18 Concepts library [concepts]

18.5 Comparison concepts [concepts.compare]

18.5.5 Concept totally_ordered [concept.totallyordered]

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template<class T> concept totally_ordered = equality_comparable<T> && partially-ordered-with<T, T>;
1
#
Given a type T, let a, b, and c be lvalues of type const remove_reference_t<T>.
T models totally_ordered only if
  • (1.1)
    Exactly one of bool(a < b), bool(a > b), or bool(a == b) is true.
  • (1.2)
    If bool(a < b) and bool(b < c), then bool(a < c).
  • (1.3)
    bool(a <= b) == !bool(b < a).
  • (1.4)
    bool(a >= b) == !bool(a < b).
🔗
template<class T, class U> concept totally_ordered_with = totally_ordered<T> && totally_ordered<U> && equality_comparable_with<T, U> && totally_ordered< common_reference_t< const remove_reference_t<T>&, const remove_reference_t<U>&>> && partially-ordered-with<T, U>;
2
#
Given types T and U, let t and t2 be lvalues denoting distinct equal objects of types const remove_reference_t<T> and remove_cvref_t<T>, respectively, let u and u2 be lvalues denoting distinct equal objects of types const remove_reference_t<U> and remove_cvref_t<U>, respectively, and let C be: common_reference_t<const remove_reference_t<T>&, const remove_reference_t<U>&> T and U model totally_ordered_with<T, U> only if
  • (2.1)
    bool(t < u) == bool(CONVERT_TO_LVALUE<C>(t2) < CONVERT_TO_LVALUE<C>(u2)).
  • (2.2)
    bool(t > u) == bool(CONVERT_TO_LVALUE<C>(t2) > CONVERT_TO_LVALUE<C>(u2)).
  • (2.3)
    bool(t <= u) == bool(CONVERT_TO_LVALUE<C>(t2) <= CONVERT_TO_LVALUE<C>(u2)).
  • (2.4)
    bool(t >= u) == bool(CONVERT_TO_LVALUE<C>(t2) >= CONVERT_TO_LVALUE<C>(u2)).
  • (2.5)
    bool(u < t) == bool(CONVERT_TO_LVALUE<C>(u2) < CONVERT_TO_LVALUE<C>(t2)).
  • (2.6)
    bool(u > t) == bool(CONVERT_TO_LVALUE<C>(u2) > CONVERT_TO_LVALUE<C>(t2)).
  • (2.7)
    bool(u <= t) == bool(CONVERT_TO_LVALUE<C>(u2) <= CONVERT_TO_LVALUE<C>(t2)).
  • (2.8)
    bool(u >= t) == bool(CONVERT_TO_LVALUE<C>(u2) >= CONVERT_TO_LVALUE<C>(t2)).