How to turn a uniform random bit generator into a uniform random floating-point [0,1] generator in JavaScript

uniform_01.js
human-readable source code and explanation
uniform_01.html
example application
uniform_01.asm.js
hand-compiled asm.js source code
uniform_01.asm.html
example application, with asm.js
histogram_01.html
d3.js histogram to spot-check uniformity
histogram_01.asm.html
d3.js histogram to spot-check uniformity slightly faster