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.

低功耗近似加法器（LPAA）的设计空间探索非常重要，因为它成功地以可接受的精度交换了功率，面积和延迟改进。根据给定的应用程序需求和合适的错误度量来评估广阔设计空间中的所有潜在选择，使面向应用程序的设计空间探索颇具挑战性。这需要对错误评估指标（例如均方误差（MSE）和均方误差（ME））进行感知输入，快速且准确的计算。本文提出了一种正式方法，该方法可以精确计算任何给定具有线性时间和空间复杂度的输入模式下LPAA的MSE和ME。实验结果显示，与使用1000个样本的蒙特卡洛采样方法相比，MSE计算至少快58倍。此外，