In this paper, we propose a scalable approximate multiplier design, scaleTRIM, that approximates the multiplication operation using fitted linear functions, also referred to as linearization. We show that multiplication operations can be completely replaced by low-cost addition and bit-wise shift operations by exploiting linearization. Moreover, our proposed design utilizes a lookup table (LUT)-based compensation unit as a novel error-reduction method. In essence, input operands are truncated to a reduced bit-width representation (i.e., h bits) based on their leading-one positions. Then, a curve-fitting method is employed to map the product term to a linear function. Additionally, a piecewise constant error-correction term is used to reduce the approximation error. To compute the piecewise constant, we divide the function space into M segments and average the errors within each segment. In particular, our multiplier supports various degrees of truncation and error compensation to offer a range of accuracy-efficiency trade-offs. The proposed multiplier improves the Mean Relative Error Distance (MRED) by about 15.2% while satisfying the efficiency constraint and improves the Power Delay Product (PDP) by about 22.8% while satisfying the accuracy and efficiency constraints compared to different state-of-the-art approximate multipliers. From a usability perspective, our evaluation of the proposed design for image classification using Deep Neural Networks (DNNs) demonstrates that scaleTRIM offers a better accuracy-efficiency trade-off than state-of-the-art approximate multiplier designs.

翻译：本文提出一种可伸缩的近似乘法器设计——scaleTRIM，通过拟合线性函数（即线性化技术）来逼近乘法运算。研究表明，利用线性化可将乘法操作完全替换为低成本加法与按位移位操作。此外，本设计创新性地采用基于查找表的补偿单元作为降误差方法。具体而言，输入操作数根据其前导1位置被截断为缩减位宽表示（即h位），随后采用曲线拟合法将乘积项映射为线性函数，并利用分段常数误差校正项降低近似误差。为计算该分段常数，我们将函数空间划分为M个区间并取各区间误差均值。特别地，本乘法器支持不同程度的截断与误差补偿，以提供多种精度-效率权衡方案。相较于当前最优近似乘法器，本设计在满足效率约束条件下将平均相对误差距离提升了约15.2%，在满足精度与效率双重约束条件下将功耗延迟积改善了约22.8%。从实用性角度而言，我们基于深度神经网络图像分类任务的评估表明：scaleTRIM相比现有最优近似乘法器设计能实现更优的精度-效率权衡。