A division-free algorithm for fixed-point power exponential function in embedded system

摘要

This work presents a division-free algorithm for fixed-point power exponential function (PEF) using Newton's method. Such a mechanism can improve the computational speed of PEF and is suitable for low-cost embedded systems without floating-point units (FPU). To achieve the goal, this work develops a fast square method to effectively describe a PEF in the form of multiplicative representation. Such representation can be separated into integer and fraction parts. For computing the base term of fraction part in fast square method, a division-free Newton's method is proposed in this paper. The proposed one utilizes two-stage iterations to modify the conventional solving strategy to reduce iteration times when the exponential term is positive. The experimental results show that the proposed algorithm can reduce the execution period about 1.8 times than the baseline one. Additionally, the performance of the proposed algorithm can reach five times higher than that of the system using a floating architecture. The computational precision of the proposed algorithm is also closed to that of the algorithm using floating operations.