There is a loop of is it close enough or not something like that. It is a brute force. Atan2 purely looks like that to me.

It’s not just guessing, there is theory to prove convergence and rates of converge.

Many algorithms require iteration.

I don't think these functions are programmed as it looks like they are in their Math form. Atan2 is something like a line-to rotating, if the given point is close to any pixel of line-to, returns how many times the line to is rotated. It is almost a motion but an algorithm. This is why I'm telling it is a brute force.