Not a Number

If you are writing programs in an environment where NaNs (Not-a-Number) crop up a lot, as I am, then turning on assertion checking beyond require level is not, in general, practical. The problem is not performance, but the fact that no NaN compares equal to any number, including itself. And for good reason.

So when you encounter a postcondition such as this from class ARRAY:

put (v: like item; i: INTEGER_32)
			-- Replace `i'-th entry, if in index interval, by `v'.
		require -- from TABLE
			valid_key: valid_index (i)
		require -- from TO_SPECIAL
			valid_index: valid_index (i)
			area.put (v, i - lower)
		ensure then -- from INDEXABLE
			insertion_done: item (i) = v
		ensure -- from TO_SPECIAL
			inserted: item (i) = v

you will get a violation if item is of type REAL_64 (for instance), and v is a NaN.

And such postconditions are pervasive.

This is a serious difficulty with Eiffel at the moment. So I am putting forward the following proposal as a starter to kick off a community discussion.

The essence of my proposal is to add a routine named is_numerically_equal (a_other: NUMERIC): BOOLEAN to class NUMERIC.

This will differ from is_equal in that if either operand is a NaN, then the result is guaranteed to be False. Whereas is_equal will return True if both operands are NaNs.

Now it is important that the = operator can continue to be used in the traditional mathmatical sense for numbers. So it will have to differ in its definition for class NUMERIC from all other classes. This will be a language change, since ECMA states that = uses is_equal.

This means that postcondition like:

insertion_done: item (i) = v

from INDEXABLE need to be re-written to use ~.