/* 
newton-raphson method for root finding.

*/

#include <iostream>
#include <cstdlib>
#include <cmath>

using std::endl;
using std::cout;

// define function:

double func_y(double x){
  return pow(x,3.0) + 1.0;
}


//define first derivative of function:

double func_dydx(double s){
  return 3.0*pow(s,2.0);
}


int main() 
{    
   int N= 0;
   int N_limit = 1000;           // max number of trys
   double s = -1.1;              // initial guess for root
   double tol = 1.0e-5;          // tolerance for finding zero

   while ((fabs(func_y(s)) >= tol) && (N < N_limit)){
     s = s - func_y(s)/func_dydx(s);
     ++N;
        }

   if(N >= N_limit){
     cout << "iteration limit exceeded" << endl;
     return 0;
   }

   if (N <= N_limit){
     cout << "estimated root = " << s << " with " << N << " iterations." << endl;
   }

   return 0;
}