Linear-time error calculation for approximate adders

Abstract

Design space exploration of Low Power Approximate Adders (LPAAs) has become significant as it successfully trades acceptable amounts of accuracy for the power, area, and delay improvements. Evaluating all potential choices in the vast design space over given application requirements and suitable error metrics makes application-oriented design space exploration quite challenging. This entails a need for input-aware, fast and accurate computation of error evaluation metrics such as Mean Squared Error (MSE) and Mean Error (ME). This paper proposes a formal approach that accurately calculates the MSE and ME of LPAAs for any given input pattern with linear time and space complexity. Experimental results exhibit at least 58 times speed up in the MSE calculation over the Monte Carlo sampling methods with 1000 samples. Furthermore, the proposed approach is integrated with an automatic LPAA generation tool to produce LPAAs with superior performance and energy-efficiency compared to their existing counterparts.