DREAMx: A Data-Driven Error Estimation Methodology for Adders Composed of Cascaded Approximate Units

Abstract

Due to the significance and broad utilization of adders in computing systems, the design of low-power approximate adders (LPAAs) has received a significant amount of attention from the system design community. However, the selection and deployment of appropriate approximate modules require a thorough design space exploration, which is (in general) an extremely time-consuming process. Toward reducing the exploration time, different error estimation techniques have been proposed in the literature for evaluating the quality metrics of approximate adders. However, most of them are based on certain assumptions that limit the usability of such techniques for real-world settings. In this work, we highlight the impact of those assumptions on the quality of error estimates provided by the state-of-the-art techniques and how they limit the use of such techniques for real-world settings. Moreover, we highlight the significance of considering input data characteristics to improve the quality of error estimation. Based on our analysis, we propose a systematic data-driven error estimation methodology, DREAMx, for adders composed of cascaded approximate units, which covers a predominant set of LPAAs. DREAMx in principle factors in the dependence between input bits based on the given input distribution to compute the probability mass function (PMF) of error value at the output of an approximate adder. It achieves improved results compared to the state-of-the-art techniques while offering a substantial decrease in the overall execution(/exploration) time compared to exhaustive simulations. Our results further show that there exists a delicate tradeoff between the achievable quality of error estimates and the overall execution time.