Improving the accuracy of the fast inverse square root algorithm

We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or similar computational cost. The main idea of our work consists in modifying the Newton-Raphson method and demanding that the maximal error is as small as possible. Such modification is possible when the distribution of Newton-Raphson corrections is not symmetric (e.g., if they are non-positive functions).