#include <iostream>
#include <math.h>
using namespace std;

enum state { ITERATING, SUCCESS, WONTSTOP, NEARZERO, SAMESIGN };
typedef double (*func)(double);
state newton(func, func, double&);


const double toosmall = 5.0E-30;
const double delta = 5.0E-7;
const double eps = 5.0E-8;
const int maxiter = 100;

state newton(func f, func f1, double &x)   //f1 = f'(x)
{
       int iter = 0;
       state s = ITERATING;
       while (s == ITERATING)
	 {
	   double  fx = f(x), f1x = f1(x), dx;
	   cout << iter << "\t" << x << "\n";
	   if (++iter == maxiter) 
              s = WONTSTOP;
           else if (fabs(f1x) < toosmall)
	      s = NEARZERO;
	   else
	     {  
	       x += (dx = -fx/f1x);
               if (fabs(dx) < delta || fabs(f(x)) < eps)
 		 s = SUCCESS;
       	     }
	 }
       return s;
  
}



inline double F(double x) { return x - exp(-x);}
inline double F1(double x) { return 1. + exp(-x);}

main()
{
       double root;
       cout << "initial guess = ";
       cin >> root;
       state s = newton(F, F1, root);
       switch(s){
       case SUCCESS: 
	 cout << "root = " << root << "\n"; 
	 break;
       case WONTSTOP: 
       case NEARZERO:
         cout << "not convergent!\n"; 
	 break;
       default: cout << "that's very peculiar!\n"; break;
       }

}