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[concept.totallyordered]

18 Concepts library [concepts]

18.5 Comparison concepts [concepts.compare]

18.5.5 Concept totally_ordered [concept.totallyordered]

Given a type T, let a, b, and c be lvalues of type const remove_reference_t<T>.

T models totally_ordered only if

  • Exactly one of bool(a < b), bool(a > b), or bool(a == b) is true.

  • If bool(a < b) and bool(b < c), then bool(a < c).

  • bool(a <= b) == !bool(b < a).

  • bool(a >= b) == !bool(a < b).

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

  • bool(t < u) == bool(CONVERT_TO_LVALUE<C>(t2) < CONVERT_TO_LVALUE<C>(u2)).

  • bool(t > u) == bool(CONVERT_TO_LVALUE<C>(t2) > CONVERT_TO_LVALUE<C>(u2)).

  • bool(t <= u) == bool(CONVERT_TO_LVALUE<C>(t2) <= CONVERT_TO_LVALUE<C>(u2)).

  • bool(t >= u) == bool(CONVERT_TO_LVALUE<C>(t2) >= CONVERT_TO_LVALUE<C>(u2)).

  • bool(u < t) == bool(CONVERT_TO_LVALUE<C>(u2) < CONVERT_TO_LVALUE<C>(t2)).

  • bool(u > t) == bool(CONVERT_TO_LVALUE<C>(u2) > CONVERT_TO_LVALUE<C>(t2)).

  • bool(u <= t) == bool(CONVERT_TO_LVALUE<C>(u2) <= CONVERT_TO_LVALUE<C>(t2)).

  • bool(u >= t) == bool(CONVERT_TO_LVALUE<C>(u2) >= CONVERT_TO_LVALUE<C>(t2)).