基于 CORDIC 算法求解平方根的研究与 FPGA 实现.PDFVIP

中国科技论文在线 基于CORDIC算法求解平方根的研究与FPGA 实现 刘荣华，李艳萍* （太原理工大学信息工程学院，太原 030024） 摘要：现代数字信号处理中，加减乘除运算使用最为频繁。开平方运算虽然没有上述运算使 用的那么广泛，但作为一种基本的数学运算，其在工程实践中仍然有较为重要的应用，例如 三角学，二次方程求解，数值分析，概率统计，图像处理等领域，开平方计算有很多不同的 算法，牛顿迭代法、SRT-冗余算法、非冗余算法、CORDIC 算法等，经过分析，本文采用了 更适合FPGA实现的坐标旋转数字计算（Coordinate Rotation Digital Computer,CORDIC） 这种算法来求解平方根，重点分析了对起始向量的输入坐标的选择，对定点与浮点计算的性 能做了比较，给出了用FPGA实现基于CORDIC算法的开平方计算的两种模型，并对流水线结 构的算法与Xilinx 公司 CORDIC Square Root IP核做了仿真综合性能的对比，综合报告表 明采用的算法时钟频率略低于CORDIC Square Root IP核，但资源消耗更低，而且同样可以 达到非常高的计算精度。 关键词：坐标旋转数字计算；流水线结构; 平方根 中图分类号：TN914 Research on Solving Square Root and FPGA Implementation Based on CORDIC Algorithm Liu Ronghua,Li Yanping (School of Information Engineering,Taiyuan University of Technology,TaiYuan 030024) Abstract: At modern digital signal processing,addition,subtraction ,multiplication and division are the most frequently used, Although solving the square root is not used so widely compared to the operations above,as a kind of basic mathematical operations in engineering practice, it still play an important part in many fields such as trigonometry,solving quadratic equation,Numerical Analysis,Probability and Statistics,Image processing. Various algorithms including Newton-Raphson method,SRT-Redundant method,Non-Redundant method,CORDIC can be applied to solve the square root.This paper selects the CORDIC Algorithm which is more suitable for the FPGA implementation.This paper focus on the selection of coordinates of initial vector,making a comparison to the performance between fixed-point calculation and float-point calculation,then two models based on CORDIC algorithm are given for solving square root with th