Performance Evaluation of the Calculation Programs of Electron Repulsion Integrals

Yuichi INADOMIa,b*, Shigeru OBARAc and Umpei NAGASHIMAa,b

aNational Institute of Advanced Industrial Science and Technology, Research Institute for Computational Sciences
Central 2, 1-1-1 Umezono, Tsukuba, 305-8568, JAPAN
bCore Research for Evolutional Science and Technology, Japan Science and Technology Agency
Kawaguchi Center building, 4-1-8 Honcho, Kawaguchi, 332-0012, JAPAN
cHokkaido University of Education, Kushiro Campus
1-15-55 Shiroyama, Kushiro, Hokkaido, 085-8580, JAPAN

(Received: July 28, 2005; Accepted for publication: November 7, 2005; Published on Web: December 15, 2005)

Performance evaluation of two programs for electron repulsion integral calculation was done using the performance counter on Intel Pentium 4 processor (3.6GHz, EM64T, 1GB L2 cache). The programs were of the new Obara method [6, 7], and of the hybrid method of Vertical Recurrence Relation method (VRR)[5] and Horizontal Recurrence Relation method (HRR)[8]. Though the floating point operations of the new Obara method are almost 20% smaller than those of the hybrid method, the total clock cycle, corresponding to the wall clock time, was more than 30% larger than that for the hybrid. The performance decrease is mainly due to memory access because load/store instructions of the new Obara method are almost 3 times larger, and the level 1 data cache difference is 25 times larger than that of the hybrid.
It becomes clear that the reduction of the memory accesses is very important to improve the performance of integral calculation as well as the reduction of the number of floating point operations.

Keywords: Two-electron integral, Performance counter, Memory access

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