How to properly compare an integer and a floating-point value?

Question

How do I compare an integer and a floating-point value the right way™?

The builtin comparsion operators give incorrect results in some edge cases, for examp

Answer 1

To compare a FP f and integer i for equality:

(Code is representative and uses comparison of float and long long as an example)

1. If f is a NaN, infinity, or has a fractional part (perhaps use frexp()), f is not equal to i.

   float ipart;
   // C++
   if (frexp(f, &ipart) != 0) return not_equal;
   // C
   if (frexpf(f, &ipart) != 0) return not_equal;
   

2. Convert the numeric limits of i into exactly representable FP values (powers of 2) near those limits.^** Easy to do if we assume FP is not a rare base 10 encoding and range of double exceeds the range on the i. Take advantage that integer limits magnitudes are or near Mersenne Number. (Sorry example code is C-ish)

   #define FP_INT_MAX_PLUS1 ((LLONG_MAX/2 + 1)*2.0)
   #define FP_INT_MIN (LLONG_MIN*1.0)
   

3. Compare f to is limits

   if (f >= FP_INT_MAX_PLUS1) return not_equal;
   if (f < FP_INT_MIN) return not_equal;
   

4. Convert f to integer and compare

   return (long long) f == i;
   

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To compare a FP f and integer i for <, >, == or not comparable:

(Using above limits)

1. Test f >= lower limit

   if (f >= FP_INT_MIN) {
   

2. Test f <= upper limit

     // reform below to cope with effects of rounding
     // if (f <= FP_INT_MAX_PLUS1 - 1)
     if (f - FP_INT_MAX_PLUS1 <= -1.0) {
   

3. Convert f to integer/fraction and compare

       // at this point `f` is in the range of `i`
       long long ipart = (long long) f;
       if (ipart < i) return f_less_than_i;
       if (ipart > i) return f_more_than_i;
   
       float frac = f - ipart;
       if (frac < 0) return f_less_than_i;
       if (frac > 0) return f_more_than_i;
       return equal;
     }
   

4. Handle edge cases

     else return f_more_than_i;
   }
   if (f < 0.0) return f_less_than_i;
   return not_comparable;
   

Simplifications possible, yet I wanted to convey the algorithm.

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^** Additional conditional code needed to cope with non 2's complement integer encoding. It is quite similar to the MAX code.