Can overflow double to negative values?

Hi i am using g ++ compiler and i am experiencing (what i think is) not enough doubles, is it possible and if so how is the behavior defined

I downloaded the csv format of the covariance matrix (51x51) here: http://pastebin.com/r0fx1qsx

This is the code (boost is required in C ++) I use to calculate the determinant (I have since switched to long doubles and had no effect):

int determinant_sign(const boost::numeric::ublas::permutation_matrix<std ::size_t>& pm)
{
    int pm_sign=1;
    std::size_t size = pm.size();
    for (std::size_t i = 0; i < size; ++i)
        if (i != pm(i))
            pm_sign *= -1.0; // swap_rows would swap a pair of rows here, so we change sign
    return pm_sign;
}

long double determinant( boost::numeric::ublas::matrix<long double>& m ) {
    boost::numeric::ublas::permutation_matrix<std ::size_t> pm(m.size1());
    long double det = 1.0;

    if( boost::numeric::ublas::lu_factorize(m,pm) ) {
        det = 0.0;
    } else {
        for(int i = 0; i < (int)m.size1(); i++)
            det *= m(i,i); // multiply by elements on diagonal
        det = det * determinant_sign( pm );
    }
    return det;
}

      

        
        
        
      

    

As a result, I get the data -3.59916e-183

.

When I run the following matlab

code:

M = csvread('path/to/csv');
det(M)
the result I get is:

4.2014e-173

      

        
        
        
      

    

As you can see, one is (slightly) positive, whereas one is (slightly) negative