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

using namespace std;
//
//  We can declare NEWTON and F1 here, and they will be usable by
//  any function within this file.
//
double newton ( double x, double f ( double x ), double fp ( double x ) );
double f1 ( double x );
double fp1 ( double x );

int main ( )
//
//  NEWTON_F1 is a program which uses NEWTON to solve for a solution
//  of F1(X) = 0.  
//
{
//
//  X0 is the starting value.
//
  double x0 = -0.0, x;

  x = newton ( x0, f1, fp1 );

  cout << "\n";
  cout << "NEWTON returned solution estimate X = " << x << "\n";
  cout << "F1(X) = " << f1 ( x ) << "\n";

  return 0;
}
double newton ( double x0, double f ( double x ), double fp ( double x ) )
{
  int step;
  double fx1, x1;
//
//  Initialization.
//
  step = 0;
  cout << step << "  " << x0 << "  " << f ( x0 ) << "\n";
//
//  Iteration loop.
//
  while ( true )
  {
    x1 = x0 - f ( x0 ) / fp ( x0 );
    fx1 = f ( x1 );
    step = step + 1;
    cout << step << "  " << x1 << "  " << f ( x1 ) << "\n";
//
//  Can we accept the new point?
//
    if ( fabs ( fx1 ) < 0.00000001 ) 
    {
      break;
    }
//
//  Quit if we take too many steps!
//
    if ( 15 <= step )
    {
      cerr << "NEWTON - Too many steps!\n";
      exit ( 1 );
    }
//
//  Prepare for next step.
//
    x0 = x1;
  }
  return x1;
}
double f1 ( double x )
//
//  F1 is our "cosine" function.
//
{
  double value;

  value = cos ( x ) - x;

  return value;
}
double fp1 ( double x )
//
//  FP1 is the derivative of F1.
//
{
  double value;

  value = - sin ( x ) - 1;

  return value;
}