6 Basics [basic]

6.8 Types [basic.types]

6.8.1 General [basic.types.general]

1
#
[Note 1: 
[basic.types] and the subclauses thereof impose requirements on implementations regarding the representation of types.
There are two kinds of types: fundamental types and compound types.
Types describe objects, references, or functions.
— end note]
2
#
For any object (other than a potentially-overlapping subobject) of trivially copyable type T, whether or not the object holds a valid value of type T, the underlying bytes ([intro.memory]) making up the object can be copied into an array of char, unsigned char, or std​::​byte ([cstddef.syn]).28
If the content of that array is copied back into the object, the object shall subsequently hold its original value.
[Example 1: constexpr std::size_t N = sizeof(T); char buf[N]; T obj; // obj initialized to its original value std::memcpy(buf, &obj, N); // between these two calls to std​::​memcpy, obj might be modified std::memcpy(&obj, buf, N); // at this point, each subobject of obj of scalar type holds its original value — end example]
3
#
For two distinct objects obj1 and obj2 of trivially copyable type T, where neither obj1 nor obj2 is a potentially-overlapping subobject, if the underlying bytes ([intro.memory]) making up obj1 are copied into obj2,29 obj2 shall subsequently hold the same value as obj1.
[Example 2: T* t1p; T* t2p; // provided that t2p points to an initialized object ... std::memcpy(t1p, t2p, sizeof(T)); // at this point, every subobject of trivially copyable type in *t1p contains // the same value as the corresponding subobject in *t2p — end example]
4
#
The object representation of an object of type T is the sequence of N unsigned char objects taken up by the object of type T, where N equals sizeof(T).
The value representation of an object of type T is the set of bits that participate in representing a value of type T.
Bits in the object representation that are not part of the value representation are padding bits.
For trivially copyable types, the value representation is a set of bits in the object representation that determines a value, which is one discrete element of an implementation-defined set of values.30
5
#
A class that has been declared but not defined, an enumeration type in certain contexts ([dcl.enum]), or an array of unknown bound or of incomplete element type, is an incompletely-defined object type.31
Incompletely-defined object types and cv void are incomplete types ([basic.fundamental]).
[Note 2: 
Objects cannot be defined to have an incomplete type ([basic.def]).
— end note]
6
#
A class type (such as “class X”) can be incomplete at one point in a translation unit and complete later on; the type “class X” is the same type at both points.
The declared type of an array object can be an array of incomplete class type and therefore incomplete; if the class type is completed later on in the translation unit, the array type becomes complete; the array type at those two points is the same type.
The declared type of an array object can be an array of unknown bound and therefore be incomplete at one point in a translation unit and complete later on; the array types at those two points (“array of unknown bound of T” and “array of N T”) are different types.
[Note 3: 
The type of a pointer or reference to array of unknown bound permanently points to or refers to an incomplete type.
An array of unknown bound named by a typedef declaration permanently refers to an incomplete type.
In either case, the array type cannot be completed.
— end note]
[Example 3: 
🔗
class X; // X is an incomplete type extern X* xp; // xp is a pointer to an incomplete type extern int arr[]; // the type of arr is incomplete typedef int UNKA[]; // UNKA is an incomplete type UNKA* arrp; // arrp is a pointer to an incomplete type UNKA** arrpp; void foo() { xp++; // error: X is incomplete arrp++; // error: incomplete type arrpp++; // OK, sizeof UNKA* is known } struct X { int i; }; // now X is a complete type int arr[10]; // now the type of arr is complete X x; void bar() { xp = &x; // OK; type is “pointer to X'' arrp = &arr; // OK; qualification conversion ([conv.qual]) xp++; // OK, X is complete arrp++; // error: UNKA can't be completed } — end example]
7
#
[Note 4: 
The rules for declarations and expressions describe in which contexts incomplete types are prohibited.
— end note]
8
#
An object type is a (possibly cv-qualified) type that is not a function type, not a reference type, and not cv void.
9
#
Arithmetic types ([basic.fundamental]), enumeration types, pointer types, pointer-to-member types ([basic.compound]), std​::​nullptr_t, and cv-qualified versions of these types are collectively called scalar types.
Scalar types, trivially copyable class types ([class.prop]), arrays of such types, and cv-qualified versions of these types are collectively called trivially copyable types.
Scalar types, trivial class types ([class.prop]), arrays of such types and cv-qualified versions of these types are collectively called trivial types.
Scalar types, standard-layout class types ([class.prop]), arrays of such types and cv-qualified versions of these types are collectively called standard-layout types.
Scalar types, implicit-lifetime class types ([class.prop]), array types, and cv-qualified versions of these types are collectively called implicit-lifetime types.
10
#
A type is a literal type if it is:
  • (10.1)
    cv void; or
  • (10.2)
    a scalar type; or
  • (10.3)
    a reference type; or
  • (10.4)
    an array of literal type; or
  • (10.5)
    a possibly cv-qualified class type that has all of the following properties:
    • (10.5.1)
      it has a constexpr destructor ([dcl.constexpr]),
    • (10.5.2)
      all of its non-static non-variant data members and base classes are of non-volatile literal types, and
    • (10.5.3)
      it
      • (10.5.3.1)
        is a closure type ([expr.prim.lambda.closure]),
      • (10.5.3.2)
        is an aggregate union type that has either no variant members or at least one variant member of non-volatile literal type,
      • (10.5.3.3)
        is a non-union aggregate type for which each of its anonymous union members satisfies the above requirements for an aggregate union type, or
      • (10.5.3.4)
        has at least one constexpr constructor or constructor template (possibly inherited ([namespace.udecl]) from a base class) that is not a copy or move constructor.
[Note 5: 
A literal type is one for which it might be possible to create an object within a constant expression.
It is not a guarantee that it is possible to create such an object, nor is it a guarantee that any object of that type will be usable in a constant expression.
— end note]
11
#
Two types cv1 T1 and cv2 T2 are layout-compatible types if T1 and T2 are the same type, layout-compatible enumerations, or layout-compatible standard-layout class types.
28)28)
By using, for example, the library functions ([headers]) std​::​memcpy or std​::​memmove.
29)29)
By using, for example, the library functions ([headers]) std​::​memcpy or std​::​memmove.
30)30)
The intent is that the memory model of C++ is compatible with that of the C programming language.
31)31)
The size and layout of an instance of an incompletely-defined object type is unknown.

6.8.2 Fundamental types [basic.fundamental]

1
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There are five standard signed integer types: “signed char”, “short int”, “int”, “long int”, and “long long int”.
In this list, each type provides at least as much storage as those preceding it in the list.
There may also be implementation-defined extended signed integer types.
The standard and extended signed integer types are collectively called signed integer types.
The range of representable values for a signed integer type is to (inclusive), where N is called the width of the type.
[Note 1: 
Plain ints are intended to have the natural width suggested by the architecture of the execution environment; the other signed integer types are provided to meet special needs.
— end note]
2
#
For each of the standard signed integer types, there exists a corresponding (but different) standard unsigned integer type: “unsigned char”, “unsigned short int”, “unsigned int”, “unsigned long int”, and “unsigned long long int”.
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.
An unsigned integer type has the same width N as the corresponding signed integer type.
The range of representable values for the unsigned type is 0 to (inclusive); arithmetic for the unsigned type is performed modulo .
[Note 2: 
Unsigned arithmetic does not overflow.
Overflow for signed arithmetic yields undefined behavior ([expr.pre]).
— end note]
3
#
An unsigned integer type has the same object representation, value representation, and alignment requirements ([basic.align]) as the corresponding signed integer type.
For each value x of a signed integer type, the value of the corresponding unsigned integer type congruent to x modulo has the same value of corresponding bits in its value representation.32
[Example 1: 
The value of a signed integer type has the same representation as the largest value of the corresponding unsigned type.
— end example]
Table 14: Minimum width [tab:basic.fundamental.width]
Type
Minimum width N
signed char
8
short int
16
int
16
long int
32
long long int
64
4
#
The width of each signed integer type shall not be less than the values specified in Table 14.
The value representation of a signed or unsigned integer type comprises N bits, where N is the respective width.
Each set of values for any padding bits ([basic.types.general]) in the object representation are alternative representations of the value specified by the value representation.
[Note 3: 
Padding bits have unspecified value, but cannot cause traps.
In contrast, see ISO C 6.2.6.2.
— end note]
[Note 4: 
The signed and unsigned integer types satisfy the constraints given in ISO C 5.2.4.2.1.
— end note]
Except as specified above, the width of a signed or unsigned integer type is implementation-defined.
5
#
Each value x of an unsigned integer type with width N has a unique representation , where each coefficient is either 0 or 1; this is called the base-2 representation of x.
The base-2 representation of a value of signed integer type is the base-2 representation of the congruent value of the corresponding unsigned integer type.
The standard signed integer types and standard unsigned integer types are collectively called the standard integer types, and the extended signed integer types and extended unsigned integer types are collectively called the extended integer types.
6
#
A fundamental type specified to have a signed or unsigned integer type as its underlying type has the same object representation, value representation, alignment requirements ([basic.align]), and range of representable values as the underlying type.
Further, each value has the same representation in both types.
7
#
Type char is a distinct type that has an implementation-defined choice of “signed char” or “unsigned char” as its underlying type.
The three types char, signed char, and unsigned char are collectively called ordinary character types.
The ordinary character types and char8_t are collectively called narrow character types.
For narrow character types, each possible bit pattern of the object representation represents a distinct value.
[Note 5: 
This requirement does not hold for other types.
— end note]
[Note 6: 
A bit-field of narrow character type whose width is larger than the width of that type has padding bits; see [basic.types.general].
— end note]
8
#
Type wchar_t is a distinct type that has an implementation-defined signed or unsigned integer type as its underlying type.
9
#
Type char8_t denotes a distinct type whose underlying type is unsigned char.
Types char16_t and char32_t denote distinct types whose underlying types are uint_least16_t and uint_least32_t, respectively, in <cstdint>.
10
#
Type bool is a distinct type that has the same object representation, value representation, and alignment requirements as an implementation-defined unsigned integer type.
The values of type bool are true and false.
[Note 7: 
There are no signed, unsigned, short, or long bool types or values.
— end note]
11
#
The types char, wchar_t, char8_t, char16_t, and char32_t are collectively called character types.
The character types, bool, the signed and unsigned integer types, and cv-qualified versions ([basic.type.qualifier]) thereof, are collectively termed integral types.
A synonym for integral type is integer type.
[Note 8: 
Enumerations ([dcl.enum]) are not integral; however, unscoped enumerations can be promoted to integral types as specified in [conv.prom].
— end note]
12
#
The three distinct types float, double, and long double can represent floating-point numbers.
The type double provides at least as much precision as float, and the type long double provides at least as much precision as double.
The set of values of the type float is a subset of the set of values of the type double; the set of values of the type double is a subset of the set of values of the type long double.
The types float, double, and long double, and cv-qualified versions ([basic.type.qualifier]) thereof, are collectively termed standard floating-point types.
An implementation may also provide additional types that represent floating-point values and define them (and cv-qualified versions thereof) to be extended floating-point types.
The standard and extended floating-point types are collectively termed floating-point types.
[Note 9: 
Any additional implementation-specific types representing floating-point values that are not defined by the implementation to be extended floating-point types are not considered to be floating-point types, and this document imposes no requirements on them or their interactions with floating-point types.
— end note]
Except as specified in [basic.extended.fp], the object and value representations and accuracy of operations of floating-point types are implementation-defined.
13
#
Integral and floating-point types are collectively termed arithmetic types.
[Note 10: 
Properties of the arithmetic types, such as their minimum and maximum representable value, can be queried using the facilities in the standard library headers <limits>, <climits>, and <cfloat>.
— end note]
14
#
A type cv void is an incomplete type that cannot be completed; such a type has an empty set of values.
It is used as the return type for functions that do not return a value.
Any expression can be explicitly converted to type cv void ([expr.type.conv], [expr.static.cast], [expr.cast]).
An expression of type cv void shall be used only as an expression statement ([stmt.expr]), as an operand of a comma expression ([expr.comma]), as a second or third operand of ?: ([expr.cond]), as the operand of typeid, noexcept, or decltype, as the expression in a return statement ([stmt.return]) for a function with the return type cv void, or as the operand of an explicit conversion to type cv void.
15
#
A value of type std​::​nullptr_t is a null pointer constant ([conv.ptr]).
Such values participate in the pointer and the pointer-to-member conversions ([conv.ptr], [conv.mem]).
sizeof(std​::​nullptr_t) shall be equal to sizeof(void*).
16
#
The types described in this subclause are called fundamental types.
[Note 11: 
Even if the implementation defines two or more fundamental types to have the same value representation, they are nevertheless different types.
— end note]
32)32)
This is also known as two's complement representation.

6.8.3 Optional extended floating-point types [basic.extended.fp]

1
#
If the implementation supports an extended floating-point type ([basic.fundamental]) whose properties are specified by the ISO/IEC/IEEE 60559 floating-point interchange format binary16, then the typedef-name std​::​float16_t is defined in the header <stdfloat> and names such a type, the macro __STDCPP_FLOAT16_T__ is defined ([cpp.predefined]), and the floating-point literal suffixes f16 and F16 are supported ([lex.fcon]).
2
#
If the implementation supports an extended floating-point type whose properties are specified by the ISO/IEC/IEEE 60559 floating-point interchange format binary32, then the typedef-name std​::​float32_t is defined in the header <stdfloat> and names such a type, the macro __STDCPP_FLOAT32_T__ is defined, and the floating-point literal suffixes f32 and F32 are supported.
3
#
If the implementation supports an extended floating-point type whose properties are specified by the ISO/IEC/IEEE 60559 floating-point interchange format binary64, then the typedef-name std​::​float64_t is defined in the header <stdfloat> and names such a type, the macro __STDCPP_FLOAT64_T__ is defined, and the floating-point literal suffixes f64 and F64 are supported.
4
#
If the implementation supports an extended floating-point type whose properties are specified by the ISO/IEC/IEEE 60559 floating-point interchange format binary128, then the typedef-name std​::​float128_t is defined in the header <stdfloat> and names such a type, the macro __STDCPP_FLOAT128_T__ is defined, and the floating-point literal suffixes f128 and F128 are supported.
5
#
If the implementation supports an extended floating-point type with the properties, as specified by ISO/IEC/IEEE 60559, of radix (b) of 2, storage width in bits (k) of 16, precision in bits (p) of 8, maximum exponent (emax) of 127, and exponent field width in bits (w) of 8, then the typedef-name std​::​bfloat16_t is defined in the header <stdfloat> and names such a type, the macro __STDCPP_BFLOAT16_T__ is defined, and the floating-point literal suffixes bf16 and BF16 are supported.
6
#
[Note 1: 
A summary of the parameters for each type is given in Table 15.
The precision p includes the implicit 1 bit at the beginning of the mantissa, so the storage used for the mantissa is bits.
ISO/IEC/IEEE 60559 does not assign a name for a type having the parameters specified for std​::​bfloat16_t.
— end note]
Table 15: Properties of named extended floating-point types [tab:basic.extended.fp]
Parameter
float16_t
float32_t
float64_t
float128_t
bfloat16_t
ISO/IEC/IEEE 60559 name
binary16
binary32
binary64
binary128
k, storage width in bits
16
32
64
128
16
p, precision in bits
11
24
53
113
8
emax, maximum exponent
15
127
1023
16383
127
w, exponent field width in bits
5
8
11
15
8
7
#
Recommended practice: Any names that the implementation provides for the extended floating-point types described in this subsection that are in addition to the names defined in the <stdfloat> header should be chosen to increase compatibility and interoperability with the interchange types _Float16, _Float32, _Float64, and _Float128 defined in ISO/IEC TS 18661-3 and with future versions of ISO/IEC 9899.

6.8.4 Compound types [basic.compound]

1
#
Compound types can be constructed in the following ways:
2
#
These methods of constructing types can be applied recursively; restrictions are mentioned in [dcl.meaning].
Constructing a type such that the number of bytes in its object representation exceeds the maximum value representable in the type std​::​size_t ([support.types]) is ill-formed.
3
#
The type of a pointer to cv void or a pointer to an object type is called an object pointer type.
[Note 1: 
A pointer to void does not have a pointer-to-object type, however, because void is not an object type.
— end note]
The type of a pointer that can designate a function is called a function pointer type.
A pointer to an object of type T is referred to as a “pointer to T”.
[Example 1: 
A pointer to an object of type int is referred to as “pointer to int” and a pointer to an object of class X is called a “pointer to X”.
— end example]
Except for pointers to static members, text referring to “pointers” does not apply to pointers to members.
Pointers to incomplete types are allowed although there are restrictions on what can be done with them ([basic.align]).
Every value of pointer type is one of the following:
A value of a pointer type that is a pointer to or past the end of an object represents the address of the first byte in memory ([intro.memory]) occupied by the object34 or the first byte in memory after the end of the storage occupied by the object, respectively.
[Note 2: 
A pointer past the end of an object ([expr.add]) is not considered to point to an unrelated object of the object's type, even if the unrelated object is located at that address.
A pointer value becomes invalid when the storage it denotes reaches the end of its storage duration; see [basic.stc].
— end note]
For purposes of pointer arithmetic ([expr.add]) and comparison ([expr.rel], [expr.eq]), a pointer past the end of the last element of an array x of n elements is considered to be equivalent to a pointer to a hypothetical array element n of x and an object of type T that is not an array element is considered to belong to an array with one element of type T.
The value representation of pointer types is implementation-defined.
Pointers to layout-compatible types shall have the same value representation and alignment requirements ([basic.align]).
[Note 3: 
Pointers to over-aligned types have no special representation, but their range of valid values is restricted by the extended alignment requirement.
— end note]
4
#
Two objects a and b are pointer-interconvertible if:
  • (4.1)
    they are the same object, or
  • (4.2)
    one is a union object and the other is a non-static data member of that object ([class.union]), or
  • (4.3)
    one is a standard-layout class object and the other is the first non-static data member of that object or any base class subobject of that object ([class.mem]), or
  • (4.4)
    there exists an object c such that a and c are pointer-interconvertible, and c and b are pointer-interconvertible.
If two objects are pointer-interconvertible, then they have the same address, and it is possible to obtain a pointer to one from a pointer to the other via a reinterpret_cast ([expr.reinterpret.cast]).
[Note 4: 
An array object and its first element are not pointer-interconvertible, even though they have the same address.
— end note]
5
#
A byte of storage b is reachable through a pointer value that points to an object x if there is an object y, pointer-interconvertible with x, such that b is within the storage occupied by y, or the immediately-enclosing array object if y is an array element.
6
#
A pointer to cv void can be used to point to objects of unknown type.
Such a pointer shall be able to hold any object pointer.
An object of type “pointer to cv void” shall have the same representation and alignment requirements as an object of type “pointer to cv char”.
33)33)
Static class members are objects or functions, and pointers to them are ordinary pointers to objects or functions.
34)34)
For an object that is not within its lifetime, this is the first byte in memory that it will occupy or used to occupy.

6.8.5 CV-qualifiers [basic.type.qualifier]

1
#
Each type other than a function or reference type is part of a group of four distinct, but related, types: a cv-unqualified version, a const-qualified version, a volatile-qualified version, and a const-volatile-qualified version.
The types in each such group shall have the same representation and alignment requirements ([basic.align]).35
A function or reference type is always cv-unqualified.
  • (1.1)
    A const object is an object of type const T or a non-mutable subobject of a const object.
  • (1.2)
    A volatile object is an object of type volatile T or a subobject of a volatile object.
  • (1.3)
    A const volatile object is an object of type const volatile T, a non-mutable subobject of a const volatile object, a const subobject of a volatile object, or a non-mutable volatile subobject of a const object.
[Note 1: 
The type of an object ([intro.object]) includes the cv-qualifiers specified in the decl-specifier-seq ([dcl.spec]), declarator ([dcl.decl]), type-id ([dcl.name]), or new-type-id ([expr.new]) when the object is created.
— end note]
2
#
Except for array types, a compound type ([basic.compound]) is not cv-qualified by the cv-qualifiers (if any) of the types from which it is compounded.
3
#
An array type whose elements are cv-qualified is also considered to have the same cv-qualifications as its elements.
[Note 2: 
Cv-qualifiers applied to an array type attach to the underlying element type, so the notation “cv T”, where T is an array type, refers to an array whose elements are so-qualified ([dcl.array]).
— end note]
[Example 1: typedef char CA[5]; typedef const char CC; CC arr1[5] = { 0 }; const CA arr2 = { 0 };
The type of both arr1 and arr2 is “array of 5 const char”, and the array type is considered to be const-qualified.
— end example]
4
#
[Note 3: 
See [dcl.fct] and [over.match.funcs] regarding function types that have cv-qualifiers.
— end note]
5
#
There is a partial ordering on cv-qualifiers, so that a type can be said to be more cv-qualified than another.
Table 16 shows the relations that constitute this ordering.
Table 16: Relations on const and volatile [tab:basic.type.qualifier.rel]
no cv-qualifier
<
const
no cv-qualifier
<
volatile
no cv-qualifier
<
const volatile
const
<
const volatile
volatile
<
const volatile
6
#
In this document, the notation cv (or cv1, cv2, etc.)
, used in the description of types, represents an arbitrary set of cv-qualifiers, i.e., one of {const}, {volatile}, {const, volatile}, or the empty set.
For a type cv T, the top-level cv-qualifiers of that type are those denoted by cv.
[Example 2: 
The type corresponding to the type-id const int& has no top-level cv-qualifiers.
The type corresponding to the type-id volatile int * const has the top-level cv-qualifier const.
For a class type C, the type corresponding to the type-id void (C​::​* volatile)(int) const has the top-level cv-qualifier volatile.
— end example]
35)35)
The same representation and alignment requirements are meant to imply interchangeability as arguments to functions, return values from functions, and non-static data members of unions.

6.8.6 Conversion ranks [conv.rank]

1
#
Every integer type has an integer conversion rank defined as follows:
  • (1.1)
    No two signed integer types other than char and signed char (if char is signed) have the same rank, even if they have the same representation.
  • (1.2)
    The rank of a signed integer type is greater than the rank of any signed integer type with a smaller width.
  • (1.3)
    The rank of long long int is greater than the rank of long int, which is greater than the rank of int, which is greater than the rank of short int, which is greater than the rank of signed char.
  • (1.4)
    The rank of any unsigned integer type equals the rank of the corresponding signed integer type.
  • (1.5)
    The rank of any standard integer type is greater than the rank of any extended integer type with the same width.
  • (1.6)
    The rank of char equals the rank of signed char and unsigned char.
  • (1.7)
    The rank of bool is less than the rank of all standard integer types.
  • (1.8)
    The ranks of char8_t, char16_t, char32_t, and wchar_t equal the ranks of their underlying types ([basic.fundamental]).
  • (1.9)
    The rank of any extended signed integer type relative to another extended signed integer type with the same width is implementation-defined, but still subject to the other rules for determining the integer conversion rank.
  • (1.10)
    For all integer types T1, T2, and T3, if T1 has greater rank than T2 and T2 has greater rank than T3, then T1 has greater rank than T3.
[Note 1: 
The integer conversion rank is used in the definition of the integral promotions ([conv.prom]) and the usual arithmetic conversions ([expr.arith.conv]).
— end note]
2
#
Every floating-point type has a floating-point conversion rank defined as follows:
  • (2.1)
    The rank of a floating point type T is greater than the rank of any floating-point type whose set of values is a proper subset of the set of values of T.
  • (2.2)
    The rank of long double is greater than the rank of double, which is greater than the rank of float.
  • (2.3)
    Two extended floating-point types with the same set of values have equal ranks.
  • (2.4)
    An extended floating-point type with the same set of values as exactly one cv-unqualified standard floating-point type has a rank equal to the rank of that standard floating-point type.
  • (2.5)
    An extended floating-point type with the same set of values as more than one cv-unqualified standard floating-point type has a rank equal to the rank of double.
[Note 2: 
The conversion ranks of floating-point types T1 and T2 are unordered if the set of values of T1 is neither a subset nor a superset of the set of values of T2.
This can happen when one type has both a larger range and a lower precision than the other.
— end note]
3
#
Floating-point types that have equal floating-point conversion ranks are ordered by floating-point conversion subrank.
The subrank forms a total order among types with equal ranks.
The types std​::​float16_t, std​::​float32_t, std​::​float64_t, and std​::​float128_t ([stdfloat.syn]) have a greater conversion subrank than any standard floating-point type with equal conversion rank.
Otherwise, the conversion subrank order is implementation-defined.
4
#
[Note 3: 
The floating-point conversion rank and subrank are used in the definition of the usual arithmetic conversions ([expr.arith.conv]).
— end note]