位宽优化中乘法运算的一种自动范围分析方法

A range analysis in automatic word length optimization for multiplication

乘法是硬件平台中最基本的非线性运算,而且在自动位宽优化过程中,目前的范围分析方法没有在精确的范围分析结果和计算复杂度之间做很好折衷.为了在较低的计算复杂度前提下更准确地分析乘法运算结果的范围,提出了改进的仿射近似法(NAA).在改进的仿射近似法中,利用额外噪声项来表示近似产生的误差,并根据误差的特点把误差分成两部分,在不增加计算复杂度的前提下更准确地估计误差的范围.新方法的计算复杂度是O(M1),其中M1是乘法的两个操作数中非零噪声个数的和.实例分析表明,利用该方法得到的乘法结果范围的准确程度是用简单估计法得到的准确程度的1.47倍,和切比雪夫近似法的准确度接近.

To achieve more accurate result and lower computational complexity of range analysis for multiplication in automatic word length optimization, this paper presents a novel refined affine approximation method of multiplication for range analysis in automatic word length optimization, which is rtamed novel affine arithmetic approximation （NAA）. In NAA, a new noise term represents the error which is caused by approximation. This error is estimated more accurately without increasing the computational complexity. The computational complexity of NAA is O（M1 ）, where Ml denotes the total of the nonzero noise of the two multipliers. In experiments, the accuracy of the range using NAA is 1.47 times of that using trivial range estimation, and the same as that using Chebyshev approximation.