Trait core::cmp::PartialOrd

1.0.0 · source · [−]
pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
    fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;

    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 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);
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
    }
}
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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
    }
}
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Examples

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

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

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));
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When comparison is impossible:

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

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);
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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);
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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);
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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

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.

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

Implements comparison of vectors lexicographically.