I'm trying to find an RNG to generate a stream of pseudorandom bits. I have found that Mersenne Twister (MT19937) is a widely used RNG that generates good 32-bit unsigned integers and that implementations have been done to generate apparently good double-precision floats (generating a 53-bit integer). But I don't seem to find any references to it being well-behaved on the bit side of things.
Marsaglia expressed some concerns about the randomness of Mersenne Twister that are making me doubt about using it.
Does anybody know if Mersenne Twister has a significant bias used to generate pseudorandom bits? If it is the case, does anyone know a good pseudorandom bit generator?