Floating Point comparison problem

Next month I will start to work on a C++ based Software named CAT++ which
is going to provide FORTRAN like arrays in C++ and will be used within
Scientific Community and hence will heavily depend on
Numerical-Computations. I was reading 29.16 ans 29.17 sections of FAQs:

http://www.para****ft.com/c++-faq-lite/newbie.html#faq-29.16


as a test, I just tried this program on Linux, GCC 4.2.2 and it gave me 2
different results:

 
#include <iostream>                                                       
                                                                    
#include <string>                                                         
                                                                    
#include <vector>                                                         
                                                                    
                                                                          
                                                                    
int main()                                                                
                                                                    
{                                                                         
                                                                    
  const double x = 0.05;                                                  
                                                                    
  const double y = 0.07;                                                  
                                                                    
  const double z = x + y;                                                 
                                                                    
  const double key_num = x + y;                                           
                                                                    
                                                                          
                                                                    
  if( key_num == z )                                                      
                                                                    
    {                                                                     
                                                                    
      std::cout << "==\n";                                                
                                                                    
    }                                                                     
                                                                    
  else                                                                    
                                                                    
    {                                                                     
                                                                    
      std::cout << "!=\n";                                                
                                                                    
    }                                                                     
                                                                    
                                                                          
                                                                    
  return 0;                                                               
                                                                    
}                                                                         
                                                                    

========== OUTPUT ============

/home/arnuld/programs $ g++ -ansi -pedantic -Wall -Wextra test2.cpp       
                                                           
/home/arnuld/programs $ ./a.out                                           
                                            
==                                                                        
                                                                    
/home/arnuld/programs $  


it always outputs == , Now i changed key_num to this:   
 
     const double key_num = 0.12;  

and this program now always outputs !=  

/home/arnuld/programs $ g++ -ansi -pedantic -Wall -Wextra test2.cpp
/home/arnuld/programs $ ./a.out
!=
/home/arnuld/programs $


As FAQ explains Floating-Point is inaccurate but my project is heavily
oriented towards number-crunching, so I was thinking of stop developing
that sofwtare in C++ and simply use FORTRAN for this specific
application in a special domain.

                                                                        

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