In recent years, several approximate adders have been proposed which are targeted for energy-efficient system design specific to error-tolerant applications. An approximate least significant bit (LSB) adder (ALA) is one such class of adder which is composed of two adder segments: one accurate most significant adder segment and one LSB adder segment approximated with inexact adder components. Error metrics such as mean error distance (MED), mean square error distance (MSED), and worst case error (WCE) have been used widely in existing studies to characterize and compare various approximate adders. In this article, we propose three independent algorithms to compute exact values of MED, MSED, and WCE, respectively, for an ALA. The algorithms are based on an iterative computation of intermediate parameters from least significant sub-adder block to the most significant sub-adder block constituting the ALA. The simulation results show that for 16-bit ALAs, the proposed MED and MSED computation algorithms are, respectively, about $2.4\times 10^{3}$ and $2.6\times 10^{3}$ times faster than Monte Carlo (MC) simulation with 2¹⁶ samples. Similarly, WCE computation method is $10.4\times 10^{3}$ times faster compared to the MC simulation with 2¹⁶ samples.

中文翻译：

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近似LSB加法器误差度量的快速精确计算

近年来，已经提出了几种近似加法器，它们针对特定于容错应用的节能系统设计。近似最低有效位 (LSB) 加法器 (ALA) 是一种此类加法器，它由两个加法器段组成：一个精确的最高有效加法器段和一个用不精确的加法器组件近似的 LSB 加法器段。诸如平均误差距离 (MED)、均方误差距离 (MSED) 和最坏情况误差 (WCE) 等误差指标已在现有研究中广泛用于表征和比较各种近似加法器。在本文中，我们提出了三种独立的算法来分别计算 ALA 的 MED、MSED 和 WCE 的精确值。该算法基于从最低有效子加法器块到构成 ALA 的最高有效子加法器块的中间参数的迭代计算。仿真结果表明，对于 16 位 ALA，提出的 MED 和 MSED 计算算法分别约为 $2.4\乘以 10^{3}$ 和 $2.6\乘以 10^{3}$ 比使用 2 ^{16 个}样本的Monte Carlo (MC) 模拟快几倍。同理，WCE 的计算方法是 $10.4\乘以 10^{3}$ 与 2 ^{16 个}样本的 MC 模拟相比，速度快了数倍。