指数函数CORDIC算法的FPGA定点化技术  

FPGA Fixed-Point Technology of Exponential Function Achieved by CORDIC Algorithm

作　　者：唐文明[1] 刘桂雄[1] 

机构地区：[1]华南理工大学机械与汽车工程学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2016年第7期9-14,共6页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家重大科学仪器设备开发专项(2013YQ230575);广州市科技计划项目(201509010008)~~

摘　　要：CORDIC算法广泛应用于多种超越函数求值,但其通用迭代算法难以用现场可编程门阵列(FPGA)计算宽范围定义域指数函数求解.为此,文中提出一种FPGA定点化技术,通过收敛域扩张与迭代结构优化实现CORDIC算法的指数函数求值器.首先,应用区间压缩方法实现指数函数CORDIC算法的收敛域扩张;其次,对CORDIC算法的迭代结构进行优化;最后,通过对指数函数求值器的仿真分析与FPGA实现,采用15级流水线结构,用双曲系统CORDIC算法求解指数函数,实现指数函数CORDIC算法的收敛域扩张.仿真与实验表明:相比于通用CORDIC算法,所提算法的迭代模式节省约1/3硬件资源,少至2个乘法单元,使收敛域由[-1.1182,1.1182]扩张到[-6,6],运算结果相对误差达10-3.Although CORDIC algorithm has been widely used in various transcendental functions, its general iterativealgorithm is inefficient in using FPGA （Field Programmable Gate Array） to solve the exponential function in awide-range domain. In order to solve this problem, an FPGA fixed-point technology, which expands the convergenceregion and optimizes the iteration structure to implement CORDIC algorithm solver, is designed. In the investigation, firstly, range compression method is employed to realize the convergence domain expansion of exponentialfunction achieved by CORDIC algorithm. Secondly, the iteration structure of CORDIC algorithm is optimized.Then, the exponential function achieved by CORDIC algorithm is analyzed in a simulative way and implemented inFPGA. Finally, a 15-grade pipeline structure as well as a hyperbolic method is used to implement the expansion inconvergence domain of CORDIC algorithm. Simulated and experimental results show that, in comparison with thegeneral CORDIC algorithm, the proposed algorithm saves about 1/3 hardware resources, uses only two DSP multiplexerunits, expands the convergence domain from [ -1.1182, 1.1182] to [ - 6 ,6 ] , and achieves a relative errorlow to 10^-3.

关 键 词：CORDIC算法 指数函数 区间压缩 收敛域 迭代结构优化 现场可编程门阵列 

分 类 号：TH878.2[机械工程—仪器科学与技术]