Dividing by constant or by variable zero

Consider the following code:

#include <iostream>

int main()
{
    double zero = 0;
    const double ZERO = 0.;
    std::cout << 0/zero << "\n"; // -nan
    std::cout << 0/0. << "\n";   // nan
    std::cout << 0/ZERO << "\n"; // nan
}

Why does 0/zero produces -nan, why it differs from 0/0. and what is the meaning of -nan?

Live demo here for clang. GCC gives -nan for all these cases. Trying to compile with MSVC leads to complile error for const values and -nan for variable.

Which compiler is the more correct by Standard in this case?