A novel error metric for evaluating the error correction capability of approximate units

The use of Approximate Arithmetic Units (AAUs) in an error-tolerant application enhance circuit performance and reduce power consumption. Recently, a lot of technical work is reported on the Approximate High-Level Synthesis (AHLS) where these AAUs are used to create high-quality approximate system-level designs. To enhance the quality of approximate designs produced by AHLS, the existing studies primarily focus on search algorithms within AHLS, while neglecting the fact that the optimal approximate designs exhibit a higher frequency of effective error capability. Therefore, the objective of this contribution is to delve into the error correction capabilities of AAUs that have not received adequate attention and integrate them in AHLS. This effort provides new perspectives and methods to improve the quality of AHLS design exploration. To achieve this, we propose a novel metric for evaluating the error correction capabilities of AAUs, detailing its calculation method and properties. We apply this metric to two AHLS cases, and the experimental results show that the metric helps each case achieve more than a twofold improvement in exploration results and reduces the number of iterations by approximately three.