Uniting extrinsic vectorization and shell structure for efficient SIMD evaluation of electron repulsion integrals

Future computer architectures are likely to feature greater reliance on single instruction multiple data (SIMD) processing for high throughput processing of data-intensive workloads. For algorithms that rely heavily on electron repulsion integrals (ERIs), exploitation of SIMD processing requires extrinsic vectorization, i.e. the sorting of ERIs into sets with equivalent class that may be computed with an identical instruction stream. Such sorting is incongruous with the commonly exploited shell structure whereby ERI are generated over shells such that initialization/bootstrap values may be reused, yielding significant savings in ERI evaluation time. In this work, we discuss how extrinsic vectorization may be unified with shell structure through the exploitation of memory access locality.