#include <iostream>
#include <cmath>
#include "functions.h"

ldouble_t ld_power(ldouble_t x, int power)
{
    ldouble_t result = x;

    for(int i = 1; i < power; i++)
        result *= x;

    return result;
}

ldouble_t G(ldouble_t x, int i)
{
    // ((-1)^(i!) * x^(2i - 1)) / (x^i + cos(ix))

    return ld_power(x, 2 * i - 1) / (ld_power(x, i) + cos(i * x));
}

ldouble_t F(ldouble_t x, int N)
{
    ldouble_t result = 1.0;
    for(int i = 2; i <= N; i++)
    {
        ldouble_t g = G(x, i);
        result += g;

        std::cout << "\n\ti=" << i << "\tG=" << g << "\tF=" << result;
    }
    return result;
}