exp n terms 3 calls

02.exp.cpp

// 02.exp.cpp
// juanfc 2024-10-22
// calculate the factorial directly by adding n terms
// of its series development
// Look at https://en.wikipedia.org/wiki/Taylor_series
// https://gist.github.com/juanfal/2b9d94a665b6f730a79a84c98e2d62a6

#include <iostream>
using namespace std;

int main()
{
    double exp(double x, int n=10);

    for (double x = 1; x < 100; x+=10)
        cout << "exp(" << x << ")= " << exp(x) << endl;

    return 0;
}

double exp(double x, int n=10)
{
    double fact(int n);
    double pot(double b, int exponent);

    double s = 0;

    for (int i = 1; i <= n; ++i)
        s += pot(x, i)/fact(i);

    return s;
}

double fact(int n)
{
    double f = 1;
    for (int i = 2; i <= n; ++i)
        f *= i;
    return f;
}

double pot(double b, int exponent)
{
    double p = 1;
    for (int i = 0; i < exponent; ++i)
        p *= b;
    return p;
}