That formula is a variation of a common method used to determine if a1 and a2 can be considered
equal. It does not tell you which one is larger if they are not equal.
In mathematics, exactly one of the following statements is true for any two real numbers a1 and a2:
A similar list for floating-point numbers is:
- a1 < a2
- a1 ≈ a2 (a1 is approximately-equal to a2)
- a1 > a2
- a1 and a2 are incommensurable (one or both are not-a-number)
If your intent is simply to return the smaller value (and you're sure you don't have to worry about the NaN case), then go ahead and use comparison operators. You can't predict which value is returned when the numbers are nearly equal, but that shouldn't matter because the values are nearly equal.
- if (a1 < a2)
-
return a1;
-
else
-
return a2;
-
If your intent is to select different execution paths for less-than, nearly-equal, and greater-then (and you're sure you don't have to handle the NaN case) then you need to be more careful. Look at
Comparing Floating Point Numbers for a discussion of what the AlmostEqualRelative function has to be. (By the way, the almost-equal leg
has to come first in the code snippet.)
- if (AlmostEqualRelative(a1,a2,epsilon))
-
<nearly-equal execution path>
-
else if (a1 < a2)
-
<less-than execution path>
-
else
-
<greater-than execution path>
You'll have to handle the incommensurable (NaN) case to be fully complete. I'll leave that for another time. (By the way, I can't recall if the Infinities also bring you to that incommensurable case.)
The most valuable thing you'll read in the linked article comes near the beginning:
"[Floating-point] math is hard." 
94
