Generating random floating-point values based on random bit stream

Given a random source (a generator of random bit stream), how do I generate a uniformly distributed random floating-point value in a given range?

Assume that my random source looks something like:

unsigned int GetRandomBits(char* pBuf, int nLen);

And I want to implement

double GetRandomVal(double fMin, double fMax);

Notes:

• I don't want the result precision to be limited (for example only 5 digits).
• Strict uniform distribution is a must
• I'm not asking for a reference to an existing library. I want to know how to implement it from scratch.
• For pseudo-code / code, C++ would be most appreciated