Inverse sqrt for fixed point

Question

I am looking for the best inverse square root algorithm for fixed point 16.16 numbers. The code below is what I have so far(but basically it takes the square root and divide

Answer 1

The trick is to apply Newton's method to the problem x - 1/y^2 = 0. So, given x, solve for y using an iterative scheme.

Y_(n+1) = y_n * (3 - x*y_n^2)/2

The divide by 2 is just a bit shift, or at worst, a multiply by 0.5. This scheme converges to y=1/sqrt(x), exactly as requested, and without any true divides at all.

The only problem is that you need a decent starting value for y. As I recall there are limits on the estimate y for the iterations to converge.