Efficient Floating -Point Square Root and Reciprocal Square Root Algorithms

Several algorithms for calculating square roots and inverse square roots are developed. These are oriented on normalized numbers with a floating point for single and double accuracy. The fast inverse square root (FISR) method, on the basis of which the new algorithms have been created, is described. This method demonstrates high efficiency for two iterations with single accuracy and three iterations with double accuracy. The Householder iteration method, which has second order convergence, is used. The optimal parameters of the iterative process are calculated by balancing the values of the positive and negative errors. In comparison with known algorithms, the proposed algorithms reduce the error during the first iteration. For single accuracy, 23.67 correct bits are obtained during the second iteration and for double accuracy 52.00 correct bits are obtained during the third iteration. The same results are obtained during the square root calculation. For single accuracy, 23.43 correct bitsare obtained during the second iteration and for double accuracy 52.00 correct bits are obtained during the third iteration. An algorithm has been developed that performs one multiplication operation less without losing accuracy. This increases the speed of computing the reciprocal of the square root by 12 %.