17 Language support library [support]

17.12 Comparisons [cmp]

17.12.4 Concept three_­way_­comparable [cmp.concept]

template<class T, class Cat> concept compares-as = // exposition only same_­as<common_comparison_category_t<T, Cat>, Cat>; template<class T, class U> concept partially-ordered-with = // exposition only requires(const remove_reference_t<T>& t, const remove_reference_t<U>& u) { { t < u } -> boolean-testable; { t > u } -> boolean-testable; { t <= u } -> boolean-testable; { t >= u } -> boolean-testable; { u < t } -> boolean-testable; { u > t } -> boolean-testable; { u <= t } -> boolean-testable; { u >= t } -> boolean-testable; };
Let t and u be lvalues of types const remove_­reference_­t<T> and const remove_­reference_­t<U>, respectively.
T and U model partially-ordered-with<T, U> only if:
  • t < u, t <= u, t > u, t >= u, u < t, u <= t, u > t, and u >= t have the same domain.
  • bool(t < u) == bool(u > t) is true,
  • bool(u < t) == bool(t > u) is true,
  • bool(t <= u) == bool(u >= t) is true, and
  • bool(u <= t) == bool(t >= u) is true.
template<class T, class Cat = partial_ordering> concept three_­way_­comparable = weakly-equality-comparable-with<T, T> && partially-ordered-with<T, T> && requires(const remove_reference_t<T>& a, const remove_reference_t<T>& b) { { a <=> b } -> compares-as<Cat>; };
Let a and b be lvalues of type const remove_­reference_­t<T>.
T and Cat model three_­way_­comparable<T, Cat> only if:
  • (a <=> b == 0) == bool(a == b) is true,
  • (a <=> b != 0) == bool(a != b) is true,
  • ((a <=> b) <=> 0) and (0 <=> (b <=> a)) are equal,
  • (a <=> b < 0) == bool(a < b) is true,
  • (a <=> b > 0) == bool(a > b) is true,
  • (a <=> b <= 0) == bool(a <= b) is true,
  • (a <=> b >= 0) == bool(a >= b) is true, and
  • if Cat is convertible to strong_­ordering, T models totally_­ordered ([concept.totallyordered]).
template<class T, class U, class Cat = partial_ordering> concept three_­way_­comparable_­with = three_­way_­comparable<T, Cat> && three_­way_­comparable<U, Cat> && comparison-common-type-with<T, U> && three_­way_­comparable< common_reference_t<const remove_reference_t<T>&, const remove_reference_t<U>&>, Cat> && weakly-equality-comparable-with<T, U> && partially-ordered-with<T, U> && requires(const remove_reference_t<T>& t, const remove_reference_t<U>& u) { { t <=> u } -> compares-as<Cat>; { u <=> t } -> compares-as<Cat>; };
Let t and t2 be lvalues denoting distinct equal objects of types const remove_­reference_­t<T> and remove_­cvref_­t<T>, respectively, and let u and u2 be lvalues denoting distinct equal objects of types const remove_­reference_­t<U> and remove_­cvref_­t<U>, respectively.
Let C be common_­reference_­t<const remove_­reference_­t<T>&, const remove_­reference_­t<U>&>.
Let CONVERT_­TO_­LVALUE<C>(E) be defined as in [concepts.compare.general].
T, U, and Cat model three_­way_­comparable_­with<T, U, Cat> only if:
  • t <=> u and u <=> t have the same domain,
  • ((t <=> u) <=> 0) and (0 <=> (u <=> t)) are equal,
  • (t <=> u == 0) == bool(t == u) is true,
  • (t <=> u != 0) == bool(t != u) is true,
  • Cat(t <=> u) == Cat(CONVERT_­TO_­LVALUE<C>(t2) <=> CONVERT_­TO_­LVALUE<C>(u2)) is true,
  • (t <=> u < 0) == bool(t < u) is true,
  • (t <=> u > 0) == bool(t > u) is true,
  • (t <=> u <= 0) == bool(t <= u) is true,
  • (t <=> u >= 0) == bool(t >= u) is true, and
  • if Cat is convertible to strong_­ordering, T and U model totally_­ordered_­with<T, U> ([concept.totallyordered]).