17 Language support library [support]

17.11 Comparisons [cmp]

17.11.2 Comparison category types [cmp.categories]

17.11.2.1 Preamble [cmp.categories.pre]

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The types partial_ordering, weak_ordering, and strong_ordering are collectively termed the comparison category types.
Each is specified in terms of an exposition-only data member named value whose value typically corresponds to that of an enumerator from one of the following exposition-only enumerations: enum class ord { equal = 0, equivalent = equal, less = -1, greater = 1 }; // exposition only enum class ncmp { unordered = -127 }; // exposition only
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[Note 1: 
The type strong_ordering corresponds to the term total ordering in mathematics.
— end note]
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The relational and equality operators for the comparison category types are specified with an anonymous parameter of unspecified type.
This type shall be selected by the implementation such that these parameters can accept literal 0 as a corresponding argument.
[Example 1: 
nullptr_t meets this requirement.
— end example]
In this context, the behavior of a program that supplies an argument other than a literal 0 is undefined.
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For the purposes of subclause [cmp.categories], substitutability is the property that f(a) == f(b) is true whenever a == b is true, where f denotes a function that reads only comparison-salient state that is accessible via the argument's public const members.

17.11.2.2 Class partial_ordering [cmp.partialord]

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The partial_ordering type is typically used as the result type of a three-way comparison operator ([expr.spaceship]) for a type that admits all of the six two-way comparison operators ([expr.rel], [expr.eq]), for which equality need not imply substitutability, and that permits two values to be incomparable.198
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namespace std { class partial_ordering { int value; // exposition only bool is_ordered; // exposition only // exposition-only constructors constexpr explicit partial_ordering(ord v) noexcept : value(int(v)), is_ordered(true) {} // exposition only constexpr explicit partial_ordering(ncmp v) noexcept : value(int(v)), is_ordered(false) {} // exposition only public: // valid values static const partial_ordering less; static const partial_ordering equivalent; static const partial_ordering greater; static const partial_ordering unordered; // comparisons friend constexpr bool operator==(partial_ordering v, unspecified) noexcept; friend constexpr bool operator==(partial_ordering v, partial_ordering w) noexcept = default; friend constexpr bool operator< (partial_ordering v, unspecified) noexcept; friend constexpr bool operator> (partial_ordering v, unspecified) noexcept; friend constexpr bool operator<=(partial_ordering v, unspecified) noexcept; friend constexpr bool operator>=(partial_ordering v, unspecified) noexcept; friend constexpr bool operator< (unspecified, partial_ordering v) noexcept; friend constexpr bool operator> (unspecified, partial_ordering v) noexcept; friend constexpr bool operator<=(unspecified, partial_ordering v) noexcept; friend constexpr bool operator>=(unspecified, partial_ordering v) noexcept; friend constexpr partial_ordering operator<=>(partial_ordering v, unspecified) noexcept; friend constexpr partial_ordering operator<=>(unspecified, partial_ordering v) noexcept; }; // valid values' definitions inline constexpr partial_ordering partial_ordering::less(ord::less); inline constexpr partial_ordering partial_ordering::equivalent(ord::equivalent); inline constexpr partial_ordering partial_ordering::greater(ord::greater); inline constexpr partial_ordering partial_ordering::unordered(ncmp::unordered); }
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constexpr bool operator==(partial_ordering v, unspecified) noexcept; constexpr bool operator< (partial_ordering v, unspecified) noexcept; constexpr bool operator> (partial_ordering v, unspecified) noexcept; constexpr bool operator<=(partial_ordering v, unspecified) noexcept; constexpr bool operator>=(partial_ordering v, unspecified) noexcept;
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Returns: For operator@, v.is_ordered && v.value @ 0.
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constexpr bool operator< (unspecified, partial_ordering v) noexcept; constexpr bool operator> (unspecified, partial_ordering v) noexcept; constexpr bool operator<=(unspecified, partial_ordering v) noexcept; constexpr bool operator>=(unspecified, partial_ordering v) noexcept;
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Returns: For operator@, v.is_ordered && 0 @ v.value.
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constexpr partial_ordering operator<=>(partial_ordering v, unspecified) noexcept;
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Returns: v.
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constexpr partial_ordering operator<=>(unspecified, partial_ordering v) noexcept;
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Returns: v < 0 ? partial_ordering​::​greater : v > 0 ? partial_ordering​::​less : v.
198)198)
That is, a < b, a == b, and a > b might all be false.

17.11.2.3 Class weak_ordering [cmp.weakord]

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The weak_ordering type is typically used as the result type of a three-way comparison operator ([expr.spaceship]) for a type that admits all of the six two-way comparison operators ([expr.rel], [expr.eq]) and for which equality need not imply substitutability.
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namespace std { class weak_ordering { int value; // exposition only // exposition-only constructors constexpr explicit weak_ordering(ord v) noexcept : value(int(v)) {} // exposition only public: // valid values static const weak_ordering less; static const weak_ordering equivalent; static const weak_ordering greater; // conversions constexpr operator partial_ordering() const noexcept; // comparisons friend constexpr bool operator==(weak_ordering v, unspecified) noexcept; friend constexpr bool operator==(weak_ordering v, weak_ordering w) noexcept = default; friend constexpr bool operator< (weak_ordering v, unspecified) noexcept; friend constexpr bool operator> (weak_ordering v, unspecified) noexcept; friend constexpr bool operator<=(weak_ordering v, unspecified) noexcept; friend constexpr bool operator>=(weak_ordering v, unspecified) noexcept; friend constexpr bool operator< (unspecified, weak_ordering v) noexcept; friend constexpr bool operator> (unspecified, weak_ordering v) noexcept; friend constexpr bool operator<=(unspecified, weak_ordering v) noexcept; friend constexpr bool operator>=(unspecified, weak_ordering v) noexcept; friend constexpr weak_ordering operator<=>(weak_ordering v, unspecified) noexcept; friend constexpr weak_ordering operator<=>(unspecified, weak_ordering v) noexcept; }; // valid values' definitions inline constexpr weak_ordering weak_ordering::less(ord::less); inline constexpr weak_ordering weak_ordering::equivalent(ord::equivalent); inline constexpr weak_ordering weak_ordering::greater(ord::greater); }
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constexpr operator partial_ordering() const noexcept;
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Returns: value == 0 ? partial_ordering::equivalent : value < 0 ? partial_ordering::less : partial_ordering::greater
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constexpr bool operator==(weak_ordering v, unspecified) noexcept; constexpr bool operator< (weak_ordering v, unspecified) noexcept; constexpr bool operator> (weak_ordering v, unspecified) noexcept; constexpr bool operator<=(weak_ordering v, unspecified) noexcept; constexpr bool operator>=(weak_ordering v, unspecified) noexcept;
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Returns: v.value @ 0 for operator@.
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constexpr bool operator< (unspecified, weak_ordering v) noexcept; constexpr bool operator> (unspecified, weak_ordering v) noexcept; constexpr bool operator<=(unspecified, weak_ordering v) noexcept; constexpr bool operator>=(unspecified, weak_ordering v) noexcept;
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Returns: 0 @ v.value for operator@.
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constexpr weak_ordering operator<=>(weak_ordering v, unspecified) noexcept;
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Returns: v.
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constexpr weak_ordering operator<=>(unspecified, weak_ordering v) noexcept;
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Returns: v < 0 ? weak_ordering​::​greater : v > 0 ? weak_ordering​::​less : v.

17.11.2.4 Class strong_ordering [cmp.strongord]

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The strong_ordering type is typically used as the result type of a three-way comparison operator ([expr.spaceship]) for a type that admits all of the six two-way comparison operators ([expr.rel], [expr.eq]) and for which equality does imply substitutability.
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namespace std { class strong_ordering { int value; // exposition only // exposition-only constructors constexpr explicit strong_ordering(ord v) noexcept : value(int(v)) {} // exposition only public: // valid values static const strong_ordering less; static const strong_ordering equal; static const strong_ordering equivalent; static const strong_ordering greater; // conversions constexpr operator partial_ordering() const noexcept; constexpr operator weak_ordering() const noexcept; // comparisons friend constexpr bool operator==(strong_ordering v, unspecified) noexcept; friend constexpr bool operator==(strong_ordering v, strong_ordering w) noexcept = default; friend constexpr bool operator< (strong_ordering v, unspecified) noexcept; friend constexpr bool operator> (strong_ordering v, unspecified) noexcept; friend constexpr bool operator<=(strong_ordering v, unspecified) noexcept; friend constexpr bool operator>=(strong_ordering v, unspecified) noexcept; friend constexpr bool operator< (unspecified, strong_ordering v) noexcept; friend constexpr bool operator> (unspecified, strong_ordering v) noexcept; friend constexpr bool operator<=(unspecified, strong_ordering v) noexcept; friend constexpr bool operator>=(unspecified, strong_ordering v) noexcept; friend constexpr strong_ordering operator<=>(strong_ordering v, unspecified) noexcept; friend constexpr strong_ordering operator<=>(unspecified, strong_ordering v) noexcept; }; // valid values' definitions inline constexpr strong_ordering strong_ordering::less(ord::less); inline constexpr strong_ordering strong_ordering::equal(ord::equal); inline constexpr strong_ordering strong_ordering::equivalent(ord::equivalent); inline constexpr strong_ordering strong_ordering::greater(ord::greater); }
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constexpr operator partial_ordering() const noexcept;
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Returns: value == 0 ? partial_ordering::equivalent : value < 0 ? partial_ordering::less : partial_ordering::greater
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constexpr operator weak_ordering() const noexcept;
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Returns: value == 0 ? weak_ordering::equivalent : value < 0 ? weak_ordering::less : weak_ordering::greater
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constexpr bool operator==(strong_ordering v, unspecified) noexcept; constexpr bool operator< (strong_ordering v, unspecified) noexcept; constexpr bool operator> (strong_ordering v, unspecified) noexcept; constexpr bool operator<=(strong_ordering v, unspecified) noexcept; constexpr bool operator>=(strong_ordering v, unspecified) noexcept;
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Returns: v.value @ 0 for operator@.
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constexpr bool operator< (unspecified, strong_ordering v) noexcept; constexpr bool operator> (unspecified, strong_ordering v) noexcept; constexpr bool operator<=(unspecified, strong_ordering v) noexcept; constexpr bool operator>=(unspecified, strong_ordering v) noexcept;
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Returns: 0 @ v.value for operator@.
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constexpr strong_ordering operator<=>(strong_ordering v, unspecified) noexcept;
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Returns: v.
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constexpr strong_ordering operator<=>(unspecified, strong_ordering v) noexcept;
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Returns: v < 0 ? strong_ordering​::​greater : v > 0 ? strong_ordering​::​less : v.