std::strong_ordering(3)

NAME
std::strong_ordering - std::strong_ordering

Synopsis
   Defined in header <compare>
   class strong_ordering; (since C++20)
   The class type std::strong_ordering is the result type of a three-way comparison
   that:
     * Admits all six relational operators (==, !=, <, <=, >, >=).
     * Implies substitutability: if a is equivalent to b, f(a) is also equivalent to
       f(b), where f denotes a function that reads only comparison-salient state that
       is accessible via the argument's public const members. In other words,
       equivalent values are indistinguishable.
     * Does not allow incomparable values: exactly one of a < b, a == b, or a > b must
       be true.

Constants
   The type std::strong_ordering has four valid values, implemented as const static
   data members of its type:
   Member constant Definition
   less(inline constexpr) a valid value of the type std::strong_ordering
   [static] indicating less-than (ordered before) relationship
                        (public static member constant)
                        a valid value of the type std::strong_ordering
   equivalent(inline constexpr) indicating equivalence (neither ordered before nor
   [static] ordered after), the same as equal
                        (public static member constant)
                        a valid value of the type std::strong_ordering
   equal(inline constexpr) indicating equivalence (neither ordered before nor
   [static] ordered after), the same as equivalent
                        (public static member constant)
   greater(inline constexpr) a valid value of the type std::strong_ordering
   [static] indicating greater-than (ordered after) relationship
                        (public static member constant)

Conversions
   std::strong_ordering is the strongest of the three comparison categories: it is not
   implicitly-convertible from any other category and is implicitly-convertible to the
   other two.
   operator partial_ordering implicit conversion to std::partial_ordering
                        (public member function) std::strong_ordering::operator partial_ordering
   constexpr operator partial_ordering() const noexcept;

Return value
   std::partial_ordering::less if v is less, std::partial_ordering::greater if v is
   greater, std::partial_ordering::equivalent if v is equal or equivalent.
   operator weak_ordering implicit conversion to std::weak_ordering
                        (public member function) std::strong_ordering::operator weak_ordering
   constexpr operator weak_ordering() const noexcept;

Return value
   std::weak_ordering::less if v is less, std::weak_ordering::greater if v is greater,
   std::weak_ordering::equivalent if v is equal or equivalent.

Comparisons
   Comparison operators are defined between values of this type and literal 0. This
   supports the expressions a <=> b == 0 or a <=> b < 0 that can be used to convert the
   result of a three-way comparison operator to a boolean relationship; see std::is_eq,
   std::is_lt, etc.
   These functions are not visible to ordinary unqualified or qualified lookup, and can
   only be found by argument-dependent lookup when std::strong_ordering is an
   associated class of the arguments.
   The behavior of a program that attempts to compare a strong_ordering with anything
   other than the integer literal 0 is undefined.
   operator==
   operator<
   operator> compares with zero or a strong_ordering
   operator<= (function)
   operator>=
   operator<=> operator==
   friend constexpr bool (1)
   operator==( strong_ordering v, /*unspecified*/ u ) noexcept;
   friend constexpr bool (2)
   operator==( strong_ordering v, strong_ordering w ) noexcept = default;

Parameters
   v, w - std::strong_ordering values to check
   u - an unused parameter of any type that accepts literal zero argument

Return value
   1) true if v is equivalent or equal, false if v is less or greater
   2) true if both parameters hold the same value, false otherwise. Note that equal is
   the same as equivalent. operator<
   friend constexpr bool operator<( strong_ordering v, /*unspecified*/ u ) (1)
   noexcept;
   friend constexpr bool operator<( /*unspecified*/ u, strong_ordering v ) (2)
   noexcept;

Parameters
   v - a std::strong_ordering value to check
   u - an unused parameter of any type that accepts literal zero argument

Return value
   1) true if v is less, and false if v is greater, equivalent, or equal
   2) true if v is greater, and false if v is less, equivalent, or equal operator<=
   friend constexpr bool operator<=( strong_ordering v, /*unspecified*/ u ) (1)
   noexcept;
   friend constexpr bool operator<=( /*unspecified*/ u, strong_ordering v ) (2)
   noexcept;

Parameters
   v - a std::strong_ordering value to check
   u - an unused parameter of any type that accepts literal zero argument

Return value
   1) true if v is less, equivalent, or equal, and false if v is greater
   2) true if v is greater, equivalent, or equal, and false if v is less operator>
   friend constexpr bool operator>( strong_ordering v, /*unspecified*/ u ) (1)
   noexcept;
   friend constexpr bool operator>( /*unspecified*/ u, strong_ordering v ) (2)
   noexcept;

Parameters
   v - a std::strong_ordering value to check
   u - an unused parameter of any type that accepts literal zero argument

Return value
   1) true if v is greater, and false if v is less, equivalent, or equal
   2) true if v is less, and false if v is greater, equivalent, or equal operator>=
   friend constexpr bool operator>=( strong_ordering v, /*unspecified*/ u ) (1)
   noexcept;
   friend constexpr bool operator>=( /*unspecified*/ u, strong_ordering v ) (2)
   noexcept;

Parameters
   v - a std::strong_ordering value to check
   u - an unused parameter of any type that accepts literal zero argument

Return value
   1) true if v is greater, equivalent, or equal, and false if v is less
   2) true if v is less, equivalent, or equal, and false if v is greater operator<=>
   friend constexpr strong_ordering (1)
   operator<=>( strong_ordering v, /*unspecified*/ u ) noexcept;
   friend constexpr strong_ordering (2)
   operator<=>( /*unspecified*/ u, strong_ordering v ) noexcept;

Parameters
   v - a std::strong_ordering value to check
   u - an unused parameter of any type that accepts literal zero argument

Return value
   1) v.
   2) greater if v is less, less if v is greater, otherwise v.

Example
// Run this code
 #include <compare>
 #include <iostream>
 struct Point
 {
     int x{}, y{};
     friend constexpr std::strong_ordering operator<=>(Point lhs, Point rhs)
     {
         if (lhs.x < rhs.x or (lhs.x == rhs.x and lhs.y < rhs.y))
             return std::strong_ordering::less;
         if (lhs.x > rhs.x or (lhs.x == rhs.x and lhs.y > rhs.y))
             return std::strong_ordering::greater;
         return std::strong_ordering::equivalent;
     }
     friend std::ostream& operator<<(std::ostream& os, Point s)
     {
         return os << '(' << s.x << ',' << s.y << ')';
     }
 };
 void print_three_way_comparison(const auto& p, const auto& q)
 {
     const auto cmp{p <=> q};
     std::cout << p
               << (cmp < 0 ? " < " : cmp > 0 ? " > " : " == " ) // compares with 0
               << q << '\n';
 }
 void print_two_way_comparison(const auto& p, const auto& q)
 {
     std::cout << p
               << (p < q ? " < " : p > q ? " > " : " == ") // compares p and q
               << q << '\n';
 }
 int main()
 {
     const Point p1{0, 1}, p2{0, 1}, p3{0, 2};
     print_three_way_comparison(p1, p2);
     print_two_way_comparison(p1, p2);
     print_three_way_comparison(p2, p3);
     print_two_way_comparison(p2, p3);
     print_three_way_comparison(p3, p2);
     print_two_way_comparison(p3, p2);
 }

Output:
 (0,1) == (0,1)
 (0,1) == (0,1)
 (0,1) < (0,2)
 (0,1) < (0,2)
 (0,2) > (0,1)
 (0,2) > (0,1)

See also
   weak_ordering the result type of 3-way comparison that supports all 6 operators
   (C++20) and is not substitutable
                    (class)
   partial_ordering the result type of 3-way comparison that supports all 6 operators,
   (C++20) is not substitutable, and allows incomparable values
                    (class)