## Paeth’s Method (Square Roots, Part VII)

March 13, 2018

In Graphics Gems [1], Paeth proposes a fast (but quite approximate) method for the rapid computation of hypotenuse,

$\displaystyle h=\sqrt{x^2+y^2}$.

The goal here is to get rid of the big bad $\sqrt{}$ because it is deemed “too expensive”—I wonder if that’s still actually true. First, he transforms the above equation: