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

std::partial_ordering - cppreference.com

class partial_ordering;

(since C++20)

The class type std::partial_ordering is the result type of a three-way comparison that:

Admits all six relational operators (==, !=, <, <=, >, >=).

Does not imply substitutability: if a is equivalent to b, f(a) may not be 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 may be distinguishable.
Admits incomparable values: a < b, a == b, and a > b may all be false.

[edit] Constants

The type std::partial_ordering has four valid values, implemented as const static data members of its type:

Name Definition

inline constexpr std::partial_ordering less

[static]

a valid value indicating less-than (ordered before) relationship
(public static member constant)

inline constexpr std::partial_ordering equivalent

[static]

a valid value indicating equivalence (neither ordered before nor ordered after)
(public static member constant)

inline constexpr std::partial_ordering greater

[static]

a valid value indicating greater-than (ordered after) relationship
(public static member constant)

inline constexpr std::partial_ordering unordered

[static]

a valid value indicating relationship with an incomparable value
(public static member constant) [edit] Conversions

std::partial_ordering cannot be implicitly converted to other comparison category types, while both std::strong_ordering and std::weak_ordering are implicitly-convertible to partial_ordering.

[edit] Comparisons

Comparison operators are defined between values of this type and literal â0â. 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::partial_ordering is an associated class of the arguments.

The behavior of a program that attempts to compare a partial_ordering with anything other than the integer literal â0â is undefined.

operator==operator<operator>operator<=operator>=operator<=>

compares with zero or a partial_ordering
(function) operator==

friend constexpr bool operator==( partial_ordering v, /*unspecified*/ u ) noexcept;

(1)

friend constexpr bool operator==( partial_ordering v, partial_ordering w ) noexcept = default;

(2) Parameters v, w - std::partial_ordering values to check u - an unused parameter of any type that accepts literal zero argument Return value

1) true if v is equivalent, false if v is less, greater, or unordered

2) true if both parameters hold the same value, false otherwise

operator<

friend constexpr bool operator<( partial_ordering v, /*unspecified*/ u ) noexcept;

(1)

friend constexpr bool operator<( /*unspecified*/ u, partial_ordering v ) noexcept;

(2) Parameters v - a std::partial_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 unordered

2) true if v is greater, and false if v is less, equivalent, or unordered

operator<=

friend constexpr bool operator<=( partial_ordering v, /*unspecified*/ u ) noexcept;

(1)

friend constexpr bool operator<=( /*unspecified*/ u, partial_ordering v ) noexcept;

(2) Parameters v - a std::partial_ordering value to check u - an unused parameter of any type that accepts literal zero argument Return value

1) true if v is less or equivalent, and false if v is greater or unordered

2) true if v is greater or equivalent, and false if v is less or unordered

operator>

friend constexpr bool operator>( partial_ordering v, /*unspecified*/ u ) noexcept;

(1)

friend constexpr bool operator>( /*unspecified*/ u, partial_ordering v ) noexcept;

(2) Parameters v - a std::partial_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 unordered

2) true if v is less, and false if v is greater, equivalent, or unordered

operator>=

friend constexpr bool operator>=( partial_ordering v, /*unspecified*/ u ) noexcept;

(1)

friend constexpr bool operator>=( /*unspecified*/ u, partial_ordering v ) noexcept;

(2) Parameters v - a std::partial_ordering value to check u - an unused parameter of any type that accepts literal zero argument Return value

1) true if v is greater or equivalent, and false if v is less or unordered

2) true if v is less or equivalent, and false if v is greater or unordered

operator<=>

friend constexpr partial_ordering operator<=>( partial_ordering v, /*unspecified*/ u ) noexcept;

(1)

friend constexpr partial_ordering operator<=>( /*unspecified*/ u, partial_ordering v ) noexcept;

(2) Parameters v - a std::partial_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.

[edit] Notes

The built-in operator<=> between floating-point values uses this ordering: the positive zero and the negative zero compare equivalent, but can be distinguished, and NaN values compare unordered with any other value.

[edit] Example [edit] See also the result type of 3-way comparison that supports all 6 operators and is substitutable
(class) [edit] the result type of 3-way comparison that supports all 6 operators and is not substitutable
(class) [edit]

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