std::three_way_comparable,std::three_way_comparable_with(3) | C++ Standard Libary | std::three_way_comparable,std::three_way_comparable_with(3) |
NAME¶
std::three_way_comparable,std::three_way_comparable_with - std::three_way_comparable,std::three_way_comparable_with
Synopsis¶
Defined in header <compare>
template<class T, class Cat = std::partial_ordering>
concept three_way_comparable =
__WeaklyEqualityComparableWith<T, T> &&
__PartiallyOrderedWith<T, T> && (1) (since C++20)
requires(const std::remove_reference_t<T>& a,
const std::remove_reference_t<T>& b) {
{ a <=> b } -> __ComparesAs<Cat>;
};
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< (2) (since C++20)
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>;
};
template<class T, class Cat>
concept __ComparesAs = // exposition only (3) (since C++20)
std::same_as<std::common_comparison_category_t<T, Cat>, Cat>;
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
modify only 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_comparable specifies that operator == is an equivalence
relation
equality_comparable_with (concept)
(C++20)
totally_ordered specifies that the comparison operators on the type yield a
totally_ordered_with total order
(C++20) (concept)
2022.07.31 | http://cppreference.com |