numerical precision in recursive functions

Question

I am puzzled, when evaluating the following function it produces number till F(0.8, 172, 1), but when I increase 172 to 173, the result becomes infinite. I suspect there is a numerical precision problem?

double F(double d, int c, int t) {
    // base cases
    if ((c==1 && t==1) || (c==0 && t==0))
        return 1.;
    if (c==0 || t==0)
        return 0.;
    if (t>c)
        return 0.;
    return F(d,c-1,t-1) + (c-1 - t*d)*F(d,c-1,t);
}

Answer 1

I do not know what your function is supposed to do, but given the arguments: F(0.8, 172, 1) the return value is 4.41861e+306 which is just short of the maximum value a double can represent:

// 1.79769e+308
std::cout << std::numeric_limits<double>::max() << std::endl;

When 172 is replaced with 173, the return value exceeds the maximum value a double can represent and becomes positive infinity. This is made clear by changing the return type of F to be long double which results in the value 7.56466e+308