A parallel algorithm for accurate dot product

Authors:
N. Yamanaka;T. Ogita;S. M. Rump;S. Oishi
Affiliations:
Graduate School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan;Department of Mathematics, Tokyo Woman's Christian University, Tokyo 167-8585, Japan and Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan;Institute for Reliable Computing, Hamburg University of Technology, Hamburg 21071, Germany;Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
Venue:
Parallel Computing
Year:
2008

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Abstract

Parallel algorithms for accurate summation and dot product are proposed. They are parallelized versions of fast and accurate algorithms of calculating sum and dot product using error-free transformations which are recently proposed by Ogita et al. [T. Ogita, S.M. Rump, S. Oishi, Accurate sum and dot product, SIAM J. Sci. Comput. 26 (6) (2005) 1955-1988]. They have shown their algorithms are fast in terms of measured computing time. However, due to the strong data dependence in the process of their algorithms, it is difficult to parallelize them. Similarly to their algorithms, the proposed parallel algorithms in this paper are designed to achieve the results as if computed in K-fold working precision with keeping the fastness of their algorithms. Numerical results are presented showing the performance of the proposed parallel algorithm of calculating dot product.