//Robert Kristof, Mateusz Urbanek Task 3
//This program calculates Cos(x) without use of cmath library

#include "pch.h"
#include <iostream>
using namespace std;

double Power(double number, int power) {
	if (power == 0) { return 1; }
	else {}
	double Powered = number;
	for (int i = 1; i < power; i++) {
		Powered *= number;
	}
	return Powered;
}

double Factorial(double Fact) {

	if (Fact < 0) { return 0; }		//Factorial of number less than 0 does not exist
	if (Fact == 0) { return 1; }	//Factorial of 0 is always equal to 1

	double Result = 1;
	for (int i = 1; i <= Fact; i++) {
		Result *= i;
	}
	return Result;
}

double Cosinus(double x, double y) {

	int True = 1;
	double PreviousX = 1;
	double ResultOfCosine = 0;		//Result of Cosinus(x) function
	int Iter = 1;

	while (True == 1) {
		//cout << "Iteration number     " << Iter << endl;
		double FirstVariable = Power(-1, Iter);
		//cout << "I did first one     " << FirstVariable << endl;
		double SecondVariable = Power(x, 2 * Iter);
		//cout << "I did second one     " << SecondVariable << endl;
		double ThirdVariable = Factorial(2 * Iter);
		//cout << "I did third one     " << ThirdVariable << endl;
		ResultOfCosine = ((FirstVariable * SecondVariable) / ThirdVariable) + PreviousX;
		//cout << "afterfirst Result" << endl;
		//cout << ResultOfCosine << endl;
		//cout << "Previous      " << PreviousX << endl;
		if (((PreviousX - ResultOfCosine <= y) && (PreviousX - ResultOfCosine >= 0)) || ((ResultOfCosine - PreviousX <= y) && (ResultOfCosine - PreviousX >= 0))) {
			True = 0;
			//cout << "Setting True" << endl;
		}
		else { True = 1; }
		PreviousX = ResultOfCosine;
		Iter++;
	}
	cout << "Your cosinus of x is equal to:\t" << ResultOfCosine << endl;
	cout << "Number of iterations is equal to:\t" << Iter - 1 << endl;
	return 1;
}

int main() {
	double x0;				//x0
	double Acc;				//Accuracy
	cout << "Input x0" << endl;
	cin >> x0;
	cout << "What is your accuracy?" << endl;
	cin >> Acc;
	Cosinus(x0, Acc);
}