Question

I stumbled upon the following example on wikipedia (http://en.wikipedia.org/wiki/Type_conversion#Implicit_type_conversion).

#include <stdio.h>

int main()
{
    int i_value   = 16777217;
    float f_value = 16777217.0;
    printf("The integer is: %i\n", i_value); // 16777217
    printf("The float is:   %f\n", f_value); // 16777216.000000
    printf("Their equality: %i\n", i_value == f_value); // result is 0
}

Their explanation: “This odd behavior is caused by an implicit cast of i_value to float when it is compared with f_value; a cast which loses precision, making the values being compared different.”

Isn’t this wrong? If i_value were cast to float, then both would have the same loss in precision and they would be equal.
So i_value must be cast to double.

Answer 1

No, in the case of the equality operator, the “usual arithmetic conversions” occur, which start off:

• First, if the corresponding real type of either operand is long double, the other operand is converted, without change of type
  domain, to a type whose corresponding real type is long double.
• Otherwise, if the corresponding real type of either operand is double, the other operand is converted, without change of type
  domain, to a type whose corresponding real type is double.
• Otherwise, if the corresponding real type of either operand is float, the other operand is converted, without change of type
  domain, to a type whose corresponding real type is float.

This last case applies here: i_value is converted to float.

The reason that you can see an odd result from the comparison, despite this, is because of this caveat to the usual arithmetic conversions:

The values of floating operands and of the results of floating
expressions may be represented in greater precision and range than
that required by the type; the types are not changed thereby.

This is what is happening: the type of the converted i_value is still float, but in this expression your compiler is taking advantage of this latitude and representing it in greater precision than float. This is typical compiler behaviour when compiling for 387-compatible floating point, because the compiler leaves temporary values on the floating point stack, which stores floating point numbers in an 80bit extended precision format.

If your compiler is gcc, you can disable this additional precision by giving the -ffloat-store command-line option.