/*    ATK IV - Numerical Programming (2006)      */
/*  Excercise 6.3 -  General Iteration Formula   */

#include<stdio.h>
#include<math.h>
#define Pi 3.141592654

/* We have to transfer the equation tan(x)=x => x = arctan(x) (+ n*Pi)  */
/* because in the general iteration formula the necessary condition for */
/* convergence is that f(x) is defined and differentiable in such way   */
/* that the values of the function are bounded in a given interval.     */
/* Additionally, in the neighbourhood of the root, one has to have      */
/* |f'(x)| = k < 1. For tan(x) this is not the case, but for arctan(x), */
/* however, it is!                                                      */

float f(float x, int n){ return atan(x)+n*Pi;}
float giter(float x,float acc);

int n;

int main(void){
  float acc=1.0e-5;
  float x=0.0;
  float y;
  int i;

  for(i=0;i<3;i++){
    n=i;
    y=giter(x,acc);
    printf("%d %f\n",i+1,y);
  }

  return 0;

}

float giter(float x,float acc){

  float x1=x;
  float x2=f(x1,n);

  while(fabs(x1-x2)>acc){
    
    x1=x2;
    x2=f(x1,n);

  }

  return x2;
}