C++ Chudnovsky Formula for Pi

Question

I am trying to make a C++ application calculate pi for me. I have tried to implement the Chudnovsky formula with no luck.

Here is my code:

#include <iostream>
#include <cmath>

long fac(long num) {
    if (num == 1)
        return 1;
    return fac(num - 1) * num;
}

int main() {
    using namespace std;
    double pi;
    for (long k = 0; k < 10; k++) {
        pi += (pow(-1, k) * fac(6 * k) * (13591409 + (545140134 * k))) / (fac(3 * k) * pow(fac(k), 3) * pow(640320, 3 * k + 3/2));
    }
    pi *= 12;
    cout << 1 / pi << endl;
    system("pause");
    return 0;
}

The goal of this was to have the program output 10 iterations of the Chudnovsky formula. Instead, I got this:

call of overloaded `pow(int, long int&)' is ambiguous 

Answer 1

You never initialize pi, so your code has undefined behaviour.

Your fac function does not correctly handle 0 (fac(0) should be 1).

3/2 evaluates to 1 (because it uses integer division, which truncates), and this makes your formula evaluate to the completely wrong answer.

Answer 2

You almost certainly want to do all the math on doubles, to avoid lot of time-killing conversions. You probably also want to use an iterative implementation of fac instead of a recursive one (not that recursion is going to be a big problem, but this is a prime example of when recursion should really be avoided because it gains you nothing). Of course you also need to initialize pi as others have already pointed out.

#include <iostream>
#include <iomanip>
#include <cmath>

double fac(double num) {
    double result = 1.0;
    for (double i=2.0; i<num; i++)
       result *= i;
    return result;
}

int main() {
    using namespace std;
    double pi=0.0;
    for (double k = 0.0; k < 10.0; k++) {
        pi += (pow(-1.0,k) * fac(6.0 * k) * (13591409.0 + (545140134.0 * k))) 
            / (fac(3.0 * k) * pow(fac(k), 3.0) * pow(640320.0, 3.0 * k + 3.0/2.0));
    }
    pi *= 12.0;
    cout << setprecision(15) << 1.0 / pi << endl;
    return 0;
}

Answer 3

pow(-1, k) is ineffective as it is a direct translation from math formula to the code.

Use this instead:

      (k%2==1?-1.0:1.0)*fac(...

Edit:

Also your fac code is far from optimal too.