Modified Fast Inverse Square Root and Square Root Approximation Algorithms: The Method of Switching Magic Constants

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 NewtonRaphson method and demanding that the maximal error is as small as possible. ...

Fast calculation of inverse square root with the use of magic constant - analytical approach

We present a mathematical analysis of transformations used in fast calculation of inverse square root for single-precision floating-point numbers. Optimal values of the so called magic constants are derived in a systematic way, minimizing either absolute or relative errors at subsequent stages of the discussed algorithm.

An Approximation for the Inverse Square Root Function

Fast Floating Point Square Root

Hain and Freire have proposed different floating point square root algorithms that can be efficiently implemented in hardware. The algorithms are compared and evaluated on both performance and precision.

High-Speed Double-Precision Computation of Reciprocal, Division, Square Root and Inverse Square Root

A new method for the high-speed computation of double-precision floating-point reciprocal, division, square root, and inverse square root operations is presented in this paper. This method employs a second-degree minimax polynomial approximation to obtain an accurate initial estimate of the reciprocal and the inverse square root values, and then performs a modified Goldschmidt iteration. The hi...