#include<iostream>
#include<stdio.h>
#include<math.h>
#include <stdlib.h>
#include<iomanip>
#include<fstream>
#include <stdlib.h>
#define MAX_ITERATION 10000
#define EPS 1e-16

using namespace std;

long double f1(long double x) {
    //return sin(x/4)*sin(x/4) - x;
    //return x*x*x +/4*x - 20;
     //return exp(5)*x*x*x +20;
}

long double f2(long double x) {
    return tan(2*x)-x-1;
    //return (x-1)*x*x +8*x;
}

long double isConcurrent(long double(*f)(long double), long double x) {
    if (((f(x + EPS) - f(x)) / EPS ) > 1)
        return false;
    else
        return true;
}

long double derivative(long double(*f)(long double), long double x) {
    return (f(x + EPS) - f(x)) / EPS;
}

long double pickard_f1(long double x) {
    return sin(x/4)*sin(x/4);
}

long double pickard_f2(long double x) {
    return atan(x+1)/2;

}

string show_function1() {
    return "sin^2(x/4)- x = 0";
}

string show_function2() {
    return "tan(2x)- x - 1 = 0";
}

void writeTitleToFile(ofstream &file) {
        file << setw(5) << "Lp." << setw(20) << right << "Przyblizenie Xn" << setw(20) << right <<
        "Estymator " << setw(20) << right << "Residuum" << endl << endl;
}

void writeResultToFile(ofstream &file, int i, double result, double estimator, double residuum) {
        file.width(5);
        file << i <<".";
        file.width(20);
        file << right << result;
        file.width(20);
        file << right << estimator;
        file.width(20);
        file << right << residuum << endl;
}

double Pickard_function(long double (*f)(long double), long double (*pickard_f)(long double), long double x0, ofstream &file) {
    long double estimator = 0;
    long double residuum = 0;
    long double x;
    writeTitleToFile(file);
        for(int i = 1; i< MAX_ITERATION; i++) {
            x = pickard_f(x0);
            residuum = fabs(f(x0));
            estimator = fabs(x - x0);
            x0 = x;

            writeResultToFile(file, i, x, estimator, residuum);

            if(residuum < EPS) {
                break;
            }
            if(estimator < EPS) {
                break;
            }
        }
    return x;
}

double Bisekcja_function(long double (*f)(long double), long double a, long double b, ofstream &file) {
    long double estimator = 0;
    long double residuum = 0;
    long double x;
    writeTitleToFile(file);
    for(int i = 1; i< MAX_ITERATION; i++) {
        x = (a+b)/2;
        estimator = fabs((b-a)/2);
        residuum = fabs(f(x));

        writeResultToFile(file, i, x, estimator, residuum);

        if(residuum < EPS) {
            break;
        }
        if(estimator < EPS) {
            break;
        }

        if(f(a)*f(x)<0)
            b = x;
        else
            a = x;

    }
    return x;
}

double Newton_function(long double (*f)(long double), long double x0, ofstream &file){
    long double estimator = 0;
    long double residuum = 0;
    long double x;
    writeTitleToFile(file);

    for(int i = 1; i<MAX_ITERATION; i++) {
        x = x0 - f(x0)/derivative(f,x0);
        estimator = fabs(x0 - x);
        residuum = fabs(f(x));
        x0 = x;

        writeResultToFile(file, i, x, estimator, residuum);

        if(residuum < EPS) {
            break;
        }
        if(estimator < EPS) {
            break;
        }
    }
    return x;
}

double Sieczna_function(long double (*f)(long double), long double a, long double b, ofstream &file) {
    long double estimator = 0;
    long double residuum = 0;
    long double x;
    writeTitleToFile(file);

    for(int i = 1; i<MAX_ITERATION; i++) {
        double tmp = b;
        b = b - f(b)*(b-a)/(f(b) - f(a));
        a = tmp ;
        estimator = fabs(a-b);
        residuum = fabs(f(b));

        writeResultToFile(file, i, x, estimator, residuum);

        if(residuum < EPS) {
            break;
        }
        if(estimator < EPS) {
            break;
        }
    }
    return a;
    }


int main()
{
    cout << setprecision(10);
    cout << setw(20) <<"========== " << show_function1() << " =========="  << endl << endl;
    ofstream Pickard1;
    Pickard1.open("pickard1.txt", ios::out);
    double arg_p1 = -8;
    if(isConcurrent(pickard_f1, arg_p1)) {
        cout << setw(20) << "Pickard " << setw(5) << "x0 = " << Pickard_function(f1, pickard_f1, arg_p1, Pickard1) << endl;
    } else {
         cout << "Nie można policzyć Pickarda. Funkcja rozbiezna!" << endl;
    }

    ofstream Bisekcja1;
    Bisekcja1.open("bisekcja1.txt", ios::out);
    double arg_b1 = -2;
    double arg_b2 = 4;

    if(f1(arg_b1)*f1(arg_b2)> 0 || arg_b1> arg_b2) {
        cout << "Nie można policzyć bisekcji. Podano zly przedzial!" << endl;
    } else {
        cout << setw(20) << "Bisekcja " << setw(5) << "x0 = " << Bisekcja_function(f1, arg_b1, arg_b2, Bisekcja1)<< endl;
    }

    ofstream Newton1;
    double arg_n1 = 8;
    Newton1.open("newton1.txt", ios::out);
    cout << setw(20) <<  "Newton " <<  setw(5) << "x0 = " << Newton_function(f1, arg_n1, Newton1) << endl;

    ofstream Sieczna1;
    double arg_s1 = -4;
    double arg_s2 = -2;
    Sieczna1.open("sieczna1.txt", ios::out);
    cout << setw(20) << "Sieczna " <<  setw(5) << "x0 = " <<Sieczna_function(f1, arg_s1, arg_s2, Sieczna1) << endl;

    /****************************************************************************************************************/
    /****************************************************************************************************************/
    cout << endl;
    cout << setw(20) <<"========== " << show_function2() << " =========="  << endl << endl;
    ofstream Pickard2;
    Pickard2.open("pickard2.txt", ios::out);
    double arg_p2 = -8;
    if(isConcurrent(pickard_f2, arg_p2)) {
        cout << setw(20) << "Pickard " << setw(5) << "x0 = " << Pickard_function(f2, pickard_f2, arg_p2, Pickard2) << endl;
    } else {
         cout << "Nie można policzyć Pickarda. Funkcja rozbiezna!" << endl;
    }

    ofstream Bisekcja2;
    Bisekcja2.open("bisekcja2.txt", ios::out);
    double arg_b21 = 0;
    double arg_b22 = 0.6;

    if(f2(arg_b21)*f2(arg_b22)> 0 || arg_b21> arg_b22) {
        cout << "Nie można policzyć bisekcji. Podano zly przedzial!" << endl;
    } else {
        cout << setw(20) << "Bisekcja " << setw(5) << "x0 = " << Bisekcja_function(f2, arg_b21, arg_b22, Bisekcja2)<< endl;
    }

    ofstream Newton2;
    double arg_n2 = 8;
    Newton2.open("newton2.txt", ios::out);
    cout << setw(20) <<  "Newton " <<  setw(5) << "x0 = " << Newton_function(f2, arg_n2, Newton2) << endl;

    ofstream Sieczna2;
    double arg_s21 = -5;
    double arg_s22 = 18;
    Sieczna2.open("sieczna2.txt", ios::out);
    cout << setw(20) << "Sieczna " <<  setw(5) << "x0 = " <<Sieczna_function(f2, arg_s21, arg_s22, Sieczna2) << endl;

    return 0;
}