NAN -> distinguish between a division by zero and an exponent with a very large negative value

I included a check for nan's in my testsuite.

Now a SIGFPE is thrown at the following line

const double retVal =exp(exponent); 

The exponent has a value of approximately value -4000. This is of course very near to zero and without the nan check the calculation goes on with zero.

The signal SIGFPE is now been thrown. I assume that this is a denormal number (represented as NAN).

How can I distinguish between a division by zero and an exponent with a very large negative value?

In the second case, doing further calculations with zero works in my case, since I do not need to distinguish between +0 and -0.

EDIT: I tried what @user2079303 suggested. My code looks like this

#include <signal.h>
void fpe_handler(int signo, siginfo_t *info, void *context) {
    switch(info->si_code) {
        case FPE_INTDIV: // division by zero
            break;
        case FPE_FLTUND: // underflow
            break;
        // other cases ...
    }
}

int main() {
    struct sigaction action = {};
    action.sa_flags     = SA_SIGINFO;
    action.sa_sigaction = fpe_handler;
    sigaction(SIGFPE, &action, NULL);
    const double a = 0.0/0.0;
    if (a>0) 
        return 0;
    else
        return 1;
}

This compiles, but does not throw a signal or an error message.