Trait PartialOrd

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 { ... }
}

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.

This trait should only contain the comparison logic for a type if one plans on only implementing PartialOrd but not Ord. Otherwise the comparison logic should be in Ord and this trait implemented with Some(self.cmp(other)).

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 relations must satisfy the following conditions (for all a, b, c of type A, B, C):

• Transitivity: if A: PartialOrd<B> and B: PartialOrd<C> and A: PartialOrd<C>, then a < b and b < c implies a < c. The same must hold for both == and >. This must also work for longer chains, such as when A: PartialOrd<B>, B: PartialOrd<C>, C: PartialOrd<D>, and A: PartialOrd<D> all exist.
• Duality: if A: PartialOrd<B> and B: PartialOrd<A>, then a < b if and only if b > a.

Note that the B: PartialOrd<A> (dual) and A: PartialOrd<C> (transitive) impls are not forced to exist, but these requirements apply whenever they do exist.

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.

Cross-crate considerations

Upholding the requirements stated above can become tricky when one crate implements PartialOrd for a type of another crate (i.e., to allow comparing one of its own types with a type from the standard library). The recommendation is to never implement this trait for a foreign type. In other words, such a crate should do impl PartialOrd<ForeignType> for LocalType, but it should not do impl PartialOrd<LocalType> for ForeignType.

This avoids the problem of transitive chains that criss-cross crate boundaries: for all local types T, you may assume that no other crate will add impls that allow comparing T < U. In other words, if other crates add impls that allow building longer transitive chains U1 < ... < T < V1 < ..., then all the types that appear to the right of T must be types that the crate defining T already knows about. This rules out transitive chains where downstream crates can add new impls that “stitch together” comparisons of foreign types in ways that violate transitivity.

Not having such foreign impls also avoids forward compatibility issues where one crate adding more PartialOrd implementations can cause build failures in downstream crates.

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)

Strict and non-strict partial orders

The < and > operators behave according to a strict partial order. However, <= and >= do not behave according to a non-strict partial order. That is because mathematically, a non-strict partial order would require reflexivity, i.e. a <= a would need to be true for every a. This isn’t always the case for types that implement PartialOrd, for example:

let a = f64::sqrt(-1.0);
assert_eq!(a <= a, false);

Derivable

This trait can be used with #[derive].

When derived on structs, it will produce a lexicographic ordering based on the top-to-bottom declaration order of the struct’s members.

When derived on enums, variants are primarily ordered 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, PartialOrd)]
enum E {
    Top,
    Bottom,
}

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

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

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

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

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;

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
    }
}

impl Eq for Person {}

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
    }
}

Examples of incorrect PartialOrd implementations

use std::cmp::Ordering;

#[derive(PartialEq, Debug)]
struct Character {
    health: u32,
    experience: u32,
}

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

let a = Character {
    health: 10,
    experience: 5,
};
let b = Character {
    health: 10,
    experience: 77,
};

// Mistake: `PartialEq` and `PartialOrd` disagree with each other.

assert_eq!(a.partial_cmp(&b).unwrap(), Ordering::Equal); // a == b according to `PartialOrd`.
assert_ne!(a, b); // a != b according to `PartialEq`.

Examples

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

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

Required Methods

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));

When comparison is impossible:

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

Provided Methods

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

Tests less than (for self and other) and is used by the < operator.

Examples

assert_eq!(1.0 < 1.0, false);
assert_eq!(1.0 < 2.0, true);
assert_eq!(2.0 < 1.0, false);

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

Tests less than or equal to (for self and other) and is used by the <= operator.

Examples

assert_eq!(1.0 <= 1.0, true);
assert_eq!(1.0 <= 2.0, true);
assert_eq!(2.0 <= 1.0, false);

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

Tests greater than (for self and other) and is used by the > operator.

Examples

assert_eq!(1.0 > 1.0, false);
assert_eq!(1.0 > 2.0, false);
assert_eq!(2.0 > 1.0, true);

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

Examples

assert_eq!(1.0 >= 1.0, true);
assert_eq!(1.0 >= 2.0, false);
assert_eq!(2.0 >= 1.0, true);

Implementors

impl PartialOrd for AsciiChar

impl PartialOrd for Infallible

impl PartialOrd for IpAddr

impl PartialOrd for SocketAddr

impl PartialOrd for Ordering

impl PartialOrd for bool

impl PartialOrd for char

impl PartialOrd for f16

impl PartialOrd for f32

impl PartialOrd for f64

impl PartialOrd for f128

impl PartialOrd for i8

impl PartialOrd for i16

impl PartialOrd for i32

impl PartialOrd for i64

impl PartialOrd for i128

impl PartialOrd for isize

impl PartialOrd for !

impl PartialOrd 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.

impl PartialOrd for u8

impl PartialOrd for u16

impl PartialOrd for u32

impl PartialOrd for u64

impl PartialOrd for u128

impl PartialOrd for ()

impl PartialOrd for usize

impl PartialOrd for TypeId

impl PartialOrd for CpuidResult

Available on x86 or x86-64 only.

impl PartialOrd for CStr

impl PartialOrd for Error

impl PartialOrd for PhantomPinned

impl PartialOrd for Ipv4Addr

impl PartialOrd for Ipv6Addr

impl PartialOrd for SocketAddrV4

impl PartialOrd for SocketAddrV6

impl PartialOrd for Alignment

impl PartialOrd for Duration

impl PartialOrd<IpAddr> for Ipv4Addr

impl PartialOrd<IpAddr> for Ipv6Addr

impl PartialOrd<Ipv4Addr> for IpAddr

impl PartialOrd<Ipv6Addr> for IpAddr

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

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

where A: PartialOrd<B> + ?Sized,

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

where A: PartialOrd<B> + ?Sized,

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

impl<F: FnPtr> PartialOrd for F

impl<Ptr: Deref, Q: Deref> PartialOrd<Pin<Q>> for Pin<Ptr>

where Ptr::Target: PartialOrd<Q::Target>,

impl<T> PartialOrd for (T₁, T₂, …, Tₙ)

where T: ?Sized + PartialOrd,

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

impl<T> PartialOrd for NonZero<T>

where T: ZeroablePrimitive + PartialOrd,

impl<T, const N: usize> PartialOrd for Mask<T, N>

where T: MaskElement + PartialOrd, LaneCount<N>: SupportedLaneCount,

impl<T, const N: usize> PartialOrd for Simd<T, N>

where LaneCount<N>: SupportedLaneCount, T: SimdElement + PartialOrd,

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

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

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

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

impl<T: PartialOrd> PartialOrd for [T]

Implements comparison of slices lexicographically.

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

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

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

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

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

Implements comparison of arrays lexicographically.

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

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

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

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

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

impl<Y: PartialOrd, R: PartialOrd> PartialOrd for CoroutineState<Y, R>