/**

  \brief solving roots of a function by dichotomy

  \author SUN Yazhou, asia.rabbit@163.com

  \date Created: 2020/05/04 Last revised: 2020/05/14 by SUN Yazhou

  \copyright 2020, SUN Yazhou

*/

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

// the objective function

// f(x) = 0 

double fun(double x){

  return sin(x) - x*x/4.;

}

int main(){

  // [a,b] is the initial search domain //

  double a = 1.5, b = 2.;

  // tolerated errors for x (epsilon0) and f(x) (epsilon1)

  double epsilon0 = 1e-2, epsilon1 = 1e-3;

  int Nmax = 100; // the maximum iteration times

  double fa = fun(a), fb = fun(b); // f(a), f(b)

  double m = (a + b) / 2.;

  // prepare for the iterations //

  int k = 0; // the iteration number

  // start the iteratons //

  while(fabs(a - b) > epsilon0 && k < Nmax){

    m = (a + b) / 2.;

    fb = fun(m); // SUPPOSE m is the end of the new search domain

    if(fabs(fb) < epsilon1) break;

    // reset the search domain

    if(fb * fa < 0.) b = m; // confirm the ASSUMPTION

    else{ // ASSUMPTION failed, a set as the end of the new search domain

      a = m;

      fa = fb;

    }

    k++;

    printf("m: %10.8f\n", m);

    getchar();

  } // end while

  printf("The program has iterated %d times.\n", k);

  printf("The obtained root is f(%10.8f) = %10.8f\n", m, fun(m));

  printf("Bye.\n\n");

  return 0;

} // end of the main function