Automated Verifiability-Driven Design of Approximate Circuits: Exploiting Error Analysis

approximate computing, approximate arithmetic circuit, formal analysis, constrained verification

A fundamental assumption for search-based circuit approximation methods is the ability to massively and efficiently traverse the search space and evaluate candidate solutions. For complex approximate circuits (adders and multipliers), common error metrics, and error analysis approaches (SAT solving, BDD analysis), we perform a detailed analysis to understand the behavior of the error analysis methods under constrained resources, such as limited execution time. In addition, we show that when evaluating the error of a candidate approximate circuit, it is highly beneficial to reuse knowledge obtained during the evaluation of previous circuit instances to reduce the total design time. When an adaptive search strategy that drives the search towards promptly verifiable approximate circuits is employed, the method can discover circuits that exhibit better trade-offs between error and desired parameters (such as area) than the same method with unconstrained verification resources and within the same overall time budget. For 16-bit and 20-bit approximate multipliers, it was possible to achieve a 75% reduction in area when compared with the baseline method.