Implementation of McMurchie–Davidson Algorithm for Gaussian AO Integrals Suited for SIMD Processors
Andrey Asadchev, Edward F. Valeev
TL;DR
This paper presents a new way to compute Gaussian integrals using modern processors, achieving high performance and open-source availability.
Contribution
A novel SIMD-optimized implementation of the McMurchie–Davidson algorithm for Gaussian AO integrals using standard C++.
Findings
The implementation achieves up to 50% of the theoretical hardware peak FP64 performance on SIMD platforms.
Speedups of up to 30x are observed compared to state-of-the-art one-shellset-at-a-time implementations.
The code is portable and uses upcoming C++ features like std::simd without explicit code generation.
Abstract
We report an implementation of the McMurchie–Davidson evaluation scheme for 1- and 2-particle Gaussian AO integrals designed for processors with Single Instruction Multiple Data (SIMD) instruction sets. Like in our recent MD implementation for graphical processing units (GPUs) [ AsadchevA., ; ValeevE. F., . J. Chem. Phys. 2024, 160, 244109.]38934632 10.1063/5.0217001, variable-sized batches of shellsets of integrals are evaluated at a time. By optimizing for the floating point instruction throughput rather than minimizing the number of operations, this approach achieves up to 50% of the theoretical hardware peak FP64 performance for many common SIMD-equipped platforms (AVX2, AVX512, NEON), which translates to speedups of up to 30 over the state-of-the-art one-shellset-at-a-time implementation of Obara–Saika-type schemes in Libint for a variety of primitive and contracted integrals.…
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Taxonomy
TopicsBlind Source Separation Techniques · Target Tracking and Data Fusion in Sensor Networks · Optical Polarization and Ellipsometry