Abstract
This paper compares several fault-tolerance methods for the detection and correction of floating-point errors in matrix-matrix multiplication. These methods include replication, triplication, Algorithm-Based Fault Tolerance (ABFT) and residual checking (RC). Error correction for ABFT can be achieved either by solving a small-size linear system of equations, or by recomputing corrupted coefficients. We show that both approaches can be used for RC. We provide a synthetic presentation of all methods before discussing their pros and cons. We have implemented all these methods with calls to optimized BLAS routines, and we provide performance data for a wide range of failure rates and matrix sizes.
This work was supported in part by the U.S. National Science Foundation awards 1645514 and 1563744.
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Fèvre, V.L., Herault, T., Langou, J., Robert, Y. (2021). A Comparison of Several Fault-Tolerance Methods for the Detection and Correction of Floating-Point Errors in Matrix-Matrix Multiplication. In: Balis, B., et al. Euro-Par 2020: Parallel Processing Workshops. Euro-Par 2020. Lecture Notes in Computer Science(), vol 12480. Springer, Cham. https://doi.org/10.1007/978-3-030-71593-9_24
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