exp function using c++

Question

I can't figure out why I keep getting the result 1.#INF from my_exp() when I give it 1 as input. Here is the code:

double factorial(const int k)
{
    int prod = 1;
    for(int i=1; i<=k; i++)
        prod = i * prod;
    return prod;
}

double power(const double base, const int exponent)
{
    double result = 1;
    for(int i=1; i<=exponent; i++)
        result = result * base;
    return result;
}

double my_exp(double x)
{
    double sum = 1 + x;
    for(int k=2; k<50; k++)
        sum = sum + power(x,k) / factorial(k);
    return sum;
}

Answer 1

You have an integer overflow in your factorial function. This causes it to output zero. 49! is divisible by 2^32, so your factorial function will return zero.

Then you divide by it causing it to go infinity. So the solution is to change prod to double:

double prod = 1;

Answer 2

Instead of completely evaluating the power and the factorial terms for each term in your expansion, you should consider how the k'th term is related to the k-1'th term and just update each term based on this relationship. That will avoid the nasty overflows in your power and factorial functions (which you will no longer need). E.g.

double my_exp(double x)
{
    double sum = 1.0 + x;
    double term = x;                 // term for k = 1 is just x
    for (int k = 2; k < 50; k++)
    {
        term = term * x / (double)k; // term[k] = term[k-1] * x / k
        sum = sum + term;
    }
    return sum;
}