Robust atan(y,x) on GLSL for converting XY coordinate to angle

Question

In GLSL (specifically 3.00 that I\'m using), there are two versions of atan(): atan(y_over_x) can only return angles between -PI/2, PI/2, while

Answer 1

A formula that gives an angle in the four quadrants for any value

of coordinates x and y. For x=y=0 the result is undefined.

f(x,y)=pi()-pi()/2*(1+sign(x))* (1-sign(y^2))-pi()/4*(2+sign(x))*sign(y)

   -sign(x*y)*atan((abs(x)-abs(y))/(abs(x)+abs(y)))