Can cstdint typedefs bind to some implementation specific types std::numeric_limits is not specialized for?

Is it possible, at least theoretically, that cstdint typedefs bind to some implementation specific types std::numeric_limits is not specialized for?

According http://www.cplusplus.com/reference/limits/numeric_limits , let me quote, "[std::numeric_limits] is specialized for every fundamental arithmetic type, with its members describing the properties of type T. This template shall not be specialized for any other type."

According to http://en.cppreference.com/w/cpp/types/numeric_limits , let me quote again, "implementations may provide specializations of std::numeric_limits for implementation-specific types".

"May", cppreference says. So they don't have to.

And finally, according to http://www.cplusplus.com/reference/cstdint , the typedefs defined in the header "are typedefs of fundamental integral types or extended integral types".

So, to sum up - it seems that cstdint typedefs might bind to extended integral types (whatever they are), which are not fundamental integral types (again, whatever they are), and therefore might be incompatible with std::numeric_limits . Is this correct?

However, the documentations I linked to seem to be slightly inconsistent on one point. Isn't cplusplus.com's prohibition that std::numeric_limits must not be specialized for any non-fundamental arithmetic type in opposition of cppreference's allowance that std::numeric_limits might be specialized for implementation-specific types? Unless, of course, these implementation-specific types actually are fundamental integral types, in which case, hopefully, std::numeric_limits would have to be specialized for all cstdint typedefs.

The documentations confuse me. So I ask my question here :)

EDIT.

According to http://eel.is/c++draft/cstdint , cstdint must bind to integer types. And according to http://eel.is/c++draft/limits.numeric , "Specializations shall be provided for each arithmetic type, both floating point and integer, including bool". Is the understanding that integer type is an arithmetic type and therefore std::numeric_limits must be specialized for cstdint typedefs correct?

Solution

The specializations such as std::numeric_limits<std::int_fast32_t> must exist.

3.9.1/2:

There are five standard signed integer types: "signed char", "short int", "int", "long int", and "long long int". ... There may also be implementation-defined extended signed integer types. The standard and extended signed integer types are collectively called signed integer types.

3.9.1/3:

For each of the standard signed integer types, there exists a corresponding (but different) standard unsigned integer type.... Likewise, for each of the extended signed integer types there exists a corresponding extended unsigned integer type.... The standard and extended unsigned integer types are collectively called unsigned integer types.

3.9.1/7:

Types bool, char, char16_t, char32_t, wchar_t, and the signed and unsigned integer types are collectively called integral types. A synonym for integral type is integer type.

3.9.1/8:

Integral and floating types are collectively called arithmetic types. Specializations of the standard template std::numeric_limits (18.3) shall specify the maximum and minimum values of each arithmetic type for an implementation.

18.3.2.1/2:

Specializations [of numeric_limits] shall be provided for each arithmetic type, both floating point and integer, including bool.

18.4.1:

namespace std {
  typedef signed_integer_type int8_t;    // optional
  //...
  typedef unsigned_integer_type uint8_t; // optional
  //...
}

So the types defined in <cstdint> might be extended types, but are definitely integer types and therefore must have corresponding specializations of std::numeric_limits.

Also, all integral types are "fundamental" in the sense used in the Standard (3.9), though not all are standard types.