#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

const double EPSILON = 1e-10;
const int MAX_ITERATIONS = 100;

double f(double x) {
   return x*x*x-5*x-1;
}

double fPrime(double x) {
    return 3*x*x-5;
}

// stolen from on line
template <typename T> int sgn(T val) {
    return (T(0) < val) - (val < T(0));
}


void Bisection(double a, double b) {

   double mid, value;
   
   int count = 0;

   if (sgn(f(a)) == sgn(f(b))) {
      cout << "Error, bisection requires  different signs " << endl;
      return ;
   }

   mid =  (a+b)/2.0;
   value = f(mid);   

   while  (count < MAX_ITERATIONS and abs(value)>  EPSILON) {
       cout << count <<"\t" << a << "\t" << b << "\t" << value << endl;
       if (sgn(f(a)) == sgn(value)) {
           a = mid;
       } else {
           b = mid;
       }
       count ++;
       mid =  (a+b)/2.0;
       value = f(mid);   
   }
   cout << count <<"\t" << a << "\t" << b << "\t" << value << endl;
   return; 
}

void Newton(double a) {
    int count;

    while (abs(f(a)) > EPSILON and count < MAX_ITERATIONS) {
        cout << count << "\t" << a <<"\t" << f(a) << endl;
        count ++;
	a = a - f(a)/fPrime(a);
    }
    cout << count << "\t" << a <<"\t" << f(a) << endl;

    return;
}

void RegulaFalsi(double a, double b) {
    int count=0;
    double newPos,value;

    if (sgn(f(a)) == sgn(f(b))) {
      cout << "Error, regula falsi requires  different signs " << endl;
      return ;
    }


    newPos = b-(f(b)*(b-a))/(f(b)-f(a));
    value = f(newPos);

    while (abs(value) > EPSILON and count < MAX_ITERATIONS) {
       cout << count <<"\t" << a << "\t" << b << "\t" << value << endl;
       if (sgn(value) == sgn(f(a))) {
          a = newPos;
       } else {
          b = newPos;
       }
       count ++;
       newPos = b-(f(b)*(b-a))/(f(b)-f(a));
       value = f(newPos);
    }
    cout << count <<"\t" << a << "\t" << b << "\t" << value << endl;
    return;

     
}


int main () {

    cout << fixed << setprecision(15);
    cout << "Bisection Method " << endl;
    Bisection(0,3);
    cout << endl << endl;
    cout << "Regula Falsi" << endl;
    RegulaFalsi(0,3);
    cout << endl << endl;
    cout << "Newton" << endl;
    Newton(3);
     
}