Is it possible to get 0 by subtracting two unequal floating point numbers?

Question

Is it possible to get division by 0 (or infinity) in the following example?

public double calculation(double a, double          


        

Answer 1

In olden times before IEEE 754, it was quite possible that a != b didn't imply a-b != 0 and vice versa. That was one of the reasons to create IEEE 754 in the first place.

With IEEE 754 it is almost guaranteed. C or C++ compilers are allowed to do an operation with higher precision than needed. So if a and b are not variables but expressions, then (a + b) != c doesn't imply (a + b) - c != 0, because a + b could be calculated once with higher precision, and once without higher precision.

Many FPUs can be switched to a mode where they don't return denormalized numbers but replace them with 0. In that mode, if a and b are tiny normalised numbers where the difference is smaller than the smallest normalised number but greater than 0, a != b also doesn't guarantee a == b.

"Never compare floating-point numbers" is cargo cult programming. Among the people who have the mantra "you need an epsilon", most have no idea how to choose that epsilon properly.