Accurate Reliability Boundary Evaluation of Approximate Arithmetic Circuit

Approximate arithmetic circuit (AAC) has emerged as a promising high-performance and energy-efficient circuit paradigm, which can be used in many applications with inherent error tolerance. To guarantee the usability of AACs and the availability of resilient applications, it is necessary to analyze the reliability of AACs. Most current literature focus on the error characteristics of AACs and few methods can be applied to estimate the reliability of AACs. These methods mostly have exponential time complexities and evaluate the average reliability assuming the input combinations are equally likely. In reality, the primary input (PI) signals can be given with any probability from 0 to 1. In this article, we assume that the PIs have random signal probabilities and propose approaches to reliability boundary estimation for AACs. First, we propose a new efficient and accurate method to evaluate the reliability of AACs. The method mainly calculates the AAC reliability for an input vector set, and furthermore, during the calculation, the correlation problem is considered to increase accuracy. Then, based upon the proposed AAC reliability evaluation method, we present the approaches to finding the reliability boundary. Randomly given signal probabilities of every PI, two heuristic search algorithms are utilized to find the lowest reliability. A comparison of the results on three series of AACs and the circuits in the EvoApprox8b library confirms that the proposed reliability evaluation method is more accurate and efficient than the previous method. Further experiments verify the plausibility of the calculated reliability boundary of AACs.