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Message: [QUOTE="Lawrence D'Oliveiro, post: 3880744"] Doesn't seem to be necessary, if I interpret the following correctly <[URL]http://en.wikipedia.org/wiki/Box-Muller_transform#Polar_form[/URL]>: Given u and v, independent and uniformly distributed in the closed interval [âˆ’1, +1], set s = R2 = u2 + v2. (Clearly \scriptstyle R = \sqrt{s}.) If s = 0 or s > 1, throw u and v away and try another pair (u, v). Continue until a pair with s in the open interval (0, 1) is found. Since s is supposed to be in an open interval, I don't see how it makes any difference if u and v are chosen from an open or semiopen interval. The probability of hitting the exact endpoints is 0, after all. [/QUOTE]