An automated design flow for approximate circuits based on reduced precision redundancy

Reduced Precision Redundancy (RPR) is a popular Approximate Computing technique, in which a circuit operated in Voltage Over-Scaling (VOS) is paired to a reduced-bitwidth and faster replica so that VOS-induced timing errors are partially recovered by the replica, and their impact is mitigated. Previous works have provided various examples of effective implementations of RPR, which however suffer from three limitations: first, these circuits are designed using ad-hoc procedures, and no generalization is provided; second, error impact analysis is carried out statistically, thus neglecting issues like non-elementary data distribution and temporal correlation. Last, only dynamic power was considered in the optimization. In this work we propose a new generalized approach to RPR that allows to overcome all these limitations, leveraging the capabilities of state-of-the-art synthesis and simulation tools. By sacrificing theoretical provability in favor of an empirical input-based analysis, we build a design tool able to automatically add RPR to a preexisting gate-level netlist. Thanks to this method, we are able to confute some of the conclusions drawn in previous works, in particular those related to statistical assumptions on inputs; we show that a given inputs distribution may yield extremely different results depending on their temporal behavior.