Improving the accuracy of the fast inverse square root algorithm.

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