Compare floating point numbers as integers

Question

Can two floating point values (IEEE 754 binary64) be compared as integers? Eg.

long long a = * (long long *) ptr_to_double1,
          b = * (long long *) ptr_to_double2;
if (a < b) {...}

assuming the size of long long and double is the same.

Answer 1

No. Two floating point values (IEEE 754 binary64) cannot compare simply as integers with if (a < b).

IEEE 754 binary64

The order of the values of double is not the same order as integers (unless you are are on a rare sign-magnitude machine). Think positive vs. negative numbers.

double has values like 0.0 and -0.0 which have the same value but different bit patterns.

double has "Not-a-number"s that do not compare like their binary equivalent integer representation.

If both the double values were x > 0 and not "Not-a-number", endian, aliasing, and alignment, etc. were not an issue, OP's idea would work.

Alternatively, a more complex if() ... condition would work - see below

[non-IEEE 754 binary64]

Some double use an encoding where there are multiple representations of the same value. This would differ from an "integer" compare.

---

Tested code: needs 2's complement, same endian for double and the integers, does not account for NaN.

int compare(double a, double b) {
  union {
    double d;
    int64_t i64;
    uint64_t u64;
  } ua, ub;
  ua.d = a;
  ub.d = b;
  // Cope with -0.0 right away
  if (ua.u64 == 0x8000000000000000) ua.u64 = 0;
  if (ub.u64 == 0x8000000000000000) ub.u64 = 0;
  // Signs differ?
  if ((ua.i64 < 0) != (ub.i64 < 0)) {
    return ua.i64 >= 0 ? 1 : -1;
  }
  // If numbers are negative
  if (ua.i64 < 0) {
    ua.u64 = -ua.u64;
    ub.u64 = -ub.u64;
  }
  return (ua.u64 > ub.u64)  - (ua.u64 < ub.u64);
}

Thanks to @David C. Rankin for a correction.

Test code

void testcmp(double a, double b) {
  int t1 = (a > b) - (a < b);
  int t2 = compare(a, b);
  if (t1 != t2) {
    printf("%le %le %d %d\n", a, b, t1, t2);
  }

}

#include <float.h>
void testcmps() {
  // Various interesting `double`
  static const double a[] = { 
      -1.0 / 0.0, -DBL_MAX, -1.0, -DBL_MIN, -0.0, 
      +0.0, DBL_MIN, 1.0, DBL_MAX, +1.0 / 0.0 };

  int n = sizeof a / sizeof a[0];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      testcmp(a[i], a[j]);
    }
  }
  puts("!");
}