Matrix multiplication has always been a cornerstone in computer science. In fact, linear algebra tools permeate a wide variety of applications: from weather forecasting, to financial market prediction, radio signal processing, computer vision, and more. Since many of the aforementioned applications typically impose strict performance and/or fault tolerance constraints, the demand for fast and reliable matrix multiplication (MxM) is at an all-time high. Typically, increased reliability is achieved through redundancy. However, coarse-grain duplication incurs an often prohibitive overhead, higher than 100%. Thanks to the peculiar characteristics of the MxM algorithm, more efficient algorithm-based hardening solutions have been designed to detect (and even correct) some types of errors with lower overhead. We show that, despite being more efficient, current solutions are still sub-optimal in certain scenarios, particularly when considering persistent faults in Field-Programmable Gate-Arrays (FPGAs). Based on a thorough analysis of the fault model, we propose an error detection technique for MxM that decreases both algorithmic and architectural costs by over a polynomial degree, when compared to existing algorithm-based strategies. Furthermore, we report arithmetic overheads at the application level to be under 1% for three state-of-the-art Convolutional Neural Networks (CNNs).

Novel computing architectures offer the possibility to execute float point operations with different precisions. The execution of reduced precision operations, when acceptable for certain applications, is likely to reduce both the execution time and the power consumption. However, the application's error rate and the device's reliability can also be impacted by these precision changes. In this paper, we study the impact of data and operation precision changes on the reliability of modern architectures. We consider Xilinx Field-Programmable Gate-Arrays (FPGA), Intel Xeon Phis, and NVIDIA Graphics Processing Units (GPUs) executing a set of codes implemented in double, single, and half-precision IEEE754-compliant float point data. On FPGAs, the reduced area and performance improvements brought by reduced precision operations increase reliability. On Xeon Phis the compiler biases significantly double and single-precision instructions execution. This raises the drawback of increasing single-precision error rates when compared to double-precision operations. NVIDIA GPUs make use of dedicated mixed-precision cores, which draw nontrivial effects on the device reliability. Generically speaking, on GPUs half-precision allows a higher number of executions to be correctly completed before experimenting a failure. Finally, we also evaluate how transient faults impact the output correctness. Our study shows that for most applications faults in a single or half-precision data or operation are more likely to significantly modify the output value than errors in double-precision data.