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.

中文翻译：

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珠峰

近似计算已成为具有固有错误恢复能力的应用程序的一种有效设计方法。低功耗近似加法器 (LPAA)，例如 IMPACT 和 InXA，被提倡作为近似计算硬件的构建块。为了实际采用，需要预先评估由这些单元引起的误差，并与应用程序的最大允许误差范围进行比较。为了解决这个问题，我们提出了 PEAL，一种概率错误分析方法论低功耗近似单层和多层加法器架构，同时考虑给定多位加法器设计的输入操作数的每一位的可变概率。PEAL 是高度通用的、线性可扩展的，并且适用于任何加法器类型。该分析提供了成功的概率，这对于单层加法器架构是准确的，并为多层架构提供了一个下限。我们已经证明，只有当输入概率非常高（>0.8）或非常低（<0.2）时，最先进的 LPAA 才能作为近似计算的有效构建块。有趣的是，据我们所知，采用最广泛的最先进的 LPAA 单元都没有表现出对中等概率（0.3-0.7）的有效性。我们还分析解释了这种可用性限制的原因并提出了解决方案。而且，