$w == 0 will occur only when $u1 == $u2 == 1/2, which will happen rarely enough that I can't see it skewing the results noticeably - even if you only have 32-bit random numbers, you'll hit this case only 1.27 in 2^64 times.

(That 1.27 is based on my rusty attempts to calculate how many times we loop until we get $w < 1. I think the probability of a success is arcsin(1)/2, which is about 0.78.)

Hugo