A Sub-Range Error Characterization based Selection Methodology for Approximate Arithmetic Units

Error characterization is a fundamental step in selection of a suitable approximate arithmetic unit (AU) for a given application. For error characterization and comparison of complex AUs, researchers rely on simulations, which are typically done over the full range of input operands of an AU while assuming uniform distribution. In this paper, we demonstrate that the inputs to AUs in many practical applications are neither uniform nor spread over the full range and the error behavior of approximate AUs may vary across different sub-ranges of inputs (segments of the full range). We present a novel design methodology for selecting suitable approximate AUs for an application, which incorporates the sub-range error behavior of AUs, statistical analysis of application input, and a selection algorithm. We demonstrate the efficacy of the proposed methodology using two practical applications (JPEG compression and Gaussian filtering) with several approximate multipliers from the literature. The results show that the multiplier suggested by our proposed methodology leads to an increase in application-level quality (increase in PSNR of up to 9dB for JPEG and 7dB for Gaussian filtering) when compared to the multiplier from the traditional full-range based error characterization.