Effective usage of approximate circuits for various performance trade-offs requires accurate computation of error. MCAC is a novel model counting framework for exact computation of several average and worst-case error metrics that are used to evaluate approximate circuits. Unlike other methods in the literature, our framework uses the same error miter for all metrics. It requires a single synthesis of the system consisting of the exact and approximate circuits followed by a subtractor that finds the difference of the two outputs. Existing miter-based methods require multiple calls to the model counter, one for each output of the miter. MCAC uses the CNF formula of the system to compute all metrics. Our algorithm converts the formula to a tree and uses message passing to compute all metrics. We propose data structures to efficiently store and perform sparse computations required for conversion to a tree and message passing. Results for all the error metrics for several benchmark instances show a significant speedup over using off-the-shelf model counters along with specialized miters for each metric.

翻译：为有效利用近似电路实现各种性能权衡，需要精确计算误差。MCAC是一种新颖的模型计数框架，用于精确计算评估近似电路常用的多种平均误差和最坏情况误差指标。与文献中其他方法不同，我们的框架对所有指标使用相同的误差验证器。它只需综合一次由精确电路和近似电路组成的系统，再通过减法器找出两个输出的差值。现有的基于验证器的方法需要对模型计数器进行多次调用，验证器的每个输出对应一次调用。MCAC利用系统的合取范式公式计算所有指标。我们的算法将公式转换为树结构，并通过消息传递计算所有指标。我们提出了有效存储并执行转换为树结构和消息传递所需的稀疏计算的数据结构。多个基准实例的所有误差指标结果表明，与使用现成模型计数器配合各指标专用验证器的方法相比，我们的方法实现了显著加速。