// Recursive binary search root-finder
//   version of January 21st, 2003 - 21:30

// ----------------------------------------------------
//     (c) Copyright 2003  Julian V. Noble.          //
//       Permission is granted by the author to      //
//       use this software for any application pro-  //
//       vided this copyright notice is preserved.   //
// ----------------------------------------------------


#include <math.h>
#include <stdio.h>

double bin_root ( double, double, double, double (*pn) (double) );
double f1 ( double );
void initialize( double a, double b, double (*pn) (double)  );

// global variables

    double ra, rb;


int main(void)
{
    typedef double (*PFI) ( double );
    PFI n;       // define a pointer to simple functions

    double a, b, eps, result;

    printf("What are a, b, and epsilon? ");
    scanf(" %le%le%le", &a, &b, &eps);

    printf( " %.10le\n %.10e\n %.10e\n", a, b, eps ) ;

    n = f1;

    initialize ( a, b, n );
    result = bin_root( a, b, eps, n );

    printf( " Root is %.10le\n", result );

    return 0;
}


double f1 ( double x)
{
    return x * exp (x) - 1;
}


void initialize( double a, double b, double (*pn) (double)  )
{
    ra = (*pn) (a) ;
    rb = (*pn) (b) ;

    if ( ra * rb > 0 )
        { printf( " Even number of roots\n");
          abort();
        }
}


double bin_root ( double a, double b, double eps, double (*pn) (double) )
{
    double c, rc ;

    c = 0.5 * ( a + b ) ;


    if ( fabs( a - b ) < eps )
        { return c;
        }

    rc = (*pn) (c) ;
    if ( ra * rc > 0 )
            { a = c;
              ra = rc;
            }
    else
            { b = c;
              rb = rc;
            }

    return bin_root( a, b, eps, pn );
}