[class.compare]

# 11 Classes [[class]](./#class)

## 11.10 Comparisons [class.compare]

### [11.10.1](#default) Defaulted comparison operator functions [[class.compare.default]](class.compare.default)

[1](#default-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6562)

A defaulted comparison operator function ([[over.binary]](over.binary "12.4.3 Binary operators"))
shall be a non-template function
that

- [(1.1)](#default-1.1)

is a non-static member or friend of some class C,

- [(1.2)](#default-1.2)

is defined as defaulted in C or in
a context where C is complete, and

- [(1.3)](#default-1.3)

either has
two parameters of type const C& or
two parameters of type C,
where the implicit object parameter (if any) is considered to be
the first parameter[.](#default-1.sentence-1)

Such a comparison operator function is termeda defaulted comparison operator function for class C[.](#default-1.sentence-2)

Name lookups and access checks in
the implicit definition ([[dcl.fct.def.default]](dcl.fct.def.default "9.6.2 Explicitly-defaulted functions"))
of a comparison operator function
are performed from a context equivalent to
its [*function-body*](dcl.fct.def.general#nt:function-body "9.6.1 General [dcl.fct.def.general]")[.](#default-1.sentence-3)

A definition of a comparison operator as
defaulted that appears in a class shall be the first declaration
of that function[.](#default-1.sentence-4)

[*Example [1](#default-example-1)*: struct S;bool operator==(S, S) = default; // error: S is not completestruct S {friend bool operator==(S, const S&) = default; // error: parameters of different types};enum E { };bool operator==(E, E) = default; // error: not a member or friend of a class — *end example*]

[2](#default-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6604)

A defaulted <=> or == operator function for class Cis defined as deleted if
any non-static data member of C is of reference type orC has variant members ([[class.union.anon]](class.union.anon "11.5.2 Anonymous unions"))[.](#default-2.sentence-1)

[3](#default-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6612)

A binary operator expression a @ b is[*usable*](#def:usable,binary_operator_expression "11.10.1 Defaulted comparison operator functions [class.compare.default]") if either

- [(3.1)](#default-3.1)

a or b is of class or enumeration type and
overload resolution ([[over.match]](over.match "12.2 Overload resolution")) as applied to a @ b results in a usable candidate, or

- [(3.2)](#default-3.2)

neither a nor b is of class or enumeration type anda @ b is a valid expression[.](#default-3.sentence-1)

[4](#default-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6627)

If the [*member-specification*](class.mem.general#nt:member-specification "11.4.1 General [class.mem.general]") does not explicitly declare
any member or friend named operator==,
an == operator function is declared implicitly
for each three-way comparison operator function
defined as defaulted in the [*member-specification*](class.mem.general#nt:member-specification "11.4.1 General [class.mem.general]"),
with the same access and [*function-definition*](dcl.fct.def.general#nt:function-definition "9.6.1 General [dcl.fct.def.general]") and
in the same class scope as
the respective three-way comparison operator function,
except that the return type is replaced with bool and
the [*declarator-id*](dcl.decl.general#nt:declarator-id "9.3.1 General [dcl.decl.general]") is replaced with operator==[.](#default-4.sentence-1)

[*Note [1](#default-note-1)*:

Such an implicitly-declared == operator for a class X is defined as defaulted
in the definition of X and
has the same [*parameter-declaration-clause*](dcl.fct#nt:parameter-declaration-clause "9.3.4.6 Functions [dcl.fct]") and
trailing [*requires-clause*](temp.pre#nt:requires-clause "13.1 Preamble [temp.pre]") as
the respective three-way comparison operator[.](#default-4.sentence-2)

It is declared with friend, virtual, constexpr,
or consteval if
the three-way comparison operator function is so declared[.](#default-4.sentence-3)

If the three-way comparison operator function
has no [*noexcept-specifier*](except.spec#nt:noexcept-specifier "14.5 Exception specifications [except.spec]"),
the implicitly-declared == operator function
has an implicit exception specification ([[except.spec]](except.spec "14.5 Exception specifications")) that
can differ from the implicit exception specification of
the three-way comparison operator function[.](#default-4.sentence-4)

— *end note*]

[*Example [2](#default-example-2)*: template<typename T> struct X {friend constexpr std::partial_ordering operator<=>(X, X) requires (sizeof(T) != 1) = default; // implicitly declares: friend constexpr bool operator==(X, X) requires (sizeof(T) != 1) = default;[[nodiscard]] virtual std::strong_ordering operator<=>(const X&) const = default; // implicitly declares: [[nodiscard]] virtual bool operator==(const X&) const = default;}; — *end example*]

[*Note [2](#default-note-2)*:

The == operator function is declared implicitly even if
the defaulted three-way comparison operator function
is defined as deleted[.](#default-4.sentence-5)

— *end note*]

[5](#default-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6673)

The direct base class subobjects of C,
in the order of their declaration in the [*base-specifier-list*](class.derived.general#nt:base-specifier-list "11.7.1 General [class.derived.general]") of C,
followed by the non-static data members of C,
in the order of their declaration in the [*member-specification*](class.mem.general#nt:member-specification "11.4.1 General [class.mem.general]") of C,
form a list of subobjects[.](#default-5.sentence-1)

In that list, any subobject of array type is recursively expanded
to the sequence of its elements, in the order of increasing subscript[.](#default-5.sentence-2)

Let xi be an lvalue denoting the ith element
in the expanded list of subobjects for an object x (of length n),
where xi is
formed by a sequence of
derived-to-base conversions ([[over.best.ics]](over.best.ics "12.2.4.2 Implicit conversion sequences")),
class member access expressions ([[expr.ref]](expr.ref "7.6.1.5 Class member access")), and
array subscript expressions ([[expr.sub]](expr.sub "7.6.1.2 Subscripting")) applied to x[.](#default-5.sentence-3)

### [11.10.2](#class.eq) Equality operator [[class.eq]](class.eq)

[1](#class.eq-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6693)

A defaulted equality operator function ([[over.binary]](over.binary "12.4.3 Binary operators"))
shall have a declared return type bool[.](#class.eq-1.sentence-1)

[2](#class.eq-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6697)

A defaulted == operator function for a class C is defined as deleted
unless, for each xi in the expanded list of subobjects
for an object x of type C,xi == xi is usable ([[class.compare.default]](#default "11.10.1 Defaulted comparison operator functions"))[.](#class.eq-2.sentence-1)

[3](#class.eq-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6705)

The return value of a defaulted == operator function
with parameters x and y is determined
by comparing corresponding elements xi and yi in the expanded lists of subobjects for x and y (in increasing index order)
until the first index i where xi == yi yields a result value which,
when contextually converted to bool, yields false[.](#class.eq-3.sentence-1)

The return value is false if such an index exists
and true otherwise[.](#class.eq-3.sentence-2)

[4](#class.eq-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6717)

[*Example [1](#class.eq-example-1)*: struct D {int i; friend bool operator==(const D& x, const D& y) = default; // OK, returns x.i == y.i}; — *end example*]

### [11.10.3](#class.spaceship) Three-way comparison [[class.spaceship]](class.spaceship)

[1](#class.spaceship-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6731)

The [*synthesized three-way comparison*](#def:three-way_comparison,synthesized "11.10.3 Three-way comparison [class.spaceship]") of type R ([[cmp.categories]](cmp.categories "17.12.2 Comparison category types"))
of glvalues a and b of the same type
is defined as follows:

- [(1.1)](#class.spaceship-1.1)

  If a <=> b is usable ([[class.compare.default]](#default "11.10.1 Defaulted comparison operator functions")) and
can be explicitly converted to R using static_cast,static_cast<R>(a <=> b)[.](#class.spaceship-1.1.sentence-1)

- [(1.2)](#class.spaceship-1.2)

  Otherwise, if a <=> b is usable or
overload resolution for a <=> b is performed and
finds at least one viable candidate,
the synthesized three-way comparison is not defined[.](#class.spaceship-1.2.sentence-1)

- [(1.3)](#class.spaceship-1.3)

  Otherwise, if R is not a comparison category type, or either
the expression a == b or the expression a < b is not usable,
the synthesized three-way comparison is not defined[.](#class.spaceship-1.3.sentence-1)

- [(1.4)](#class.spaceship-1.4)

  Otherwise, if R is strong_ordering, thena == b ? strong_ordering::equal : a < b ? strong_ordering::less : strong_ordering::greater

- [(1.5)](#class.spaceship-1.5)

  Otherwise, if R is weak_ordering, thena == b ? weak_ordering::equivalent : a < b ? weak_ordering::less : weak_ordering::greater

- [(1.6)](#class.spaceship-1.6)

  Otherwise (when R is partial_ordering),a == b ? partial_ordering::equivalent : a < b ? partial_ordering::less : b < a ? partial_ordering::greater : partial_ordering::unordered

[*Note [1](#class.spaceship-note-1)*:

A synthesized three-way comparison is ill-formed
if overload resolution finds usable candidates
that do not otherwise meet the requirements implied by the defined expression[.](#class.spaceship-1.sentence-2)

— *end note*]

[2](#class.spaceship-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6786)

Let R be the declared return type of
a defaulted three-way comparison operator function, and
let xi be the elements of
the expanded list of subobjects for
an object x of type C[.](#class.spaceship-2.sentence-1)

- [(2.1)](#class.spaceship-2.1)

  If R is auto, then
let cvi Ri be
the type of the expression xi <=> xi[.](#class.spaceship-2.1.sentence-1)
  The operator function is defined as deleted
if that expression is not usable or
if Ri is not
a comparison category type ([[cmp.categories.pre]](cmp.categories.pre "17.12.2.1 Preamble")) for any i[.](#class.spaceship-2.1.sentence-2)
  The return type is deduced as
the common comparison type (see below) ofR0, R1, …, Rn−1[.](#class.spaceship-2.1.sentence-3)

- [(2.2)](#class.spaceship-2.2)

  Otherwise, R shall not contain a placeholder type[.](#class.spaceship-2.2.sentence-1)
  If the synthesized three-way comparison of type R between any objects xi and xi is not defined,
the operator function is defined as deleted[.](#class.spaceship-2.2.sentence-2)

[3](#class.spaceship-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6813)

The return value of type R of the defaulted three-way comparison operator function
with parameters x and y of the same type
is determined by comparing corresponding elementsxi and yi in the expanded lists of subobjects for x and y (in increasing index order)
until the first index i where
the synthesized three-way comparison of type R between xi and yi yields a result value vi where vi!=0,
contextually converted to bool, yields true[.](#class.spaceship-3.sentence-1)

The return value is a copy of vi if such an index exists andstatic_cast<R>(std​::​strong_ordering​::​equal) otherwise[.](#class.spaceship-3.sentence-2)

[4](#class.spaceship-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6830)

The [*common comparison type*](#def:common_comparison_type "11.10.3 Three-way comparison [class.spaceship]") U of a possibly-empty list of n comparison category typesT0, T1, …, Tn−1 is defined as follows:

- [(4.1)](#class.spaceship-4.1)

  If at least one Ti is std​::​partial_ordering,U is std​::​partial_ordering ([[cmp.partialord]](cmp.partialord "17.12.2.2 Class partial_­ordering"))[.](#class.spaceship-4.1.sentence-1)

- [(4.2)](#class.spaceship-4.2)

  Otherwise, if at least one Ti is std​::​weak_ordering,U is std​::​weak_ordering ([[cmp.weakord]](cmp.weakord "17.12.2.3 Class weak_­ordering"))[.](#class.spaceship-4.2.sentence-1)

- [(4.3)](#class.spaceship-4.3)

  Otherwise, U is std​::​strong_ordering ([[cmp.strongord]](cmp.strongord "17.12.2.4 Class strong_­ordering"))[.](#class.spaceship-4.3.sentence-1)
  [*Note [2](#class.spaceship-note-2)*:
  In particular, this is the result when n is 0[.](#class.spaceship-4.3.sentence-2)
 — *end note*]

### [11.10.4](#secondary) Secondary comparison operators [[class.compare.secondary]](class.compare.secondary)

[1](#secondary-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6855)

A [*secondary comparison operator*](#def:secondary_comparison_operator "11.10.4 Secondary comparison operators [class.compare.secondary]") is
a relational operator ([[expr.rel]](expr.rel "7.6.9 Relational operators")) or the != operator[.](#secondary-1.sentence-1)

A defaulted operator function ([[over.binary]](over.binary "12.4.3 Binary operators"))
for a secondary comparison operator @ shall have a declared return type bool[.](#secondary-1.sentence-2)

[2](#secondary-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6863)

The operator function with parameters x and y is defined as deleted if

- [(2.1)](#secondary-2.1)

a first overload resolution ([[over.match]](over.match "12.2 Overload resolution")),
as applied to x @ y,
  * [(2.1.1)](#secondary-2.1.1)

does not result in a usable candidate, or

  * [(2.1.2)](#secondary-2.1.2)

the selected candidate is not a rewritten candidate, or

- [(2.2)](#secondary-2.2)

a second overload resolution for
the expression resulting from the interpretation of x @ y using the selected rewritten candidate ([[over.match.oper]](over.match.oper "12.2.2.3 Operators in expressions"))
does not result in a usable candidate
(for example, that expression might be (x <=> y) @ 0), or

- [(2.3)](#secondary-2.3)

x @ y cannot be implicitly converted to bool[.](#secondary-2.sentence-1)

In any of the two overload resolutions above,
the defaulted operator function is not considered as
a candidate for the @ operator[.](#secondary-2.sentence-2)

Otherwise, the operator function yields x @ y[.](#secondary-2.sentence-3)

[3](#secondary-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/classes.tex#L6892)

[*Example [1](#secondary-example-1)*: struct HasNoLessThan { };

struct C {friend HasNoLessThan operator<=>(const C&, const C&); bool operator<(const C&) const = default; // OK, function is deleted}; — *end example*]