expr series with functions. Two ways

04.fexp.cpp

// 01.exp.cpp
// juanfc 2024-10-23
// expr series with functions. Two ways
// https://en.wikipedia.org/wiki/Taylor_series
// https://gist.github.com/juanfal/99504b4df2590c909b91a7ead0e96c5c

#include <iostream>
using namespace std;


int main()
{
    double exp(double x, int n);
    double exp(double x, float precision=0.001);
    // testing the functions
    for (float x = 0; x <= 50; x+=10) {
        cout << "exp(" << x << ")= "
             << exp(x, 20) << endl;
        cout << "exp(" << x << ")= "
             << exp(x) << endl;
    }

    return 0;
}


double exp(double x,  int n)
{
    double pot(double x, int n);
    double fact(int n);

    double s = 0; // result
    for (int i = 0; i < n; ++i)
        s += pot(x, i)/fact(i);

    return s;
}

double exp(double x, float precision)
{
    double pot(double x, int n);
    double fact(int n);

    double s = 0; // result
    int i = 0;
    double term = pot(x, 0)/fact(0);
    do {
        s += term;
        ++i;
        term = pot(x, i)/fact(i);
    } while (term > precision);
    return s;
}





double pot(double x, int n)
{
    double r = 1;
    for (int i = 0; i < n; ++i)
        r *= x;
    return r;
}

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