WEID: Worst-case Error Improvement in Approximate Dividers

Abstract

Approximate integer dividers suffer from unreasonably high worst-case relative errors (such as 50% or 100%), which can adversely affect the application-level output. In this paper, we propose WEID, which is a novel lightweight method to improve the worst-case relative errors in approximate integer dividers. We first present an in-depth analysis to gain insights into the cause of the high worst-case relative error. Based on our insights, we propose a novel method to detect when an error occurs in an approximate divider, and modify the output to reduce the error. Further, we present the hardware realization of WEID method and demonstrate that it can be generically coupled with several state-of-the-art approximate dividers. Our results show that for 32-by-16 dividers, WEID reduces worst-case relative errors from 100% to $\sim 20$%, while still achieving $\sim 80$% and $\sim 70$% reduction in delay and energy compared to an accurate array divider.