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A GPU method for the analysis stage of the SPTRSV kernel

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Abstract

The solution of sparse triangular linear systems of equations (SPTRSV) is often the main computational bottleneck of many numerical methods in science and engineering. In GPUs, this operation is solved using mainly two approaches. Level-set strategies perform a costly pre-processing (called analysis stage) to examine the dependencies between rows of the matrix and derive a static schedule for the subsequent solution stage. On the other hand, synchronization-free methods discover this scheduling dynamically and avoid the analysis stage, although some hybrid synchronization-free methods can leverage the level-set analysis to improve the performance. In this work, we present an efficient GPU routine to compute the analysis stage and then apply some of these ideas to accelerate a synchronization-free solver that does not require analysis. The experimental comparison with the well-known cusparse library shows up to 40\(\times \) speedups in the solution of triangular linear systems, and up to 262\(\times \) concerning the level-set analysis phase.

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Availability of data and materials

The source code is available on Github (https://github.com/HCL-Fing/SPTRSV). The sparse matrices used for the experimental evaluation are available in the SuiteSparse matrix collection.

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Acknowledgements

This work is partially funded by the UDELAR CSIC-INI project CompactDisp: Formatos dispersos eficientes para arquitecturas de hardware modernas. The authors also thank PEDECIBA Informática and the University of the Republic, Uruguay.

Funding

Manuel Freire received funding from the UDELAR CSIC-INI project CompactDisp: Formatos dispersos eficientes para arquitecturas de hardware modernas. The authors also thank PEDECIBA Informática and the University of the Republic, Uruguay.

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Authors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, INCO, Universidad de la República, Montevideo, Uruguay

    Manuel Freire, Juan Ferrand, Franco Seveso, Ernesto Dufrechou & Pablo Ezzatti

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  1. Manuel Freire
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  2. Juan Ferrand
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  3. Franco Seveso
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  4. Ernesto Dufrechou
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  5. Pablo Ezzatti
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Contributions

MF, JF and FS equally contributed to the design, implementation and evaluation of the analysis and solver routine, which was part of their final graduation project in Computer Engineering. PE and ED were the supervisors of the project.

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Correspondence to Manuel Freire.

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Freire, M., Ferrand, J., Seveso, F. et al. A GPU method for the analysis stage of the SPTRSV kernel. J Supercomput 79, 15051–15078 (2023). https://doi.org/10.1007/s11227-023-05238-8

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  • DOI: https://doi.org/10.1007/s11227-023-05238-8

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