C++ Bc. 9 cpp

#include <iostream>
#include <iomanip>
#include <cmath>

struct Chyba
{
   template <typename T> Chyba(T t) : text(t) {}

   std::string text;
};

double maclaurin (double x, int a, int& iter, double rel_chyba = 1e-12);

int main ()
{
  using namespace std;

  double m, mstd;
  int    pocet_iteraci;

  for (double x = -1.20; x <= 1.21; x += 0.4)
    {
      for (int a = -2; a <= 2; a++)
	{
	  try
	    {
	      cout.setf (ios_base::fixed, ios_base::floatfield);
	      // explicitne se uvadi znamenko '+'
	      cout.setf (ios_base::showpos); 
	      
	      cout << setprecision(2) << setw (3) << x
		   << ' ' << setw(3) << a
		   << ' ';

	      m    = maclaurin (x, a, pocet_iteraci);
	      mstd = pow (1 + x, a);

	      cout << setprecision( 6) << setw (10) << m
		   << ' ' << setw (10) << mstd;
	      
	      cout.setf  (ios_base::scientific, ios_base::floatfield);
	      cout.unsetf(ios_base::showpos);
	      
	      cout << ' ' << std::abs(m - mstd);
	      
	      cout.setf (ios_base::fixed);
	      cout << ' ' << pocet_iteraci << endl;
	    }
	  catch (Chyba& err)
	    {
	      cout << err.text << endl;
	    }
	}
      for (int i = 0; i < 72; i++)
	{
	  cout << "-";
	}
      cout << endl;
    }

  return 0;
}

double maclaurin (double x, int a, int& iter, double rel_chyba)
{

  if ( a < 0 && (x >= 1.0 || x <= -1.0))
    {
      throw Chyba (" ...");
    }
  
  double dif      = a * x;
  double vysledek = 1.0 + dif;
  int    n        = 2;
  
  while (std::abs (dif) / rel_chyba > std::abs (vysledek))
    {
      dif      *= x * (a - (n - 1)) / n;
      vysledek += dif;
      n++;
    }

  iter = n;

  return vysledek;
}

Příklad výstupu:

-1.20  -2  ...
-1.20  -1  ...
-1.20   0  +1.000000  +1.000000 0.000000e+00 2
-1.20  +1  -0.200000  -0.200000 0.000000e+00 3
-1.20  +2  +0.040000  +0.040000 5.551115e-17 4
------------------------------------------------------------------------
-0.80  -2 +25.000000 +25.000000 8.908785e-11 133
-0.80  -1  +5.000000  +5.000000 1.834444e-11 118
-0.80   0  +1.000000  +1.000000 0.000000e+00 2
-0.80  +1  +0.200000  +0.200000 0.000000e+00 3
-0.80  +2  +0.040000  +0.040000 6.938894e-18 4
------------------------------------------------------------------------
-0.40  -2  +2.777778  +2.777778 1.755041e-12 34
-0.40  -1  +1.666667  +1.666667 7.680523e-13 31
-0.40   0  +1.000000  +1.000000 0.000000e+00 2
-0.40  +1  +0.600000  +0.600000 0.000000e+00 3
-0.40  +2  +0.360000  +0.360000 0.000000e+00 4
------------------------------------------------------------------------
+0.00  -2  +1.000000  +1.000000 2.220446e-16 2
+0.00  -1  +1.000000  +1.000000 1.110223e-16 2
+0.00   0  +1.000000  +1.000000 0.000000e+00 2
+0.00  +1  +1.000000  +1.000000 0.000000e+00 2
+0.00  +2  +1.000000  +1.000000 2.220446e-16 2
------------------------------------------------------------------------
+0.40  -2  +0.510204  +0.510204 1.236788e-13 36
+0.40  -1  +0.714286  +0.714286 1.315614e-13 32
+0.40   0  +1.000000  +1.000000 0.000000e+00 2
+0.40  +1  +1.400000  +1.400000 0.000000e+00 3
+0.40  +2  +1.960000  +1.960000 0.000000e+00 4
------------------------------------------------------------------------
+0.80  -2  +0.308642  +0.308642 1.266764e-13 153
+0.80  -1  +0.555556  +0.555556 2.191580e-13 128
+0.80   0  +1.000000  +1.000000 0.000000e+00 2
+0.80  +1  +1.800000  +1.800000 0.000000e+00 3
+0.80  +2  +3.240000  +3.240000 4.440892e-16 4
------------------------------------------------------------------------
+1.20  -2  ...
+1.20  -1  ...
+1.20   0  +1.000000  +1.000000 0.000000e+00 2
+1.20  +1  +2.200000  +2.200000 0.000000e+00 3
+1.20  +2  +4.840000  +4.840000 0.000000e+00 4

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