Why is the statement "f == (float)(double)f;" wrong?
Assuming IEC 60559, the result of f == (float)(double) f depends on the type of f.
Further assuming f is a float, then there's nothing "wrong" about the expression - it will evaluate to true (unless f held NaN, in which case the expression will evaluate to false).
On the other hand, x == (int)(double)x (assuming x is a int) is (potentially) problematic, since a double precision IEC 60559 floating point value only has 53 bits for the significand1, which cannot represent all possible values of an int if it uses more than 53 bits for its value on your platform (admittedly rare). So it will evaluate to true on platforms where ints are 32-bit (using 31 bits for the value), and might evaluate to false on platforms where ints are 64-bit (using 63 bits for the value) (depending on the value).
Relevant quotes from the C standard (6.3.1.4 and 6.3.1.5) :
When a value of integer type is converted to a real floating type, if the value being converted can be represented exactly in the new type, it is unchanged.
When a finite value of real floating type is converted to an integer type other than
_Bool, the fractional part is discarded (i.e., the value is truncated toward zero). If the value of the integral part cannot be represented by the integer type, the behavior is undefined.
When a value of real floating type is converted to a real floating type, if the value being converted can be represented exactly in the new type, it is unchanged.
1 a double precision IEC 60559 floating point value consists of 1 bit for the sign, 11 bits for the exponent, and 53 bits for the significand (of which 1 is implied and not stored) - totaling 64 (stored) bits.