//	Bisect2.cc

//	Recursive function
//			Example: Find the solution by bisection

//	Version 2: f(x) is globally declared and defined
//		   epsilon as global constant

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

const double EPS = 1e-6;		// global constant

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

double Bisect2(const double a, const double b);	// declaration of Bisect2

main()
{
 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;

 x0 = Bisect2(a,b);			// call recursive function
 
 cout << endl;
 cout << " point of zero = " << x0 << endl;
 cout << endl;
}

//	---------------------------------------------------------------
//	Recursive  function Bisect2
//	---------------------------------------------------------------

double Bisect2(const double a, const double b)	// definition of Bisect2
{
 double x0, fc, c = (a+b)/2;
 
 fc = f(c);
 if ( fabs(fc) < EPS )
  {
   x0 = c;			// end of recursion
  }
 else if (  fc > 0.0 )
  {
   x0 = Bisect2(c,b);		// search in right intervall
  }
 else 				// i.e., fc < 0.0
  {
   x0 = Bisect2(a,c);		// search in left intervall
  } 

 return x0;			// return with solution
}