std::three_way_comparable, std::three_way_comparable_with

 

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Defined in header <compare>
template< class T, class Cat = std::partial_ordering > concept three_way_comparable =     __WeaklyEqualityComparableWith<T, T> &&     __PartiallyOrderedWith<T, T> &&     requires(const std::remove_reference_t<T>& a,              const std::remove_reference_t<T>& b) {         { a <=> b } -> __ComparesAs<Cat>;     };	(1)	(since C++20)
template< class T, class U, class Cat = std::partial_ordering > concept three_way_comparable_with =     std::three_way_comparable<T, Cat> &&     std::three_way_comparable<U, Cat> &&     __ComparisonCommonTypeWith<T, U> &&     std::three_way_comparable<         std::common_reference_t<             const std::remove_reference_t<T>&,             const std::remove_reference_t<U>&>, Cat> &&     __WeaklyEqualityComparableWith<T, U> &&     __PartiallyOrderedWith<T, U> &&     requires(const std::remove_reference_t<T>& t,              const std::remove_reference_t<U>& u) {         { t <=> u } -> __ComparesAs<Cat>;         { u <=> t } -> __ComparesAs<Cat>;     };	(2)	(since C++20)
template< class T, class Cat > concept __ComparesAs =     std::same_as<std::common_comparison_category_t<T, Cat>, Cat>;	(3)	(exposition only*)

1) The concept std::three_way_comparable specifies that the three way comparison operator <=> on T yield results consistent with the comparison category implied by Cat.

2) The concept std::three_way_comparable_with specifies that the three way comparison operator <=> on (possibly mixed) T and U operands yield results consistent with the comparison category implied by Cat. Comparing mixed operands yields results equivalent to comparing the operands converted to their common type.

__WeaklyEqualityComparableWith, __PartiallyOrderedWith, and __ComparisonCommonTypeWith are exposition-only concepts. See descriptions of equality_comparable and totally_ordered.

Semantic requirements

These concepts are modeled only if they are satisfied and all concepts they subsume are modeled.

1) T and Cat model std::three_way_comparable<T, Cat> only if, given lvalues a and b of type const std::remove_reference_t<T>, following are true:

• (a <=> b == 0) == bool(a == b),
• (a <=> b != 0) == bool(a != b),
• ((a <=> b) <=> 0) and (0 <=> (b <=> a)) are equal,
• bool(a > b) == bool(b < a),
• bool(a >= b) == !bool(a < b),
• bool(a <= b) == !bool(b < a),
• (a <=> b < 0) == bool(a < b),
• (a <=> b > 0) == bool(a > b),
• (a <=> b <= 0) == bool(a <= b), and
• (a <=> b >= 0) == bool(a >= b), and
• if Cat is convertible to std::strong_ordering, T models totally_ordered.

2) T, U, and Cat model std::three_way_comparable_with<T, U, Cat> only if given

• t and t2, lvalues denoting distinct equal objects of types const std::remove_reference_t<T> and std::remove_reference_t<T> respectively, and
• u and u2, lvalues denoting distinct equal objects of types const std::remove_reference_t<U> and std::remove_reference_t<U> respectively.

Let C be std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t<U>&> and given an expression E and a type C, let CONVERT_TO<C>(E) be:

static_cast<C>(std::as_const(E)).	(until C++23)
static_cast<const C&>(std::as_const(E)) if that is a valid expression, static_cast<const C&>(std::move(E)) otherwise.	(since C++23)

the following are true:

• t <=> u and u <=> t have the same domain,
• ((t <=> u) <=> 0) and (0 <=> (u <=> t)) are equal,
• (t <=> u == 0) == bool(t == u),
• (t <=> u != 0) == bool(t != u),
• Cat(t <=> u) == Cat(CONVERT_TO<C>(t2) <=> CONVERT_TO<C>(u2)),
• (t <=> u < 0) == bool(t < u),
• (t <=> u > 0) == bool(t > u),
• (t <=> u <= 0) == bool(t <= u),
• (t <=> u >= 0) == bool(t >= u), and
• if Cat is convertible to std::strong_ordering, T and U model std::totally_ordered_with<T, U>.

Equality preservation

Expressions declared in requires expressions of the standard library concepts are required to be equality-preserving (except where stated otherwise).

Implicit expression variations

A requires expression that uses an expression that is non-modifying for some constant lvalue operand also requires implicit expression variations.

See also

equality_comparableequality_comparable_with (C++20)	specifies that operator == is an equivalence relation (concept)
totally_orderedtotally_ordered_with (C++20)	specifies that the comparison operators on the type yield a total order (concept)