Constant expressions

From cppreference.com
< cpp‎ | language
 
 
C++ language
General topics
Flow control
Conditional execution statements
if
Iteration statements (loops)
for
range-for (C++11)
Jump statements
Functions
Function declaration
Lambda function expression
inline specifier
Dynamic exception specifications (until C++17*)
noexcept specifier (C++11)
Exceptions
Namespaces
Types
Specifiers
const/volatile
decltype (C++11)
auto (C++11)
constexpr (C++11)
consteval (C++20)
constinit (C++20)
Storage duration specifiers
Initialization
Expressions
Alternative representations
Literals
Boolean - Integer - Floating-point
Character - String - nullptr (C++11)
User-defined (C++11)
Utilities
Attributes (C++11)
Types
typedef declaration
Type alias declaration (C++11)
Casts
Memory allocation
Classes
Class-specific function properties
explicit (C++11)
static

Special member functions
Templates
Miscellaneous
 
 

Defines an expression that can be evaluated at compile time.

Such expressions can be used as non-type template arguments, array sizes, and in other contexts that require constant expressions, e.g.

int n = 1;
std::array<int, n> a1;  // Error: “n” is not a constant expression
const int cn = 2;
std::array<int, cn> a2; // OK: “cn” is a constant expression

Definition

An expression that belongs to any of the constant expression categories listed below is a constant expression.

C++98 constant expression categories

Integral constant expression (C++98)

In the following places, C++ requires expressions that evaluate to an integral or enumeration constant:

An expression satisfying all following conditions is an integral constant-expression :

  • It only involves the following entities:
  • literals of arithmetic types
  • enumerators
  • variables or static data members satisfying all following conditions:
  • They are const-qualified.
  • They are not volatile-qualified.
  • They are of integral or enumeration types.
  • They are initialized with constant expressions.
  • It does not use any floating-point literals, unless they are explicitly converted to integral or enumeration types.
  • It does not apply any conversion to non-integral and non-enumeration types.
  • It does not use any of the following entities except in the operands of sizeof:
  • function
  • class object
  • pointer
  • reference
  • assignment operator
  • increment operator
  • decrement operator
  • function-call operator
  • comma operator

Other constant expression categories

Other expressions are considered constant expressions only for the purpose of constant initialization. Such a constant expression must be one of the following expressions:

  • an expression that evaluates to a null pointer value
  • an expression that evaluates to a null pointer-to-member value
  • an arithmetic constant expression
  • an address constant expression
  • a reference constant expression
  • an address constant expression for a complete object type, plus or minus an integral constant expression
  • a pointer-to-member constant expression

An arithmetic constant expression is an expression satisfying the requirements for an integral constant expression, with the following exceptions:

  • Floating-point literals can be used without explicit conversion.
  • Conversions to floating-point types can be applied.

An address constant expression is an expression of pointer type satisfying all following conditions:

  • explicitly using the address-of operator
  • implicitly using a non-type template parameter of pointer type
  • using an expression of array or function type
  • The expression does not call any function.
  • The expression uses explicit pointer conversions (except dynamic_cast) and the following operators without accessing the result object:
  • subscript operator
  • indirection operator
  • address-of operator
  • member access operator
  • If the subscript operator is used, one of its operands is an integral constant expression.

A reference constant expression is an expression of reference type satisfying all following conditions:

  • The reference designates an object of static storage duration, a non-type template parameter of reference type, or a function. The reference does not designate a member or base class of non-POD class type.
  • The expression does not call any function.
  • The expression uses explicit reference conversions (except dynamic_cast) and the following operators without accessing the result object:
  • subscript operator
  • indirection operator
  • address-of operator
  • member access operator
  • If the subscript operator is used, one of its operands is an integral constant expression.

A pointer-to-member constant expression is an expression of pointer-to-member type where the pointer is created by applying the address-of operator to a qualified identifier, optionally preceded by an explicit pointer-to-member conversion.

(until C++11)

The following expressions are collectively called constant expressions :

  • the address of an object with static storage duration
  • the address of a function
  • a null pointer value
(since C++11)
(until C++14)

The following entities are permitted results of a constant expression :

  • temporary objects with static storage duration
  • non-temporary objects with static storage duration whose values satisfy the constraints listed below
  • non-immediate (since C++20)functions

A constant expression is either a glvalue core constant expression that refers to an entity that is a permitted result of a constant expression, or a prvalue core constant expression whose value satisfies the following constraints:

  • If the value is an object of class type, each non-static data member of reference type refers to an entity that is a permitted result of a constant expression.
  • If the value is an object of scalar type, it does not have an indeterminate value.
  • If the value is of pointer type, it is one of the following values:
  • the address of an object with static storage duration
  • the address past the end of an object with static storage duration
  • the address of a non-immediate(since C++20) function
  • a null pointer value
  • If the value is of pointer-to-member-function type, it does not designate an immediate function.
(since C++20)
  • If the value is an object of class or array type, each subobject satisfies these constraints for the value.
(since C++14)
(until C++26)

A constant expression is either a glvalue core constant expression that refers to an object or a non-immediate function, or a prvalue core constant expression whose value satisfies the following constraints:

(since C++26)

When determining whether an expression is a constant expression, copy elision is assumed not to be performed.

The C++98 definition of constant expressions is entirely within the collpase box. The following description applies to C++11 and later C++ versions.

Literal type

The following types are collectively called literal types :

  • possibly cv-qualified void
  • scalar type
  • reference type
  • an array of literal type
  • possibly cv-qualified class type that satisfies all following conditions:
  • It has a trivial destructor(until C++20)constexpr destructor(since C++20).
  • All of its non-static non-variant data members and base classes are of non-volatile literal types.
  • It is one of the following types:
(since C++17)
  • an aggregate union type that satisfies one of the following conditions:
  • It has no variant member.
  • It has at least one variant member of non-volatile literal type.
  • a non-union aggregate type, and each of its anonymous union members satisfies one of the following conditions:
  • It has no variant member.
  • It has at least one variant member of non-volatile literal type.
  • a type with at least one constexpr constructor (template) that is not a copy or move constructor

Only objects of literal types can be created within a constant expression.

Core constant expression

A core constant expression is any expression whose evaluation would not evaluate any one of the following language constructs:

Language construct     Version     Paper(s)
the this pointer, except in a constexpr function that is being evaluated as part of the expression, or when appearing in an implicit or explicit class member access expression N2235
a control flow that passes through a declaration of a block variable with static or thread storage duration that is not usable in constant expressions (since C++23) P2242R3
  1. a function call expression that calls a function (or a constructor) that is not declared constexpr
    constexpr int n = std::numeric_limits<int>::max(); // OK: max() is constexpr
    constexpr int m = std::time(nullptr); // Error: std::time() is not constexpr
  2. a function call to a constexpr function which is declared, but not defined
  3. a function call to a constexpr function/constructor template instantiation where the instantiation fails to satisfy constexpr function/constructor requirements.
  4. a function call to a constexpr virtual function, invoked on an object whose dynamic type is constexpr-unknown
  5. an expression that would exceed the implementation-defined limits
  6. an expression whose evaluation leads to any form of core language undefined or erroneous(since C++26) behavior, except for any potential undefined behavior introduced by standard attributes.
    constexpr double d1 = 2.0 / 1.0; // OK
    constexpr double d2 = 2.0 / 0.0; // Error: not defined
    constexpr int n = std::numeric_limits<int>::max() + 1; // Error: overflow
    int x, y, z[30];
    constexpr auto e1 = &y - &x;        // Error: undefined
    constexpr auto e2 = &z[20] - &z[3]; // OK
    constexpr std::bitset<2> a; 
    constexpr bool b = a[2]; // UB, but unspecified if detected
  7. (until C++17) a lambda expression
  8. an lvalue-to-rvalue implicit conversion unless applied to...
    1. a glvalue of type (possibly cv-qualified) std::nullptr_t
    2. a non-volatile literal-type glvalue that designates an object that is usable in constant expressions
      int main()
      {
          const std::size_t tabsize = 50;
          int tab[tabsize]; // OK: tabsize is a constant expression
                            // because tabsize is usable in constant expressions
                            // because it has const-qualified integral type, and
                            // its initializer is a constant initializer
       
          std::size_t n = 50;
          const std::size_t sz = n;
          int tab2[sz]; // Error: sz is not a constant expression
                        // because sz is not usable in constant expressions
                        // because its initializer was not a constant initializer
      }
    3. a non-volatile literal-type glvalue that refers to a non-volatile object whose lifetime began within the evaluation of this expression
  9. an lvalue-to-rvalue implicit conversion or modification applied to a non-active member of a union or its subobject (even if it shares a common initial sequence with the active member)
  10. an lvalue-to-rvalue implicit conversion on an object whose value is indeterminate
  11. an invocation of implicit copy/move constructor/assignment for a union whose active member is mutable (if any), with lifetime beginning outside the evaluation of this expression
  12. (until C++20) an assignment expression that would change the active member of a union
  13. conversion from pointer to void to a pointer-to-object type T* unless the pointer holds a null pointer value or points to an object whose type is similar to T(since C++26)
  14. dynamic_cast whose operand is a glvalue that refers to an object whose dynamic type is constexpr-unknown(since C++20)
  15. reinterpret_cast
  16. (until C++20) pseudo-destructor call
  17. (until C++14) an increment or a decrement operator
  18. (since C++14) modification of an object, unless the object has non-volatile literal type and its lifetime began within the evaluation of the expression
    constexpr int incr(int& n)
    {
        return ++n;
    }
     
    constexpr int g(int k)
    {
        constexpr int x = incr(k); // Error: incr(k) is not a core constant
                                   // expression because lifetime of k
                                   // began outside the expression incr(k)
        return x;
    }
     
    constexpr int h(int k)
    {
        int x = incr(k); // OK: x is not required to be initialized
                         // with a core constant expression
        return x;
    }
     
    constexpr int y = h(1); // OK: initializes y with the value 2
                            // h(1) is a core constant expression because
                            // the lifetime of k begins inside the expression h(1)
  19. (since C++20) a destructor call or pseudo destructor call for an object whose lifetime did not begin within the evaluation of this expression
  20. a typeid expression applied to a glvalue of polymorphic type and that glvalue refers to an object whose dynamic type is constexpr-unknown(since C++20)
  21. a new expression, unless one of the following conditions is satisfied:(since C++20)
    • The selected allocation function is a replaceable global allocation function and the allocated storage is deallocated within the evaluation of this expression.
    (since C++20)
    • The selected allocation function is a non-allocating form with an allocated type T, and the placement argument satisfies all following conditions:
    • It points to:
    • an object whose type is similar to T, if T is not an array type, or
    • the first element of an object of a type similar to T, if T is an array type.
    • It points to storage whose duration began within the evaluation of this expression.
    (since C++26)
  22. a delete expression, unless it deallocates a region of storage allocated within the evaluation of this expression(since C++20)
  23. (since C++20) Coroutines: an await-expression or a yield-expression
  24. (since C++20) a three-way comparison when the result is unspecified
  25. an equality or relational operator whose result is unspecified
  26. (until C++14) an assignment or a compound assignment operator
  27. (until C++26) a throw expression
  28. (since C++26) a construction of an exception object, unless the exception object and all of its implicit copies created by invocations of std::current_exception or std::rethrow_exception are destroyed within the evaluation of this expression
    constexpr void check(int i)
    {
        if (i < 0)
            throw i;
    }
     
    constexpr bool is_ok(int i)
    {
        try {
            check(i);
        } catch (...) {
            return false;
        }
        return true;
    }
     
    constexpr bool always_throw()
    {
        throw 12;
        return true;
    }
     
    static_assert(is_ok(5)); // OK
    static_assert(!is_ok(-1)); // OK since C++26
    static_assert(always_throw()); // Error: uncaught exception
  29. an asm-declaration
  30. an invocation of the va_arg macro
  31. a goto statement
  32. a dynamic_cast or typeid expression or new expression(since C++26) that would throw an exception where no definition of the exception type is reachable(since C++26)
  33. inside a lambda expression, a reference to this or to a variable defined outside that lambda, if that reference would be an odr-use
    void g()
    {
        const int n = 0;
     
        constexpr int j = *&n; // OK: outside of a lambda-expression
     
        [=]
        {
            constexpr int i = n;   // OK: 'n' is not odr-used and not captured here.
            constexpr int j = *&n; // Ill-formed: '&n' would be an odr-use of 'n'.
        };
    }

    note that if the ODR-use takes place in a function call to a closure, it does not refer to this or to an enclosing variable, since it accesses a closure's data member instead

    // OK: 'v' & 'm' are odr-used but do not occur in a constant-expression
    // within the nested lambda
    auto monad = [](auto v){ return [=]{ return v; }; };
    auto bind = [](auto m){ return [=](auto fvm){ return fvm(m()); }; };
     
    // OK to have captures to automatic objects created during constant expression evaluation.
    static_assert(bind(monad(2))(monad)() == monad(2)());
    (since C++17)

Extra requirements

Even if an expression E does not evaluate anything stated above, it is implementation-defined whether E is a core constant expression if evaluating E would result in runtime-undefined behavior.

Even if an expression E does not evaluate anything stated above, it is unspecified whether E is a core constant expression if evaluating E would evalute any of the following:

For the purposes of determining whether an expression is a core constant expression, the evaluation of the body of a member function of std::allocator<T> is ignored if T is a literal type.

For the purposes of determining whether an expression is a core constant expression, the evaluation of a call to a trivial copy/move constructor or copy/move assignment operator of a union is considered to copy/move the active member of the union, if any.

For the purposes of determining whether an expression is a core constant expression, the evaluation of an identifier expression that names a structured binding bd has the following semantics:

  • If bd is an lvalue referring to the object bound to an invented reference ref, the behavior is as if ref were nominated.
  • Otherwise, if bd names an array element, the behavior is that of evaluating e[i], where e is the name of the variable initialized from the initializer of the structured binding declaration, and i is the index of the element referred to by bd.
  • Otherwise, if bd names a class member, the behavior is that of evaluating e.m, where e is the name of the variable initialized from the initializer of the structured binding declaration, and m is the name of the member referred to by bd.
(since C++26)

During the evaluation of the expression as a core constant expression, all identifier expressions and uses of *this that refer to an object or reference whose lifetime began outside the evaluation of the expression are treated as referring to a specific instance of that object of that object or reference whose lifetime and that of all subobjects (including all union members) includes the entire constant evaluation.

  • For such an object that is not usable in constant expressions(since C++20), the dynamic type of the object is constexpr-unknown.
  • For such a reference that is not usable constant expression(since C++20)s, the reference is treated as binding to an unspecified object of the referenced type whose lifetime and that of all subobjects includes the entire constant evaluation and whose dynamic type is constexpr-unknown.

Integral constant expression

Integral constant expression is an expression of integral or unscoped enumeration type implicitly converted to a prvalue, where the converted expression is a core constant expression.

If an expression of class type is used where an integral constant expression is expected, the expression is contextually implicitly converted to an integral or unscoped enumeration type.

Converted constant expression

A converted constant expression of type T is an expression implicitly converted to type T, where the converted expression is a constant expression, and the implicit conversion sequence contains only:

(since C++17)

And if any reference binding takes place, it can only be direct binding.

The following contexts require a converted constant expression:

(since C++14)
(since C++26)

A contextually converted constant expression of type bool is an expression, contextually converted to bool, where the converted expression is a constant expression and the conversion sequence contains only the conversions above.

The following contexts require a contextually converted constant expression of type bool:

(until C++23)
(since C++17)
(until C++23)
(since C++20)


Constituent entities

The constituent values of an object obj are defined as follows:

  • If obj has scalar type, the constituent value is the value of obj.
  • Otherwise, the constituent values are the constituent values of any direct subobjects of obj other than inactive union members.

The constituent references of an object obj include the following references:

  • any direct members of obj that have reference type
  • the constituent references of any direct subobjects of obj other than inactive union members

The constituent values and constituent references of a variable var are defined as follows:

  • If var declares an object, the constituent values and references are the constituent values and references of that object.
  • If var declares a reference, the constituent reference is that reference.

For any constituent reference ref of a variable var, if ref is bound to a temporary object or subobject thereof whose lifetime is extended to that of ref, the constituent values and references of that temporary object are also constituent values and references of var, recursively.

Constexpr-representable entities

Objects with static storage duration is constexpr-referenceable at any point in the program.

An object obj with automatic storage duration is constexpr-referenceable from a point P if the smallest scope enclosing the variable var and the smallest scope enclosing P that are the same function parameter scope that does not associate with the parameter list of a requires expression, where var is the variable corresponding to obj’s complete object or the variable to whose lifetime that of obj is extended.

An object or reference x is constexpr-representable at a point P if all following conditions are satisfied:

  • For each constituent value of x that points to an object obj, obj is constexpr-referenceable from P.
  • For each constituent value of x that points past an object obj, obj is constexpr-referenceable from P.
  • For each constituent reference of x that refers to an object obj, obj is constexpr-referenceable from P.
(since C++26)

Constant-initialized entities

A variable or temporary object obj is constant-initialized if all following conditions are satisfied:

  • Either it has an initializer, or its type is const-default-constructible.
  • The full-expression of its initialization is a constant expression in the context of requiring a constant expression, except that if obj is an object, that full-expression may also invoke constexpr constructors for obj and its subobjects even if those objects are of non-literal class types.
(until C++26)

A variable var is constant-initializable if all following conditions are satisfied:

  • The full-expression of its initialization is a constant expression in the context of requiring a constant expression.
  • Immediately after the initializing declaration of var, the object or reference declared by var is constexpr-representable.
  • If the object or reference x declared by var has static or thread storage duration, x is constexpr-representable at the nearest point whose immediate scope is a namespace scope that follows the initializing declaration of var.

A constant-initializable variable is constant-initialized if either it has an initializer, or its type is const-default-constructible.

(since C++26)

Usable in constant expressions

A variable is potentially-constant if it is a constexpr variable or it has reference or non-volatile const-qualified integral or enumeration type.

A constant-initialized potentially-constant variable var is usable in constant expressions at a point P if var’s initializing declaration D is reachable from P and any of the following conditions is satisfied:

  • var is a constexpr variable.
  • var is not initialized to a TU-local value.
  • P is in the same translation unit as D.

An object or reference is usable in constant expressions at a point P if it is one of the following entities:

  • a variable that is usable in constant expressions at P
  • a temporary object of non-volatile const-qualified literal type whose lifetime is extended to that of a variable that is usable in constant expressions at P
  • a template parameter object
  • a string literal object
  • a non-mutable subobject of any of the above
  • a reference member of any of the above
(until C++26)

An object or reference is potentially usable in constant expressions at a point P if it is one of the following entities:

  • a variable that is usable in constant expressions at P
  • a temporary object of non-volatile const-qualified literal type whose lifetime is extended to that of a variable that is usable in constant expressions at P
  • a template parameter object
  • a string literal object
  • a non-mutable subobject of any of the above
  • a reference member of any of the above

An object or reference is usable in constant expressions at point P if it is an object or reference that is potentially usable in constant expressions at P and is constexpr-representable at P.

(since C++26)

Manifestly constant-evaluated expressions

The following expressions (including conversions to the destination type) are manifestly constant-evaluated :

Whether an evaluation occurs in a manifestly constant-evaluated context can be detected by std::is_constant_evaluated and if consteval(since C++23).

(since C++20)

Functions and variables needed for constant evaluation

Following expressions or conversions are potentially constant evaluated:

A function is needed for constant evaluation if it is a constexpr function and named by an expression that is potentially constant evaluated.

A variable is needed for constant evaluation if it is either a constexpr variable or is of non-volatile const-qualified integral type or of reference type and the identifier expression that denotes it is potentially constant evaluated.

Definition of a defaulted function and instantiation of a function template specialization or variable template specialization(since C++14) are triggered if the function or variable(since C++14) is needed for constant evaluation.

Constant subexpression

A constant subexpression is an expression whose evaluation as subexpression of an expression e would not prevent e from being a core constant expression, where e is not any of the following expressions:

(since C++20)

Notes

Feature-test macro Value Std Feature
__cpp_constexpr_in_decltype 201711L (C++20)
(DR11)
Generation of function and variable definitions when needed for constant evaluation
__cpp_constexpr_dynamic_alloc 201907L (C++20) Operations for dynamic storage duration in constexpr functions
__cpp_constexpr 202306L (C++26) constexpr cast from void*: towards constexpr type-erasure
202406L (C++26) constexpr placement new and new[]
__cpp_constexpr_exceptions 202411L (C++26) constexpr exceptions

Example

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior
CWG 94 C++98 arithmetic constant expressions could not
involve variables and static data members
they can
CWG 366 C++98 expressions involving string literals
could be integral constant expressions
they are not
CWG 457 C++98 expressions involving volatile variables
could be integral constant expressions
they are not
CWG 1293 C++11 it was unclear whether string literals
are usable in constant expressions
they are usable
CWG 1311 C++11 volatile glvalues could be used in constant expressions prohibited
CWG 1312 C++11 reinterpret_cast is prohibited in constant expressions,
but casting to and from void* could achieve the same effect
prohibited conversions
from type cv void* to
a pointer-to-object type
CWG 1313 C++11 undefined behavior was permitted;
all pointer subtraction was prohibited
UB prohibited; same-array
pointer subtraction OK
CWG 1405 C++11 for objects that are usable in constant expressions,
their mutable subobjects were also usable
they are not usable
CWG 1454 C++11 passing constants through constexpr
functions via references was not allowed
allowed
CWG 1455 C++11 converted constant expressions could only be prvalues can be lvalues
CWG 1456 C++11 an address constant expression could not
designate the address one past the end of an array
allowed
CWG 1535 C++11 a typeid expression whose operand is of a
polymorphic class type was not a core constant
expression even if no runtime check is involved
the operand constraint
is limited to glvalues of
polymorphic class types
CWG 1581 C++11 functions needed for constant evaluation were
not required to be defined or instantiated
required
CWG 1613 C++11 core constant expressions could evaluate any
ODR-used reference inside lambda expressions
some references could
not be evaluated
CWG 1694 C++11 binding the value of a temporary to a static storage
duration reference was a constant expression
it is not a
constant expression
CWG 1872 C++11 core constant expressions could invoke constexpr function template
insantiations that do not satisfy the constexpr function requirements
such instantiations
cannot be invoked
CWG 1952 C++11 standard library undefined behaviors
were required to be diagnosed
unspecified whether
they are diagnosed
CWG 2022 C++98 the determination of constant expression might
depend on whether copy elision is performed
assume that copy elision
is always performed
CWG 2126 C++11 constant initialized lifetime-extended temporaries of const-
qualified literal types were not usable in constant expressions
usable
CWG 2129 C++11 integer literals were not constant expressions they are
CWG 2167 C++11 non-member references local to an evaluation
made the evaluation non-constexpr
non-member
references allowed
CWG 2278 C++98 the resolution of CWG issue 2022 was not implementable assume that copy elision
is never performed
CWG 2299 C++14 it was unclear whether macros in <cstdarg>
can be used in constant evaluation
va_arg forbidden,
va_start unspecified
CWG 2400 C++11 invoking a constexpr virtual function on an object not usable
in constant expressions and whose lifetime began outside the
expression containing the invocation could be a constant expression
it is not a
constant expression
CWG 2490 C++20 (pseudo) destructor calls lacked
restrictions in constant evaluation
restriction added
CWG 2552 C++23 when evaluating a core constant expression, the control
flow could not pass through a declaration of a non-block variable
it can
CWG 2558 C++11 an indeterminate value could be a constant expression not a constant expression
CWG 2647 C++20 variables of volatile-qualified types could be potentially-constant they are not
CWG 2763 C++11 the violation of [[noreturn]] was not required
to be detected during constant evaluation
required
CWG 2851 C++11 converted constant expressions did
not allow floating-point conversions
allow non-narrowing
floating-point conversions
CWG 2907 C++11 core constant expressions could not apply
lvalue-to-rvalue conversions to std::nullptr_t glvalues
can apply such
conversions
CWG 2909 C++20 a variable without an initializer could only be
constant-initialized if its default-initialization
results in some initialization being performed
can only be constant-
initialized if its type is
const-default-initializable
CWG 2924 C++11
C++23
it was unspecified whether an expression violating
the constraints of [[noreturn]] (C++11) or
[[assume]] (C++23) is a core constant expression
it is
implementation-defined
P2280R4 C++11 evaluating an expression containing an identifier expression
or *this that refers to an object or reference whose lifetime
began outside this evaluation is not a constant expression
it can be a
constant expression

See also

constexpr specifier(C++11) specifies that the value of a variable or function can be computed at compile time
(C++11)(deprecated in C++17)(removed in C++20)
checks if a type is a literal type
(class template)
C documentation for Constant expressions