If operator< works properly for floating-point types, why can't we use it for equality testing?

Question

Properly testing two floating-point numbers for equality is something that a lot of people, including me, don\'t fully understand. Today, however, I thought about how some s

Answer 1

The ==, <, >, <=, >=, and != operators work just fine with floating-point numbers.

You seem to have the premise that some reasonable implementation of < ought to compare (double)0.7f equal to 0.7. This is not the case. If you cast 0.7f to a double, you get 0x1.666666p-1. However, 0.7 is equal to 0x1.6666666666666p-1. These are not numerically equal; in fact, (double)0.7f is considerably smaller than 0.7 --- it would be ridiculous for them to compare equal.

When working with floating-point numbers, it is important to remember that they are floating-point numbers, rather than real numbers or rational numbers or any other such thing. You have to take into account their properties and not the properties everyone wants them to have. Do this and you automatically avoid most of the commonly-cited "pitfalls" of working with floating-point numbers.