High precision Taylor Expansion and Piecewise Calculation Square Root algorithm of microcomputer protection

Abstract

Microcomputer Protection System usually needs to carry on Square Root Operations, such as Newton iterative algorithm, traditional Taylor Expansion algorithm, etc. However, there is not enough high precision to calculate for traditional Square Root Operations. Address to this issue, Taylor Expansion and Piecewise Calculation Square Root algorithm is purposed. In this algorithm, square root algorithm of Taylor Expansion and piecewise calculation are used, and then by successive approximation method the error is reduced. At last, by piecewise calculation the radicand is lessening. Simulation shows that, compared error between uniform segment method and non-uniform segment method, Taylor Expansion and Piecewise Calculation Square Root algorithm has the characters such as high precision and low computation. The precision of this algorithm is high enough to the Microcomputer Protection System, in which there is not more than the error 1.5 $\times$ 10 ${}^{-8}$ .