A Modification of the Fast Inverse Square Root Algorithm

We present a new algorithm for the approximate evaluation of the inverse square root for single-precision floating-point numbers. This is a modification of the famous fast inverse square root code. We use the same "magic constant" to compute the seed solution, but then, we apply Newton-Raphson corrections with modified coefficients. As compared to the original fast inverse square root code, the new algorithm is two-times more accurate in the case of one Newton-Raphson correction and almost seven-times more accurate in the case of two corrections. We discuss relative errors within our analytical approach and perform numerical tests of our algorithm for all numbers of the type float.