# Default comparisons (since C++20)

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Comparison operator functions can be explicitly defaulted to request the compiler to generate the corresponding default comparison for a class.

### Definition

A defaulted comparison operator function is a non-template comparison operator function (i.e. `<=>`, `==`, `!=`, `<`, `>`, `<=`, or `>=`) satisfying all following conditions:

- It is a non-static member or friend of some class `C`.
- It is defined as defaulted in `C` or in a context where `C` is complete.
- It has two parameters of type const C& or two parameters of type `C`, where the implicit object parameter (if any) is considered to be the first parameter.

Such a comparison operator function is termed a defaulted comparison operator function for class `C`.

    struct X
    {
        bool operator==(const X&) const = default; // OK
        bool operator==(const X&) = default;       // Error: the implicit object
                                                   //        parameter type is X&
        bool operator==(this X, X) = default;      // OK
    };

    struct Y
    {
        friend bool operator==(Y, Y) = default;        // OK
        friend bool operator==(Y, const Y&) = default; // Error: different parameter types
    };

    bool operator==(const Y&, const Y&) = default;     // Error: not a friend of Y

Name lookups and access checks in the implicit definition of a comparison operator function are performed from a context equivalent to its function body. A definition of a comparison operator function as defaulted that appears in a class must be the first declaration of that function.

### Default comparison order

Given a class `C`, a subobject list is formed by the following subjects in order:

- The direct base class subobjects of `C`, in declaration order.
- The non-static data members of `C`, in declaration order.

  - If any member subobject is of array type, it is expanded to the sequence of its elements, in the order of increasing subscript. The expansion is recursive: array elements of array types will be expanded again until there is no subobject of array type.

For any object x of type `C`, in the following descriptions:

- Let n be the number of subobjects in the (expanded) subobject list for x.
- Let x_i be the ith subobject in the (expanded) subobject list for x, where x_i is formed by a sequence of derived-to-base conversions, class member access expressions, and array subscript expressions applied to x.

    struct S {};

    struct T : S
    {
        int arr[2][2];
    } t;

    // The subobject list for “t” consists of the following 5 subobjects in order:
    // (S)t → t[0][0] → t[0][1] → t[1][0] → t[1][1]

### Three-way comparison

An operator<=> for a class type can be defined as defaulted with any return type.

#### Comparison category types

There are three comparison category types:

- `std::strong_ordering`
- `std::weak_ordering`
- `std::partial_ordering`

Type | Equivalent values are.. | Incomparable values are..
--- | --- | ---
`std::strong_ordering` | indistinguishable | not allowed
`std::weak_ordering` | distinguishable | not allowed
`std::partial_ordering` | distinguishable | allowed

#### Synthesized three-way comparison

The synthesized three-way comparison of type `T` between glvalues a and b of the same type is defined as follows:

- If the overload resolution for a <=> b results in a usable candidate, and can be explicitly converted to `T` using `static_cast`, the synthesized comparison is static_cast<T>(a <=> b).
- Otherwise, if any of the following condition is satisfied, the synthesized comparison is not defined:

  - The overload resolution for a <=> b finds at least one viable candidate.
  - `T` is not a comparison category type.
  - The overload resolution for a == b does not result in a usable candidate.
  - The overload resolution for a < b does not result in a usable candidate.

- Otherwise, if `T` is `std::strong_ordering`, the synthesized comparison is

    a == b ? std::strong_ordering::equal :
    a < b  ? std::strong_ordering::less :
             std::strong_ordering::greater

- Otherwise, if `T` is `std::weak_ordering`, the synthesized comparison is

    a == b ? std::weak_ordering::equivalent :
    a < b  ? std::weak_ordering::less :
             std::weak_ordering::greater

- Otherwise (`T` is `std::partial_ordering`), the synthesized comparison is

    a == b ? std::partial_ordering::equivalent :
    a < b  ? std::partial_ordering::less :
    b < a  ? std::partial_ordering::greater :
             std::partial_ordering::unordered

#### Placeholder return type

If the declared return type of a defaulted three-way comparison operator function (operator<=>) for a class type `C` is auto, the return type is deduced from the return types of the three-way comparisons between the corresponding subobjects of an object x of type `C`.

For each subobject x_i in the (expanded) subobject list for x:

1. Perform overload resolution for x_i <=> x_i, if the overload resolution does not result in a usable candidate, the defaulted operator<=> is defined as deleted.
2. Denote the cv-unqualified version of the type of x_i <=> x_i as `R_i`, if `R_i` is not a comparison category type, the defaulted operator<=> is defined as deleted.

If the defaulted operator<=> is not defined as deleted, its return type is deduced as std::common_comparison_category_t <R_1, R_2, ..., R_n>.

#### Non-placeholder return type

If the declared return type of the defaulted operator<=> is not auto, it cannot contain any placeholder type (e.g. decltype(auto)).

If there is a subobject x_i in the (expanded) subobject list for x such that the synthesized three-way comparison of the declared return type between x_i and x_i is not defined, the defaulted operator<=> is defined as deleted.

#### Comparison result

Let x and y be the parameters of a defaulted operator<=>, denote each subobject in the (expanded) subobject list for x and y as x_i and y_i respectively. The default three-way comparison between x and y is performed by comparing corresponding subobjects x_i and y_i with increasing i order.

Let `R` be the (possibly-deduced) return type, the comparison result between x_i and y_i is the result of the synthesized three-way comparison of type `R` between x_i and y_i.

- During the default three-way comparison between x and y, if a subobject-wise comparison between x_i and y_i generates a result v_i such that contextually converting v_i != 0 to bool yields true, the return value is a copy of v_i (the remaining subobjects will not be compared).
- Otherwise, the return value is static_cast<R>(std::strong_ordering::equal).

Run this code

    #include <compare>
    #include <iostream>
    #include <set>

    struct Point
    {
        int x;
        int y;
        auto operator<=>(const Point&) const = default;
        /* non-comparison functions */
    };

    int main()
    {
        Point pt1{1, 1}, pt2{1, 2};
        std::set<Point> s; // OK
        s.insert(pt1);     // OK

        // two-way comparison operator functions are not required to be explicitly defined:
        // operator== is implicitly declared (see below)
        // the overload resolutions of other candidates will select rewritten candidates
        std::cout << std::boolalpha
            << (pt1 == pt2) << ' '  // false
            << (pt1 != pt2) << ' '  // true
            << (pt1 <  pt2) << ' '  // true
            << (pt1 <= pt2) << ' '  // true
            << (pt1 >  pt2) << ' '  // false
            << (pt1 >= pt2) << ' '; // false
    }

### Equality comparison

#### Explicit declaration

An operator== for a class type can be defined as defaulted with return type bool.

Given a class `C` and an object x of type `C`, if there is a subobject x_i in the (expanded) subobject list for x such that the overload resolution for x_i == x_i does not result in a usable candidate, the defaulted operator== is defined as deleted.

Let x and y be the parameters of a defaulted operator==, denote each subobject in the (expanded) subobject list for x and y as x_i and y_i respectively. The default equality comparison between x and y is performed by comparing corresponding subobjects x_i and y_i with increasing i order.

The comparison result between x_i and y_i is the result of x_i == y_i.

- During the default equality comparison between x and y, if a subobject-wise comparison between x_i and y_i generates a result v_i such that contextually converting v_i to bool yields false, the return value is false (the remaining subobjects will not be compared).
- Otherwise, the return value is true.

Run this code

    #include <iostream>

    struct Point
    {
        int x;
        int y;
        bool operator==(const Point&) const = default;
        /* non-comparison functions */
    };

    int main()
    {
        Point pt1{3, 5}, pt2{2, 5};
        std::cout << std::boolalpha
            << (pt1 != pt2) << '\n'  // true
            << (pt1 == pt1) << '\n'; // true

        struct [[maybe_unused]] { int x{}, y{}; } p, q;
        // if (p == q) {} // Error: operator== is not defined
    }

#### Implicit declaration

If a class `C` does not explicitly declare any member or friend named operator==, an `` operator function is declared implicitly for each operator<=> defined as defaulted. Each implicity-declared operator== have the same access and function definition and in the same class scope as the respective defaulted operator<=>, with the following changes:

- The declarator identifier is replaced with operator==.
- The return type is replaced with bool.

    template<typename T>
    struct X
    {
        friend constexpr std::partial_ordering operator<=>(X, X)
            requires (sizeof(T) != 1) = default;
        // implicitly declares: friend constexpr bool operator==(X, X)
        //                          requires (sizeof(T) != 1) = default;

        [[nodiscard]] virtual std::strong_ordering operator<=>(const X&) const = default;
        // implicitly declares: [[nodiscard]] virtual bool
        //                          operator==(const X&) const = default;
    };

### Secondary comparison

A secondary comparison operator function (`!=`, `<`, `>`, `<=`, or `>=`) for a class type can be defined as defaulted with return type bool.

Let `@` be one of the five secondary comparison operators, for each defaulted operator@ with parameters x and y, up to two overloads resolutions are performed (not considering the defaulted operator@ as a candidate) to determine whether it is defined as deleted.

- The first overload resolution is performed for x @ y. If the overload resolution does not result in a usable candidate, or the selected candidate is not a rewritten candidate, the defaulted operator@ is defined as deleted. There is no second overload resolution in these cases.
- The second overload resolution is performed for the selected rewritten candidate of x @ y. If the overload resolution does not result in a usable candidate, the defaulted operator@ is defined as deleted.

If is x @ y cannot be implicitly converted to bool, the defaulted operator@ is defined as deleted.

If the defaulted operator@ is not defined as deleted, it yields x @ y.

    struct HasNoRelational {};

    struct C
    {
        friend HasNoRelational operator<=>(const C&, const C&);
        bool operator<(const C&) const = default; // OK, function is defaulted
    };

### Keywords

`default`

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
CWG 2539 | C++20 | the synthesized three-way comparison would choose static_cast even if the explicit conversion is not available | does not choose static_cast in this case
CWG 2546 | C++20 | the defaulted secondary operator@ was not defined as deleted if the overload resolution of x @ y selects a non-usable rewritten candidate | defined as deleted in this case
CWG 2547 | C++20 | it was unclear whether comparison operator functions for non-classes can be defaulted | they cannot be defaulted
CWG 2568 | C++20 | the implicit definition of comparison operator functions might violate member access rules | access checks are performed from a context equivalent to their function bodies

### See also

- overload resolution in a call to an overloaded operator
- Built-in three-way comparison operator
- Operator overloading for comparison operators

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