Investigating and Mitigating Critical Faults in Floating-Point and Posit Arithmetic Hardware

Abstract

Mature computing formats, such as Floating-Point (FP), provide optimal accuracy to process real values and are essential in most scientific domains. However, the massive market adoption of highly parallel systems, with advanced technology nodes, in several domains exacerbates the need for highly reliable systems. Formerly, most reliability evaluations targeted FP hardware. Unfortunately, fine-grain assessments on cores with recent arithmetic format alternatives, such as Posit (particularly suited for Artificial Intelligence), have remained partially unexplored. Similarly, the effects of corruption on operations due to faulty hardware are not well-known, which may prevent the proposal of effective mitigation mechanisms. This work exhaustively evaluates the fine-grain effects of permanent faults in the hardware of arithmetic cores for the three most extensively used operations in modern applications (Add, Multiply, and Multiply and Add), including machine learning, implemented in Posit and FP. Our results indicate that Posit cores are less fault-vulnerable than FP ones. However, Posit cores are more prone to induce significant operational corruption than FP ones (5.2% to 7.5%). We also found that absolute errors in faulty FP cores are higher by up to 2 orders of magnitude than in Posit ones. Finally, we applied and evaluated three mitigation mechanisms (Self-Check and repair, Dual Modular Redundancy, and Triple Modular Redundancy), effectively reducing the most critical errors with moderate area costs (20% to 110%).