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

double f1 (double);
double df1 (double);
double d2f1 (double);
double f2 (double);
double df2 (double);
double d2f2 (double);
double f3 (double);
double df3 (double);
double d2f3 (double);
double get_masheps ();
double get_h (int, int, double);
double get_dpm (double, double (*f) (double), double);
double get_dp (double, double (*f) (double), double);
double get_dpdm (double, double (*f) (double), double);
double get_diff (double, double (*df) (double), double);
void calculate (double (*f) (double), double (*df) (double), double (*d2f) (double), double, double);

double f1 (double x)
{
  return sin (x);
}

double df1 (double x)
{
  return cos (x);
}

double d2f1 (double x)
{
  return (-sin (x));
}

double f2 (double x)
{
  return 100 * 100 * 10 * sin (x);
}

double df2 (double x)
{
  return 100 * 100 * 10 * cos (x);
}

double d2f2 (double x)
{
  return -100 * 100 * 10 * sin (x);
}

double f3 (double x)
{
  return tan (x);
}

double df3 (double x)
{
  return 1. / (cos (x) * cos (x));
}

double d2f3 (double x)
{
  return 2. * sin (x) / (cos (x) * cos (x) * cos (x));
}

double get_masheps ()
{
  double tmp = 1.;
  while (tmp + 1. > 1.)
    tmp /= 2.;
  return tmp * 2.;
}

double get_h (int k, int m, double eps)
{
  double res = 0.;
  res = pow (10, k) * pow (eps, 1. / m);
  return res;
}

double get_dpm (double h, double (*f) (double), double x)
{
  double tmp = 0.;
  tmp = (f (x + h) - f (x - h)) / (2. * h);
  return tmp;
}

double get_dp (double h, double (*f) (double), double x)
{
  double tmp = 0.;
  tmp = (f (x + h) - f (x)) / h;
  return tmp;
}

double get_dpdm (double h, double (*f) (double), double x)
{
  double tmp = 0.;
  tmp = (f (x + h) - 2 * f (x) + f (x - h)) / (h * h);
  return tmp;
}

double get_diff (double my_df, double (*df) (double), double x)
{
  double res = 0.;
  res = fabs (my_df - df (x));
  return res;
}

void calculate (double (*f) (double), double (*df) (double), double (*d2f) (double), double x, double eps)
{
  double h = 0., dpm = 0., dp = 0., dpdm = 0., res = 0.;
  int m = 0;

  m = 3;
  for (int k = -2; k < 3; k++)
    {
      h = get_h (k, m, eps);
      dpm = get_dpm (h, f, x);
      res = get_diff (dpm, df, x);
      printf ("h = %.2e,  dpm = %.10e, diff = %e\n", h, dpm, res);
    }
  printf ("\n");

  m = 2;
  for (int k = -2; k < 3; k++)
    {
      h = get_h (k, m, eps);
      dp = get_dp (h, f, x);
      res = get_diff (dp, df, x);
      printf ("h = %.2e,   dp = %.10e, diff = %e\n", h, dp, res);
    }
  printf ("\n");

  m = 4;
  for (int k = -2; k < 3; k++)
    {
      h = get_h (k, m, eps);
      dpdm = get_dpdm (h, f, x);
      res = get_diff (dpdm, d2f, x);
      printf ("h = %.2e, dpdm = %.10e, diff = %e\n", h, dpdm, res);
    }
  printf ("\n");
}

int main (void)
{
  double eps = 0.;
  double x = 1.;
  eps = get_masheps ();
  printf ("eps = %e\n", eps);

  printf ("----------- sin(x) -----------\n");
  calculate (f1, df1, d2f1, x, eps);

  printf ("----------- 10^5 * sin(x) -----------\n");
  calculate (f2, df2, d2f2, x, eps);

  printf ("----------- tg(x) -----------\n");
  x = 1.59;
  calculate (f3, df3, d2f3, x, eps);

  return 0;
}