Trait Ord

1.0.0 · Source

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 { ... }
}

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) -> std::cmp::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 · 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 · 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);

1.21.0 · 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);

1.50.0 · 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);

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Trait OrdCopy 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

Dyn Compatibility§

Implementors§

impl Ord for MaybeRelocatable

impl Ord for Infallible

impl Ord for Ordering

impl Ord for AsciiChar

impl Ord for IpAddr

impl Ord for SocketAddr

impl Ord for std::io::error::ErrorKind

impl Ord for ark_std::io::error::ErrorKind

impl Ord for BigEndian

impl Ord for LittleEndian

impl Ord for Sign

impl Ord for bool

impl Ord for char

impl Ord for i8

impl Ord for i16

impl Ord for i32

impl Ord for i64

impl Ord for i128

impl Ord for isize

impl Ord for !

impl Ord for str

impl Ord for u8

impl Ord for u16

impl Ord for u32

impl Ord for u64

impl Ord for u128

impl Ord for ()

impl Ord for usize

impl Ord for String

impl Ord for Felt

impl Ord for Relocatable

impl Ord for TypeId

impl Ord for Error

impl Ord for PhantomPinned

impl Ord for Alignment

impl Ord for Duration

impl Ord for CString

impl Ord for CpuidResult

impl Ord for CStr

impl Ord for Ipv4Addr

impl Ord for Ipv6Addr

impl Ord for SocketAddrV4

impl Ord for SocketAddrV6

impl Ord for OsStr

impl Ord for OsString

impl Ord for Components<'_>

impl Ord for Path

impl Ord for PathBuf

impl Ord for PrefixComponent<'_>

impl Ord for Instant

impl Ord for SystemTime

impl Ord for Lsb0

impl Ord for Msb0

impl Ord for Limb

impl Ord for lambdaworks_math::field::element::FieldElement<MontgomeryBackendPrimeField<MontgomeryConfigStark252PrimeField, 4>>

impl Ord for lambdaworks_math::field::element::FieldElement<MontgomeryBackendPrimeField<MontgomeryConfigU64GoldilocksPrimeField, 1>>

impl Ord for lambdaworks_math::field::element::FieldElement<MontgomeryBackendPrimeField<MontgomeryConfigMersenne31PrimeField, 1>>

impl Ord for Mersenne31Field

impl Ord for U56x8

impl Ord for Goldilocks64Field

impl Ord for num_bigint::bigint::BigInt

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,

impl<'a, T, O> Ord for IterOnes<'a, T, O>
where T: Ord + 'a + BitStore, O: Ord + BitOrder,

impl<'a, T, O> Ord for IterZeros<'a, T, O>
where T: Ord + 'a + BitStore, O: Ord + BitOrder,

impl<A> Ord for &A
where A: Ord + ?Sized,

impl<A> Ord for &mut A
where A: Ord + ?Sized,

impl<A, O> Ord for BitArray<A, O>
where A: BitViewSized, O: BitOrder,

impl<B> Ord for Cow<'_, B>
where B: Ord + ToOwned + ?Sized,

impl<Dyn> Ord for DynMetadata<Dyn>
where Dyn: ?Sized,

impl<F> Ord for F
where F: FnPtr,

impl<Inner> Ord for Frozen<Inner>
where Inner: Ord + Mutability,

impl<K, V, A> Ord for BTreeMap<K, V, A>
where K: Ord, V: Ord, A: Allocator + Clone,

impl<L, R> Ord for Either<L, R>
where L: Ord, R: Ord,

impl<M, T> Ord for Address<M, T>
where M: Mutability,

impl<M, T, O> Ord for BitRef<'_, M, T, O>
where M: Mutability, T: BitStore, O: BitOrder,

impl<M, T, O> Ord for BitPtr<M, T, O>
where M: Mutability, T: BitStore, O: BitOrder,

impl<P> Ord for CubicExtField<P>
where P: CubicExtConfig,

impl<P> Ord for QuadExtField<P>
where P: QuadExtConfig,

impl<P, const N: usize> Ord for Fp<P, N>
where P: FpConfig<N>,

impl<Ptr> Ord for Pin<Ptr>
where Ptr: Deref, <Ptr as Deref>::Target: Ord,

impl<R> Ord for BitEnd<R>
where R: Ord + BitRegister,

impl<R> Ord for BitIdx<R>
where R: Ord + BitRegister,

impl<R> Ord for BitIdxError<R>
where R: Ord + BitRegister,

impl<R> Ord for BitMask<R>
where R: Ord + BitRegister,

impl<R> Ord for BitPos<R>
where R: Ord + BitRegister,

impl<R> Ord for BitSel<R>
where R: Ord + BitRegister,

impl<T> Ord for Option<T>
where T: Ord,

impl<T> Ord for Poll<T>
where T: Ord,

impl<T> Ord for BitPtrError<T>
where T: Ord + BitStore,

impl<T> Ord for BitSpanError<T>
where T: Ord + BitStore,

impl<T> Ord for *const T
where T: ?Sized,

impl<T> Ord for *mut T
where T: ?Sized,

impl<T> Ord for [T]
where T: Ord,

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

impl<T> Ord for Reverse<T>
where T: Ord,

impl<T> Ord for Cell<T>
where T: Ord + Copy,

impl<T> Ord for RefCell<T>
where T: Ord + ?Sized,

impl<T> Ord for PhantomData<T>
where T: ?Sized,

impl<T> Ord for ManuallyDrop<T>
where T: Ord + ?Sized,

impl<T> Ord for cairo_vm::with_std::num::NonZero<T>
where T: ZeroablePrimitive + Ord,

impl<T> Ord for Saturating<T>
where T: Ord,

impl<T> Ord for cairo_vm::with_std::num::Wrapping<T>
where T: Ord,

impl<T> Ord for NonNull<T>
where T: ?Sized,

impl<T> Ord for CapacityError<T>
where T: Ord,

impl<T> Ord for MisalignError<T>
where T: Ord,