Reduced Precision Checking to Detect Errors in Floating Point Arithmetic

We use reduced precision checking (RPC) to detect errors in floating point arithmetic. Prior work explored RPC for addition and multiplication. In this work, we extend RPC to a complete floating point unit (FPU), including division and square root, and we present precise analyses of the errors undetectable with RPC that show bounds that are smaller than prior work. We implement RPC for a complete FPU in RTL and experimentally evaluate its error coverage and cost.