Algorithms for Calculating the Square Root and Inverse Square Root Based on the Second-Order Householder's Method

This article proposes a set of algorithms for calculating the square root and inverse square root for normalized single and double precision floating-point numbers. They are based on the combination of the Householder's method of cubic convergence and the Newton-Raphson method of quadratic convergence using the magic constant to obtain the initial approximation. The advantage of the algorithms is to increase the accuracy of calculations of these functions without the use of division operation and lookup tables.