-precision calculations. The AVX512F kernels show $\sim 1.6\times$ speedup relative to the AVX kernels and compare favorably to a theoretical maximum of $2\times$. In addition, by pruning pairs with too large of a minimum possible separation, we achieve a $\sim 5-10\%$ speedup across all the SIMD kernels. Such speedups highlight the importance of programming explicitly with SIMD vector intrinsics for complex calculations that can not be efficiently vectorized by compilers. Corrfunc is publicly available at https://github.com/manodeep/Corrfunc/.

• The paper introduces manually implemented AVX512F kernels that achieve up to fourfold speed improvements in correlation function calculations.
• It details optimizations like space partitioning, SIMD vectorization, and bounding box pruning to significantly reduce unnecessary computations.
• The enhanced performance enables efficient large-scale cosmological simulations, providing critical advantages in astrophysical data analysis.

Corrfunc: Blazing Fast Correlation Functions with AVX512F SIMD Intrinsics

The paper presents significant enhancements to the Corrfunc software, focused on augmenting the efficiency of calculating correlation functions using AVX512F SIMD intrinsics. These functions are crucial in extra-galactic astrophysics and cosmology for understanding galaxy distribution and constraining cosmological parameters.

Corrfunc is an open-source package that efficiently computes multiple correlation functions. The authors have introduced manually implemented AVX512F kernels, achieving up to a fourfold speed increase compared to compiler-generated double-precision codes. The AVX512F kernels offer a 1.6× speedup over their AVX counterparts, aligning well with the theoretical upper limit of a 2× improvement offered by these advancements in instruction set architecture.

Methodology and Implementation

The implementation detailed in the paper involves leveraging the newest AVX512F instruction set, which facilitates processing 16 floats or 8 doubles simultaneously. Important optimizations include:

• Space Partitioning: The paper outlines partitioning datasets into cells matching potential maximum separation distances, thereby reducing unnecessary distance calculations.
• SIMD Vectorization: They improve runtime by processing distances using SIMD intrinsics, avoiding the limitations of automatic compiler vectorization.
• Bounding Box Pruning: By calculating the minimum possible separation between particles, the method effectively prunes cell pairs that are unlikely to include the desired separations, thereby enhancing computational efficiency by 5-10%.

Performance Evaluation

Benchmarked on platforms supporting the AVX512F instruction set, the AVX512F kernels demonstrate robust performance improvements across variable correlation function configurations. Specifically, the kernels maintain superior speed when working with both typical and extensive ranges of separation thresholds. The performance benefits are particularly pronounced in scenarios demanding high computational loads.

Implications

This paper underlines the importance of utilizing advanced vector instructions and domain-specific optimizations in computational astrophysics. By manually coding SIMD intrinsics, the researchers circumvent limitations inherent to automated compiling processes, achieving remarkable speedups. This work enhances the ability to perform large-scale cosmological simulations efficiently, a critical component in adapting to the ever-increasing scale of astrophysical data.

Future Directions

Potential future endeavors could focus on extending these optimization techniques to other critical algorithms within astrophysics and exploring their scalability on emerging hardware platforms. Additionally, integrating more dynamic methods for optimizing grid sizes and partitioning strategies based on dataset characteristics could yield further efficiency gains.

In conclusion, the paper's contributions significantly advance the capabilities of Corrfunc, positioning it as an essential tool for researchers in astrophysics needing to perform fast and accurate correlation function computations.