Approximate computing has emerged as an efficient design approach for applications with inherent error resilience. Low-power approximate adders (LPAAs), for instance, IMPACT and InXA, are being advocated as building blocks for approximate computing hardware. For their practical adoption, the error caused by these units needs to be pre-evaluated and compared with maximum allowable error bounds for an application. To address this problem, we present PEAL, a Probabilistic error analysis methodology for Low-power Approximate Single and Multi-layered Adder Architectures , while considering variable probabilities for each bit of input operands for a given multi-bit adder design. PEAL is highly generic, linearly scalable, and applicable to any adder type. The analysis provides probability of success, which is accurate for single-layered adder architectures and provides a lower bound for multi-layered architectures. We have shown that state-of-the-art LPAAs can serve as effective building blocks of approximate computing only when the input probabilities are either very high (>0.8) or very low (<0.2). Interestingly, none of the state-of-the-art LPAA units, which to the best of our knowledge are the most widely adopted, has demonstrated effectiveness for mid-range probabilities (0.3–0.7). We have also analytically explained the cause of this usability limitation and proposed its solution. Moreover, we have proposed a method for estimating the Mean-squared Error of datapaths composed of LPAAs, to quantify the magnitude of error introduced in the output due to approximation of the adder units.

Low-power approximate adders provide basic building blocks for approximate computing hardware that have shown remarkable energy efficiency for error-resilient applications (like image/video processing, computer vision, etc.), especially for battery-driven portable systems. In this paper, we present a novel scalable, fast yet accurate analytical method to evaluate the output error probability of multi-bit low power adders for a predetermined probability of input bits. Our method recursively computes the error probability by considering the accurate cases only, which are considerably smaller than the erroneous ones. Our method can handle the error analysis of a wider-range of adders with negligible computational overhead. To ensure its rapid adoption in industry and academia, we have open-sourced our LabVIEW and MATLAB libraries.