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

Improving Performance of Iterative Methods by Lossy Checkponting

Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks in parallel, they have to checkpoint the dynamic variables periodically in case of unavoidable fail-stop errors, requiring fast I/O systems and large storage space. To this end, significantly reducing the checkpointing overhead is critical to improving the overall performance of iterative methods. Our contribution is fourfold. (1) We propose a novel lossy checkpointing scheme that can significantly improve the checkpointing performance of iterative methods by leveraging lossy compressors. (2) We formulate a lossy checkpointing performance model and derive theoretically an upper bound for the extra number of iterations caused by the distortion of data in lossy checkpoints, in order to guarantee the performance improvement under the lossy checkpointing scheme. (3) We analyze the impact of lossy checkpointing (i.e., extra number of iterations caused by lossy checkpointing files) for multiple types of iterative methods. (4)We evaluate the lossy checkpointing scheme with optimal checkpointing intervals on a high-performance computing environment with 2,048 cores, using a well-known scientific computation package PETSc and a state-of-the-art checkpoint/restart toolkit. Experiments show that our optimized lossy checkpointing scheme can significantly reduce the fault tolerance overhead for iterative methods by 23%~70% compared with traditional checkpointing and 20%~58% compared with lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1

Improving Energy Saving of One-sided Matrix Decompositions on CPU-GPU Heterogeneous Systems

One-sided dense matrix decompositions (e.g., Cholesky, LU, and QR) are the key components in scientific computing in many different fields. Although their design has been highly optimized for modern processors, they still consume a considerable amount of energy. As CPU-GPU heterogeneous systems are commonly used for matrix decompositions, in this work, we aim to further improve the energy saving of one-sided matrix decompositions on CPU-GPU heterogeneous systems. We first build an Algorithm-Based Fault Tolerance protected overclocking technique (ABFT-OC) to enable us to exploit reliable overclocking for key matrix decomposition operations. Then, we design an energy-saving matrix decomposition framework, Bi-directional Slack Reclamation(BSR), that can intelligently combine the capability provided by ABFT-OC and DVFS to maximize energy saving and maintain performance and reliability. Experiments show that BSR is able to save up to 11.7% more energy compared with the current best energy saving optimization approach with no performance degradation and up to 14.1% Energy * Delay^2 reduction. Also, BSR enables the Pareto efficient performance-energy trade-off, which is able to provide up to 1.43x performance improvement without costing extra energy

Toward Resilience and Data Reduction in Exascale Scientific Computing

Because of the ever-increasing execution scale, reliability and data management are becoming more and more important for scientific applications. On the one hand, exascale systems are anticipated to be more susceptible to soft errors ,e.g. silent data corruptions, due to the reduction in the size of transistors and the increase of the number of components. These errors will lead to corrupted results without warning, making the output of the computation untrustable. On the other hand, large volumes of highly variable data are produced by scientific computing with high velocity on exascale systems or advanced instruments, and the I/O time on storing these data is prohibitive due to the I/O bottleneck in parallel file systems. In this work, we leverage algorithm-based fault tolerance (ABFT) and error-bound lossy compression to tackle the two problems, in order to support efficient scientific computing on exascale systems.We propose an efficient fault tolerant scheme to tolerant soft errors in Fast Fourier Transform (FFT), one of the most important computation kernels widely used in scientific computing. Traditional redundancy approaches will at least double the execution time or resources, limiting the usage in practice because of the large overhead. Previous works on offline ABFT algorithms for FFT mitigate this problem by providing resilient FFT with lower overhead, but these algorithms fail to make progress in vulnerable environments with high error rates because they can only detect and correct errors after the whole computation finishes. We propose an online ABFT scheme for large-scale FFT inspired by the divide-and-conquer nature of the FFT computation. We devise fault tolerant schemes for both computational and memory errors in FFT, with both serial and parallel optimizations. Experimental results demonstrate that the proposed approach provides more timely error detection and recovery as well as better fault coverage with less overhead, compared to the offline ABFT algorithm.To alleviate the I/O bottleneck in the parallel file systems, we work on a prediction-based error-bounded lossy compressor to significantly reduce the size of scientific datasets while retaining the accuracy of the decompressed data, with adaptive prediction algorithms and compression models. We first propose a regression-based predictor for better prediction accuracy than traditional approaches under large error bounds, followed by an adaptive algorithm that dynamically selects between the traditional Lorenzo predictor and the proposed regression-based predictor, leading to very high compression ratios with little visual distortion. We further unify the prediction-based model and transform-baed model by using transform-based compressors as a predictor, with novel optimizations toward efficient coefficient encoding for both the two models. The proposed adaptive multi-algorithm design provides better compression ratios given the same distortion, significantly reducing storage requirements and I/O time.We further adapt the compression algorithms and compressors to different requirements and/or objectives in realistic scenarios. We leverage a logarithmic transform to precondition the data, which turns a relative-error-bound compression problem into an absolute-error-bound compression problem. This transform aligns two different error requirements while improving the compression quality, efficiently reducing the workload for compressor design. We also correlate the compression algorithm with system information to achieve better I/O performance compared to traditional single compressor deployment. These studies further improve the efficiency of lossy compression from the perspective of efficient I/O in the context of scientific simulation, making scientific applications running on exascale systems more efficient