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Showing content from https://en.cppreference.com/w/cpp/language/../../cpp/utility/compare/three_way_comparable.html below:

std::three_way_comparable, std::three_way_comparable_with - cppreference.com

(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> && __ComparisonCommonTypeWith<T, U> && std::three_way_comparable< std::common_reference_t< const std::remove_reference_t<T>&, const std::remove_reference_t&>, Cat> && __WeaklyEqualityComparableWith<T, U> && __PartiallyOrderedWith<T, U> && requires(const std::remove_reference_t<T>& t, const std::remove_reference_t& u) { { t <=> u } -> __ComparesAs<Cat>; { u <=> t } -> __ComparesAs<Cat>; }; (2) (since C++20) (3) (exposition only*)

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.

__WeaklyEqualityComparableWith, __PartiallyOrderedWith, and __ComparisonCommonTypeWith are exposition-only concepts. See descriptions of equality_comparable and totally_ordered.

[edit] Semantic requirements

These concepts are modeled only if they are satisfied 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 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 and std::remove_reference_t respectively.

Let C be std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t&> 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:

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(CONVERT_TO<C>(t2) <=> CONVERT_TO<C>(u2)),
(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>.

[edit] Equality preservation

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

[edit] Implicit expression variations

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

[edit] See also

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