Proposed resolution:

This wording is relative to N4606.

1. Modify [cmath.syn] as indicated:

   -2- For each set of overloaded functions within <cmath>, with the exception of abs, there shall be additional overloads sufficient to ensure:

   1. If any argument of arithmetic type corresponding to a double parameter has type long double, then all arguments of arithmetic type (3.9.1) corresponding to double parameters are effectively cast to long double.

   2. Otherwise, if any argument of arithmetic type corresponding to a double parameter has type double or an integer type, then all arguments of arithmetic type corresponding to double parameters are effectively cast to double.

   3. Otherwise, all arguments of arithmetic type corresponding to double parameters have type float.

   [Note: abs is exempted from these rules in order to stay compatible with C. — end note]

   See also: ISO C 7.5, 7.10.2, 7.10.6.

[ 2016-07 Chicago ]

Monday: Some of this has been changed in N4606; the rest of the changes may be editorial.

Fri PM: Move to Tentatively Ready

Consider this C++98 program:

#include <cmath>
#include <cstdlib>

int main() {
  return std::abs(static_cast<short>(23)) % 42;
}

This works fine with C++98 compilers. At the std::abs(short) call, short gets promoted to int and std::abs(int) is called.

C++11 added the following wording on page 1083 §26.9 p15 b2 [c.math]:

Otherwise, if any argument of arithmetic type corresponding to a double parameter has type double or an integer type, then all arguments of arithmetic type corresponding to double parameters are effectively cast to double.

C++17 draft additionally adds on page 1080 §26.9 p10 [c.math]:

If abs() is called with an argument of type X for which is_unsigned<X>::value is true and if X cannot be converted to int by integral promotion (4.5), the program is ill-formed. [Note: Arguments that can be promoted to int are permitted for compatibility with C. — end note]

It is somewhat confusing and probably even contradictory to on the one hand specify abs() in terms of integral promotion in §26.9 p10 and on the other hand demand all integral types to be converted to double in §26.9 p15 b2.

Most compilers (each with their own respective library implementation) I tested (MSVC, Clang, older GCC) appear to not consider §26.9 p15 b2 for std::abs and compile the code successfully. GCC 4.5-5.3 (for std::abs but not for ::abs) as well as GCC >=6.0 (for both std::abs and ::abs) fail to compile in the following way: Taking §26.9 p15 b2 literally and applying it to abs() (which is listed in §26.9 p12) results in abs(short) returning double, and with operator% not being specified for double, this makes the programm ill-formed.

I do acknowledge the reason for the wording and semantics demanded by §26.9 p15 b2, i.e. being able to call math functions with integral types or with partly floating point types and partly integral types. Converting integral types to double certainly makes sense here for all the other floating point math functions. However, abs() is special. abs() has overloads for the 3 wider integral types which return integral types. abs() originates in the C standard in stdlib.h and had originally been specified for integral types only. Calling it in C with a short argument returns an int. Calling std::abs(short) in C++98 also returns an int. Calling std::abs(short) in C++11 and later with §26.9 p15 b2 applied to abs() suddenly returns a double.

Additionally, this behaviour also breaks third-party C headers which contain macros or inline functions calling abs(short).

As per discussion on std-discussion, my reading of the standard as well as GCC's interpretation seem valid. However, as can be seen, this breaks existing code.

In addition to the compatibilty concerns, having std::abs(short) return double is also very confusing and unintuitive.

The other (possibly, depending on their respective size relative to int) affected types besides short are signed char, unsigned char and unsigned short, and also char, char16_t, char32_t and wchar_t, (all of these are or may be promotable to int). Wider integral types are not affected because explicit overloads are specified for those types by §26.9 p6, §26.9 p7 and §26.9 p9. div() is also not affected because it is neither listed in §26.9 p12, nor does it actually provide any overload for double at all.

As far as I can see, the proposed or implemented solutions for LWG 2294, 2192 and/or 2086 do not resolve this issue.

I think both, §26.9 p10 [c.math] and §26.9 p15 [c.math] need some correction and clarification.

(Note: These changes would explicitly render the current implementation in GCC's libstdc++ non-conforming, which would be a good thing, as outlined above.)

Previous resolution [SUPERSEDED]:

This wording is relative to N4594.

1. Modify [c.math] as indicated:

   -10- If abs() is called with an argument of type X for which is_unsigned<X>::value is true and if X cannot be converted to int by integral promotion (4.5), the program is ill-formed. If abs() is called with an argument of type X which can be converted to int by integral promotion (4.5), the argument is promoted to int. [Note: Arguments that can be promoted to int are promoted to int in order to keeppermitted for compatibility with C. — end note]

   […]

   -15- Moreover, there shall be additional overloads for these functions, with the exception of abs(), sufficient to ensure:

   1. If any argument of arithmetic type corresponding to a double parameter has type long double, then all arguments of arithmetic type (3.9.1) corresponding to double parameters are effectively cast to long double.

   2. Otherwise, if any argument of arithmetic type corresponding to a double parameter has type double or an integer type, then all arguments of arithmetic type corresponding to double parameters are effectively cast to double.

   3. Otherwise, all arguments of arithmetic type corresponding to double parameters have type float.

   See also: ISO C 7.5, 7.10.2, 7.10.6.

   [Note: abs() is exempted from these rules in order to stay compatible with C. — end note]