An Efficient Method for Calculating the Error Statistics of Block-Based Approximate Adders

Adders are key building blocks of many error-tolerant applications. Recently, a number of approximate adders were proposed. Many of them are block-based approximate adders. For approximate circuits, besides normal metrics such as area and delay, the other important design metrics are the various error statistics, such as error rate (ER), mean error distance (MED), and mean square error (MSE). Given the popularity of block-based approximate adders, in this work, we propose an efficient method to obtain their error statistics. We first show how to calculate the ER. Then, we demonstrate an approach to get the error distribution, which can be used to calculate other metrics, such as MED and MSE. Our method is applicable to an arbitrary block-based approximate adder. It is accurate for the uniformly distributed inputs. Experimental results also demonstrated that it produces error metrics close to the accurate ones for various types of non-uniform input distributions. Compared to the state-of-the-art algorithm for obtaining the error distributions of block-based approximate adders, for the uniform input distribution, our method improves the runtime by up to <inline-formula><tex-math notation="LaTeX">$4.8\times 10^4$</tex-math><alternatives> <inline-graphic xlink:href="qian-ieq1-2859960.gif"/></alternatives></inline-formula> times with the same accuracy; for non-uniform input distributions, it achieves a speed-up of up to 400 times with very similar accuracy.