微机保护测控装置定点数的开方计算方法

Fixed-point square root algorithm for microprocessor-based protection and monitoring devices

微机保护测控装置中经常遇到开方计算,其计算速度和精度直接影响到微机保护测控装置的性能。牛顿迭代法用于开方计算的主要难点是选取合适的迭代初值。分析了牛顿迭代法应用于开方计算所具有的特征,并利用其特征针对2种不同形式的开方运算分别提出了相对误差小且速度快的迭代初值选取方法。对于整数开方计算,根据被开方数二进制的位数确定最优的迭代初值;对于复数模形式的开方计算,根据复数的实部和虚部确定最优的迭代初值。与工程上传统采用的算法相比,该算法计算精度更高,计算量小(至多进行一次除法运算),主要针对定点数(整型数)的计算,但其算法思想及其关于迭代初值的选取方法和结论对于浮点数的开方计算也具有指导意义。

Square root calculation is very normal in microprocessor-based protection and monitoring devices,and its speed and precision influence device performance directly. Selecting proper initial value is the key in application of Newton iteration. The characteristics of Newton iteration method used in square root calculation is analyzed,based on which the way to select the proper initial value is proposed for two kinds of faster and more precise square root calculation. For the integers,the initial value is Jet according to its binary bit number;for the magnitude of complex,the initial value is set according to its real and imaginary parts. The proposed algorithm is simpler（at most one division operation ） and more precise than the classical square root calculations. Though the proposed square root algorithm is discussed for fixed-point number（integer）,its concept and the way of initial value selection is useful for floating-point number.