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;
}