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Time and energy modeling of a high-performance multi-threaded Cholesky factorization

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Abstract

We present accurate time and energy piece-wise models of high-performance multi-threaded implementations for the general matrix multiplication, triangular system solve with multiple right-hand sides, and symmetric rank-k update. Furthermore, these are then assembled to provide accurate models of the Cholesky factorization built on top of these Level-3 BLAS operations. Our models consider the costs, in terms of time and energy, of the floating-point operations involved in the routines as well as the overhead due to data movements across the levels of the memory hierarchy. The accuracy of the multi-threaded models is tested on an Intel Xeon E5-2620 processor, reporting relative errors for the Cholesky factorization that are, respectively, around 2.4 and 2.9 % on average for time and energy.

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Acknowledgments

This work was supported by the CICYT projects TIN2014-53495-R and CICYT-TIN 2012-32180 of the MINECO and FEDER, the EU FET Project FP7 318793 “EXA2GREEN”, and the FPU program of MECD.

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Authors and Affiliations

  1. Depto. Ingeniería y Ciencia de Computadores, Universidad Jaume I, Castellón, Spain

    Sandra Catalán, Rafael Mayo, Rafael Rodríguez-Sánchez & Enrique S. Quintana-Ortí

  2. Depto. de Arquitectura de Computadores y Automática, Universidad Complutense de Madrid, Madrid, Spain

    Francisco D. Igual

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  1. Sandra Catalán
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  2. Francisco D. Igual
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  3. Rafael Mayo
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  4. Rafael Rodríguez-Sánchez
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  5. Enrique S. Quintana-Ortí
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Correspondence to Sandra Catalán.

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Catalán, S., Igual, F.D., Mayo, R. et al. Time and energy modeling of a high-performance multi-threaded Cholesky factorization. J Supercomput 73, 139–151 (2017). https://doi.org/10.1007/s11227-016-1654-6

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  • DOI: https://doi.org/10.1007/s11227-016-1654-6

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