[basic.fundamental] It is unclear whether negative zero is negative

[eisenwave]

Reference (section label): [basic.fundamental]

Issue description

#include <complex>
auto c = std::polar(std::copysign(0.0, -1.0));

If negative zero is negative, the Preconditions element of std::polar is not satisfied, and the behavior is undefined. However, the intent is for negative zero and positive zero to be largely interchangeable.

C23 5.2.4.2.2 [Characteristics of floating types <float.h>] clarifies as follows:

A value is negative if and only if it compares less than 0. Thus, negative zeros and NaNs are not negative values.

Library wording such as in [tab:format.sign] already treats negative zero as distinct from the negative numbers:

Indicates that a sign should be used for negative numbers and negative zero only (this is the default behavior).

Suggested resolution

Immediately prior to [basic.fundamental] paragraph 14, insert a new paragraph:

+? A value is negative if and only if it compares less than 0.
+Thus, negative zeros and NaNs are not negative values.

 14 Integral and floating-point types are collectively termed arithmetic types.

[frederick-vs-ja]

I wonder whether this specific case should be handled in an LWG issue. We can say "rho >= 0 is true" instead of "rho is non-negative and non-NaN".

[eisenwave]

The term "non-negative" appears 50 times in the standard, and at least some of these occurrences relate to floating-point numbers; "negative" appears 150+ times. Whether we fix this one little Preconditions element or not, we have a problem if we don't ever say what "negative" means.

I would expect LWG to tell me that this should be clarified in the core language rather than treating any use of the word "negative" for floating-point numbers as inherently ambiguous. That's clearly unsustainable.

[frederick-vs-ja]

Oh, I found that [tab:format.sign] is already implying that negative zero is a non-negative number. But perhaps clarification is still needed.