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


double  diffaitken( double (*fct)(double), double x, double h0, double tau) {

  assert (tau > 0);

  double phi = 0;
  double phip = 0;
  double hp = 0;
  double help = 1;
  double h = 0;
  int n= 0;
  int j = 0;
  double erg = 0;

  double *diff = malloc(1*sizeof(double));
  double *aitk = malloc (1*sizeof(double));

  for (n=0;1 ; n++) {


    for (j = 1;j < n+4 ;j++) {     // ACHTUNG MIT 1 ANGEFANGEN

    phip = phi;

    hp = h;

    if (j == 1) {

      h = h0;

    }

    else {

      help = help *2;

      h = 1/(2*help*h0);
  }
    phi = (fct(x+h)-fct(x))/h;

    diff = realloc (diff,j*sizeof(double));

    diff[j-1]=phi;


    }


    aitk = realloc (aitk,(n+1)*sizeof(double));

    aitk[n] = diff[n] - ((diff[n+1]-diff[n])*(diff[n+1]-diff[n]))/(diff[n+2]-2*diff[n+1]+diff[n]);


    if (fabs(aitk[n]) <= tau) {

    if (fabs(aitk[n-1]-aitk[n]) <= tau) {

      //printf("%f\n",aitk[n]);

      erg= aitk[n];

      return erg;

    }

      }
      else {

    if (fabs(aitk[n-1]-aitk[n]) <= tau * aitk[n]) {

      // printf("%f\n",aitk[n]);
      erg = aitk[n];
      return erg;
    }
      }


    printf("h_n= %f\n",h);
    printf("|y_n-y_n-1| = %f\n",fabs(aitk[n+1]-aitk[n]));
    printf("y_n = %f\n",aitk[n+1]);
    printf("\n");

}

}


double fct( double x) {

  return x*x*x;
}


int main () {

  double x = 0;
  double h= 0;
  double tau= 0;
  double z = 0;


  printf("Geben Sie einen Auswertungspunkt x ein:");
  scanf("%lf",&x);

  printf("Geben Sie eine Schrittweite h ein:");
  scanf("%lf",&h);

  printf("Geben Sie ein tau ein:");
  scanf("%lf",&tau);

  fct(x) ;

 z= diffaitken(fct,x,h,tau);

 printf("Das Ergebnis ist: %f",z);
}