一种基于CORDIC算法的高精度反正切求解  

A high precision arctangent solution based on CORDIC algorithm

作　　者：仲雅莉 吴俊辉 刘炫 高萍 段晓辉[1,4] Zhong Yali;Wu Junhui;Liu Xuan;Gao Ping;Duan Xiaohui(National Supercomputing Center in Wuxi,Wuxi 214072,China;Jiangnan University,Wuxi 214122,China;Shandong University,Jinan 250100,China;Tsinghua University,Beijing 100084,China)

机构地区：[1]国家超级计算无锡中心,江苏无锡214072 [2]江南大学,江苏无锡214122 [3]山东大学,山东济南250100 [4]清华大学,北京100084

出　　处：《电子技术应用》2022年第1期12-17,共6页Application of Electronic Technique

基　　金：国家重点研发计划(2019YFA0709400);国家自然科学基金青年基金(62102114)。

摘　　要：传统的CORDIC(坐标旋转计算机)算法进行高精度反正切求解时存在迭代次数多、收敛速度慢、资源消耗大等问题,提出一种改进的高精度CORDIC算法。该方法利用传统的CORDIC算法迭代数次后得到正弦信息,并利用角度和正弦值近似的原理,对迭代后的结果进行误差补偿,有效提高了相同迭代步数下的计算精度。实验数据表明:32位改进的CORDIC算法,保证绝对误差小于5×10-9情况下,查找表资源消耗降低了64.8%,触发器资源消耗降低了35.3%,输出时延降低了53.3%。在分子动力学应用场景下,触发器资源消耗可降低63.2%,输出时延可降低60%。改进的CORDIC算法在资源消耗、输出时延方面优于传统CORDIC算法,适用于高精度计算的场景。The traditional CORDIC(Coordinate Rotation Computer)algorithm has many iterations,slow convergence speed,and large resource consumption for high-precision arctangent.An improved high-precision CORDIC algorithm is proposed.This method uses the traditional CORDIC algorithm to obtain the sine information after several iterations,and uses the sine value to compensate the error of iteration results,which effectively improves the calculation accuracy.Experimental data shows that the 32 bit improved CORDIC algorithm ensures that the absolute error is less than 5×10;,the resource consumption of the lookup table is reduced by64.8%,the resource consumption of the flip-flop is reduced by 35.3%,and the output delay is reduced by 53.3%.In molecular dynamics application scenarios,flip-flop resource consumption can be reduced by 63.2%,and output delay can be reduced by60%.The improved CORDIC algorithm is superior to the traditional CORDIC algorithm in terms of resource consumption and output delay,and is suitable for high-precision computing applications.

关 键 词：反正切求解 迭代收敛 误差补偿 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]