Approximate computing (AC) has become a prominent solution to improve the performance, area, and power/energy efficiency of a digital design at the cost of output accuracy. We propose a novel scalable approximate multiplier that utilizes a lookup table-based compensation unit. To improve energy-efficiency, input operands are truncated to a reduced bitwidth representation (e.g., h bits) based on their leading one positions. Then, a curve-fitting method is employed to map the product term to a linear function, and a piecewise constant error-correction term is used to reduce the approximation error. For computing the piecewise constant error-compensation term, we partition the function space into M segments and compute the compensation factor for each segment by averaging the errors in the segment. The multiplier supports various degrees of truncation and error-compensation to exploit accuracy-efficiency trade-off. The proposed approximate multiplier offers better error metrics such as mean and standard deviation of absolute relative error (MARED and StdARED) compare to a state-of-the-art integer approximate multiplier. The proposed approximate multiplier improves the MARED and StdARED by about 38% and 32% when its energy consumption is about equal to the state-of-the-art approximate multiplier. Moreover, the performance of the proposed approximate multiplier is evaluated in image classification applications using a Deep Neural Network (DNN). The results indicate that the degradation of DNN accuracy is negligible especially due to the compensation properties of our approximate multiplier.

翻译：近似计算（AC）已成为在牺牲输出精度的前提下提升数字设计性能、面积和功耗/能效的重要解决方案。我们提出了一种新颖的可伸缩近似乘法器，采用基于查找表的补偿单元。为提升能效，输入操作数根据其前导一位位置被截断为简化的位宽表示（例如h位）。随后，采用曲线拟合方法将乘积项映射为线性函数，并利用分段常数误差校正项来降低近似误差。为计算分段常数误差补偿项，我们将函数空间划分为M个区间，通过取各区间内误差的平均值来计算每个区间的补偿因子。该乘法器支持不同程度的截断与误差补偿，以利用精度-效率权衡。与最先进的整数近似乘法器相比，所提出的近似乘法器在平均绝对相对误差（MARED）和标准绝对相对误差（StdARED）等误差指标上表现更优。当能耗与最先进近似乘法器大致相当时，该乘法器将MARED和StdARED分别改善了约38%和32%。此外，我们使用深度神经网络（DNN）在图像分类应用中评估了所提近似乘法器的性能。结果表明，尤其是得益于该近似乘法器的补偿特性，DNN精度的退化几乎可忽略不计。