Should C++ std::uniform_real_distribution

I was trying to generate some random doubles in C++ (MSVC, though that isn't too important to me—I just didn't have another compiler to test) and I noticed that my quick program never generated negative numbers:

#include <iostream>
#include <random>
#include <ctime>

int main() {
    std::mt19937 generator(clock());
    std::uniform_real_distribution<double>
        rand_dbl(std::numeric_limits<double>::min(),
                 std::numeric_limits<double>::max());

    std::cout << "Double Limits: (" << std::numeric_limits<double>::min()
              << "," << std::numeric_limits<double>::max() << ")"
              << std::endl << std::endl;

    int total_neg = 0;
    for (int i=0; i<100; i++) {
        double d = rand_dbl(generator);
        if (d<0) total_neg++;
        std::cout << d << " ";
    }
    std::cout << std::endl << std::endl
              << "Total negative random double is: " << total_neg << std::endl;

    return 0;
}

No matter how many numbers I have it generate, it never generates a negative one. I understand why most of the numbers generated are in the 10³⁰⁷ - 10³⁰⁸ range (which isn't exactly what I wanted), but not why the numbers are always positive. I tried a few different generators (default, mt19937, minstd_rand0) without any difference in this aspect.

Can anyone describe why this is the case?