c - casting signed to double different result than casting to float then double -

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Then, as part of an assignment, I am working on an expression: (double) (float) x == (Double) x 1 or not. (X is a signed integer)

It works for every value except INT_MAX. I was wondering why this is so? If I print the values, then they both show the same value for INT_MAX. 

  x = INT_MAX; Printf ("signed X:% d \ n", x); Float fx1 = (float) x; Double dx 1 = (double) x; Double dfx = (double) (float) x; Printf ("(double) x:% g \ n", dx1); Printf ("(float) x:% f \ n", fx1); Printf ("(double) (float) x:% g \ n", dfx); If ((double) (float) x == (double) x) {printf ("RESULT:% d \ n", ((double) (float x == (double) x)); }   
 Edit: The entire program:  
  contains # lt; Stdio.h & gt; #to & lt include, stdlib.h & gt; #to & lt include, limits.h & gt; Int main (int argc, char * argv []) {// create random values ​​int x = INT_MAX; Printf ("signed X:% d \ n", x); Float fx1 = (float) x; Double dx 1 = (double) x; Double dfx = (double) (float) x; Printf ("(double) x:% g \ n", dx1); Printf ("(float) x:% f \ n", fx1); Printf ("(double) (float) x:% g \ n", dfx); If ((double) (float) x == (double) x) {printf ("RESULT:% d \ n", ((double) (float x == (double) x); } Return 0;   
} The end of the main task   
 
 
  Int < / Code> and  float  in their representation is likely to have the same number of bits, i.e. 32. In  float  there is a mantissa, an exponent and a signal bit, so i Must be at least bitta, which is required for large  int  values ​​like  INT_MAX . Therefore, lack of accuracy while storing in  float

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