// A program that explores floating point arithmetic in the IEEE 
// floating point standard.  The source code is SourcesOfError.C.

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

int main() {

   float  xs, ys, zs, ws;  // Some single precision variables.
   double yd;              // A double precision variable.

   
   xs = 204.;         // Take an exponential that is out of range.
   ys = exp(xs);
   cout << "The single precision exponential of " << xs << 
           " is " << ys << endl;
   yd = exp ( xs );   // In double precision, it is in range.
   cout << "The double precision exponential of " << xs << 
           " is " << yd << endl;
 
   
   zs = xs / ys;      // Divide a normal number by infinity.
   cout << xs << " divided by " << ys  << " gives " << zs << endl;
   
   ws = ys;           // Divide infinity by infinity.
   zs = ws / ys;
   cout << ws << " divided by " << ys << " gives " << zs << endl;
   
   zs = sqrt( -1.) ;  // sqrt(-1) should be NaN.
   cout << "sqrt(-1.) is " << zs << endl;
   
   ws = xs + zs;      // Add NaN to a normal number.
   cout << xs << " + " << zs << " gives " << ws << endl;
   
   xs =        sin(1.); // Some generic single precision numbers.
   ys = 100.  *sin(2.);
   zs = 10000.*sin(3.);
   float xsPys, ysPxs, xsPzs, zsPxs;  // xsPzx holds xs + zs, etc.
   xsPys = xs + ys;   
   ysPxs = ys + xs;   // Try commuting pairs.
   xsPzs = xs + zs;
   zsPxs = zs + xs;  
   if ( ( xsPys == ysPxs ) && ( xsPzs == zsPxs ) ) 
      cout << "Adding " << xs << "  " << ys << " and "<< zs <<
              " in pairs commutes." << endl;
     else
       cout << "Adding " << xs << "  " << ys << " and "<< zs <<
               " in pairs does not commute." << endl; 
              
   float xsPysPzs, ysPzsPxs;     // Test for associativity.
   xsPysPzs = ( xs + ys ) + zs;
   ysPzsPxs = ( ys + zs ) + xs;
   if ( xsPysPzs == ysPzsPxs ) 
      cout << "Adding " << xs << "  " << ys << " and "<< zs <<
              " is associative." << endl;
     else 
       cout << "Adding " << xs << "  " << ys << " and "<< zs <<
               " is not associative." << endl;
               
   int xi, yi; //   Some integer variables.
   xi =  9;    // Compute the quotient using integer
   yi = 10;    // and floating point arithmetic.
   zs = xi/yi;  
   ws = ( (float) xi ) / ( (float) yi ); // Convert, then divide.
   cout << "Integer division of " << xi << " by " << yi << " gives " <<
           zs << ".  Floating point gives " << ws << endl;
        
   return(0);
   
   }