std::three_way_comparable, std::three_way_comparable_with

 

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Defined in header <compare>
template<class T, class U>   concept __PartiallyOrderedWith =      // exposition only     requires(const std::remove_reference_t<T>& t,              const std::remove_reference_t<U>& u) {       { t <  u } -> std::boolean;       { t >  u } -> std::boolean;       { t <= u } -> std::boolean;       { t >= u } -> std::boolean;       { u <  t } -> std::boolean;       { u >  t } -> std::boolean;       { u <= t } -> std::boolean;       { u >= t } -> std::boolean;     };	(1)	(since C++20)
template<class T, class Cat>   concept __ComparesAs =                // exposition only     std::same_as<std::common_comparison_category_t<T, Cat>, Cat>;	(2)	(since C++20)
template<class T, class Cat = std::partial_ordering>   concept three_way_comparable =     __WeaklyEqualityComparableWith<T, T> &&     __PartiallyOrderedWith<T, T> &&     requires(const std::remove_reference_t<T>& a,              const std::remove_reference_t<T>& b) {       { a <=> b } -> __ComparesAs<Cat>;     };	(3)	(since C++20)
template<class T, class U, class Cat = std::partial_ordering>   concept three_way_comparable_with =     __WeaklyEqualityComparableWith<T, U> &&     __PartiallyOrderedWith<T, U> &&     std::three_way_comparable<T, Cat> &&     std::three_way_comparable<U, Cat> &&     std::common_reference_with<       const std::remove_reference_t<T>&,       const std::remove_reference_t<U>&> &&     three_way_comparable<       std::common_reference_t<         const std::remove_reference_t<T>&,         const std::remove_reference_t<U>&>, Cat> &&     requires(const std::remove_reference_t<T>& t,              const std::remove_reference_t<U>& u) {       { t <=> u } -> __ComparesAs<Cat>;       { u <=> t } -> __ComparesAs<Cat>;     };	(4)	(since C++20)

1) The exposition-only concept __PartiallyOrderedWith<T, U> specifies that an object of type T and an object 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.

More formally, T and U model __PartiallyOrderedWith<T, U> only if given

• t, an lvalue of type const std::remove_reference_t<T> and
• u, an lvalue 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).

3) The concept three_way_comparable<T, Cat> specifies that the three way comparison operator <=> on T yield results consistent with the comparison category implied by Cat.

T and Cat model three_way_comparable<T, Cat> only if, given lvalues a and b type const std::remove_reference_t<T>, following are true:

• (a <=> b == 0) == bool(a == b),
• (a <=> b != 0) == bool(a != b),
• ((a <=> b) <=> 0) and (0 <=> (b <=> a)) are equal,
• bool(a > b) == bool(b < a),
• bool(a >= b) == !bool(a < b),
• bool(a <= b) == !bool(b < a),
• (a <=> b < 0) == bool(a < b),
• (a <=> b > 0) == bool(a > b),
• (a <=> b <= 0) == bool(a <= b), and
• (a <=> b >= 0) == bool(a >= b); and
• if Cat is convertible to std::strong_ordering, T models totally_ordered.

4) The concept three_way_comparable_with<T, U, Cat> specifies that the three way comparison operator <=> on (possibly mixed) T and U operands yield results consistent with the comparison category implied by Cat. Comparing mixed operands yields results equivalent to comparing the operands converted to their common type.

Formally, T, U, and Cat model three_way_comparable_with<T, U, Cat> only if given

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

Let C be std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t<U>&>, the following are true:

• t <=> u and u <=> t have the same domain;
• ((t <=> u) <=> 0) and (0 <=> (u <=> t)) are equal;
• (t <=> u == 0) == bool(t == u),
• (t <=> u != 0) == bool(t != u),
• Cat(t <=> u) == Cat(C(t) <=> C(u)),
• (t <=> u < 0) == bool(t < u),
• (t <=> u > 0) == bool(t > u),
• (t <=> u <= 0) == bool(t <= u),
• (t <=> u >= 0) == bool(t >= u); and
• if Cat is convertible to std::strong_ordering, T and U model std::totally_ordered_with<T, U>.

where __WeaklyEqualityComparableWith is an exposition-only concept also used by equality_comparable.

Equality preservation

An expression is equality preserving if it results in equal outputs given equal inputs.

• The inputs to an expression consist of its operands.
• The outputs of an expression consist of its result and all operands modified by the expression (if any).

Every expression required to be equality preserving is further required to be stable: two evaluations of such an expression with the same input objects must have equal outputs absent any explicit intervening modification of those input objects.

Unless noted otherwise, every expression used in a requires-expression is required to be equality preserving and stable, and the evaluation of the expression may only modify its non-constant operands. Operands that are constant must not be modified.

Implicit expression variations

A requires-expression that uses an expression that is non-modifying for some constant lvalue operand also implicitly requires additional variations of that expression that accept a non-constant lvalue or (possibly constant) rvalue for the given operand unless such an expression variation is explicitly required with differing semantics. These implicit expression variations must meet the same semantic requirements of the declared expression. The extent to which an implementation validates the syntax of the variations is unspecified.

See also

equality_comparableequality_comparable_with (C++20)	specifies that operator == is an equivalence relation (concept)
totally_orderedtotally_ordered_with (C++20)	specifies that the comparison operators on the type yield a total order (concept)