Fast inverse square root isn't that ultra fancy. It just happens that the IEEE representation lines up the exponent to the left, allowing you to do the obvious

Fast inverse square root isn't that ultra fancy. It just happens that the IEEE representation lines up the exponent to the left, allowing you to do the obvious multiply-the-exponent thing, but in integer mode, followed by a standard Newton-Raphson round. The only surprising part was that this was faster than calling the CPU's native floating point instructions.