Abstract
High precision arithmetic can improve the convergence of Krylov subspace methods; however, it is very costly. One system of high precision arithmetic is double-double (DD) arithmetic, which uses more than 20 double precision operations for one DD operation. We accelerated DD arithmetic using AVX SIMD instructions. The performances of vector operations in 4 threads are 51–59 % of peak performance in a cache and bounded by the memory access speed out of the cache. For SpMV, we used a double precision sparse matrix A and DD vector x to reduce memory access and achieved performances of 17–41 % of peak performance using padding in execution. We also achieved performances that were 9–33 % of peak performance for a transposed SpMV. For these cases, the performances were not bounded by memory access.
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The authors would like to thank the reviewers for their helpful comments.
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Hishinuma, T., Fujii, A., Tanaka, T., Hasegawa, H. (2014). AVX Acceleration of DD Arithmetic Between a Sparse Matrix and Vector. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55224-3_58
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DOI: https://doi.org/10.1007/978-3-642-55224-3_58
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