一种满刻度无溢出的圆周旋转CORDIC算法

A Full-scale and Overflow-free Circular Rotation CORDIC Algorithm

CORDIC算法是一种经典的算法,在其工程实现中,有限的级数和处理位数可能会发生溢出,导致输出结果产生误差甚至符号位翻转。以圆周旋转CORDIC算法为例提出一种算法,在每级CORDIC运算之后,通过构建当前角度跟踪理论角度值对本级输出的余弦和正弦值逐级进行修正,并在最后一级根据输入相位初值对输出结果进行修正。经过仿真验证,本方法能够解决每级的溢出问题,输出结果能完整覆盖-1~1的赋值区间,并和相位初值的理论cos/sin值保持一致,实现高精度、满刻度输出。

The CORDIC algorithm is a classic algorithm.In its engineering implementation, the limited stage number and processing bits may overflow, which results in the output error or even sign bit reverse.Taking the circular rotation CORDIC algorithm as an example, this paper proposes an algorithm.After each stage of CORDIC operation, the cosine and sine values of the output of this stage are corrected step by step through constructing the current angle tracking theoretical angle value, and in the last stage, the output result is corrected according to the initial input phase value.This method can solve the overflow problem of each stage through simulation verification, and the output result can completely cover the assignment range from-1 to 1,and is consistent with the theoretical cos/sin value of the initial phase value, so high-precision and full-scale output is achieved.