跳跃迭代的高速高精CORDIC算法及FPGA实现  

High-Speed and High-Precision CORDIC Algorithm with Skip Iteration and FPGA Implementation

作　　者：胡雄龙 陈进华[2] 乔海[2] 唐军[1] HU Xiong-long;CHEN Jin-hua;QIAO Hai;TANG Jun(Mechanical and Electrical Engineering,Jiangxi University of Science and Technology,Ganzhou Jiangxi 341000,China;Ningbo Institute of Materials Technology and Engineering,Chinese Academy of Sciences,Ningbo Zhejiang 315201,China)

机构地区：[1]江西理工大学机电工程学院,江西赣州341000 [2]中国科学院宁波材料技术与工程研究所,浙江宁波315201

出　　处：《计算机仿真》2023年第10期365-370,398,共7页Computer Simulation

基　　金：国家自然科学基金青年科学基金(51807194);宁波市科技创新2025重大专项(2019B10077,2020Z067)。

摘　　要：针对传统坐标旋转数字计算机(coordinate rotation digital computer, CORDIC)算法在计算过程中存在冗余迭代的问题,提出了一种跳跃迭代的CORDIC算法,可根据迭代残差匹配查找近似预选角度,跳过冗余迭代,减少迭代次数;对随之引起的模数因子的改变进行了分析并提出了传统加跳跃综合迭代的矫正方法,保证了计算结果的精度。在MATLAB进行仿真分析,并在现场可编程门阵列(field programmable gate array, FPGA)实现验证;结果表明,以32位输出为例;在计算正切值时,跳跃迭代平均迭代次数减少了67.91%,在计算正余弦函数时,其平均迭代次数减少了33%。因此上述算法在实时性强,硬件资源有限,精度要求高的数字信号处理系统中具有潜在的应用价值。For the traditional coordinate rotation digital computer(CORDIC)algorithm,there is a redundant iteration problem in the calculation process.This paper proposes a skip iterative CORDIC algorithm,which can find approximate preselected angles according to iterative residual matching,skip redundant iterations,and reduce the number of iterations.The consequent change in the modulus factor is analysed and a conventional plus jump synthesis iteration correction method is proposed to ensure the accuracy of the calculation results.Simulations are carried out in MATLAB and verified in a field programmable gate array(FPGA)implementation.The results show that the average number of iterations of the jump iteration is reduced by 67.91%for the calculation of the tangent and by 33%for the calculation of the sine and cosine functions,for example,with a 32-bit output.Therefore,the algorithm has potential applications in digital signal processing systems with high real-time performance,limited hardware resources and high accuracy requirements.

关 键 词：坐标旋转数字计算机算法 最佳逼近角 跳跃迭代 现场可编程门阵列 三角函数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]