/* ===================================================================*\

  filename: bisection.c  

  THE PROGRAM IS TO IMPLEMENT THE BISECTION METHOD FOR ROOT FINDING      

  PROGRAMMER:  RiNN
  INSTRUCTOR:  Dr. Robert Sczech 
  Class:       CS102 S98
  Date:        Tuesday February 10, 1998 



\*=====================================================================*/

#include                   //iostream Header
#include                       //math     Header

// GLOBAL VARABLES
const double delta   = 0.00001   ;     //CONSTANT DELTA
const double epsilon = 0.000001  ;     //CONSTANT EPSILON

//PROTOTYPES
double bisect(double (*f)(double x), double a, double b);
double FuncOne  (double x);  //f(x)=x2-2,     [a,b]=[1,2]
double FuncTwo  (double x);  //f(x)=cos(x/2), [a,b]=[3.0,3.2]
double FuncThree(double x);  //f(x)=ln(x)-1,  [a,b]=[2.71,2.72]

void main ()
{ cout << "\n" << bisect(FuncOne,  1    ,2   ) << endl;  
  cout << "\n" << bisect(FuncTwo,  3.0  ,3.2 ) << endl;
  cout << "\n" << bisect(FuncThree,2.71 ,2.72) << endl;
return 0;
}

double bisect(double (*f)(double x), double a, double b){
  double mid = ((a+b)/2);       //Midpoint declared and calculated
  cout << "\tBisect: interval=[" << a << " , " << b << "]" << endl;
 if ((fabs( a - b) < delta) || (fabs(f(mid)) < epsilon))
   return (mid = (( a+b )/2));  //Stop when Values are < delta/epsilon
 else if ( f(a)*f(mid) < 0)     //Is point in between the a & mid?
   return bisect(f, a, mid);    //Return if it is true
 else                           
   return bisect(f, mid,b);     //Return if the point is between mid & b
}

double FuncOne(double x){       
 return ((x * x) -2);
}

double FuncTwo(double x){
 return (cos(x/2));
}

double FuncThree(double x){ 
 return ( log(x) - 1);
}