We present the automatic formal verification of a state-of-the-art algorithm from the GMP library that computes the square root of a 64-bit integer. Although it uses only integer operations, the best way to understand the program is to view it as a fixed-point arithmetic algorithm that implements Newton's method. The C code is short but intricate, involving magic constants and intentional arithmetic overflows. We have verified the algorithm using the Why3 tool and automated solvers such as Gappa.