A proposal for a type trait to detect narrowing conversions

ISO/IEC JTC1 SC22 WG21 P0870R4 2020-09-15

Project: Programming Language C++

Audience: Library Evolution Working Group, Study Group 6 (Numerics)

Table of Contents

• 1. Introduction
• 2. Changelog
• 3. Motivation and Scope
• 4. Impact On The Standard
• 5. Design Decisions
• 6. Technical Specifications
• Appendix A
• Appendix B

§ 1. Introduction

This paper proposes a new type trait for the C++ Standard Library, is_convertible_without_narrowing, to detect whether a type is implictly convertible to another type without going through a narrowing conversion.

§ 1.1 Tony Tables

// list initialization forbids narrowing for e.g. int,
// but not for types "wrapping" int (like
// optional<int>, variant<int>, etc.):


template <typename T>
struct optional
{
    template <typename U = T>
    optional(U&& u)

    { ~~~ }
};

int some_int{3.14};               // ERROR
optional<int> optional_int{3.14}; // OK, but possibly not wanted

// make it possible to block narrowing for int,
// as well as anything "wrapping" int:



template <typename T>
struct optional
{
    template <typename U = T>
    optional(U&& u)
    requires std::is_convertible_without_narrowing_v<U&&, T>
    { ~~~ }
};

int some_int{3.14};               // ERROR
optional<int> optional_int{3.14}; // ERROR

template <typename T>
class complex;

// Each floating point specialization of complex defines conversion
// constructors which are implicit if and only if they don't narrow

template <>
class complex<float>
{
    float re; float im;
public:
    explicit complex(const complex<double>& other);
    explicit complex(const complex<long double>& other);
};

template <>
class complex<double>
{
    double re; double im;
public:
    /* implicit */ complex(const complex<float>& other);
    explicit complex(const complex<long double>& other);
};

// repeat for long double, extended floating point [P1467R4], etc.

template <typename T>
class complex;

// Just one converting constructor template that uses explicit(bool)
// (it's pointless to also check for convertibility, floating points
// always convert to each other)

template <std::floating_point T>
class complex
{
    T re; T im;
public:
    template <std::floating_point U>
    explicit(!std::is_convertible_without_narrowing_v<U, T>)
    complex(const complex<U>& other);
};

// simplified from QObject

template <typename Func1, typename Func2>
bool connect(QObject *sender, Func1 signal,
             QObject *receiver, Func2 slot)
{
    // Check that the signal is compatible with the slot.
    // This means:
    // * that the signal carries at least as many arguments
    //   than the slot;
    // * that each positional argument of the signal is convertible
    //   to the respective argument of the slot;
    // * etc.

    static_assert(detail::check_argument_count<Func1, Func2>,
                 "The slot requires more arguments than the signal provides.");

    static_assert(detail::check_convertible_arguments<Func1, Func2>,
                  "Signal and slot arguments are not compatible.");

    return detail::connect_impl(~~~);
}

// When the temperature changes, emits a signal carrying a double
BodyThermometer *thermometer = ~~~;

// Has a slot that shows an integer value on the screen
IntLabel *label = ~~~;

// OK, but likely a mistake: will silently truncate the double
// emitted with the signal. For instance, 37.0 and 37.99 would
// be both displayed as "37".
// Still, it compiles, because double is implicitly convertible to int...
connect(thermometer, &BodyThermometer::temperatureChanged,
        label, &IntLabel::setValue);

// simplified from QObject

template <typename Func1, typename Func2>
bool connect(QObject *sender, Func1 signal,
             QObject *receiver, Func2 slot)
{
    // Same checks, but refine the convertibility check so that no argument
    // carried by the signal needs a narrowing conversion
    // in order to be converted to the respective argument in of the slot





    static_assert(detail::check_argument_count<Func1, Func2>,
                 "The slot requires more arguments than the signal provides.");

    static_assert(detail::check_convertible_without_narrowing_arguments<Func1, Func2>,
                  "Signal and slot arguments are not compatible/would narrow.");

    return detail::connect_impl(~~~);
}


BodyThermometer *thermometer = ~~~;


IntLabel *label = ~~~;




// ERROR: failing static_assert, would narrow
connect(thermometer, &BodyThermometer::temperatureChanged,
        label, &IntLabel::setValue);

§ 2. Changelog

• P0870R4
  • Incorporated the feedback after a review of the paper on the lib-ext mailing list.
  • Changed the proposed name of the trait to is_convertible_without_narrowing following a poll on the mailing list; the semantics have been adapted.
  • Added Tony Tables with more examples.
  • Change the target audience to LEWG.
• P0870R3
  • Clarified that the implementation using an array won't work with certain datatypes (void, etc.).
  • Added a feature test macro.
  • Rebased the proposed wording on top of N4861.
  • Improved the proposed wording.
  • Editorial fixes: numbered the sections, fixed misspellings.
• P0870R2
  • Incorporated feedback from the LEWGI, EWGI, EWG sessions in Prague. In the LEWGI session this proposal was met favourably (2-10-2-1-0). EWGI and EWG didn't have any direct feedback (and also no particular concerns).
  • Elaborated on possible implementations.
  • Elaborated more on design decisions, especially regarding whether user-defined types should be handled, and whether this proposal would constrain core language evolution. Unlike R1, we now also include user-defined types in narrow conversion sequences (but like R1, we stick to [dcl.init.list] semantics, which are not customizable).
  • Updated reference to P0608R3.
  • Referenced other papers.
  • Incorporated the changes to [dcl.init.list] introduced by P1957R2.
  • Added SG6 to the target audience.
  • Improved spelling.
• P0870R1
  • Submitted for the Prague mailing, targeting LEWGI.

§ 3. Motivation and Scope

A narrowing conversion is formally defined by the C++ Standard in [dcl.init.list], with the intent of forbidding them from list-initializations.

It is useful in certain contexts to know whether a conversion between two types would qualify as a narrowing conversion. For instance, it may be useful to inhibit (via SFINAE) construction or conversion of "wrapper" types (like std::variant or std::optional) when a narrowing conversion is requested.

A use case the author has recently worked on was to prohibit narrowing conversions when establishing a connection in the Qt framework (see [Qt]), with the intent of making the type system more robust. Simplifying, a connection is established between a signal non-static member function of an object and a slot non-static member function of another object. The signal's and the slot's argument lists must have compatible arguments for the connection to be established: the signal must have at least as many arguments as the slot, and the each argument of the signal must be implictly convertible to the corresponding argument of the slot. In case of a mismatch, a compile-time error is generated. Bugs have been observed when connections were successfully established, but a narrowing conversion (and subsequent loss of data/precision) was happening. Detecting such narrowing conversions, and making the connection fail for such cases, would have prevented the bugs.

§ 4. Impact On The Standard

This proposal is a pure library extension.

It proposes changes to an existing header, <type_traits>, but it does not require changes to any standard classes or functions and it does not require changes to any of the standard requirement tables.

This proposal does not require any changes in the core language, and it has been implemented in standard C++.

This proposal does not depend on any other library extensions.

This proposal may help with the implementation of [P0608R3], the adopted resolution for [LEWG 227]. In particular, in [P0608R3]'s wording section, the "invented variable x" is used to detect a narrowing conversion. However, the same paragraph is also broader than the current proposal, in the sense that it special-cases boolean conversions [conv.bool], while the current proposal does not handle them in any special way. The part about boolean conversions has been anyhow removed by adoping [P1957R2].

The just mentioned [P1957R2], as a follow up of [P0608R3], made conversions from pointers to bool narrowing. It was adopted in the Prague meeting, therefore extending the definition of narrowing conversion in [dcl.init.list]. We do not see this as a problem: we aim to provide a trait to detect narrowing conversions exactly as specified by the Standard. Should the specification change, then the trait detection should also change accordingly; cf. the design decisions below.

This proposal overlaps with [P1818R1], a proposal that aims at introducing a distinction between narrowing and widening conversions. [P1818R1] is much more ambitious than this proposal; amongst other things, it aims at defining a widening trait. The wording of [P1818R1] is not complete, but we think that such a trait somehow overlaps with the semantics of the trait proposed here; it would ultimately depend on the exact definition of what constitutes a "widening conversion". Anyhow, the adoption of [P1818R1] is orthogonal to the present proposal.

[P1619R1] and [P1998R1] introduce functions (called respectively can_convert and is_value_lossless_convertable) that check whether a given value of an integer type can be represented by another integer type. This is in line with the spirit of detecting narrowing conversions, namely, preventing loss of information and/or preventing undefined behavior. While this proposal works on types, the functions examine specific values; we therefore think that the proposals are somehow orthogonal to the current proposal. Moreover, [P1619R1] and [P1998R1]'s functions only deal with integer types, while the narrowing definition in [dcl.init.list] (adopted by this proposal) also deals with floating point and enumeration types (and, following [P1957R2]'s adoption, also boolean and pointer types).

§ 5. Design Decisions

The most natural place to add the trait presented by this proposal is the already existing <type_traits> header, which collects most (if not all) of the type traits available from the Standard Library.

In the <type_traits> header the is_convertible type trait checks whether a type is implictly convertible to another type. Building upon this established name, the proposed name for the trait described by this proposal shall therefore be is_convertible_without_narrowing, with the corresponding is_convertible_without_narrowing_v type trait helper variable template.

§ 5.1 Should is_convertible_v<From, To> == true be a precondition of trying to instantiate is_convertible_without_narrowing<From, To>?

The author deems this unnecessary. Adding such a precondition would likely make the usage of the proposed trait more difficult and/or error prone.

As far as the author can see, the precondition is not going to dramatically simplify the specification for the proposed trait, or its implementation.

§ 5.2 Given a type From convertible to a type To, should is_convertible_without_narrowing_v<From, To> yield false only for the combinations of types listed in [dcl.init.list]? What about user-defined types?

The R1 revision of this paper was limiting the possibility for the trait to detect narrowing if and only if both From and To were one of the types listed in [dcl.init.list], which are all builtin types. Now, while we strongly want the type trait to match the language definition of narrowing conversion, there are some objections to simply detecting if we are in one of the those cases.

For instance, should a conversion from const double to float be considered narrowing or not? If we take the listing in [dcl.init.list] literally, then the answer would be "no" (that is, the trait would have to yield true), because const double is not in the list. However, this is not really useful, nor expected. If some code checks whether there is a conversion between two types and the conversion isn't narrowing, such code could erroneously infer that this is the case between const double and float and do the conversion. (This is in spite of the fact that list-initialization would not work, because there is a narrowing conversion in the conversion sequence).

To elaborate on this last sentence: the definition of list-initialization in [dcl.init.list] contains several cases where, if a narrowing conversion takes place, then the program is ill-formed. We believe that, more than detecting if a given conversion between two types is a narrowing conversion (as strictly per the definition), users want to detect if a conversion has a narrowing conversion, and thus would be forbidden if used in a list-initialization. As a consequence, we claim that is_convertible_without_narrowing_v<const double, float> should yield false.

This is not simply doable by stripping From and To of their cv-qualifiers (e.g. by applying std::decay_t on them), and then checking if the resulting types do not form a narrowing conversion. One must also consider all the other cases for conversions, which necessarily include user-defined types, as they may define implicit conversion operators that can be used as part of a conversion sequence that also includes a narrowing conversion. As an example:

struct S { operator double() const; };
S s;
float f1 = s;     // OK
float f2 = { s }; // ERROR: narrowing

We therefore claim that is_convertible_without_narrowing_v<S, float> should yield false. A similar example is used in [P0608R3] and then [P1957R2]'s design. Slightly adapted:

struct Bad { operator char const*() &&; };

With the adoption of [P1957R2] in the Standard, we claim that is_convertible_without_narrowing_v<Bad, bool> should yield false. For completeness, is_convertible_without_narrowing_v<Bad &, bool> should yield false (there is no conversion), and is_convertible_without_narrowing_v<Bad &&, bool> should yield false as well (narrowing).

Note that, although user-defined datatypes are involved, the detection of whether there is a narrowing conversion sticks to the list of narrowing conversions in [dcl.list.init], which deals with fixed number of cases: between certain integer and floating point types; from unscoped enumeration types to a integer or a floating point type; and from pointer types to boolean. We are not proposing to allow any customization to these cases (see below).

§ 5.3 Should is_convertible_without_narrowing<From, To> yield false for boolean conversions [conv.bool]?

The author deems this to be out of scope for the proposed trait, which should have only the semantics defined by the language regarding narrowing conversion. Another trait should be therefore added to detect (implicit) boolean conversions, which, according to the current wording of [dcl.init.list], are not considered narrowing conversions. (Note that with the adoption of [P1957R2], conversions from pointer types to boolean are indeed considered narrowing.)

It is the author's opinion that, in general, implicit boolean conversions are undesirable for the same reasons that make narrowing conversions unwanted in certain contexts — in the sense that a conversion towards bool may discard important information. However, we recognize the importance of not imbuing a type trait with extra, not yet well-defined semantics, and therefore we are excluding boolean conversions from the present proposal.

§ 5.4 Should is_convertible_without_narrowing<From, To> use some other semantics than the narrowing defined in [dcl.init.list]?

Given that narrowing is formally defined in the core language, we are strongly against deviating from that definition. If anything, proposals aiming at marking as narrowing certain conversions between user defined types should also amend the core language definition; the type trait would still stick to that definition.

§ 5.5 Should specializations of is_convertible_without_narrowing<From, To> be allowed?

We believe that specializations of the trait should be forbidden. This is consistent with the other type traits defined in [meta] (cf. [meta.rqmts]), and with the fact that the current wording of [dcl.init.list] defining narrowing conversions does not extend to user-defined types.

We are aware of broader work happening in the area, such as [P1818R1]. That proposal introduces a keyword to mark widening conversions, but one may think of an alternative approach where users are expected to specialize is_convertible_without_narrowing in order to mark a conversion as non-narrowing. In any case, lifting the above limitation on specializations would always be possible.

§ 5.6 Does providing such a trait make changes to the definition of "narrowing conversion" harder to land?

This objection has been raised during the LEWGI meeting in Prague. The objection is sound, in the sense that a future possible change to the definition of narrowing conversion will impact user code using the trait.

On the other hand, during the Prague meeting, EWGI and EWG did not raise this concern regarding this proposal.

First and foremost, we would like to remark that the trait is already implementable — and has indeed already been implemented — using standard C++ (e.g. via To{std::declval<From>()}, cf. below). Any change to the definition of narrowing would therefore already be impacting user code. The impact would likely go beyond type traits / metaprogramming, since initialization itself would change semantics. An example of such a change affecting [dcl.init.list] comes from [P1957R2], which has been adopted in Prague. That adoption changed the semantics of code like bool b = {ptr}; (making it ill-formed; was OK before).

In general, changes to the core language that affected type traits have already happened. For instance, between C++17 and C++20 the definition of "aggregate" in [dcl.init.aggr] has been changed, therefore changing the semantics of the std::is_aggregate type trait. Similarly, the definitions of "trivial class" and of "trivially copyable class" in [class.prop] have changed between C++14 and C++17; meaning that also the type traits std::is_trivial and std::is_trivially_copy_constructible have changed semantics.

We can therefore reasonably assume that the presence of a trait does not seem to preclude changes to the core language (or, if such an objection was raised when proposing these changes to the core language, it was also disregarded, as the changes did ultimately land).

Finally, it is the author's opinion that code that is using facilities to detect narrowing conversions would like to stick to the core language definition. If the definition changes, we foresee that the detection wants to change too, following the definition. Note that an ad-hoc solution (rather than a standardized trait) may fall out of sync with the core language definition, and thus start misdetecting some cases.

§ 5.7 Should there be a matching concept?

This point was raised during the LEWGI meeting in Prague, and it was deemed unnecessary at this point, because ultimately this proposal is just about a type trait. If it will be deemed useful, adding a concept could always be done at a later time, via another proposal.

§ 5.8 Bikeshedding: naming

The LEWGI review of the R3 revision of this paper discussed several options for the name of the trait.

In earlier versions we proposed the name is_narrowing_convertible; however, during the review of the paper, there was a general consensus that the majority of uses is going to be about detecting whether a conversion is possible without narrowing. As such, is_narrowing_convertible (which detects if a conversion does involve a narrowing conversion) would always need to be combined with is_convertible to achieve the desidered result, for instance like this:

~~~
// detect if From is convertible to To without a narrowing conversion
requires (is_convertible_v<From, To> && !is_narrowing_convertible_v<From, To>)
~~~

Another concern was raised about the very usage of "narrowing convertible", which is not currently a term used anywhere in the Standard.

Therefore, a poll was taken on the lib-ext mailing list, trying to find a better name, offering options for both a positive name (conversion sequence involves a narrowing conversion) or a negative one (conversion sequence does not involve a narrowing conversion). The proposed options were:

• is_narrowing_convertible
• is_convertible_with_narrowing
• is_narrowing
• is_non_narrowing_convertible
• is_nonarrowing_convertible
• is_nonnarrowing_convertible
• is_convertible_without_narrowing
• is_convertible_no_narrowing
• is_non_narrowing

The poll had very scarce participation, but is_convertible_without_narrowing emerged as the preferred option. The R4 revision of this paper renamed the trait, and, consequently, adapted the discussion regarding its semantics — that is, to detect types that are convertible through a conversion sequence that does not require a narrowing conversion. This required some rewording in a few places.

§ 6. Technical Specifications

§ 6.1. Implementation

The proposed type trait has already been implemented in various codebases using ad-hoc solutions (depending on the quality of the compiler, etc.), using standard C++ and without the need of any special compiler hooks.

One possible implementation is to exhaustively check whether a conversion between two types fall in one of the narrowing cases listed in [dcl.list.init]. This particular implementation has been done in [Qt connect()] (see this proposal's motivation about why this detection has been added to Qt in the first place); it has obviously maintenance and complexity shortcomings. The most important part is:

template<typename From, typename To, typename Enable = void>
struct AreArgumentsNarrowedBase : std::false_type
{
};

template<typename From, typename To>
struct AreArgumentsNarrowedBase<From, To, typename std::enable_if<sizeof(From) && sizeof(To)>::type>
    : std::integral_constant<bool,
          (std::is_floating_point<From>::value && std::is_integral<To>::value) ||
          (std::is_floating_point<From>::value && std::is_floating_point<To>::value && sizeof(From) > sizeof(To)) ||
          ((std::is_integral<From>::value || std::is_enum<From>::value) && std::is_floating_point<To>::value) ||
          (std::is_integral<From>::value && std::is_integral<To>::value
           && (sizeof(From) > sizeof(To)
               || (std::is_signed<From>::value ? !std::is_signed<To>::value
                   : (std::is_signed<To>::value && sizeof(From) == sizeof(To))))) ||
          (std::is_enum<From>::value && std::is_integral<To>::value
           && (sizeof(From) > sizeof(To)
               || (IsEnumUnderlyingTypeSigned<From>::value ? !std::is_signed<To>::value
                   : (std::is_signed<To>::value && sizeof(From) == sizeof(To)))))
          >
{
};

(Historical note: at the time this implementation was done, the codebase could only use C++11 features, and some compilers were unable to cope with the SFINAE solution presented below.).

The Qt implementation strictly checks for the one of narrowing cases listed in [dcl.init.list], which is not the aim of the current proposal (cf. design decisions above). Also, the snippet does not yet implement the change introduced by [P1957R2], showing an inherent limitation to such an "exhaustive" solution: it may fall out of sync with the core language.

Another, much simpler implementation is to rely on SFINAE around an expression such as To{std::declval<From>()}. However, this form is also error-prone: it may accidentally select aggregate initialization for To, or a constructor taking a std::initializer_list, and so on. If for any reason these make the expression ill-formed, then the trait is going to report that there is a narrowing conversion between the types, even when there actually isn't one (or vice-versa, depending on how one builds the trait).

[P0608R3] uses a clever workaround to avoid falling into these traps: declaring an array, that is, building an expression like To t[] = { std::declval<From>() };. This solution is now used in the Standard (in [variant.ctor] and [variant.assign]), amongst other things, in order to detect and prevent a narrowing conversion. The trait that we are proposing could be used to replace the ad-hoc solution, and clarify the intent of it.

Another possible implementation, that uses the just mentioned workaround, is the following one (courtesy of Zhihao Yuan; received via private communication, slightly adapted):

template<class From, class To>
inline constexpr bool is_convertible_without_narrowing_v = false;

template<class T, class U>
concept __construct_without_narrowing = requires (U&& x) {
    { std::type_identity_t<T[]>{std::forward<U>(x)} } -> T[1];
};

template<class From, class To> requires std::is_convertible_v<From, To>
inline constexpr bool is_convertible_without_narrowing_v<From, To> =
    __construct_without_narrowing<To, From>;

Using some sort of SFINAE around an array declaration can therefore be used as the main part of detection. A complete implementation also needs handling of the "corner cases". Types such as cv void, reference types, function types, arrays of unknown bounds, etc., require special care because they cannot be used to declare the array of To, and this may give wrong results. Note that we propose that it is legal to specialize is_convertible_without_narrowing with these types, following the precedent set by is_convertible.

This handling of "corner cases" is not much different anyhow from the practical implementations of other type traits: for instance, in both [libstdc++] and [libc++] implementations of is_convertible there is code that deals with some types in a special way.

In conclusion, it is the author's opinion that is_convertible_without_narrowing can be implemented in standard C++ without placing an unreasonable burden on implementors.

Author's note: given the amount of subtleties involved, we claim that it is extremely likely that non-experts would go for a "naïve", wrong solution (e.g. To{std::declval<From>()}). This further underlines the necessity of providing detection of narrowing conversions in the Standard Library, rather than having users reinventing it with ad-hoc solutions.

§ 6.2. Feature testing macro

We propose the usage of the __cpp_lib_is_convertible_without_narrowing macro, following the pre-existing nomenclature for the other traits in <type_traits>.

§ 6.3. Proposed wording

All changes are relative to [N4861].

In [meta.type.synop], add to the header synopsis:

  template <class From, class To> struct is_convertible;
  template <class From, class To> struct is_convertible_without_narrowing;

  template <class From, class To>
    inline constexpr bool is_convertible_v = is_convertible<From, To>::value;
  template <class From, class To>
    inline constexpr bool is_convertible_without_narrowing_v = is_convertible_without_narrowing<From, To>::value;

In [meta.rel], add a new row to the Type relationship predicates table, in the same row as is_convertible:

Template

template <class From, class To> struct is_convertible; template <class From, class To> struct is_convertible_without_narrowing;

Condition

see below

Comments

From and To shall be complete types, cv void, or arrays of unknown bound.

Modify paragraph 5 of [meta.rel]:

5. The predicate condition for a template specialization is_convertible<From, To> or a template specialization is_convertible_without_narrowing<From, To> shall be satisfied if and only if the return expression in the following code would be well-formed, including any implicit conversions to the return type of the function; for is_convertible_without_narrowing<From, To> the initialization of the return object of the function shall, moreover, not require a narrowing conversion ([dcl.init.list]):

To test() {
  return declval<From>();
}

[ Note: This requirement gives well-defined results for reference types, void types, array types, and function types. — end note ] [ Note: For the purpose of establishing whether a conversion is a narrowing conversion, the source is not considered a constant expression. — end note ]

In [version.syn], add to the list of feature testing macros in paragraph 2:

#define __cpp_lib_is_layout_compatible     201907L // also in <type_traits>
#define __cpp_lib_is_convertible_without_narrowing     TBD // also in <type_traits>
#define __cpp_lib_is_null_pointer          201309L // also in <type_traits>

The actual value is left to be determined (TBD); it should be replaced by yyyymmL, matching the year and month of adoption of this proposal.

§ Appendix

§ A. Acknowledgements

Thanks to KDAB for supporting this work.

Thanks to Marc Mutz for his feedback and championing this paper in Prague; to Zhihao Yuan for the discussion and some sample code; to Walter E. Brown and André Somers for their feedback.

All remaining errors are ours and ours only.

§ B. References

[Qt] Qt version 5.15, QT_NO_NARROWING_CONVERSIONS_IN_CONNECT, QObject class documentation

[Qt connect()] Qt version 5.15, traits for detecting narrowing conversions

[P0608R3] Zhihao Yuan, A sane variant converting constructor (LEWG 227)

[LEWG 227] Zhihao Yuan, Bug 227 - variant converting constructor allows unintended conversions

[P1957R2] Zhihao Yuan, Converting from T* to bool should be considered narrowing (re: US 212)

[P1818R1] Lawrence Crowl, Narrowing and Widening Conversions

[P1619R1] Lisa Lippincott, Functions for Testing Boundary Conditions on Integer Operations

[P1998R1] Ryan McDougall, Simple Facility for Lossless Integer Conversion

[libstdc++] libstdc++, implementation of is_convertible

[libc++] libc++, implementation of is_convertible

[N4861] Richard Smith, Thomas Koeppe, Jens Maurer, Dawn Perchik, Working Draft, Standard for Programming Language C++

[P1467R4] David Olsen, Michał Dominiak, Extended floating-point types and standard names