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Abstract-Aggressive requirements for low power and high performance in VLSI designs have led to increased interest in approximate computation. Approximate hardware modules can achieve improved energy efficiency compared to accurate hardware modules. While a number of previous works have proposed hardware modules for approximate arithmetic, these works focus on solitary approximate arithmetic operations. To utilize the benefit of approximate hardware modules, CAD tools should be able to quickly and accurately estimate the output quality of composed approximate designs. A previous work [10] proposes an interval-based approach for evaluating the output quality of certain approximate arithmetic designs. However, their approach uses sampled error distributions to store the characterization data of hardware, and its accuracy is limited by the number of intervals used during characterization.In this work, we propose an approach for output quality estimation of approximate designs that is based on a lookup table technique that characterizes the statistical properties of approximate hardwares and a regression-based technique for composing statistics to formulate output quality. These two techniques improve the speed and accuracy for several error metrics over a set of multiply-accumulator testcases. Compared to the interval-based modeling approach of [10], our approach for estimating output quality of approximate designs is 3.75× more accurate for comparable runtime on the testcases and achieves 8.4× runtime reduction for the error composition flow. We also demonstrate that our approach is applicable to general testcases.

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Abstract-Transistor aging due to bias temperature instability (BTI) is a major reliability concern in sub-32nm technology. Aging decreases performance of digital circuits over the entire IC lifetime. To compensate for aging, designs now typically apply adaptive voltage scaling (AVS) to mitigate performance degradation by elevating supply voltage. Varying the supply voltage of a circuit using AVS also causes the BTI degradation to vary over lifetime. This presents a new challenge for margin reduction in conventional signoff methodology, which characterizes timing libraries based on transistor models with pre-calculated BTI degradations for a given IC lifetime. Many works have separately addressed predictive models of BTI and the analysis of AVS, but there is no published work that considers BTI-aware signoff that accounts for the use of AVS during IC lifetime. This motivates us to study how the presence of AVS should affect aging-aware signoff. In this paper, we first simulate and analyze circuit performance degradation due to BTI in the presence of AVS. Based on our observations, we propose a ruleof-thumb for chip designers to characterize an aging-derated standardcell timing library that accounts for the impact of AVS. According to our experimental results, this aging-aware signoff approach avoids both overestimation and underestimation of aging -either of which results in power or area penalty -in AVS enabled systems.