A comparison of several fault-tolerance methods for the detection and correction of floating-point errors in matrix-matrix multiplication

Valentin Le Fèvre (1, 2) , Thomas Herault (3) , Julien Langou (4) , Yves Robert (1, 2, 3)

1 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 ICL - Innovative Computing Laboratory [Knoxville]
4 University of Colorado [Denver]

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.

Domaines: Informatique [cs]

Valentin Le Fèvre, Thomas Herault, Julien Langou, Yves Robert. A comparison of several fault-tolerance methods for the detection and correction of floating-point errors in matrix-matrix multiplication. Resilience 2020 - 12th Workshop on Resiliency in High Performance Computing in Clusters, Clouds, and Grids (colocated with Euro-Par), Aug 2020, Warsaw, Poland. pp.1-14. ⟨hal-03029309⟩