Trait core::cmp::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.

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>.

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

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 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);

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;

#[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
    }
}

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

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

This method 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

This method 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

This method 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

This method 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<AsciiChar> for AsciiChar

impl PartialOrd<Infallible> for Infallible

impl PartialOrd<IpAddr> for IpAddr

impl PartialOrd<IpAddr> for Ipv4Addr

impl PartialOrd<IpAddr> for Ipv6Addr

impl PartialOrd<SocketAddr> for SocketAddr

impl PartialOrd<Which> for Which

impl PartialOrd<Ordering> for Ordering

impl PartialOrd<bool> for bool

impl PartialOrd<char> for char

impl PartialOrd<f32> for f32

impl PartialOrd<f64> for f64

impl PartialOrd<i8> for i8

impl PartialOrd<i16> for i16

impl PartialOrd<i32> for i32

impl PartialOrd<i64> for i64

impl PartialOrd<i128> for i128

impl PartialOrd<isize> for isize

impl PartialOrd<!> for !

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.

impl PartialOrd<u8> for u8

impl PartialOrd<u16> for u16

impl PartialOrd<u32> for u32

impl PartialOrd<u64> for u64

impl PartialOrd<u128> for u128

impl PartialOrd<()> for ()

impl PartialOrd<usize> for usize

impl PartialOrd<TypeId> for TypeId

impl PartialOrd<CpuidResult> for CpuidResult

Available on x86 or x86-64 only.

impl PartialOrd<CStr> for CStr

impl PartialOrd<Error> for Error

impl PartialOrd<PhantomPinned> for PhantomPinned

impl PartialOrd<Ipv4Addr> for IpAddr

impl PartialOrd<Ipv4Addr> for Ipv4Addr

impl PartialOrd<Ipv6Addr> for IpAddr

impl PartialOrd<Ipv6Addr> for Ipv6Addr

impl PartialOrd<SocketAddrV4> for SocketAddrV4

impl PartialOrd<SocketAddrV6> for SocketAddrV6

impl PartialOrd<NonZeroI8> for NonZeroI8

impl PartialOrd<NonZeroI16> for NonZeroI16

impl PartialOrd<NonZeroI32> for NonZeroI32

impl PartialOrd<NonZeroI64> for NonZeroI64

impl PartialOrd<NonZeroI128> for NonZeroI128

impl PartialOrd<NonZeroIsize> for NonZeroIsize

impl PartialOrd<NonZeroU8> for NonZeroU8

impl PartialOrd<NonZeroU16> for NonZeroU16

impl PartialOrd<NonZeroU32> for NonZeroU32

impl PartialOrd<NonZeroU64> for NonZeroU64

impl PartialOrd<NonZeroU128> for NonZeroU128

impl PartialOrd<NonZeroUsize> for NonZeroUsize

impl PartialOrd<Alignment> for Alignment

impl PartialOrd<Duration> for Duration

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Implements comparison of vectors lexicographically.

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

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

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

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

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

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

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

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

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

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

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