A Novel Approach for Handling Soft Error in Conjugate Gradients

Soft errors or bit flips have recently become an important challenge in high performance computing. In this paper, we focus on soft errors in a particular algorithm: conjugate gradients (CG). We present a series of techniques to detect soft errors in CG. We first derive a mathematical quantity that is monotonically decreasing. Next, we add a set of heuristics and combine our approach with previously established methods. We have extensively evaluated our method considering three distinct dimensions. First, we show that the F-score of our detection is significantly better than two other methods. Second, we show that for soft errors that are not detected by our method, the resulting inaccuracy in the final results are small, and better than those with other methods. Finally, we show that the runtime overheads of our method are lower than for other methods.