- Given
*r*and φ independently uniformly distributed in (0,1], compute:- and

- Given
*x*and*y*independently uniformly distributed in [-1,1], set*r*=*x*^{2}+*y*^{2}. If*r*= 0 or*r*> 1, throw them away and try another pair (*x*,*y*). Thus, all points left after this filtering process will be uniformly distributed within a unit circle. Then, for these filtered points, compute:- and

The second method is faster because it uses only one transcendental function instead of three, even though it throws away 21% of the numbers.