lib::core::cmp

Trait Ord

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 { ... }
    fn clamp_to<R>(self, range: R) -> Self
       where Self: Sized,
             R: ClampBounds<Self> { ... }
}

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 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 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 (const: unstable) · 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 (const: unstable) · 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 (const: unstable) · 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 (const: unstable) · 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);

Source

fn clamp_to<R>(self, range: R) -> Self
where Self: Sized, R: ClampBounds<Self>,

🔬This is a nightly-only experimental API. (clamp_to)

Restrict a value to a certain range.

This is equal to max, min, or clamp, depending on whether the range is min.., ..=max, or min..=max, respectively. Exclusive ranges are not permitted.

§Panics

Panics on min..=max if min > max.

§Examples

#![feature(clamp_to)]
assert_eq!((-3).clamp_to(-2..=1), -2);
assert_eq!(0.clamp_to(-2..=1), 0);
assert_eq!(2.clamp_to(..=1), 1);
assert_eq!(5.clamp_to(7..), 7);

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors§

1.100.0 (const: unstable) · Source§

impl Ord for !

1.0.0 (const: unstable) · Source§

Trait Ord Copy item path

§Corollaries

§Derivable

§Lexicographical comparison

§How can I implement Ord?

§Examples of incorrect Ord implementations

Required Methods§

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

§Examples

Provided Methods§

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

§Examples

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

§Examples

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

§Panics

§Examples

fn clamp_to<R>(self, range: R) -> Selfwhere Self: Sized, R: ClampBounds<Self>,

§Panics

§Examples

Dyn Compatibility§

Implementors§

impl Ord for !

impl Ord for ()

impl Ord for ATerm

impl Ord for Alignment

impl Ord for AlternateHandling

impl Ord for Ansi256Color

impl Ord for AnsiColor

impl Ord for AnyCalendarKind

impl Ord for Arg

impl Ord for ArgCursor

impl Ord for AsciiChar

impl Ord for Attribute

impl Ord for Attributes

impl Ord for B0

impl Ord for B1

impl Ord for winnow::stream::bstr::BStr

impl Ord for winnow::stream::bstr::BStr

impl Ord for BidiClass

impl Ord for BigEndian

impl Ord for BigInt

impl Ord for BigUint

impl Ord for BookHebrew

impl Ord for Braced

impl Ord for ByteStr

impl Ord for ByteString

impl Ord for bytes::bytes::Bytes

impl Ord for winnow::stream::bytes::Bytes

impl Ord for winnow::stream::bytes::Bytes

impl Ord for BytesMut

impl Ord for CStr

impl Ord for CString

impl Ord for CanonicalCombiningClass

impl Ord for CharCase

impl Ord for CharULE

impl Ord for Chinese

impl Ord for ClassBytesRange

impl Ord for ClassUnicodeRange

impl Ord for Color

impl Ord for ComplexScriptULE

impl Ord for Components<'_>

impl Ord for Coptic

impl Ord for CpuidResult

impl Ord for CurrencyType

impl Ord for Dangi

impl Ord for DataIdentifierCow<'_>

impl Ord for DataMarkerAttributes

impl Ord for DataMarkerId

impl Ord for DataMarkerIdHash

impl Ord for DataMarkerInfo

impl Ord for DataRequestMetadata

impl Ord for toml_datetime::datetime::Date

impl Ord for DateGreatestDifferenceField

impl Ord for zip::types::DateTime

impl Ord for Datetime

impl Ord for Day

impl Ord for DayPeriod

impl Ord for DayPeriodULE

impl Ord for DayULE

Trait Ord

§How can I implement `Ord`?

§Examples of incorrect `Ord` implementations

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,

fn clamp_to<R>(self, range: R) -> Self
where Self: Sized, R: ClampBounds<Self>,