//	Bisect3.cc

//	Recursive function
//			Example: Find the point of zero by bisection

//	Version 3: func(x) and epsilon as parameters

#include <iostream.h>
#include <math.h>

double f(const double x)		// declaration and
  { return sin(x) - 0.5*x ; }		//   definition of function f(x)

double g(const double x)		// declaration and
  { return -(x-1.234567)*(x+0.987654) ; }//   definition of function g(x)

					// declaration of Bisect3
double Bisect3(double (* const func)(double), const double a, const double b, 
		const double eps=1e-6);

main()
{
 const double EPS = 1e-6;		// accuracy constant
       double a,b,x0;
 
 cout << endl;
 cout << " Determine point of zero in [a,b] by bisection " << endl;

 cout << "f(a) > 0,  a : "; cin >> a;
 cout << "f(b) < 0,  b : "; cin >> b;
 cout << endl;
 
 x0 = Bisect3(f,a,b,EPS);		// call recursive function with f
// x0 = Bisect3(g,a,b,EPS);		// call recursive function with g
 
 cout << endl << " point of zero = " << x0 << endl;
 cout << endl;
}

//	---------------------------------------------------------------
//	Recursive  function Bisect3
//	---------------------------------------------------------------
//	definition of Bisect3

double Bisect3(double (* const func)(double), const double a, const double b, 
		const double eps)
{
 double x0, fc, c = (a+b)/2;
 
 fc = func(c);			// calculate value of parameter function
 if ( fabs(fc) < eps )
  {
   x0 = c;			// end of recursion
  }
 else if (  fc > 0.0 )
  {
   x0 = Bisect3(func,c,b,eps);	// search in right intervall
  }
 else 			// i.e., fc < 0.0
  {
   x0 = Bisect3(func,a,c,eps);	// search in left intervall
  } 

 return x0;			// return the solution
}