#include <iostream>
#include <cmath>
#include <iomanip>
#include <cstdlib>
#include <cstring>

using namespace std;

typedef double (*ftype)(double, int);


struct I_print {    //данные для печати результатов интегрирования
    const char* name;//название функции
    double i_sum;   //значение интегральной суммы
    double i_toch;  //точное значение интеграла
    int n;  //число разбиений области интегрирования
            //при котором достигнута требуемая точность
};


void PrintTabl(I_print i_prn[], int k, char* gg);

double IntRect(ftype f, double a, double b, double eps, int& n, int mode);

double IntTrap(ftype f, double a, double b, double eps, int& n, int mode);

double i_toch(int mode);

double funcs(double x, int mode);

int main()
{
    double a = -1, b = 3;
    int n = 0;
    double eps = 0.1;
    I_print i_prn[4];
    const char* func_name[] = { "y=x ", "y=sin(22x)", "y=x^4 ", "y=arctg(x)" };
    //IntRect
    while (eps >= 0.000001) {

        cout << fixed << setw(30) << "eps = " << eps << endl;
        for (int i = 0; i < 4; i++) {
            I_print I_str = { func_name[i], IntRect(funcs, a, b, eps, n, i + 1), i_toch(i + 1), n };
            i_prn[i] = I_str;
        }
        PrintTabl(i_prn, 4, "IntRect ");
        eps /= 10;
    }
    cout << endl << endl;
    eps = 0.1;
    //IntTrap
    while (eps >= 0.000001) {

        cout << fixed << setw(30) << "eps = " << eps << endl;
        for (int i = 0; i < 4; i++) {
            I_print I_str = { func_name[i], IntTrap(funcs, a, b, eps, n, i + 1), i_toch(i + 1), n };
            i_prn[i] = I_str;
        }
        PrintTabl(i_prn, 4, "IntTrap ");
        eps /= 10;
    }
    system("pause");
    return 0;
}

void PrintTabl(I_print i_prn[], int k, char* gg)
{
    const int m = 4;//число столбцов таблицы
    int wn[m] = { 12,18,18,10 };//ширина столбцов таблицы
    const char* title[m] = { "Function","Integral", gg ,"N " };
    int size[m];
    for (int i = 0; i < m; i++)
        size[i] = strlen(title[i]);
    //шапка таблицы
    cout << char(218) << setfill(char(196));
    for (int j = 0; j < m - 1; j++)
        cout << setw(wn[j]) << char(194);
    cout << setw(wn[m - 1]) << char(191) << endl;

    cout << char(179);
    for (int j = 0; j < m; j++)
        cout << setw((wn[j] - size[j]) / 2) << setfill(' ') << ' ' << title[j]
        << setw((wn[j] - size[j]) / 2) << char(179);
    cout << endl;
    for (int i = 0; i < k; i++)
    {//заполнение таблицы
        cout << char(195) << fixed;
        for (int j = 0; j < m - 1; j++)
            cout << setfill(char(196)) << setw(wn[j]) << char(197);
        cout << setw(wn[m - 1]) << char(180) << setfill(' ') << endl;

        cout << char(179) << setw((wn[0] - strlen(i_prn[i].name)) / 2) << ' ' << i_prn[i].name
            << setw((wn[0] - strlen(i_prn[i].name)) / 2) << char(179);
        cout << setw(wn[1] - 1) << setprecision(10) << i_prn[i].i_toch << char(179)
            << setw(wn[2] - 1) << i_prn[i].i_sum << setprecision(6) << char(179)
            << setw(wn[3] - 1) << i_prn[i].n << char(179) << endl;
    }
    //низ таблицы
    cout << char(192) << setfill(char(196));
    for (int j = 0; j < m - 1; j++)
        cout << setw(wn[j]) << char(193);
    cout << setw(wn[m - 1]) << char(217) << setfill(' ') << endl;
}


double IntRect(ftype f, double a, double b, double eps, int& n, int mode)
{
    n = 1;
    double y = 0;
    double Iold = 0, Inew = 0;
    double left = a;
    do {
        n *= 2;
        Iold = Inew;
        double dx = (b - a) / n;
        while (a < b) {
            y += f(a + dx / 2, mode);
            a += dx;
        }
        a = left;
        Inew = y * dx;
        y = 0;
    } while (abs(Iold - Inew) > 3 * eps);
    return Inew;
}

double IntTrap(ftype f, double a, double b, double eps, int& n, int mode) {
    n = 1;
    double y = 0;
    double Iold = 0, Inew = 0;
    double left = a;
    do {
        n *= 2;
        Iold = Inew;
        double dx = (b - a) / n;
        while (a < b) {
            y += (f(a, mode) + f(a + dx, mode)) / 2;
            a += dx;
        }
        a = left;
        Inew = y * dx;
        y = 0;
    } while (abs(Inew - Iold) > 3 * eps);
    return Inew;
}

double funcs(double x, int mode) {
    switch (mode) {
    case 1: return x;
    case 2: return sin(22 * x);
    case 3: return x * x * x * x;
    case 4: return atan(x);
    }
}

double i_toch(int mode) {
    double a = -1, b = 3;
    switch (mode) {
    case 1: return (b * b - a * a) / 2.0;
    case 2: return (cos(a * 22.0) - cos(b * 22.0)) / 22.0;
    case 3: return (b * b * b * b * b - a * a * a * a * a) / 5.0;
    case 4: return b * atan(b) - a * atan(a) - (log(b * b + 1) - log(a * a + 1)) / 2.0;
    }
}