OPACT: Optimization of Approximate Compressor Tree for Approximate Multiplier

Approximate multipliers have attracted significant attention of researchers for designing low-power systems. The most area-consuming part of a multiplier is its compressor tree (CT). Hence, the prior works proposed various approximate compressors to reduce the area of the CT. However, the compression strategy for the approximate compressors has not been systematically studied: Most of the prior works apply their ad hoc strategies to arrange approximate compressors. In this work, we propose OPACT, a method for optimizing approximate compressor tree for approximate multiplier. An integer linear programming problem is first formulated to co-optimize CT's area and error. Moreover, since different connection orders of the approximate compressors can affect the error of an approximate multiplier, we formulate another mixed-integer programming problem for optimizing the connection order. The experimental results showed that OPACT can produce approximate multipliers with an average reduction of 24.4% and 8.4% in power-delay product and mean error distance, respectively, compared to the best existing designs with the same types of approximate compressors used.