//	Reihe.cc
//
//			Sum 1/kČ  = Pi^2 / 6  [Euler, 1736]
//			limited accuracy
//			Is s1 or s2 closer to right result ?

#include <iostream.h>
#include <math.h>
#include <float.h>

main()
{
 float s1,s2;
 int i,n ;
 
 cout << endl << "Demo for precision of float" << endl;

//		Print the index where cancelation has to be expected for float 
 cout << "The first sum will be rather precise until  n = " 
      << ceil(sqrt(1./FLT_EPSILON)) << endl;

//		Input highest index
 cout << endl << " n =  ";
 cin >> n;
// n = 65000;
 
//		Calculate in incrementing order
 s1 = 0.0; 
 for (i=1; i<=n; i++)
   {
     s1 += 1.0/i/i;
   }
 
 cout << endl << "s1 = " << s1 << endl << endl;
 
//		Calculate in decrementing order
 s2 = 0.0; 
 for (i=n; i>=1; i--)
   {
     s2 += 1.0/i/i;
//     s2 += 1.0/(i*i);	     // results in inf
//				since i*i may be longer than int supports
   }

 cout << endl << "s2 = " << s2 << endl << endl;
 
//				Compare both sums
 cout << endl << "Diff " << s2-s1 << endl << endl;
 
//				Compare sums with exact result 
 cout << endl << "Pi*Pi/6 - s1 : " << M_PI*M_PI/6-s1 << endl;
 cout << endl << "Pi*Pi/6 - s2 : " << M_PI*M_PI/6-s2 << endl << endl;

}