Compressed Multiple-Row Storage Format

Zbigniew Koza, Maciej Matyka, Sebastian Szkoda, Lukasz Miroslaw
Faculty of Physics and Astronomy, University of Wroclaw, pl. M. Borna 9, 50-205 Wroclaw, Poland
arXiv:1203.2946v1 [physics.comp-ph] (13 Mar 2012)


   author={Koza}, Z. and {Matyka}, M. and {Szkoda}, S. and {Miros{l}aw}, {L}.},

   title={"{Compressed Multiple-Row Storage Format}"},

   journal={ArXiv e-prints},




   keywords={Physics – Computational Physics, Computer Science – Distributed, Parallel, and Cluster Computing},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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A new format for storing sparse matrices is proposed for efficient sparse matrix-vector (SpMV) product calculation on modern throughput-oriented computer architectures. This format extends the standard compressed row storage (CRS) format and is easily convertible to and from it without any memory overhead. Computational performance of an SpMV kernel for the new format is determined for over 140 sparse matrices on two Fermi-class graphics processing units (GPUs) and the efficiency of the kernel, which peaks at 36 and 25 GFLOPS at single and double precision, respectively, is compared with that of five existing generic algorithms and industrial implementations. The efficiency of the new format is also measured as a function of the mean (mu) and of the standard deviation (sigma) of the number of matrix nonzero elements per row. The largest speedup is found for matrices with mu > 20 and mu > sigma > 1.5 and can be as high as 43%.
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