Approximate computing has emerged as a new paradigm for high-performance and energy-efficient design of circuits and systems. For the many approximate arithmetic circuits proposed, it has become critical to understand a design or approximation technique for a specific application to improve performance and energy efficiency with a minimal loss in accuracy. This article aims to provide a comprehensive survey and a comparative evaluation of recently developed approximate arithmetic circuits under different design constraints. Specifically, approximate adders, multipliers, and dividers are synthesized and characterized under optimizations for performance and area. The error and circuit characteristics are then generalized for different classes of designs. The applications of these circuits in image processing and deep neural networks indicate that the circuits with lower error rates or error biases perform better in simple computations, such as the sum of products, whereas more complex accumulative computations that involve multiple matrix multiplications and convolutions are vulnerable to single-sided errors that lead to a large error bias in the computed result. Such complex computations are more sensitive to errors in addition than those in multiplication, so a larger approximation can be tolerated in multipliers than in adders. The use of approximate arithmetic circuits can improve the quality of image processing and deep learning in addition to the benefits in performance and power consumption for these applications.

中文翻译：

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近似算术电路：调查、表征和最新应用


近似计算已成为电路和系统的高性能和节能设计的新范例。对于提出的许多近似算术电路，了解特定应用的设计或近似技术变得至关重要，以在精度损失最小的情况下提高性能和能源效率。本文旨在对不同设计约束下最近开发的近似算术电路进行全面的调查和比较评估。具体来说，在性能和面积优化下综合和描述了近似加法器、乘法器和除法器。然后将误差和电路特性推广到不同类别的设计。这些电路在图像处理和深度神经网络中的应用表明，错误率或错误偏差较低的电路在简单计算（例如乘积之和）中表现更好，而涉及多个矩阵乘法和卷积的更复杂的累加计算则很脆弱导致计算结果出现较大误差偏差的单边误差。这种复杂的计算对加法运算的误差比乘法运算更敏感，因此乘法器比加法器可以容忍更大的近似值。使用近似运算电路除了可以提高这些应用的性能和功耗之外，还可以提高图像处理和深度学习的质量。