High-precision and fast square root algorithm based on Newton iteration method

As the square root calculation of full-wave Fourier algorithm takes longer time,the real-time performance of microcomputer-based protection is seriously influenced. A method based on Newton iteration is proposed. To reduce the iteration times,it can select the initial value very close to the real square root with error less than 2-9 by only executing displacement instruction,referring a 256 - unit table once,and doing once or twice multiply operations with DSP hardware multiplier. The algorithm is programmed with assembly language and tested on TI DSP integrated development platform. The results of sampling tests show that,the iteration time of the square root operation for the fixed-point numbers ranging from 0000 0004.0000 H to 01FF FFFF.FFFF H is not greater than 3 with the iteration precision better than 2-16. This method needs smaller memory,very suitable for the embedded microcomputer with hardware multipliers.