std::three_way_comparable, std::three_way_comparable_with

 

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

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

2) The concept std::three_way_comparable_with 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.

In both definitions, __WeaklyEqualityComparableWith and __PartiallyOrderedWith are exposition-only concepts also used by equality_comparable and totally_ordered, respectively.

Semantic requirements

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

1) T and Cat model std::three_way_comparable<T, Cat> only if, given lvalues a and b of 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.

2) T, U, and Cat model std::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>.

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).

In specification of standard concepts, operands are defined as the largest subexpressions that include only:

• an id-expression, and
• invocations of std::move, std::forward, and std::declval.

The cv-qualification and value category of each operand is determined by assuming that each template type parameter denotes a cv-unqualified complete non-array object type.

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)