//#include "stdafx.h"
#define _USE_MATH_DEFINES
#include <math.h>
#include <iostream>
#include <cmath>

using namespace std;


void falseposition();
void newtonraphson();
void nonlinear();



int main()
{
	cout << "choose the method" << endl;
	cout << "enter 1 for false position" << endl;
	cout << "enter 2 for modified" << endl;
	cout << "enter 3 for nonlinear" << endl;

	int choice;
	cin >> choice;

	if (choice == 1) falseposition();
	if (choice == 2) newtonraphson();
	if (choice == 3) nonlinear();

	switch(choice){
		case 1: falseposition(); break;
		case 2: newtonraphson(); break;
		case 3: nonlinear(); break;
		default: falseposition();
	}

	return 0;
}

void nonlinear(){
	double u, v, dux, duy, dvx, dvy, xi, yi, xr, yr;;

	cout << "enter xi" << endl;
	cin >> xi;
	cout << "enter yi" << endl;
	cin >> yi;

	for (int i = 1; i < 1000; i++)
	{
		u = 0.45 * cos(xi) - 0.28 * cos(yi) - 0.275;
		v = 0.45 * sin(xi) - 0.28 * sin(yi) - 0.13;
		dux = -0.45 * sin(xi);
		duy = 0.28 * sin(yi);
		dvx = 0.45 * cos(xi);
		dvy = -0.28 * cos(yi);
		xr = xi - ((u * dvy - v * duy) / (dux * dvy - duy * dvx));
		yr = yi - ((v * dux - u * dvx) / (dux * dvy - duy * dvx));

		xi = xr;  yi = yr;
	}

	cout << "xr = " << xr << endl;
	cout << "yr = " << yr << endl;

}

void falseposition(){
	double tmpx, tmpy,xl, xu, fxl, fxu, xr, fxr, d = 0, error;
	int i;
	cout << "enter lower interval" << endl;
	cin >> tmpx;
	cout << "enter upper interval" << endl;
	cin >> tmpy;
	if (tmpx < tmpy) {
		xl = tmpx;
		xu = tmpy;
		}
	else {
		xl = tmpy;
		xu = tmpx;
		}

	for (i = 0; i < 10; i++){

		fxl = ((sin(2.0 * M_PI * xl / 16) * (cos(2 * M_PI * 12 * 48 / 16))) + pow(M_E, -xl)) - 0.8;
		fxu = ((sin(2.0 * M_PI * xu / 16) * (cos(2 * M_PI * 12 * 48 / 16))) + pow(M_E,-xu)) - 0.8;

		if ((fxl * fxu) < 0){
			xr = xu - (fxu * (xl - xu) / (fxl - fxu));

			fxr = ((sin(2.0 * M_PI * xr / 16) * (cos(2.0 * M_PI * 12 * 48 / 16))) + pow(M_E, -xr)) - 0.8;
			error = (xr - d) / xr;
			d = xr;

			if ((fxl * fxr) < 0){
				xu = xr;
			}
			else if ((fxl * fxr) > 0){
				xl = xr;
			}
			else if(fxr==0) {
				cout << "xr =" << xr << endl;
				cout << "error = " << error * 100 << "%" << endl;
				break;
			}
		}
		else {

			cout << "error!" << endl;
			break;
		}
	}
	if (i == 10) {
		cout << "xr = " << xr << endl;
		cout << "error = " << error * 100 << "%" << endl;
	}

}
void newtonraphson(){
	double fx, fpx, fdpx, x, xr,fxr;
	cout<< "Enter the guess value" <<endl;
	cin >> x;

	for (int i = 1; i < 1000; i++) {
		fx = pow((pow(M_E, x) + x - 20), 3);
		fpx = (pow((pow(M_E, x) + x - 20), 2)) * (3 * pow(M_E, x) + 3);
		fdpx = (pow(M_E, x) + x - 20) * (pow(M_E, x) + 1) * ((3 * pow(M_E, x) + 3)) + (pow((pow(M_E, x) + x - 20), 2)) * (3 * pow(M_E, x));
		xr = x - ((fx * fpx) / (fpx * fpx - fx * fdpx));
		x = xr;
	}


	cout << "xr = " << xr << endl;
	cout<< (fx > -0.000000001 && fx < 0.00000000001)?"converges":"diverges";



}