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std::totally_ordered, std::totally_ordered_with - cppreference.com

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Defined in header <concepts>

template< class T > concept totally_ordered = std::equality_comparable<T> && __PartiallyOrderedWith<T, T>;

 (1) (since C++20)

template< class T, class U > concept totally_ordered_with = std::totally_ordered<T> && std::totally_ordered<U> && std::equality_comparable_with<T, U> && std::totally_ordered< std::common_reference_t< const std::remove_reference_t<T>&, const std::remove_reference_t<U>&>> && __PartiallyOrderedWith<T, U>;

 (2) (since C++20)

Helper concepts

template< class T, class U > concept __PartiallyOrderedWith = requires(const std::remove_reference_t<T>& t, const std::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; };

 (3) (exposition only*)

1) The concept std::totally_ordered specifies that the comparison operators ==,!=,<,>,<=,>= on a type yield results consistent with a strict total order on the type.

2) The concept std::totally_ordered_with specifies that the comparison operators ==,!=,<,>,<=,>= on (possibly mixed) T and U operands yield results consistent with a strict total order. Comparing mixed operands yields results equivalent to comparing the operands converted to their common type.

3) The exposition-only concept __PartiallyOrderedWith specifies that a value of type T and a value of type U can be compared in a partial order with each other (in either order) using <, >, <=, and >=, and the results of the comparisons are consistent.

Semantic requirements

These concepts are modeled only if they are satisfied and all concepts they subsume are modeled.

1) std::totally_ordered<T> is modeled only if, given lvalues a, b and c of type const std::remove_reference_t<T>:

  • Exactly one of bool(a < b), bool(a > b) and bool(a == b) is true;
  • If bool(a < b) and bool(b < c) are both true, then bool(a < c) is true;
  • bool(a > b) == bool(b < a)
  • bool(a >= b) == !bool(a < b)
  • bool(a <= b) == !bool(b < a)

2) std::totally_ordered_with<T, U> is modeled only if, given

  • t and t2, lvalues denoting distinct equal objects of types const std::remove_reference_t<T> and std::remove_reference_t<T> respectively, and
  • u and u2, lvalues denoting distinct equal objects of types const std::remove_reference_t<U> and std::remove_reference_t<U> respectively,

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:

  • static_cast<C>(std::as_const(E)).
 (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:

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

3) __PartiallyOrderedWith<T, U> is modeled only if given

  • any lvalue t of type const std::remove_reference_t<T>, and
  • any lvalue u of type const std::remove_reference_t<U>,

the following are true:

  • 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);
  • bool(u < t) == bool(t > u);
  • bool(t <= u) == bool(u >= t); and
  • bool(u <= t) == bool(t >= u).

Equality preservation

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

Implicit expression variations

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

References

  • C++23 standard (ISO/IEC 14882:2024):
  • 18.5.5 Concept totally_ordered [concept.totallyordered]
  • C++20 standard (ISO/IEC 14882:2020):
  • 18.5.4 Concept totally_ordered [concept.totallyordered]

See also