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

using namespace std;
//
//  We can declare SECANT and F1 here, and they will be usable by
//  any function within this file.
//
double secant ( double a, double b, double f ( double x ) );
double f1 ( double x );


int main ( )
//
//  SECANT_F1 is a program which uses SECANT to solve for a solution
//  of F1(X) = 0.  
//
{
//
//  A and B are the "bracket" values we've chosen for our function.
//
  double a = -10.0, b = +10.0, c;

  c = secant ( a, b, f1 );

  cout << "\n";
  cout << "SECANT returned solution estimate C = " << c << "\n";
  cout << "F1(C) = " << f1 ( c ) << "\n";

  return 0;
}
double secant ( double x0, double x1, double f ( double x ) )
{
  int step;
  double fx0, fx1, fx2, x2;
//
//  Initialization.
//
  step = 0;
  fx0 = f ( x0 );
  fx1 = f ( x1 );
//
//  Iteration loop.
//
  while ( true )
  {
    x2 = ( fx1 * x0 - fx0 * x1 ) / ( fx1 - fx0 );
    fx2 = f ( x2 );
    step = step + 1;
//
//  Can we accept the new point?
//
    if ( fabs ( fx2 ) < 0.000001 ) 
    {
      break;
    }
//
//  Quit if we take too many steps!
//
    if ( 25 <= step )
    {
      cerr << "SECANT - Too many steps!\n";
      exit ( 1 );
    }
//
//  Prepare for next step.
//
    x0 = x1;
    fx0 = fx1;
    x1 = x2;
    fx1 = fx2;
  }
  return x2;
}
double f1 ( double x )
//
//  F1 is our "cosine" function.
//
{
  double value;

  value = cos ( x ) - x;

  return value;
}