For those curious, here is my (outdated and frankly in need of rewriting) write-up of the miniature talk I gave last week at the Boston Lisp meeting on how to generate a floating-point number in [0,1] uniformly at random:
https://mumble.net/~campbell/2014/04/28/uniform-random-float
Some C code implementing the idea:
https://mumble.net/~campbell/2014/04/28/random_real.c
Some JavaScript code implementing the idea, slightly simplified, and without requiring 64-bit integer arithmetic: