# Trait Ord

1.0.0 · Source

    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 { ... }
    }

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.

### §Corollaries

From the above and the requirements of `PartialOrd`, it follows that for all `a`, `b` and `c`:

- exactly one of `a < b`, `a == b` or `a > b` is true; and
- `<` is transitive: `a < b` and `b < c` implies `a < 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.

### §Derivable

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 struct’s 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. Here’s 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);

### §Lexicographical 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.

### §How 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`.

Here’s 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) -> 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`.

### §Examples 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 it’s wrong for `PartialOrd` and `PartialEq` to disagree.

## Required Methods§

1.0.0 · Source

#### fn cmp(&self, other: &Self) -> Ordering

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.

##### §Examples

    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 Methods§

1.21.0 · Source

#### fn max(self, other: Self) -> Self
where Self: Sized,

Compares and returns the maximum of two values.

Returns the second argument if the comparison determines them to be equal.

##### §Examples

    assert_eq!(1.max(2), 2);
    assert_eq!(2.max(2), 2);

    use std::cmp::Ordering;

    #[derive(Eq)]
    struct Equal(&'static str);

    impl PartialEq for Equal {
        fn eq(&self, other: &Self) -> bool { true }
    }
    impl PartialOrd for Equal {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> { Some(Ordering::Equal) }
    }
    impl Ord for Equal {
        fn cmp(&self, other: &Self) -> Ordering { Ordering::Equal }
    }

    assert_eq!(Equal("self").max(Equal("other")).0, "other");

1.21.0 · Source

#### fn min(self, other: Self) -> Self
where Self: Sized,

Compares and returns the minimum of two values.

Returns the first argument if the comparison determines them to be equal.

##### §Examples

    assert_eq!(1.min(2), 1);
    assert_eq!(2.min(2), 2);

    use std::cmp::Ordering;

    #[derive(Eq)]
    struct Equal(&'static str);

    impl PartialEq for Equal {
        fn eq(&self, other: &Self) -> bool { true }
    }
    impl PartialOrd for Equal {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> { Some(Ordering::Equal) }
    }
    impl Ord for Equal {
        fn cmp(&self, other: &Self) -> Ordering { Ordering::Equal }
    }

    assert_eq!(Equal("self").min(Equal("other")).0, "self");

1.50.0 · Source

#### fn clamp(self, min: Self, max: Self) -> Self
where Self: Sized,

Restrict a value to a certain interval.

Returns `max` if `self` is greater than `max`, and `min` if `self` is less than `min`. Otherwise this returns `self`.

##### §Panics

Panics if `min > max`.

##### §Examples

    assert_eq!((-3).clamp(-2, 1), -2);
    assert_eq!(0.clamp(-2, 1), 0);
    assert_eq!(2.clamp(-2, 1), 1);

## Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

## Implementors§

Source§

### impl Ord for AsciiChar

1.34.0 · Source§

### impl Ord for Infallible

1.0.0 · Source§

### impl Ord for ErrorKind

1.7.0 · Source§

### impl Ord for IpAddr

1.0.0 · Source§

### impl Ord for SocketAddr

1.0.0 · Source§

### impl Ord for Ordering

1.0.0 · Source§

### impl Ord for bool

1.0.0 · Source§

### impl Ord for char

1.0.0 · Source§

### impl Ord for i8

1.0.0 · Source§

### impl Ord for i16

1.0.0 · Source§

### impl Ord for i32

1.0.0 · Source§

### impl Ord for i64

1.0.0 · Source§

### impl Ord for i128

1.0.0 · Source§

### impl Ord for isize

Source§

### impl Ord for !

1.0.0 · Source§

### 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 “alphabetical” 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.

1.0.0 · Source§

### impl Ord for u8

1.0.0 · Source§

### impl Ord for u16

1.0.0 · Source§

### impl Ord for u32

1.0.0 · Source§

### impl Ord for u64

1.0.0 · Source§

### impl Ord for u128

1.0.0 · Source§

### impl Ord for ()

1.0.0 · Source§

### impl Ord for usize

1.27.0 · Source§

### impl Ord for CpuidResult

1.0.0 · Source§

### impl Ord for TypeId

Source§

### impl Ord for ByteStr

Source§

### impl Ord for ByteString

1.0.0 · Source§

### impl Ord for CStr

1.64.0 · Source§

### impl Ord for CString

1.0.0 · Source§

### impl Ord for OsStr

1.0.0 · Source§

### impl Ord for OsString

1.0.0 · Source§

### impl Ord for Error

1.33.0 · Source§

### impl Ord for PhantomPinned

1.0.0 · Source§

### impl Ord for Ipv4Addr

1.0.0 · Source§

### impl Ord for Ipv6Addr

1.0.0 · Source§

### impl Ord for SocketAddrV4

1.0.0 · Source§

### impl Ord for SocketAddrV6

1.10.0 · Source§

### impl Ord for Location<'_>

1.0.0 · Source§

### impl Ord for Components<'_>

1.0.0 · Source§

### impl Ord for Path

1.0.0 · Source§

### impl Ord for PathBuf

1.0.0 · Source§

### impl Ord for PrefixComponent<'_>

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### impl Ord for Alignment

1.0.0 · Source§

### impl Ord for String

1.3.0 · Source§

### impl Ord for Duration

1.8.0 · Source§

### impl Ord for Instant

1.8.0 · Source§

### impl Ord for SystemTime

1.0.0 · Source§

### impl<'a> Ord for Component<'a>

1.0.0 · Source§

### impl<'a> Ord for Prefix<'a>

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### impl<'a> Ord for PhantomContravariantLifetime<'a>

Source§

### impl<'a> Ord for PhantomCovariantLifetime<'a>

Source§

### impl<'a> Ord for PhantomInvariantLifetime<'a>

1.0.0 · Source§

### impl<A> Ord for &A
where A: Ord + ?Sized,

1.0.0 · Source§

### impl<A> Ord for &mut A
where A: Ord + ?Sized,

1.0.0 · Source§

### impl<B> Ord for Cow<'_, B>
where B: Ord + ToOwned + ?Sized,

Source§

### impl<Dyn> Ord for DynMetadata<Dyn>
where Dyn: ?Sized,

1.4.0 · Source§

### impl<F> Ord for F
where F: FnPtr,

1.0.0 · Source§

### impl<K, V, A> Ord for BTreeMap<K, V, A>
where K: Ord, V: Ord, A: Allocator + Clone,

1.41.0 · Source§

### impl<Ptr> Ord for Pin<Ptr>
where Ptr: Deref, <Ptr as Deref>::Target: Ord,

1.0.0 · Source§

### impl<T> Ord for Option<T>
where T: Ord,

1.36.0 · Source§

### impl<T> Ord for Poll<T>
where T: Ord,

1.0.0 · Source§

### impl<T> Ord for *const T
where T: ?Sized,

Pointer comparison is by address, as produced by the `[`<*const T>::addr`](pointer::addr)` method.

1.0.0 · Source§

### impl<T> Ord for *mut T
where T: ?Sized,

Pointer comparison is by address, as produced by the `<*mut T>::addr` method.

1.0.0 · Source§

### impl<T> Ord for [T]
where T: Ord,

Implements comparison of slices lexicographically.

1.0.0 · Source§

### impl<T> Ord for (T₁, T₂, …, Tₙ)
where T: Ord,

This trait is implemented for tuples up to twelve items long.

1.10.0 · Source§

### impl<T> Ord for Cell<T>
where T: Ord + Copy,

1.10.0 · Source§

### impl<T> Ord for RefCell<T>
where T: Ord + ?Sized,

Source§

### impl<T> Ord for PhantomContravariant<T>
where T: ?Sized,

Source§

### impl<T> Ord for PhantomCovariant<T>
where T: ?Sized,

1.0.0 · Source§

### impl<T> Ord for PhantomData<T>
where T: ?Sized,

Source§

### impl<T> Ord for PhantomInvariant<T>
where T: ?Sized,

1.20.0 · Source§

### impl<T> Ord for ManuallyDrop<T>
where T: Ord + ?Sized,

1.28.0 · Source§

### impl<T> Ord for NonZero<T>
where T: ZeroablePrimitive + Ord,

1.74.0 · Source§

### impl<T> Ord for Saturating<T>
where T: Ord,

1.0.0 · Source§

### impl<T> Ord for Wrapping<T>
where T: Ord,

1.25.0 · Source§

### impl<T> Ord for NonNull<T>
where T: ?Sized,

1.19.0 · Source§

### impl<T> Ord for Reverse<T>
where T: Ord,

1.0.0 · Source§

### impl<T, A> Ord for Box<T, A>
where T: Ord + ?Sized, A: Allocator,

1.0.0 · Source§

### impl<T, A> Ord for BTreeSet<T, A>
where T: Ord, A: Allocator + Clone,

1.0.0 · Source§

### impl<T, A> Ord for LinkedList<T, A>
where T: Ord, A: Allocator,

1.0.0 · Source§

### impl<T, A> Ord for VecDeque<T, A>
where T: Ord, A: Allocator,

1.0.0 · Source§

### impl<T, A> Ord for Rc<T, A>
where T: Ord + ?Sized, A: Allocator,

Source§

### impl<T, A> Ord for UniqueRc<T, A>
where T: Ord + ?Sized, A: Allocator,

1.0.0 · Source§

### impl<T, A> Ord for Arc<T, A>
where T: Ord + ?Sized, A: Allocator,

Source§

### impl<T, A> Ord for UniqueArc<T, A>
where T: Ord + ?Sized, A: Allocator,

1.0.0 · Source§

### impl<T, A> Ord for Vec<T, A>
where T: Ord, A: Allocator,

Implements ordering of vectors, lexicographically.

1.0.0 · Source§

### impl<T, E> Ord for Result<T, E>
where T: Ord, E: Ord,

1.0.0 · Source§

### impl<T, const N: usize> Ord for [T; N]
where T: Ord,

Implements comparison of arrays lexicographically.

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### impl<T, const N: usize> Ord for Simd<T, N>
where LaneCount<N>: SupportedLaneCount, T: SimdElement + Ord,

Lexicographic order. For the SIMD elementwise minimum and maximum, use simd_min and simd_max instead.

Source§

### impl<Y, R> Ord for CoroutineState<Y, R>
where Y: Ord, R: Ord,