[raymondh]

FWIW, there is a recipe for this in the Python docs[0]. It was developed in collaboration with Alan Downey and Tim Peters:

    from random import Random
    from math import ldexp

    class FullRandom(Random):

        def random(self):
            mantissa = 0x10_0000_0000_0000 | self.getrandbits(52)
            exponent = -53
            x = 0
            while not x:
                x = self.getrandbits(32)
                exponent += x.bit_length() - 32
            return ldexp(mantissa, exponent)

[0] https://docs.python.org/3/library/random.html#recipes