A vulnerability factor for ECC-protected memory

Fault injection studies and vulnerability analyses have been used to estimate the reliability of data structures in memory. We survey these metrics and look at their adequacy to describe the data stored in ECC-protected memory. We also introduce FEA, a new metric improving on the memory derating factor by ignoring a class of false errors. We measure all metrics using simulations and compare them to the outcomes of injecting errors in real runs. This in-depth study reveals that FEA provides more accurate results than any state-of-the-art vulnerability metric. Furthermore, FEA gives an upper bound on the failure probability due to an error in memory, making this metric a tool of choice to quantify memory vulnerability. Finally, we show that ignoring these false errors reduces the failure rate on average by 12.75% and up to over 45%.This work has been supported by the RoMoL ERC Advanced Grant (GA 321253), by the European HiPEAC Network of Excellence, by the Spanish Ministry of Economy and Competitiveness (contract TIN2015-65316- P), by the Generalitat de Catalunya (contracts 2017-SGR-1414 and 2017- SGR-1328), by the Spanish Government (Severo Ochoa grant SEV-2015- 0493) and by the European Union’s Horizon 2020 research and innovation programme (grant agreements 671697 and 779877). L. Jaulmes has been partially supported by the Spanish Ministry of Education, Culture and Sports under grant FPU2013/06982. M. Moreto and M. Casas have been partially supported by the Spanish Ministry of Economy, Industry and Competitiveness under Ramon y Cajal fellowships RYC-2016-21104 and RYC-2017-23269.Peer ReviewedPostprint (author's final draft

Correcting soft errors online in fast fourier transform

While many algorithm-based fault tolerance (ABFT) schemes have been proposed to detect soft errors offline in the fast Fourier transform (FFT) after computation finishes, none of the existing ABFT schemes detect soft errors online before the computation finishes. This paper presents an online ABFT scheme for FFT so that soft errors can be detected online and the corrupted computation can be terminated in a much more timely manner. We also extend our scheme to tolerate both arithmetic errors and memory errors, develop strategies to reduce its fault tolerance overhead and improve its numerical stability and fault coverage, and finally incorporate it into the widely used FFTW library - one of the today's fastest FFT software implementations. Experimental results demonstrate that: (1) the proposed online ABFT scheme introduces much lower overhead than the existing offline ABFT schemes; (2) it detects errors in a much more timely manner; and (3) it also has higher numerical stability and better fault coverage

Ground-truth prediction to accelerate soft-error impact analysis for iterative methods

Understanding the impact of soft errors on applications can be expensive. Often, it requires an extensive error injection campaign involving numerous runs of the full application in the presence of errors. In this paper, we present a novel approach to arriving at the ground truth-the true impact of an error on the final output-for iterative methods by observing a small number of iterations to learn deviations between normal and error-impacted execution. We develop a machine learning based predictor for three iterative methods to generate ground-truth results without running them to completion for every error injected. We demonstrate that this approach achieves greater accuracy than alternative prediction strategies, including three existing soft error detection strategies. We demonstrate the effectiveness of the ground truth prediction model in evaluating vulnerability and the effectiveness of soft error detection strategies in the context of iterative methods.This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Award Number 66905, program manager Lucy Nowell. Pacific Northwest National Laboratory is operated by Battelle for DOE under Contract DE-AC05-76RL01830.Peer ReviewedPostprint (author's final draft

Approximating a Multi-Grid Solver

Multi-grid methods are numerical algorithms used in parallel and distributed processing. The main idea of multigrid solvers is to speedup the convergence of an iterative method by reducing the problem to a coarser grid a number of times. Multi-grid methods are widely exploited in many application domains, thus it is important to improve their performance and energy efficiency. This paper aims to reach this objective based on the following observation: Given that the intermediary steps do not require full accuracy, it is possible to save time and energy by reducing precision during some steps while keeping the final result within the targeted accuracy. To achieve this goal, we first introduce a cycle shape different from the classic V-cycle used in multi-grid solvers. Then, we propose to dynamically change the floating-point precision used during runtime according to the accuracy needed for each intermediary step. Our evaluation considering a state-of-the-art multi-grid solver implementation demonstrates that it is possible to trade temporary precision for time to completion without hurting the quality of the final result. In particular, we are able to reach the same accuracy results as with full double-precision while gaining between 15% and 30% execution time improvement.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 708566 (DURO). The European Commission is not liable for any use that might be made of the information contained therein. This work has been supported by the Spanish Government (Severo Ochoa grant SEV2015-0493)Peer ReviewedPostprint (author's final draft

Exploiting asynchrony from exact forward recovery for DUE in iterative solvers

This paper presents a method to protect iterative solvers from Detected and Uncorrected Errors (DUE) relying on error detection techniques already available in commodity hardware. Detection operates at the memory page level, which enables the use of simple algorithmic redundancies to correct errors. Such redundancies would be inapplicable under coarse grain error detection, but become very powerful when the hardware is able to precisely detect errors. Relations straightforwardly extracted from the solver allow to recover lost data exactly. This method is free of the overheads of backwards recoveries like checkpointing, and does not compromise mathematical convergence properties of the solver as restarting would do. We apply this recovery to three widely used Krylov subspace methods, CG, GMRES and BiCGStab, and their preconditioned versions. We implement our resilience techniques on CG considering scenarios from small (8 cores) to large (1024 cores) scales, and demonstrate very low overheads compared to state-of-the-art solutions. We deploy our recovery techniques either by overlapping them with algorithmic computations or by forcing them to be in the critical path of the application. A trade-off exists between both approaches depending on the error rate the solver is suffering. Under realistic error rates, overlapping decreases overheads from 5.37% down to 3.59% for a non-preconditioned CG on 8 cores.This work has been partially supported by the European Research Council under the European Union's 7th FP, ERC Advanced Grant 321253, and by the Spanish Ministry of Science and Innovation under grant TIN2012-34557. L. Jaulmes has been partially supported by the Spanish Ministry of Education, Culture and Sports under grant FPU2013/06982. M. Moreto has been partially supported by the Spanish Ministry of Economy and Competitiveness under Juan de la Cierva postdoctoral fellowship JCI-2012-15047. M. Casas has been partially supported by the Secretary for Universities and Research of the Ministry of Economy and Knowledge of the Government of Catalonia and the Co-fund programme of the Marie Curie Actions of the European Union's 7th FP (contract 2013 BP B 00243).Peer ReviewedPostprint (author's final draft

Adaptive control in rollforward recovery for extreme scale multigrid

With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed algorithm-based recovery method for multigrid iterations by introducing an adaptive control. After a fault, the healthy part of the system continues the iterative solution process, while the solution in the faulty domain is re-constructed by an asynchronous on-line recovery. The computations in both the faulty and healthy subdomains must be coordinated in a sensitive way, in particular, both under and over-solving must be avoided. Both of these waste computational resources and will therefore increase the overall time-to-solution. To control the local recovery and guarantee an optimal re-coupling, we introduce a stopping criterion based on a mathematical error estimator. It involves hierarchical weighted sums of residuals within the context of uniformly refined meshes and is well-suited in the context of parallel high-performance computing. The re-coupling process is steered by local contributions of the error estimator. We propose and compare two criteria which differ in their weights. Failure scenarios when solving up to $6.9\cdot10^{11}$ unknowns on more than 245\,766 parallel processes will be reported on a state-of-the-art peta-scale supercomputer demonstrating the robustness of the method