一种面向FPGA的指/对数函数求值算法  

FPGA-oriented evaluation algorithm for exponential and logarithm functions

作　　者：牟胜梅[1] 李兆刚[2] 

机构地区：[1]海军工程大学计算机工程系,武汉430033 [2]通信指挥学院训练部,武汉430010

出　　处：《计算机工程与应用》2011年第33期59-61,共3页Computer Engineering and Applications

基　　金：海军工程大学自然科学基金(No.HGDQNJJ10028)

摘　　要：CORDIC算法常用于高效地实现多种超越函数求值,但算法的通用性使其无法针对具体函数进行优化。提出一种统一的指数/对数函数迭代求值算法LnE,实现方式与CORDIC算法类似,每次迭代同样只需进行移位、加法和简单的判断操作,拥有线性收敛速度,但LnE算法具备更多优势:只需x、y两条通路;每次迭代均进行加法操作,不需根据迭代系数di选择加法/减法,控制简单;不需进行扩展因子补偿;不需重复某些迭代以保证收敛。因此LnE算法的迭代次数和每次迭代的开销均小于CORDIC算法,相对于CORDIC算法可节省1/3以上的面积开销。CORDIC algorithm has been widely used for efficient evaluation of transcendental functions in hardware,but its generality prevents it to be optimized according to a certain function.A unified evaluation algorithm for exponential and logarithm function called LnE is proposed.It can be implemented only by shift and addition with linear convergence speed just as CORDIC algorithm does,but shows great advantages over CORDIC algorithm.LnE only needs x datapath and y datapath, and addition is needed independent of iteration coefficients di during all the iteration,which can reduce the cost of control. Moreover,LnE avoids the process of scale factor compensation and can converge without repeating some iteration.So,the number of iteration and cost of each iteration in LnE are both less than those of CORDIC,which can spare at least 1/3 of the area estate compared to CORDIC algorithm.

关 键 词：坐标旋转数字计算(CORDIC)算法 指数函数 对数函数 硬件实现 

分 类 号：TP302.2[自动化与计算机技术—计算机系统结构]