A-ABFT: Autonomous Algorithm-Based Fault Tolerance for Matrix Multiplications on Graphics Processing Units

Graphics processing units (GPUs) enable large-scale scientific applications and simulations on the desktop. To allow scientific computing on GPUs with high performance and reliability requirements, the application of software-based fault tolerance is attractive. Algorithm-Based Fault Tolerance (ABFT) protects important scientific operations like matrix multiplications. However, the application to floating-point operations necessitates the runtime classification of errors into inevitable rounding errors, allowed compute errors in the magnitude of such rounding errors, and into critical errors that are larger than those and not tolerable. Hence, an ABFT scheme needs suitable rounding error bounds to detect errors reliably. The determination of such error bounds is a highly challenging task, especially since it has to be integrated tightly into the algorithm and executed autonomously with low performance overhead. In this work, A-ABFT for matrix multiplications on GPUs is introduced, which is a new, parallel ABFT scheme that determines rounding error bounds autonomously at runtime with low performance overhead and high error coverage.