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

using namespace std;

float func(float x,float m) {
    return powf(1+x,m);
}

float approximate_func(float x,float m) {
    float result = 1;
    float temp_x = 1;
    float temp_m = 1;
    float temp_fact = 1;
    int i = 1;
    while (i<=4) {
        temp_m *= (m-i+1);
        temp_x *= x;
        temp_fact *= i;
        float value = temp_m * temp_x / temp_fact;
        result += value;
        i++;
    }
    return result;
}

int fact(int n) {
    int result = 1;
    int i = 1;
    while (i<n)
        result *= (++i);
    return result;
}

float inverse_fact(float n,int count) {
    float result = n;
    while (count > 0) {
        result *= (--n);
        count--;
    }
    return result;
}

float power(float a,int b) {
    if (b == 0)
        return 1;
    float result = a;
    for (int i=1;i<b;i++)
        result *= a;
    return result;
}

float approximate_func_without(float x,float m) {
    int i = 1;
    float result = 1;
    while (i<=4) {
        result += (inverse_fact(m,i-1) * power(x,i) / fact(i));
        i++;
    }
    return result;
}

int _tmain(int argc, _TCHAR* argv[]) {
    setlocale(0, "");
    float x;
    float m = 0;
    cout << "Введите x:";
    cin >> x;
    cout << "Значение\tПриближенное значение\tАбсолютная ошибка\tОтносительная ошибка" << endl;
    while (m <= 6) {
        float exact = func(x,m);
        float approximate = approximate_func(x,m);
        cout << exact;
        cout << "|";
        cout << approximate;
        cout << "|";
        cout << fabs(exact - approximate);
        cout << "|";
        cout << fabs(exact - approximate) / fabs(approximate);
        cout << endl;
        m += 0.5;
    }
    system("pause");
    return 0;
}