pub trait Ord: Eq + PartialOrd {
// Required method
fn cmp(&self, other: &Self) -> Ordering;
// Provided methods
fn max(self, other: Self) -> Self
where Self: Sized { ... }
fn min(self, other: Self) -> Self
where Self: Sized { ... }
fn clamp(self, min: Self, max: Self) -> Self
where Self: Sized { ... }
}
prelude_2024
)Expand description
Trait for types that form a total order.
Implementations must be consistent with the PartialOrd
implementation, and ensure max
,
min
, and clamp
are consistent with cmp
:
partial_cmp(a, b) == Some(cmp(a, b))
.max(a, b) == max_by(a, b, cmp)
(ensured by the default implementation).min(a, b) == min_by(a, b, cmp)
(ensured by the default implementation).- For
a.clamp(min, max)
, see the method docs (ensured by the default implementation).
Violating these requirements is a logic error. The behavior resulting from a logic error is not
specified, but users of the trait must ensure that such logic errors do not result in
undefined behavior. This means that unsafe
code must not rely on the correctness of these
methods.
ยงCorollaries
From the above and the requirements of PartialOrd
, it follows that for all a
, b
and c
:
- exactly one of
a < b
,a == b
ora > b
is true; and <
is transitive:a < b
andb < c
impliesa < c
. The same must hold for both==
and>
.
Mathematically speaking, the <
operator defines a strict weak order. In cases where ==
conforms to mathematical equality, it also defines a strict total order.
ยงDerivable
This trait can be used with #[derive]
.
When derive
d on structs, it will produce a
lexicographic ordering based on the
top-to-bottom declaration order of the structโs members.
When derive
d on enums, variants are ordered primarily by their discriminants. Secondarily,
they are ordered by their fields. By default, the discriminant is smallest for variants at the
top, and largest for variants at the bottom. Hereโs an example:
#[derive(PartialEq, Eq, PartialOrd, Ord)]
enum E {
Top,
Bottom,
}
assert!(E::Top < E::Bottom);
However, manually setting the discriminants can override this default behavior:
#[derive(PartialEq, Eq, PartialOrd, Ord)]
enum E {
Top = 2,
Bottom = 1,
}
assert!(E::Bottom < E::Top);
ยงLexicographical comparison
Lexicographical comparison is an operation with the following properties:
- Two sequences are compared element by element.
- The first mismatching element defines which sequence is lexicographically less or greater than the other.
- If one sequence is a prefix of another, the shorter sequence is lexicographically less than the other.
- If two sequences have equivalent elements and are of the same length, then the sequences are lexicographically equal.
- An empty sequence is lexicographically less than any non-empty sequence.
- Two empty sequences are lexicographically equal.
ยงHow can I implement Ord
?
Ord
requires that the type also be PartialOrd
, PartialEq
, and Eq
.
Because Ord
implies a stronger ordering relationship than PartialOrd
, and both Ord
and
PartialOrd
must agree, you must choose how to implement Ord
first. You can choose to
derive it, or implement it manually. If you derive it, you should derive all four traits. If you
implement it manually, you should manually implement all four traits, based on the
implementation of Ord
.
Hereโs an example where you want to define the Character
comparison by health
and
experience
only, disregarding the field mana
:
use std::cmp::Ordering;
struct Character {
health: u32,
experience: u32,
mana: f32,
}
impl Ord for Character {
fn cmp(&self, other: &Self) -> std::cmp::Ordering {
self.experience
.cmp(&other.experience)
.then(self.health.cmp(&other.health))
}
}
impl PartialOrd for Character {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl PartialEq for Character {
fn eq(&self, other: &Self) -> bool {
self.health == other.health && self.experience == other.experience
}
}
impl Eq for Character {}
If all you need is to slice::sort
a type by a field value, it can be simpler to use
slice::sort_by_key
.
ยงExamples of incorrect Ord
implementations
use std::cmp::Ordering;
#[derive(Debug)]
struct Character {
health: f32,
}
impl Ord for Character {
fn cmp(&self, other: &Self) -> std::cmp::Ordering {
if self.health < other.health {
Ordering::Less
} else if self.health > other.health {
Ordering::Greater
} else {
Ordering::Equal
}
}
}
impl PartialOrd for Character {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl PartialEq for Character {
fn eq(&self, other: &Self) -> bool {
self.health == other.health
}
}
impl Eq for Character {}
let a = Character { health: 4.5 };
let b = Character { health: f32::NAN };
// Mistake: floating-point values do not form a total order and using the built-in comparison
// operands to implement `Ord` irregardless of that reality does not change it. Use
// `f32::total_cmp` if you need a total order for floating-point values.
// Reflexivity requirement of `Ord` is not given.
assert!(a == a);
assert!(b != b);
// Antisymmetry requirement of `Ord` is not given. Only one of a < c and c < a is allowed to be
// true, not both or neither.
assert_eq!((a < b) as u8 + (b < a) as u8, 0);
use std::cmp::Ordering;
#[derive(Debug)]
struct Character {
health: u32,
experience: u32,
}
impl PartialOrd for Character {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for Character {
fn cmp(&self, other: &Self) -> std::cmp::Ordering {
if self.health < 50 {
self.health.cmp(&other.health)
} else {
self.experience.cmp(&other.experience)
}
}
}
// For performance reasons implementing `PartialEq` this way is not the idiomatic way, but it
// ensures consistent behavior between `PartialEq`, `PartialOrd` and `Ord` in this example.
impl PartialEq for Character {
fn eq(&self, other: &Self) -> bool {
self.cmp(other) == Ordering::Equal
}
}
impl Eq for Character {}
let a = Character {
health: 3,
experience: 5,
};
let b = Character {
health: 10,
experience: 77,
};
let c = Character {
health: 143,
experience: 2,
};
// Mistake: The implementation of `Ord` compares different fields depending on the value of
// `self.health`, the resulting order is not total.
// Transitivity requirement of `Ord` is not given. If a is smaller than b and b is smaller than
// c, by transitive property a must also be smaller than c.
assert!(a < b && b < c && c < a);
// Antisymmetry requirement of `Ord` is not given. Only one of a < c and c < a is allowed to be
// true, not both or neither.
assert_eq!((a < c) as u8 + (c < a) as u8, 2);
The documentation of PartialOrd
contains further examples, for example itโs wrong for
PartialOrd
and PartialEq
to disagree.
Required Methodsยง
sourcefn cmp(&self, other: &Self) -> Ordering
๐ฌThis is a nightly-only experimental API. (prelude_2024
)
fn cmp(&self, other: &Self) -> Ordering
prelude_2024
)This method returns an Ordering
between self
and other
.
By convention, self.cmp(&other)
returns the ordering matching the expression
self <operator> other
if true.
ยงExamples
use std::cmp::Ordering;
assert_eq!(5.cmp(&10), Ordering::Less);
assert_eq!(10.cmp(&5), Ordering::Greater);
assert_eq!(5.cmp(&5), Ordering::Equal);
Provided Methodsยง
sourcefn max(self, other: Self) -> Selfwhere
Self: Sized,
๐ฌThis is a nightly-only experimental API. (prelude_2024
)
fn max(self, other: Self) -> Selfwhere
Self: Sized,
prelude_2024
)Compares and returns the maximum of two values.
Returns the second argument if the comparison determines them to be equal.
ยงExamples
assert_eq!(1.max(2), 2);
assert_eq!(2.max(2), 2);
sourcefn min(self, other: Self) -> Selfwhere
Self: Sized,
๐ฌThis is a nightly-only experimental API. (prelude_2024
)
fn min(self, other: Self) -> Selfwhere
Self: Sized,
prelude_2024
)Compares and returns the minimum of two values.
Returns the first argument if the comparison determines them to be equal.
ยงExamples
assert_eq!(1.min(2), 1);
assert_eq!(2.min(2), 2);
Dyn Compatibilityยง
This trait is not dyn compatible.
In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.
Implementorsยง
impl Ord for EntityIndex
impl Ord for LibCall
impl Ord for AsciiChar
impl Ord for Ordering
impl Ord for Infallible
impl Ord for IpAddr
impl Ord for SocketAddr
impl Ord for ErrorKind
impl Ord for Level
impl Ord for LevelFilter
impl Ord for bool
impl Ord for char
impl Ord for i8
impl Ord for i16
impl Ord for i32
impl Ord for i64
impl Ord for i128
impl Ord for isize
impl Ord for !
impl Ord for str
Implements ordering of strings.
Strings are ordered lexicographically by their byte values. This orders Unicode code
points based on their positions in the code charts. This is not necessarily the same as
โalphabeticalโ order, which varies by language and locale. Sorting strings according to
culturally-accepted standards requires locale-specific data that is outside the scope of
the str
type.
impl Ord for u8
impl Ord for u16
impl Ord for u32
impl Ord for u64
impl Ord for u128
impl Ord for ()
impl Ord for usize
impl Ord for ComponentFuncIndex
impl Ord for ComponentIndex
impl Ord for ComponentInstanceIndex
impl Ord for ComponentTypeIndex
impl Ord for ComponentUpvarIndex
impl Ord for DefinedResourceIndex
impl Ord for ExportIndex
impl Ord for ImportIndex
impl Ord for LoweredIndex
impl Ord for ModuleIndex
impl Ord for ModuleInstanceIndex
impl Ord for ModuleUpvarIndex
impl Ord for ResourceIndex
impl Ord for RuntimeComponentInstanceIndex
impl Ord for RuntimeImportIndex
impl Ord for RuntimeInstanceIndex
impl Ord for RuntimeMemoryIndex
impl Ord for RuntimePostReturnIndex
impl Ord for RuntimeReallocIndex
impl Ord for StaticComponentIndex
impl Ord for TrampolineIndex
impl Ord for TypeComponentIndex
impl Ord for TypeComponentInstanceIndex
impl Ord for TypeEnumIndex
impl Ord for TypeFlagsIndex
impl Ord for TypeFuncIndex
impl Ord for TypeListIndex
impl Ord for TypeModuleIndex
impl Ord for TypeOptionIndex
impl Ord for TypeRecordIndex
impl Ord for TypeResourceTableIndex
impl Ord for TypeResultIndex
impl Ord for TypeTupleIndex
impl Ord for TypeVariantIndex
impl Ord for String
impl Ord for BuiltinFunctionIndex
impl Ord for DataIndex
impl Ord for DefinedFuncIndex
impl Ord for DefinedGlobalIndex
impl Ord for DefinedMemoryIndex
impl Ord for DefinedTableIndex
impl Ord for ElemIndex
impl Ord for EngineInternedRecGroupIndex
impl Ord for FuncIndex
impl Ord for FuncRefIndex
impl Ord for GlobalIndex
impl Ord for MemoryIndex
impl Ord for ModuleInternedRecGroupIndex
impl Ord for ModuleInternedTypeIndex
impl Ord for OwnedMemoryIndex
impl Ord for RecGroupRelativeTypeIndex
impl Ord for StaticModuleIndex
impl Ord for TableIndex
impl Ord for TagIndex
impl Ord for TypeIndex
impl Ord for TypeId
impl Ord for CpuidResult
impl Ord for CStr
impl Ord for Error
impl Ord for PhantomPinned
impl Ord for Ipv4Addr
impl Ord for Ipv6Addr
impl Ord for SocketAddrV4
impl Ord for SocketAddrV6
impl Ord for Alignment
impl Ord for Duration
impl Ord for CString
impl Ord for OsStr
impl Ord for OsString
impl Ord for Components<'_>
impl Ord for Path
impl Ord for PathBuf
impl Ord for PrefixComponent<'_>
impl Ord for Instant
impl Ord for SystemTime
impl Ord for BuildMetadata
impl Ord for Prerelease
impl Ord for Version
impl Ord for AbstractHeapType
impl Ord for AliasableResourceId
impl Ord for AnyTypeId
impl Ord for ArangeEntry
impl Ord for ArrayType
impl Ord for ColumnType
impl Ord for ComdatId
impl Ord for ComponentAnyTypeId
impl Ord for ComponentCoreInstanceTypeId
impl Ord for ComponentCoreModuleTypeId
impl Ord for ComponentCoreTypeId
impl Ord for ComponentDefinedTypeId
impl Ord for ComponentFuncTypeId
impl Ord for ComponentInstanceTypeId
impl Ord for ComponentName
impl Ord for ComponentNameKind<'_>
impl Ord for ComponentSectionId
impl Ord for ComponentTypeId
impl Ord for ComponentValueTypeId
impl Ord for CompositeInnerType
impl Ord for CompositeType
impl Ord for ContType
impl Ord for CoreTypeId
impl Ord for DemangleNodeType
impl Ord for DwAccess
impl Ord for DwAddr
impl Ord for DwAt
impl Ord for DwAte
impl Ord for DwCc
impl Ord for DwCfa
impl Ord for DwChildren
impl Ord for DwDefaulted
impl Ord for DwDs
impl Ord for DwDsc
impl Ord for DwEhPe
impl Ord for DwEnd
impl Ord for DwForm
impl Ord for DwId
impl Ord for DwIdx
impl Ord for DwInl
impl Ord for DwLang
impl Ord for DwLle
impl Ord for DwLnct
impl Ord for DwLne
impl Ord for DwLns
impl Ord for DwMacro
impl Ord for DwOp
impl Ord for DwOrd
impl Ord for DwRle
impl Ord for DwSect
impl Ord for DwSectV2
impl Ord for DwTag
impl Ord for DwUt
impl Ord for DwVirtuality
impl Ord for DwVis
impl Ord for FieldType
impl Ord for FieldType
impl Ord for FuncType
impl Ord for HeapType
impl Ord for KebabStr
impl Ord for KebabString
impl Ord for PackedIndex
impl Ord for Range
impl Ord for RecGroup
impl Ord for RecGroupId
impl Ord for RefType
impl Ord for RefType
impl Ord for Register
impl Ord for ResourceId
impl Ord for SectionId
impl Ord for SectionId
impl Ord for SectionId
impl Ord for SectionIndex
impl Ord for StandardSection
impl Ord for StandardSegment
impl Ord for StorageType
impl Ord for StorageType
impl Ord for StructType
impl Ord for SubType
impl Ord for SymbolFlags
impl Ord for SymbolId
impl Ord for SymbolIndex
impl Ord for UnpackedIndex
impl Ord for ValType
impl Ord for ValType
impl Ord for ValidatorId
impl<'a> Ord for Component<'a>
impl<'a> Ord for Prefix<'a>
impl<'a> Ord for Location<'a>
impl<'a> Ord for Metadata<'a>
impl<'a> Ord for MetadataBuilder<'a>
impl<'a> Ord for DependencyName<'a>
impl<'a> Ord for HashName<'a>
impl<'a> Ord for InterfaceName<'a>
impl<'a> Ord for ResourceFunc<'a>
impl<'a> Ord for UrlName<'a>
impl<A> Ord for &A
impl<A> Ord for &mut A
impl<A> Ord for SmallVec<A>where
A: Array,
<A as Array>::Item: Ord,
impl<B> Ord for Cow<'_, B>
impl<Dyn> Ord for DynMetadata<Dyn>where
Dyn: ?Sized,
impl<E> Ord for I16<E>where
E: Ord + Endian,
impl<E> Ord for I16Bytes<E>where
E: Ord + Endian,
impl<E> Ord for I32<E>where
E: Ord + Endian,
impl<E> Ord for I32Bytes<E>where
E: Ord + Endian,
impl<E> Ord for I64<E>where
E: Ord + Endian,
impl<E> Ord for I64Bytes<E>where
E: Ord + Endian,
impl<E> Ord for U16<E>where
E: Ord + Endian,
impl<E> Ord for U16Bytes<E>where
E: Ord + Endian,
impl<E> Ord for U32<E>where
E: Ord + Endian,
impl<E> Ord for U32Bytes<E>where
E: Ord + Endian,
impl<E> Ord for U64<E>where
E: Ord + Endian,
impl<E> Ord for U64Bytes<E>where
E: Ord + Endian,
impl<F> Ord for Fwhere
F: FnPtr,
impl<K, V> Ord for Slice<K, V>
impl<K, V, A> Ord for BTreeMap<K, V, A>
impl<Ptr> Ord for Pin<Ptr>
impl<T> Ord for Option<T>where
T: Ord,
impl<T> Ord for Poll<T>where
T: Ord,
impl<T> Ord for *const Twhere
T: ?Sized,
impl<T> Ord for *mut Twhere
T: ?Sized,
impl<T> Ord for [T]where
T: Ord,
Implements comparison of slices lexicographically.
impl<T> Ord for (Tโ, Tโ, โฆ, Tโ)
This trait is implemented for tuples up to twelve items long.
impl<T> Ord for PackedOption<T>where
T: Ord + ReservedValue,
impl<T> Ord for Cell<T>
impl<T> Ord for RefCell<T>
impl<T> Ord for Reverse<T>where
T: Ord,
impl<T> Ord for PhantomData<T>where
T: ?Sized,
impl<T> Ord for ManuallyDrop<T>
impl<T> Ord for NonZero<T>where
T: ZeroablePrimitive + Ord,
impl<T> Ord for Saturating<T>where
T: Ord,
impl<T> Ord for Wrapping<T>where
T: Ord,
impl<T> Ord for NonNull<T>where
T: ?Sized,
impl<T> Ord for DebugInfoOffset<T>where
T: Ord,
impl<T> Ord for DebugTypesOffset<T>where
T: Ord,
impl<T> Ord for Slice<T>where
T: Ord,
impl<T> Ord for Unalign<T>where
T: Unaligned + Ord,
impl<T> Ord for UnitOffset<T>where
T: Ord,
impl<T> Ord for UnitSectionOffset<T>where
T: Ord,
impl<T, A> Ord for Box<T, A>
impl<T, A> Ord for Vec<T, A>
Implements ordering of vectors, lexicographically.
impl<T, A> Ord for BTreeSet<T, A>
impl<T, A> Ord for LinkedList<T, A>
impl<T, A> Ord for VecDeque<T, A>
impl<T, A> Ord for Rc<T, A>
impl<T, A> Ord for Arc<T, A>
impl<T, B> Ord for Ref<B, [T]>where
B: ByteSlice,
T: FromBytes + Ord,
impl<T, B> Ord for Ref<B, T>where
B: ByteSlice,
T: FromBytes + Ord,
impl<T, E> Ord for Result<T, E>
impl<T, const N: usize> Ord for [T; N]where
T: Ord,
Implements comparison of arrays lexicographically.