17 Language support library [support]

17.11 Comparisons [cmp]

17.11.4 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;
    };
1
#
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:
  • (1.1)
    t < u, t <= u, t > u, t >= u, u < t, u <= t, u > t, and u >= t have the same domain.
  • (1.2)
    bool(t < u) == bool(u > t) is true,
  • (1.3)
    bool(u < t) == bool(t > u) is true,
  • (1.4)
    bool(t <= u) == bool(u >= t) is true, and
  • (1.5)
    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>;
    };
2
#
Let a and b be lvalues of type const remove_­reference_­t<T>.
T and Cat model three_­way_­comparable<T, Cat> only if:
  • (2.1)
    (a <=> b == 0) == bool(a == b) is true,
  • (2.2)
    (a <=> b != 0) == bool(a != b) is true,
  • (2.3)
    ((a <=> b) <=> 0) and (0 <=> (b <=> a)) are equal,
  • (2.4)
    (a <=> b < 0) == bool(a < b) is true,
  • (2.5)
    (a <=> b > 0) == bool(a > b) is true,
  • (2.6)
    (a <=> b <= 0) == bool(a <= b) is true,
  • (2.7)
    (a <=> b >= 0) == bool(a >= b) is true, and
  • (2.8)
    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> &&
    common_reference_with<const remove_reference_t<T>&, const remove_reference_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>;
    };
3
#
Let t and u be lvalues of types const remove_­reference_­t<T> and const remove_­reference_­t<U>, respectively.
Let C be common_­reference_­t<const remove_­reference_­t<T>&, const remove_­reference_­t<U>&>.
T, U, and Cat model three_­way_­comparable_­with<T, U, Cat> only if:
  • (3.1)
    t <=> u and u <=> t have the same domain,
  • (3.2)
    ((t <=> u) <=> 0) and (0 <=> (u <=> t)) are equal,
  • (3.3)
    (t <=> u == 0) == bool(t == u) is true,
  • (3.4)
    (t <=> u != 0) == bool(t != u) is true,
  • (3.5)
    Cat(t <=> u) == Cat(C(t) <=> C(u)) is true,
  • (3.6)
    (t <=> u < 0) == bool(t < u) is true,
  • (3.7)
    (t <=> u > 0) == bool(t > u) is true,
  • (3.8)
    (t <=> u <= 0) == bool(t <= u) is true,
  • (3.9)
    (t <=> u >= 0) == bool(t >= u) is true, and
  • (3.10)
    if Cat is convertible to strong_­ordering, T and U model totally_­ordered_­with<T, U> ([concept.totallyordered]).