#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;

double f( double ); // function whose root is sought
double secant( double, double, bool&);

int main()
{
  const double MAX_ERROR = 0.00001;
  double xGuess;
  bool rootFound;
  double rootApprox;
  cout << "Enter an initial guess for a root of f => ";
  cin >> xGuess;
  rootApprox = secant( xGuess, MAX_ERROR, rootFound );
  cout << setiosflags( ios::fixed ) <<
  setprecision( 5 );
  if (rootFound) {
    cout << "Starting with an initial guess of " << xGuess <<
        ", Secant's method " << endl << "approximates a root of f at "
        << rootApprox << endl;
    cout << "f( " << rootApprox << " ) = " << f(rootApprox) << endl;
  }
  return 0;
}
double secant( double xGuess, double okError, bool& converges )
{
  const int MAX_ITER = 25;
  double xN, xNplus1, xNminus1;
  int iter = 0;

  xN = xGuess;
  do {
    ++iter;
    xNplus1 = (xNminus1* f( xN )-xN*f ( xNminus1)) / (f (xN)- f ( xNminus1));
    xN = xNplus1;
  } while (xNplus1 >= okError && iter < MAX_ITER);

  if (xNplus1 < okError) {
    converges = true;
    return xN;
  } else {
    cout << "Newton's method did not converge to a root of f "
        << "in " << MAX_ITER << endl << "iterations using an initial"
        << " guess of " << xGuess << endl;
    converges = false;
    return xGuess;
  }
}

double f ( double xN)
{
	int x;
	return x*x+1;
}