Computation of high-precision mathematical constants in a combined cluster and grid environment

Authors:
Daisuke Takahashi;Mitsuhisa Sato;Taisuke Boku
Affiliations:
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan
Venue:
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Year:
2005

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Abstract

The computation of high-precision mathematical constants in a combined cluster and grid environment is presented. Mathematical constants (e.g., π and e) are computed from their series expansions. The binary splitting method recursively reduces the calculation of the sum of the series by effectively splitting the problem into two halves and performing the same calculation on each half. By using grid computing for part of the binary splitting process, the supercomputer computation time, which is very expensive, can be reduced. We implemented the independent binary splitting process in a grid environment using a grid RPC system called OmniRPC. We successfully achieved nearly linear speedup for larger digits on an 8-node PC cluster used over a wide-area network.