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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.

Contents

[edit] 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

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:

(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>.

[edit] Equality preservation

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

[edit] Implicit expression variations

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

[edit] See also

specifies that operator == is an equivalence relation
(concept) [edit]
specifies that the comparison operators on the type yield a total order
(concept) [edit]