Implementation of McMurchie-Davidson algorithm for Gaussian AO integrals suited for SIMD processors
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912640784138240 |
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| author | Asadchev, Andrey Valeev, Edward F. |
| author_facet | Asadchev, Andrey Valeev, Edward F. |
| contents | 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) [J. Chem. Phys. 160, 244109 (2024)], 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. As with our previous work, we rely on the standard C++ programming language -- such as the std::simd standard library feature to be included in the 2026 ISO C++ standard -- without any explicit code generation to keep the code base small and portable. The implementation is part of the open source LibintX library freely available at https://github.com/ValeevGroup/libintx. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_12501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Implementation of McMurchie-Davidson algorithm for Gaussian AO integrals suited for SIMD processors Asadchev, Andrey Valeev, Edward F. Chemical Physics Mathematical Software Computational Physics 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) [J. Chem. Phys. 160, 244109 (2024)], 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. As with our previous work, we rely on the standard C++ programming language -- such as the std::simd standard library feature to be included in the 2026 ISO C++ standard -- without any explicit code generation to keep the code base small and portable. The implementation is part of the open source LibintX library freely available at https://github.com/ValeevGroup/libintx. |
| title | Implementation of McMurchie-Davidson algorithm for Gaussian AO integrals suited for SIMD processors |
| topic | Chemical Physics Mathematical Software Computational Physics |
| url | https://arxiv.org/abs/2506.12501 |