# Trait core::cmp::PartialOrd

1.0.0 · source ·

    pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
        // Required method
        fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;

        // Provided methods
        fn lt(&self, other: &Rhs) -> bool { ... }
        fn le(&self, other: &Rhs) -> bool { ... }
        fn gt(&self, other: &Rhs) -> bool { ... }
        fn ge(&self, other: &Rhs) -> bool { ... }
    }

Expand description

Trait for types that form a partial order.

The `lt`, `le`, `gt`, and `ge` methods of this trait can be called using the `<`, `<=`, `>`, and `>=` operators, respectively.

The methods of this trait must be consistent with each other and with those of `PartialEq`. The following conditions must hold:

1. `a == b` if and only if `partial_cmp(a, b) == Some(Equal)`.
2. `a < b` if and only if `partial_cmp(a, b) == Some(Less)`
3. `a > b` if and only if `partial_cmp(a, b) == Some(Greater)`
4. `a <= b` if and only if `a < b || a == b`
5. `a >= b` if and only if `a > b || a == b`
6. `a != b` if and only if `!(a == b)`.

Conditions 2–5 above are ensured by the default implementation. Condition 6 is already ensured by `PartialEq`.

If `Ord` is also implemented for `Self` and `Rhs`, it must also be consistent with `partial_cmp` (see the documentation of that trait for the exact requirements). It’s easy to accidentally make them disagree by deriving some of the traits and manually implementing others.

The comparison must satisfy, for all `a`, `b` and `c`:

- transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
- duality: `a < b` if and only if `b > a`.

Note that these requirements mean that the trait itself must be implemented symmetrically and transitively: if `T: PartialOrd<U>` and `U: PartialOrd<V>` then `U: PartialOrd<T>` and `T: PartialOrd<V>`.

### Corollaries

The following corollaries follow from the above requirements:

- irreflexivity of `<` and `>`: `!(a < a)`, `!(a > a)`
- transitivity of `>`: if `a > b` and `b > c` then `a > c`
- duality of `partial_cmp`: `partial_cmp(a, b) == partial_cmp(b, a).map(Ordering::reverse)`

### 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 by their discriminants. By default, the discriminant is smallest for variants at the top, and largest for variants at the bottom. Here’s an example:

    #[derive(PartialEq, PartialOrd)]
    enum E {
        Top,
        Bottom,
    }

    assert!(E::Top < E::Bottom);

Run

However, manually setting the discriminants can override this default behavior:

    #[derive(PartialEq, PartialOrd)]
    enum E {
        Top = 2,
        Bottom = 1,
    }

    assert!(E::Bottom < E::Top);

Run

### How can I implement `PartialOrd`?

`PartialOrd` only requires implementation of the `partial_cmp` method, with the others generated from default implementations.

However it remains possible to implement the others separately for types which do not have a total order. For example, for floating point numbers, `NaN < 0 == false` and `NaN >= 0 == false` (cf. IEEE 754-2008 section 5.11).

`PartialOrd` requires your type to be `PartialEq`.

If your type is `Ord`, you can implement `partial_cmp` by using `cmp`:

    use std::cmp::Ordering;

    #[derive(Eq)]
    struct Person {
        id: u32,
        name: String,
        height: u32,
    }

    impl PartialOrd for Person {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            Some(self.cmp(other))
        }
    }

    impl Ord for Person {
        fn cmp(&self, other: &Self) -> Ordering {
            self.height.cmp(&other.height)
        }
    }

    impl PartialEq for Person {
        fn eq(&self, other: &Self) -> bool {
            self.height == other.height
        }
    }

Run

You may also find it useful to use `partial_cmp` on your type’s fields. Here is an example of `Person` types who have a floating-point `height` field that is the only field to be used for sorting:

    use std::cmp::Ordering;

    struct Person {
        id: u32,
        name: String,
        height: f64,
    }

    impl PartialOrd for Person {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            self.height.partial_cmp(&other.height)
        }
    }

    impl PartialEq for Person {
        fn eq(&self, other: &Self) -> bool {
            self.height == other.height
        }
    }

Run

## Examples

    let x: u32 = 0;
    let y: u32 = 1;

    assert_eq!(x < y, true);
    assert_eq!(x.lt(&y), true);

Run

## Required Methods§

source

#### fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>

This method returns an ordering between `self` and `other` values if one exists.

##### Examples

    use std::cmp::Ordering;

    let result = 1.0.partial_cmp(&2.0);
    assert_eq!(result, Some(Ordering::Less));

    let result = 1.0.partial_cmp(&1.0);
    assert_eq!(result, Some(Ordering::Equal));

    let result = 2.0.partial_cmp(&1.0);
    assert_eq!(result, Some(Ordering::Greater));

Run

When comparison is impossible:

    let result = f64::NAN.partial_cmp(&1.0);
    assert_eq!(result, None);

Run

## Provided Methods§

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#### fn lt(&self, other: &Rhs) -> bool

This method tests less than (for `self` and `other`) and is used by the `<` operator.

##### Examples

    let result = 1.0 < 2.0;
    assert_eq!(result, true);

    let result = 2.0 < 1.0;
    assert_eq!(result, false);

Run
source

#### fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for `self` and `other`) and is used by the `<=` operator.

##### Examples

    let result = 1.0 <= 2.0;
    assert_eq!(result, true);

    let result = 2.0 <= 2.0;
    assert_eq!(result, true);

Run
source

#### fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for `self` and `other`) and is used by the `>` operator.

##### Examples

    let result = 1.0 > 2.0;
    assert_eq!(result, false);

    let result = 2.0 > 2.0;
    assert_eq!(result, false);

Run
source

#### fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for `self` and `other`) and is used by the `>=` operator.

##### Examples

    let result = 2.0 >= 1.0;
    assert_eq!(result, true);

    let result = 2.0 >= 2.0;
    assert_eq!(result, true);

Run

## Implementors§

1.34.0 · source§

### impl PartialOrd<Infallible> for Infallible

1.7.0 · source§

### impl PartialOrd<IpAddr> for IpAddr

1.16.0 · source§

### impl PartialOrd<IpAddr> for Ipv4Addr

1.16.0 · source§

### impl PartialOrd<IpAddr> for Ipv6Addr

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### impl PartialOrd<SocketAddr> for SocketAddr

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### impl PartialOrd<Which> for Which

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### impl PartialOrd<Ordering> for Ordering

const: unstable · source§

### impl PartialOrd<bool> for bool

const: unstable · source§

### impl PartialOrd<char> for char

const: unstable · source§

### impl PartialOrd<f32> for f32

const: unstable · source§

### impl PartialOrd<f64> for f64

const: unstable · source§

### impl PartialOrd<i8> for i8

const: unstable · source§

### impl PartialOrd<i16> for i16

const: unstable · source§

### impl PartialOrd<i32> for i32

const: unstable · source§

### impl PartialOrd<i64> for i64

const: unstable · source§

### impl PartialOrd<i128> for i128

const: unstable · source§

### impl PartialOrd<isize> for isize

const: unstable · source§

### impl PartialOrd<!> for !

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### impl PartialOrd<str> for str

Implements comparison operations on strings.

Strings are compared lexicographically by their byte values. This compares 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. Comparing strings according to culturally-accepted standards requires locale-specific data that is outside the scope of the `str` type.

const: unstable · source§

### impl PartialOrd<u8> for u8

const: unstable · source§

### impl PartialOrd<u16> for u16

const: unstable · source§

### impl PartialOrd<u32> for u32

const: unstable · source§

### impl PartialOrd<u64> for u64

const: unstable · source§

### impl PartialOrd<u128> for u128

const: unstable · source§

### impl PartialOrd<()> for ()

const: unstable · source§

### impl PartialOrd<usize> for usize

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### impl PartialOrd<TypeId> for TypeId

1.27.0 · source§

### impl PartialOrd<CpuidResult> for CpuidResult

Available on x86 or x86-64 only.
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### impl PartialOrd<CStr> for CStr

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### impl PartialOrd<Error> for Error

1.33.0 · source§

### impl PartialOrd<PhantomPinned> for PhantomPinned

1.16.0 · source§

### impl PartialOrd<Ipv4Addr> for IpAddr

source§

### impl PartialOrd<Ipv4Addr> for Ipv4Addr

1.16.0 · source§

### impl PartialOrd<Ipv6Addr> for IpAddr

source§

### impl PartialOrd<Ipv6Addr> for Ipv6Addr

1.45.0 · source§

### impl PartialOrd<SocketAddrV4> for SocketAddrV4

1.45.0 · source§

### impl PartialOrd<SocketAddrV6> for SocketAddrV6

1.34.0 · source§

### impl PartialOrd<NonZeroI8> for NonZeroI8

1.34.0 · source§

### impl PartialOrd<NonZeroI16> for NonZeroI16

1.34.0 · source§

### impl PartialOrd<NonZeroI32> for NonZeroI32

1.34.0 · source§

### impl PartialOrd<NonZeroI64> for NonZeroI64

1.34.0 · source§

### impl PartialOrd<NonZeroI128> for NonZeroI128

1.34.0 · source§

### impl PartialOrd<NonZeroIsize> for NonZeroIsize

1.28.0 · source§

### impl PartialOrd<NonZeroU8> for NonZeroU8

1.28.0 · source§

### impl PartialOrd<NonZeroU16> for NonZeroU16

1.28.0 · source§

### impl PartialOrd<NonZeroU32> for NonZeroU32

1.28.0 · source§

### impl PartialOrd<NonZeroU64> for NonZeroU64

1.28.0 · source§

### impl PartialOrd<NonZeroU128> for NonZeroU128

1.28.0 · source§

### impl PartialOrd<NonZeroUsize> for NonZeroUsize

const: unstable · source§

### impl PartialOrd<Alignment> for Alignment

1.3.0 · source§

### impl PartialOrd<Duration> for Duration

1.10.0 · source§

### impl<'a> PartialOrd<Location<'a>> for Location<'a>

const: unstable · source§

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

source§

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

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### impl<Dyn: ?Sized> PartialOrd<DynMetadata<Dyn>> for DynMetadata<Dyn>

1.4.0 · source§

### impl<F: FnPtr> PartialOrd<F> for F

1.41.0 · source§

### impl<P: Deref, Q: Deref> PartialOrd<Pin<Q>> for Pin<P>where P::Target: PartialOrd<Q::Target>,

const: unstable · source§

### impl<T> PartialOrd<(T,)> for (T₁, T₂, …, Tₙ)where T: ?Sized + PartialOrd + PartialEq,

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

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### impl<T, const LANES: usize> PartialOrd<Mask<T, LANES>> for Mask<T, LANES>where T: MaskElement + PartialOrd, LaneCount<LANES>: SupportedLaneCount,

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

1.10.0 · source§

### impl<T: PartialOrd + Copy> PartialOrd<Cell<T>> for Cell<T>

1.20.0 · source§

### impl<T: PartialOrd + ?Sized> PartialOrd<ManuallyDrop<T>> for ManuallyDrop<T>

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### impl<T: PartialOrd> PartialOrd<Option<T>> for Option<T>

1.36.0 · source§

### impl<T: PartialOrd> PartialOrd<Poll<T>> for Poll<T>

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### impl<T: PartialOrd> PartialOrd<[T]> for [T]

Implements comparison of vectors lexicographically.

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### impl<T: PartialOrd> PartialOrd<Saturating<T>> for Saturating<T>

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### impl<T: PartialOrd> PartialOrd<Wrapping<T>> for Wrapping<T>

1.19.0 (const: unstable) · source§

### impl<T: PartialOrd> PartialOrd<Reverse<T>> for Reverse<T>

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### impl<T: PartialOrd, E: PartialOrd> PartialOrd<Result<T, E>> for Result<T, E>

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

1.10.0 · source§

### impl<T: ?Sized + PartialOrd> PartialOrd<RefCell<T>> for RefCell<T>

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### impl<T: ?Sized> PartialOrd<*const T> for *const T

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### impl<T: ?Sized> PartialOrd<*mut T> for *mut T

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### impl<T: ?Sized> PartialOrd<PhantomData<T>> for PhantomData<T>

1.25.0 · source§

### impl<T: ?Sized> PartialOrd<NonNull<T>> for NonNull<T>

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### impl<Y: PartialOrd, R: PartialOrd> PartialOrd<GeneratorState<Y, R>> for GeneratorState<Y, R>