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


double* diff( double (*fct)(double), double x, double h0, double tau, int * n) {

  assert (tau > 0);
  double phi = 0;
  double phip= 0;
  double hp= 0;
  double help = 1;
  double h = 0;

  double * z= malloc (1*sizeof(double));

  while(1) {
    phip = phi;

    hp = h;

    if (*n == 1) {
      h = h0;
    }

    else {
  help = help *2;
    h = 1/(2*help*h0);
    }

      phi = (fct(x+h)-fct(x))/h;

       z = realloc(z,*n *sizeof(double));

       z[*n-1]= phi;

     if (fabs(phi) <= tau && fabs(phip-phi)<= tau ) {

	 return z;
  }
     if ( fabs(phi) > tau && fabs (phip - phi) <= tau * fabs(phip)) {

	   return z;
	 }

     *n=*n+1;
  }
 }



double fct (double x) {
  return x*x;
}


 void printVector(double * vector, int dim) {
   int j = 0;
   for (j= 0; j < dim; j++) {
     printf("%f\n",vector[j]);
   }
 }

int main () {

  double x = 0;
  double tau = 0;
  int n = 1;
  double *folge = NULL;
  double h0 = 0;

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


  printf("Geben Sie ein h0 ein: ");
  scanf("%lf",&h0);

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

  folge= diff(fct,x,h0,tau,&n);
  printVector(folge,n);
  free (folge);
}