Any reason why 0.0/0.0 makes negative nan in C++?

Question

I found the following from SoloLearn:

I found that 0.0/0.0 makes negative nan(-nan). It makes sense to me that such a mathematical result is undefined, or "not a number". [...]

Furthermore, why is -nan+2^nan=nan?

For example:

#include <iostream>
using namespace std;

int main() {
    cout<<0.0/0.0<<endl;
    cout<<"important "+to_string(1.0/0.0)+"o:"<<endl;
    cout<<"ba"+to_string(0.0/0.0*-1)+"a"<<endl;
    cout<<(0.0/0.0)+2^(0.0/0.0*-1);//-nan+2^nan=nan
    return 0;
}

But this doesn't suffice my logic..

Answer 1

As far as the C++ language is concerned, the behaviour of the program is undefined. So, from C++ perspective there is no "reason" for anything about the behaviour of the program.

According to the IEEE-754 floating point standard, assuming your hardware and language implementation conform to it (they probably do), result of such division is NaN. IEEE-754 does not specify the sign of NaN for any operation. So from IEEE-754's perspective, the answer is: It just happened to be so on your system for whatever reason the language / hardware implementation has chosen (or simply for no particular reason).

In conclusion: You should never rely on sign of NaN being anything in particular. And you should generally avoid division by zero.