//	Bisect.ccx.cc

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

//	Version 1: f(x) is dircetly implemented in Bisect()
//		   epsilon as parameter

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


//	declaration of Bisect1
double Bisect1(const double a, const double b, const double eps);

main()
{
 const double EPS = 1e-6;		// global 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;

 x0 = Bisect1(a,b,EPS);			// call recursive function
 
 cout << endl;
 cout << " point of zero = " << x0 << endl;
 cout << endl;
}

//	---------------------------------------------------------------
//	Recursive  function Bisect1
//	---------------------------------------------------------------
//	definition of Bisect1

double Bisect1(const double a, const double b, const double eps)	
{
 double x0, fc, c = (a+b)/2;
 
 fc = sin(c) - 0.5*c;
 if ( fabs(fc) < eps )
  {
   x0 = c;			// end of recursion
  }
 else if (  fc > 0.0 )
  {
   x0 = Bisect1(c,b,eps);	// search in right intervall
  }
 else 				// i.e., fc < 0.0
  {
   x0 = Bisect1(a,c,eps);	// search in left intervall
  } 

 return x0;			// return the solution
}