This paper presents an algorithm based fault tolerance method to harden three two-sided matrix factorizations against soft errors: reduction to Hessenberg form, tridiagonal form, and bidiagonal form. These two sided factorizations are usually the prerequisites to computing eigenvalues/eigenvectors and singular value decomposition. Algorithm based fault tolerance has been shown to work on three main one-sided matrix factorizations: LU, Cholesky, and QR, but extending it to cover two sided factorizations is non-trivial because there are no obvious offline, problem specific maintenance of checksums. We thus develop an online, algorithm specific checksum scheme and show how to systematically adapt the two sided factorization algorithms used in LAPACK and ScaLAPACK packages to introduce the algorithm based fault tolerance. The resulting ABFT scheme can detect and correct arithmetic errors continuously during the factorizations that allow timely error handling. Detailed analysis and experiments are conducted to show the cost and the gain in resilience. We demonstrate that our scheme covers a significant portion of the operations of the factorizations. Our checksum scheme achieves high error detection coverage and error correction coverage compared to the state of the art, with low overhead and high scalability.
|Title of host publication||PPoPP 2017 - Proceedings of the 22nd ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming|
|Number of pages||13|
|State||Published - Jan 26 2017|
|Event||22nd ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPoPP 2017 - Austin, United States|
Duration: Feb 4 2017 → Feb 8 2017
|Name||Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP|
|Conference||22nd ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPoPP 2017|
|Period||2/4/17 → 2/8/17|
Bibliographical noteFunding Information:
The authors would like to thank the anonymous reviewers for their insightful comments and valuable suggestions. This work is partially supported by the NSF ACI-1305624, CCF-1513201, the SZSTI basic research program JCYJ20150630114942313, and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase).
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