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-//! Functionality for ordering and comparison.
-//!
-//! This module contains various tools for ordering and comparing values. In
-//! summary:
-//!
-//! * [`Eq`] and [`PartialEq`] are traits that allow you to define total and
-//!   partial equality between values, respectively. Implementing them overloads
-//!   the `==` and `!=` operators.
-//! * [`Ord`] and [`PartialOrd`] are traits that allow you to define total and
-//!   partial orderings between values, respectively. Implementing them overloads
-//!   the `<`, `<=`, `>`, and `>=` operators.
-//! * [`Ordering`] is an enum returned by the main functions of [`Ord`] and
-//!   [`PartialOrd`], and describes an ordering.
-//! * [`Reverse`] is a struct that allows you to easily reverse an ordering.
-//! * [`max`] and [`min`] are functions that build off of [`Ord`] and allow you
-//!   to find the maximum or minimum of two values.
-//!
-//! For more details, see the respective documentation of each item in the list.
-//!
-//! [`Eq`]: trait.Eq.html
-//! [`PartialEq`]: trait.PartialEq.html
-//! [`Ord`]: trait.Ord.html
-//! [`PartialOrd`]: trait.PartialOrd.html
-//! [`Ordering`]: enum.Ordering.html
-//! [`Reverse`]: struct.Reverse.html
-//! [`max`]: fn.max.html
-//! [`min`]: fn.min.html
-
-#![stable(feature = "rust1", since = "1.0.0")]
-
-use self::Ordering::*;
-
-/// Trait for equality comparisons which are [partial equivalence
-/// relations](http://en.wikipedia.org/wiki/Partial_equivalence_relation).
-///
-/// This trait allows for partial equality, for types that do not have a full
-/// equivalence relation. For example, in floating point numbers `NaN != NaN`,
-/// so floating point types implement `PartialEq` but not [`Eq`](Eq).
-///
-/// Formally, the equality must be (for all `a`, `b` and `c`):
-///
-/// - symmetric: `a == b` implies `b == a`; and
-/// - transitive: `a == b` and `b == c` implies `a == c`.
-///
-/// Note that these requirements mean that the trait itself must be implemented
-/// symmetrically and transitively: if `T: PartialEq<U>` and `U: PartialEq<V>`
-/// then `U: PartialEq<T>` and `T: PartialEq<V>`.
-///
-/// ## Derivable
-///
-/// This trait can be used with `#[derive]`. When `derive`d on structs, two
-/// instances are equal if all fields are equal, and not equal if any fields
-/// are not equal. When `derive`d on enums, each variant is equal to itself
-/// and not equal to the other variants.
-///
-/// ## How can I implement `PartialEq`?
-///
-/// `PartialEq` only requires the [`eq`] method to be implemented; [`ne`] is defined
-/// in terms of it by default. Any manual implementation of [`ne`] *must* respect
-/// the rule that [`eq`] is a strict inverse of [`ne`]; that is, `!(a == b)` if and
-/// only if `a != b`.
-///
-/// Implementations of `PartialEq`, [`PartialOrd`], and [`Ord`] *must* agree with
-/// each other. It's easy to accidentally make them disagree by deriving some
-/// of the traits and manually implementing others.
-///
-/// An example implementation for a domain in which two books are considered
-/// the same book if their ISBN matches, even if the formats differ:
-///
-/// ```
-/// enum BookFormat {
-///     Paperback,
-///     Hardback,
-///     Ebook,
-/// }
-///
-/// struct Book {
-///     isbn: i32,
-///     format: BookFormat,
-/// }
-///
-/// impl PartialEq for Book {
-///     fn eq(&self, other: &Self) -> bool {
-///         self.isbn == other.isbn
-///     }
-/// }
-///
-/// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
-/// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
-/// let b3 = Book { isbn: 10, format: BookFormat::Paperback };
-///
-/// assert!(b1 == b2);
-/// assert!(b1 != b3);
-/// ```
-///
-/// ## How can I compare two different types?
-///
-/// The type you can compare with is controlled by `PartialEq`'s type parameter.
-/// For example, let's tweak our previous code a bit:
-///
-/// ```
-/// // The derive implements <BookFormat> == <BookFormat> comparisons
-/// #[derive(PartialEq)]
-/// enum BookFormat {
-///     Paperback,
-///     Hardback,
-///     Ebook,
-/// }
-///
-/// struct Book {
-///     isbn: i32,
-///     format: BookFormat,
-/// }
-///
-/// // Implement <Book> == <BookFormat> comparisons
-/// impl PartialEq<BookFormat> for Book {
-///     fn eq(&self, other: &BookFormat) -> bool {
-///         self.format == *other
-///     }
-/// }
-///
-/// // Implement <BookFormat> == <Book> comparisons
-/// impl PartialEq<Book> for BookFormat {
-///     fn eq(&self, other: &Book) -> bool {
-///         *self == other.format
-///     }
-/// }
-///
-/// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
-///
-/// assert!(b1 == BookFormat::Paperback);
-/// assert!(BookFormat::Ebook != b1);
-/// ```
-///
-/// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
-/// we allow `BookFormat`s to be compared with `Book`s.
-///
-/// A comparison like the one above, which ignores some fields of the struct,
-/// can be dangerous. It can easily lead to an unintended violation of the
-/// requirements for a partial equivalence relation. For example, if we kept
-/// the above implementation of `PartialEq<Book>` for `BookFormat` and added an
-/// implementation of `PartialEq<Book>` for `Book` (either via a `#[derive]` or
-/// via the manual implementation from the first example) then the result would
-/// violate transitivity:
-///
-/// ```should_panic
-/// #[derive(PartialEq)]
-/// enum BookFormat {
-///     Paperback,
-///     Hardback,
-///     Ebook,
-/// }
-///
-/// #[derive(PartialEq)]
-/// struct Book {
-///     isbn: i32,
-///     format: BookFormat,
-/// }
-///
-/// impl PartialEq<BookFormat> for Book {
-///     fn eq(&self, other: &BookFormat) -> bool {
-///         self.format == *other
-///     }
-/// }
-///
-/// impl PartialEq<Book> for BookFormat {
-///     fn eq(&self, other: &Book) -> bool {
-///         *self == other.format
-///     }
-/// }
-///
-/// fn main() {
-///     let b1 = Book { isbn: 1, format: BookFormat::Paperback };
-///     let b2 = Book { isbn: 2, format: BookFormat::Paperback };
-///
-///     assert!(b1 == BookFormat::Paperback);
-///     assert!(BookFormat::Paperback == b2);
-///
-///     // The following should hold by transitivity but doesn't.
-///     assert!(b1 == b2); // <-- PANICS
-/// }
-/// ```
-///
-/// # Examples
-///
-/// ```
-/// let x: u32 = 0;
-/// let y: u32 = 1;
-///
-/// assert_eq!(x == y, false);
-/// assert_eq!(x.eq(&y), false);
-/// ```
-///
-/// [`eq`]: PartialEq::eq
-/// [`ne`]: PartialEq::ne
-#[lang = "eq"]
-#[stable(feature = "rust1", since = "1.0.0")]
-#[doc(alias = "==")]
-#[doc(alias = "!=")]
-#[rustc_on_unimplemented(
-    message = "can't compare `{Self}` with `{Rhs}`",
-    label = "no implementation for `{Self} == {Rhs}`"
-)]
-pub trait PartialEq<Rhs: ?Sized = Self> {
-    /// This method tests for `self` and `other` values to be equal, and is used
-    /// by `==`.
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn eq(&self, other: &Rhs) -> bool;
-
-    /// This method tests for `!=`.
-    #[inline]
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn ne(&self, other: &Rhs) -> bool {
-        !self.eq(other)
-    }
-}
-
-/// Derive macro generating an impl of the trait `PartialEq`.
-#[rustc_builtin_macro]
-#[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
-#[allow_internal_unstable(core_intrinsics, structural_match)]
-pub macro PartialEq($item:item) {
-    /* compiler built-in */
-}
-
-/// Trait for equality comparisons which are [equivalence relations](
-/// https://en.wikipedia.org/wiki/Equivalence_relation).
-///
-/// This means, that in addition to `a == b` and `a != b` being strict inverses, the equality must
-/// be (for all `a`, `b` and `c`):
-///
-/// - reflexive: `a == a`;
-/// - symmetric: `a == b` implies `b == a`; and
-/// - transitive: `a == b` and `b == c` implies `a == c`.
-///
-/// This property cannot be checked by the compiler, and therefore `Eq` implies
-/// [`PartialEq`], and has no extra methods.
-///
-/// ## Derivable
-///
-/// This trait can be used with `#[derive]`. When `derive`d, because `Eq` has
-/// no extra methods, it is only informing the compiler that this is an
-/// equivalence relation rather than a partial equivalence relation. Note that
-/// the `derive` strategy requires all fields are `Eq`, which isn't
-/// always desired.
-///
-/// ## How can I implement `Eq`?
-///
-/// If you cannot use the `derive` strategy, specify that your type implements
-/// `Eq`, which has no methods:
-///
-/// ```
-/// enum BookFormat { Paperback, Hardback, Ebook }
-/// struct Book {
-///     isbn: i32,
-///     format: BookFormat,
-/// }
-/// impl PartialEq for Book {
-///     fn eq(&self, other: &Self) -> bool {
-///         self.isbn == other.isbn
-///     }
-/// }
-/// impl Eq for Book {}
-/// ```
-#[doc(alias = "==")]
-#[doc(alias = "!=")]
-#[stable(feature = "rust1", since = "1.0.0")]
-pub trait Eq: PartialEq<Self> {
-    // this method is used solely by #[deriving] to assert
-    // that every component of a type implements #[deriving]
-    // itself, the current deriving infrastructure means doing this
-    // assertion without using a method on this trait is nearly
-    // impossible.
-    //
-    // This should never be implemented by hand.
-    #[doc(hidden)]
-    #[inline]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn assert_receiver_is_total_eq(&self) {}
-}
-
-/// Derive macro generating an impl of the trait `Eq`.
-#[rustc_builtin_macro]
-#[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
-#[allow_internal_unstable(core_intrinsics, derive_eq, structural_match)]
-pub macro Eq($item:item) {
-    /* compiler built-in */
-}
-
-// FIXME: this struct is used solely by #[derive] to
-// assert that every component of a type implements Eq.
-//
-// This struct should never appear in user code.
-#[doc(hidden)]
-#[allow(missing_debug_implementations)]
-#[unstable(feature = "derive_eq", reason = "deriving hack, should not be public", issue = "none")]
-pub struct AssertParamIsEq<T: Eq + ?Sized> {
-    _field: crate::marker::PhantomData<T>,
-}
-
-/// An `Ordering` is the result of a comparison between two values.
-///
-/// # Examples
-///
-/// ```
-/// use std::cmp::Ordering;
-///
-/// let result = 1.cmp(&2);
-/// assert_eq!(Ordering::Less, result);
-///
-/// let result = 1.cmp(&1);
-/// assert_eq!(Ordering::Equal, result);
-///
-/// let result = 2.cmp(&1);
-/// assert_eq!(Ordering::Greater, result);
-/// ```
-#[derive(Clone, Copy, PartialEq, Debug, Hash)]
-#[stable(feature = "rust1", since = "1.0.0")]
-pub enum Ordering {
-    /// An ordering where a compared value is less than another.
-    #[stable(feature = "rust1", since = "1.0.0")]
-    Less = -1,
-    /// An ordering where a compared value is equal to another.
-    #[stable(feature = "rust1", since = "1.0.0")]
-    Equal = 0,
-    /// An ordering where a compared value is greater than another.
-    #[stable(feature = "rust1", since = "1.0.0")]
-    Greater = 1,
-}
-
-impl Ordering {
-    /// Reverses the `Ordering`.
-    ///
-    /// * `Less` becomes `Greater`.
-    /// * `Greater` becomes `Less`.
-    /// * `Equal` becomes `Equal`.
-    ///
-    /// # Examples
-    ///
-    /// Basic behavior:
-    ///
-    /// ```
-    /// use std::cmp::Ordering;
-    ///
-    /// assert_eq!(Ordering::Less.reverse(), Ordering::Greater);
-    /// assert_eq!(Ordering::Equal.reverse(), Ordering::Equal);
-    /// assert_eq!(Ordering::Greater.reverse(), Ordering::Less);
-    /// ```
-    ///
-    /// This method can be used to reverse a comparison:
-    ///
-    /// ```
-    /// let data: &mut [_] = &mut [2, 10, 5, 8];
-    ///
-    /// // sort the array from largest to smallest.
-    /// data.sort_by(|a, b| a.cmp(b).reverse());
-    ///
-    /// let b: &mut [_] = &mut [10, 8, 5, 2];
-    /// assert!(data == b);
-    /// ```
-    #[inline]
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    pub fn reverse(self) -> Ordering {
-        match self {
-            Less => Greater,
-            Equal => Equal,
-            Greater => Less,
-        }
-    }
-
-    /// Chains two orderings.
-    ///
-    /// Returns `self` when it's not `Equal`. Otherwise returns `other`.
-    ///
-    /// # Examples
-    ///
-    /// ```
-    /// use std::cmp::Ordering;
-    ///
-    /// let result = Ordering::Equal.then(Ordering::Less);
-    /// assert_eq!(result, Ordering::Less);
-    ///
-    /// let result = Ordering::Less.then(Ordering::Equal);
-    /// assert_eq!(result, Ordering::Less);
-    ///
-    /// let result = Ordering::Less.then(Ordering::Greater);
-    /// assert_eq!(result, Ordering::Less);
-    ///
-    /// let result = Ordering::Equal.then(Ordering::Equal);
-    /// assert_eq!(result, Ordering::Equal);
-    ///
-    /// let x: (i64, i64, i64) = (1, 2, 7);
-    /// let y: (i64, i64, i64) = (1, 5, 3);
-    /// let result = x.0.cmp(&y.0).then(x.1.cmp(&y.1)).then(x.2.cmp(&y.2));
-    ///
-    /// assert_eq!(result, Ordering::Less);
-    /// ```
-    #[inline]
-    #[must_use]
-    #[stable(feature = "ordering_chaining", since = "1.17.0")]
-    pub fn then(self, other: Ordering) -> Ordering {
-        match self {
-            Equal => other,
-            _ => self,
-        }
-    }
-
-    /// Chains the ordering with the given function.
-    ///
-    /// Returns `self` when it's not `Equal`. Otherwise calls `f` and returns
-    /// the result.
-    ///
-    /// # Examples
-    ///
-    /// ```
-    /// use std::cmp::Ordering;
-    ///
-    /// let result = Ordering::Equal.then_with(|| Ordering::Less);
-    /// assert_eq!(result, Ordering::Less);
-    ///
-    /// let result = Ordering::Less.then_with(|| Ordering::Equal);
-    /// assert_eq!(result, Ordering::Less);
-    ///
-    /// let result = Ordering::Less.then_with(|| Ordering::Greater);
-    /// assert_eq!(result, Ordering::Less);
-    ///
-    /// let result = Ordering::Equal.then_with(|| Ordering::Equal);
-    /// assert_eq!(result, Ordering::Equal);
-    ///
-    /// let x: (i64, i64, i64) = (1, 2, 7);
-    /// let y: (i64, i64, i64)  = (1, 5, 3);
-    /// let result = x.0.cmp(&y.0).then_with(|| x.1.cmp(&y.1)).then_with(|| x.2.cmp(&y.2));
-    ///
-    /// assert_eq!(result, Ordering::Less);
-    /// ```
-    #[inline]
-    #[must_use]
-    #[stable(feature = "ordering_chaining", since = "1.17.0")]
-    pub fn then_with<F: FnOnce() -> Ordering>(self, f: F) -> Ordering {
-        match self {
-            Equal => f(),
-            _ => self,
-        }
-    }
-}
-
-/// A helper struct for reverse ordering.
-///
-/// This struct is a helper to be used with functions like [`Vec::sort_by_key`] and
-/// can be used to reverse order a part of a key.
-///
-/// [`Vec::sort_by_key`]: ../../std/vec/struct.Vec.html#method.sort_by_key
-///
-/// # Examples
-///
-/// ```
-/// use std::cmp::Reverse;
-///
-/// let mut v = vec![1, 2, 3, 4, 5, 6];
-/// v.sort_by_key(|&num| (num > 3, Reverse(num)));
-/// assert_eq!(v, vec![3, 2, 1, 6, 5, 4]);
-/// ```
-#[derive(PartialEq, Eq, Debug, Copy, Clone, Default, Hash)]
-#[stable(feature = "reverse_cmp_key", since = "1.19.0")]
-pub struct Reverse<T>(#[stable(feature = "reverse_cmp_key", since = "1.19.0")] pub T);
-
-#[stable(feature = "reverse_cmp_key", since = "1.19.0")]
-impl<T: PartialOrd> PartialOrd for Reverse<T> {
-    #[inline]
-    fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
-        other.0.partial_cmp(&self.0)
-    }
-
-    #[inline]
-    fn lt(&self, other: &Self) -> bool {
-        other.0 < self.0
-    }
-    #[inline]
-    fn le(&self, other: &Self) -> bool {
-        other.0 <= self.0
-    }
-    #[inline]
-    fn gt(&self, other: &Self) -> bool {
-        other.0 > self.0
-    }
-    #[inline]
-    fn ge(&self, other: &Self) -> bool {
-        other.0 >= self.0
-    }
-}
-
-#[stable(feature = "reverse_cmp_key", since = "1.19.0")]
-impl<T: Ord> Ord for Reverse<T> {
-    #[inline]
-    fn cmp(&self, other: &Reverse<T>) -> Ordering {
-        other.0.cmp(&self.0)
-    }
-}
-
-/// Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order).
-///
-/// An order is a total order if it is (for all `a`, `b` and `c`):
-///
-/// - total and asymmetric: exactly one of `a < b`, `a == b` or `a > b` is true; and
-/// - transitive, `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
-///
-/// ## Derivable
-///
-/// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
-/// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
-/// When `derive`d on enums, variants are ordered by their top-to-bottom declaration order.
-///
-/// ## How can I implement `Ord`?
-///
-/// `Ord` requires that the type also be [`PartialOrd`] and [`Eq`] (which requires [`PartialEq`]).
-///
-/// Then you must define an implementation for [`cmp`]. You may find it useful to use
-/// [`cmp`] on your type's fields.
-///
-/// Implementations of [`PartialEq`], [`PartialOrd`], and `Ord` *must*
-/// agree with each other. That is, `a.cmp(b) == Ordering::Equal` if
-/// and only if `a == b` and `Some(a.cmp(b)) == a.partial_cmp(b)` for
-/// all `a` and `b`. It's easy to accidentally make them disagree by
-/// deriving some of the traits and manually implementing others.
-///
-/// Here's an example where you want to sort people by height only, disregarding `id`
-/// and `name`:
-///
-/// ```
-/// use std::cmp::Ordering;
-///
-/// #[derive(Eq)]
-/// struct Person {
-///     id: u32,
-///     name: String,
-///     height: u32,
-/// }
-///
-/// impl Ord for Person {
-///     fn cmp(&self, other: &Self) -> Ordering {
-///         self.height.cmp(&other.height)
-///     }
-/// }
-///
-/// impl PartialOrd for Person {
-///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-///         Some(self.cmp(other))
-///     }
-/// }
-///
-/// impl PartialEq for Person {
-///     fn eq(&self, other: &Self) -> bool {
-///         self.height == other.height
-///     }
-/// }
-/// ```
-///
-/// [`cmp`]: Ord::cmp
-#[doc(alias = "<")]
-#[doc(alias = ">")]
-#[doc(alias = "<=")]
-#[doc(alias = ">=")]
-#[stable(feature = "rust1", since = "1.0.0")]
-pub trait Ord: Eq + PartialOrd<Self> {
-    /// 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);
-    /// ```
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn cmp(&self, other: &Self) -> Ordering;
-
-    /// Compares and returns the maximum of two values.
-    ///
-    /// Returns the second argument if the comparison determines them to be equal.
-    ///
-    /// # Examples
-    ///
-    /// ```
-    /// assert_eq!(2, 1.max(2));
-    /// assert_eq!(2, 2.max(2));
-    /// ```
-    #[stable(feature = "ord_max_min", since = "1.21.0")]
-    #[inline]
-    #[must_use]
-    fn max(self, other: Self) -> Self
-    where
-        Self: Sized,
-    {
-        max_by(self, other, Ord::cmp)
-    }
-
-    /// Compares and returns the minimum of two values.
-    ///
-    /// Returns the first argument if the comparison determines them to be equal.
-    ///
-    /// # Examples
-    ///
-    /// ```
-    /// assert_eq!(1, 1.min(2));
-    /// assert_eq!(2, 2.min(2));
-    /// ```
-    #[stable(feature = "ord_max_min", since = "1.21.0")]
-    #[inline]
-    #[must_use]
-    fn min(self, other: Self) -> Self
-    where
-        Self: Sized,
-    {
-        min_by(self, other, Ord::cmp)
-    }
-
-    /// 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
-    ///
-    /// ```
-    /// #![feature(clamp)]
-    ///
-    /// assert!((-3).clamp(-2, 1) == -2);
-    /// assert!(0.clamp(-2, 1) == 0);
-    /// assert!(2.clamp(-2, 1) == 1);
-    /// ```
-    #[must_use]
-    #[unstable(feature = "clamp", issue = "44095")]
-    fn clamp(self, min: Self, max: Self) -> Self
-    where
-        Self: Sized,
-    {
-        assert!(min <= max);
-        if self < min {
-            min
-        } else if self > max {
-            max
-        } else {
-            self
-        }
-    }
-}
-
-/// Derive macro generating an impl of the trait `Ord`.
-#[rustc_builtin_macro]
-#[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
-#[allow_internal_unstable(core_intrinsics)]
-pub macro Ord($item:item) {
-    /* compiler built-in */
-}
-
-#[stable(feature = "rust1", since = "1.0.0")]
-impl Eq for Ordering {}
-
-#[stable(feature = "rust1", since = "1.0.0")]
-impl Ord for Ordering {
-    #[inline]
-    fn cmp(&self, other: &Ordering) -> Ordering {
-        (*self as i32).cmp(&(*other as i32))
-    }
-}
-
-#[stable(feature = "rust1", since = "1.0.0")]
-impl PartialOrd for Ordering {
-    #[inline]
-    fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
-        (*self as i32).partial_cmp(&(*other as i32))
-    }
-}
-
-/// Trait for values that can be compared for a sort-order.
-///
-/// The comparison must satisfy, for all `a`, `b` and `c`:
-///
-/// - asymmetry: if `a < b` then `!(a > b)`, as well as `a > b` implying `!(a < b)`; and
-/// - transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
-///
-/// 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>`.
-///
-/// ## Derivable
-///
-/// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
-/// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
-/// When `derive`d on enums, variants are ordered by their top-to-bottom declaration order.
-///
-/// ## 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`].
-///
-/// Implementations of [`PartialEq`], `PartialOrd`, and [`Ord`] *must* agree with each other. It's
-/// easy to accidentally make them disagree by deriving some of the traits and manually
-/// implementing others.
-///
-/// 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: &Person) -> Option<Ordering> {
-///         Some(self.cmp(other))
-///     }
-/// }
-///
-/// impl Ord for Person {
-///     fn cmp(&self, other: &Person) -> Ordering {
-///         self.height.cmp(&other.height)
-///     }
-/// }
-///
-/// impl PartialEq for Person {
-///     fn eq(&self, other: &Person) -> 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);
-/// ```
-///
-/// [`partial_cmp`]: PartialOrd::partial_cmp
-/// [`cmp`]: Ord::cmp
-#[lang = "partial_ord"]
-#[stable(feature = "rust1", since = "1.0.0")]
-#[doc(alias = ">")]
-#[doc(alias = "<")]
-#[doc(alias = "<=")]
-#[doc(alias = ">=")]
-#[rustc_on_unimplemented(
-    message = "can't compare `{Self}` with `{Rhs}`",
-    label = "no implementation for `{Self} < {Rhs}` and `{Self} > {Rhs}`"
-)]
-pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
-    /// 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);
-    /// ```
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;
-
-    /// 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);
-    /// ```
-    #[inline]
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn lt(&self, other: &Rhs) -> bool {
-        matches!(self.partial_cmp(other), Some(Less))
-    }
-
-    /// 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);
-    /// ```
-    #[inline]
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn le(&self, other: &Rhs) -> bool {
-        matches!(self.partial_cmp(other), Some(Less | Equal))
-    }
-
-    /// 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);
-    /// ```
-    #[inline]
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn gt(&self, other: &Rhs) -> bool {
-        matches!(self.partial_cmp(other), Some(Greater))
-    }
-
-    /// 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);
-    /// ```
-    #[inline]
-    #[must_use]
-    #[stable(feature = "rust1", since = "1.0.0")]
-    fn ge(&self, other: &Rhs) -> bool {
-        matches!(self.partial_cmp(other), Some(Greater | Equal))
-    }
-}
-
-/// Derive macro generating an impl of the trait `PartialOrd`.
-#[rustc_builtin_macro]
-#[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
-#[allow_internal_unstable(core_intrinsics)]
-pub macro PartialOrd($item:item) {
-    /* compiler built-in */
-}
-
-/// Compares and returns the minimum of two values.
-///
-/// Returns the first argument if the comparison determines them to be equal.
-///
-/// Internally uses an alias to [`Ord::min`].
-///
-/// # Examples
-///
-/// ```
-/// use std::cmp;
-///
-/// assert_eq!(1, cmp::min(1, 2));
-/// assert_eq!(2, cmp::min(2, 2));
-/// ```
-#[inline]
-#[must_use]
-#[stable(feature = "rust1", since = "1.0.0")]
-pub fn min<T: Ord>(v1: T, v2: T) -> T {
-    v1.min(v2)
-}
-
-/// Returns the minimum of two values with respect to the specified comparison function.
-///
-/// Returns the first argument if the comparison determines them to be equal.
-///
-/// # Examples
-///
-/// ```
-/// #![feature(cmp_min_max_by)]
-///
-/// use std::cmp;
-///
-/// assert_eq!(cmp::min_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 1);
-/// assert_eq!(cmp::min_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
-/// ```
-#[inline]
-#[must_use]
-#[unstable(feature = "cmp_min_max_by", issue = "64460")]
-pub fn min_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
-    match compare(&v1, &v2) {
-        Ordering::Less | Ordering::Equal => v1,
-        Ordering::Greater => v2,
-    }
-}
-
-/// Returns the element that gives the minimum value from the specified function.
-///
-/// Returns the first argument if the comparison determines them to be equal.
-///
-/// # Examples
-///
-/// ```
-/// #![feature(cmp_min_max_by)]
-///
-/// use std::cmp;
-///
-/// assert_eq!(cmp::min_by_key(-2, 1, |x: &i32| x.abs()), 1);
-/// assert_eq!(cmp::min_by_key(-2, 2, |x: &i32| x.abs()), -2);
-/// ```
-#[inline]
-#[must_use]
-#[unstable(feature = "cmp_min_max_by", issue = "64460")]
-pub fn min_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
-    min_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
-}
-
-/// Compares and returns the maximum of two values.
-///
-/// Returns the second argument if the comparison determines them to be equal.
-///
-/// Internally uses an alias to [`Ord::max`].
-///
-/// # Examples
-///
-/// ```
-/// use std::cmp;
-///
-/// assert_eq!(2, cmp::max(1, 2));
-/// assert_eq!(2, cmp::max(2, 2));
-/// ```
-#[inline]
-#[must_use]
-#[stable(feature = "rust1", since = "1.0.0")]
-pub fn max<T: Ord>(v1: T, v2: T) -> T {
-    v1.max(v2)
-}
-
-/// Returns the maximum of two values with respect to the specified comparison function.
-///
-/// Returns the second argument if the comparison determines them to be equal.
-///
-/// # Examples
-///
-/// ```
-/// #![feature(cmp_min_max_by)]
-///
-/// use std::cmp;
-///
-/// assert_eq!(cmp::max_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
-/// assert_eq!(cmp::max_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 2);
-/// ```
-#[inline]
-#[must_use]
-#[unstable(feature = "cmp_min_max_by", issue = "64460")]
-pub fn max_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
-    match compare(&v1, &v2) {
-        Ordering::Less | Ordering::Equal => v2,
-        Ordering::Greater => v1,
-    }
-}
-
-/// Returns the element that gives the maximum value from the specified function.
-///
-/// Returns the second argument if the comparison determines them to be equal.
-///
-/// # Examples
-///
-/// ```
-/// #![feature(cmp_min_max_by)]
-///
-/// use std::cmp;
-///
-/// assert_eq!(cmp::max_by_key(-2, 1, |x: &i32| x.abs()), -2);
-/// assert_eq!(cmp::max_by_key(-2, 2, |x: &i32| x.abs()), 2);
-/// ```
-#[inline]
-#[must_use]
-#[unstable(feature = "cmp_min_max_by", issue = "64460")]
-pub fn max_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
-    max_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
-}
-
-// Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
-mod impls {
-    use crate::cmp::Ordering::{self, Equal, Greater, Less};
-    use crate::hint::unreachable_unchecked;
-
-    macro_rules! partial_eq_impl {
-        ($($t:ty)*) => ($(
-            #[stable(feature = "rust1", since = "1.0.0")]
-            impl PartialEq for $t {
-                #[inline]
-                fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
-                #[inline]
-                fn ne(&self, other: &$t) -> bool { (*self) != (*other) }
-            }
-        )*)
-    }
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl PartialEq for () {
-        #[inline]
-        fn eq(&self, _other: &()) -> bool {
-            true
-        }
-        #[inline]
-        fn ne(&self, _other: &()) -> bool {
-            false
-        }
-    }
-
-    partial_eq_impl! {
-        bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f32 f64
-    }
-
-    macro_rules! eq_impl {
-        ($($t:ty)*) => ($(
-            #[stable(feature = "rust1", since = "1.0.0")]
-            impl Eq for $t {}
-        )*)
-    }
-
-    eq_impl! { () bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
-
-    macro_rules! partial_ord_impl {
-        ($($t:ty)*) => ($(
-            #[stable(feature = "rust1", since = "1.0.0")]
-            impl PartialOrd for $t {
-                #[inline]
-                fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
-                    match (self <= other, self >= other) {
-                        (false, false) => None,
-                        (false, true) => Some(Greater),
-                        (true, false) => Some(Less),
-                        (true, true) => Some(Equal),
-                    }
-                }
-                #[inline]
-                fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
-                #[inline]
-                fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
-                #[inline]
-                fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
-                #[inline]
-                fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
-            }
-        )*)
-    }
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl PartialOrd for () {
-        #[inline]
-        fn partial_cmp(&self, _: &()) -> Option<Ordering> {
-            Some(Equal)
-        }
-    }
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl PartialOrd for bool {
-        #[inline]
-        fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
-            (*self as u8).partial_cmp(&(*other as u8))
-        }
-    }
-
-    partial_ord_impl! { f32 f64 }
-
-    macro_rules! ord_impl {
-        ($($t:ty)*) => ($(
-            #[stable(feature = "rust1", since = "1.0.0")]
-            impl PartialOrd for $t {
-                #[inline]
-                fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
-                    Some(self.cmp(other))
-                }
-                #[inline]
-                fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
-                #[inline]
-                fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
-                #[inline]
-                fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
-                #[inline]
-                fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
-            }
-
-            #[stable(feature = "rust1", since = "1.0.0")]
-            impl Ord for $t {
-                #[inline]
-                fn cmp(&self, other: &$t) -> Ordering {
-                    // The order here is important to generate more optimal assembly.
-                    // See <https://github.com/rust-lang/rust/issues/63758> for more info.
-                    if *self < *other { Less }
-                    else if *self == *other { Equal }
-                    else { Greater }
-                }
-            }
-        )*)
-    }
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl Ord for () {
-        #[inline]
-        fn cmp(&self, _other: &()) -> Ordering {
-            Equal
-        }
-    }
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl Ord for bool {
-        #[inline]
-        fn cmp(&self, other: &bool) -> Ordering {
-            // Casting to i8's and converting the difference to an Ordering generates
-            // more optimal assembly.
-            // See <https://github.com/rust-lang/rust/issues/66780> for more info.
-            match (*self as i8) - (*other as i8) {
-                -1 => Less,
-                0 => Equal,
-                1 => Greater,
-                // SAFETY: bool as i8 returns 0 or 1, so the difference can't be anything else
-                _ => unsafe { unreachable_unchecked() },
-            }
-        }
-    }
-
-    ord_impl! { char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
-
-    #[unstable(feature = "never_type", issue = "35121")]
-    impl PartialEq for ! {
-        fn eq(&self, _: &!) -> bool {
-            *self
-        }
-    }
-
-    #[unstable(feature = "never_type", issue = "35121")]
-    impl Eq for ! {}
-
-    #[unstable(feature = "never_type", issue = "35121")]
-    impl PartialOrd for ! {
-        fn partial_cmp(&self, _: &!) -> Option<Ordering> {
-            *self
-        }
-    }
-
-    #[unstable(feature = "never_type", issue = "35121")]
-    impl Ord for ! {
-        fn cmp(&self, _: &!) -> Ordering {
-            *self
-        }
-    }
-
-    // & pointers
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &A
-    where
-        A: PartialEq<B>,
-    {
-        #[inline]
-        fn eq(&self, other: &&B) -> bool {
-            PartialEq::eq(*self, *other)
-        }
-        #[inline]
-        fn ne(&self, other: &&B) -> bool {
-            PartialEq::ne(*self, *other)
-        }
-    }
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized, B: ?Sized> PartialOrd<&B> for &A
-    where
-        A: PartialOrd<B>,
-    {
-        #[inline]
-        fn partial_cmp(&self, other: &&B) -> Option<Ordering> {
-            PartialOrd::partial_cmp(*self, *other)
-        }
-        #[inline]
-        fn lt(&self, other: &&B) -> bool {
-            PartialOrd::lt(*self, *other)
-        }
-        #[inline]
-        fn le(&self, other: &&B) -> bool {
-            PartialOrd::le(*self, *other)
-        }
-        #[inline]
-        fn gt(&self, other: &&B) -> bool {
-            PartialOrd::gt(*self, *other)
-        }
-        #[inline]
-        fn ge(&self, other: &&B) -> bool {
-            PartialOrd::ge(*self, *other)
-        }
-    }
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized> Ord for &A
-    where
-        A: Ord,
-    {
-        #[inline]
-        fn cmp(&self, other: &Self) -> Ordering {
-            Ord::cmp(*self, *other)
-        }
-    }
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized> Eq for &A where A: Eq {}
-
-    // &mut pointers
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &mut A
-    where
-        A: PartialEq<B>,
-    {
-        #[inline]
-        fn eq(&self, other: &&mut B) -> bool {
-            PartialEq::eq(*self, *other)
-        }
-        #[inline]
-        fn ne(&self, other: &&mut B) -> bool {
-            PartialEq::ne(*self, *other)
-        }
-    }
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized, B: ?Sized> PartialOrd<&mut B> for &mut A
-    where
-        A: PartialOrd<B>,
-    {
-        #[inline]
-        fn partial_cmp(&self, other: &&mut B) -> Option<Ordering> {
-            PartialOrd::partial_cmp(*self, *other)
-        }
-        #[inline]
-        fn lt(&self, other: &&mut B) -> bool {
-            PartialOrd::lt(*self, *other)
-        }
-        #[inline]
-        fn le(&self, other: &&mut B) -> bool {
-            PartialOrd::le(*self, *other)
-        }
-        #[inline]
-        fn gt(&self, other: &&mut B) -> bool {
-            PartialOrd::gt(*self, *other)
-        }
-        #[inline]
-        fn ge(&self, other: &&mut B) -> bool {
-            PartialOrd::ge(*self, *other)
-        }
-    }
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized> Ord for &mut A
-    where
-        A: Ord,
-    {
-        #[inline]
-        fn cmp(&self, other: &Self) -> Ordering {
-            Ord::cmp(*self, *other)
-        }
-    }
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized> Eq for &mut A where A: Eq {}
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &A
-    where
-        A: PartialEq<B>,
-    {
-        #[inline]
-        fn eq(&self, other: &&mut B) -> bool {
-            PartialEq::eq(*self, *other)
-        }
-        #[inline]
-        fn ne(&self, other: &&mut B) -> bool {
-            PartialEq::ne(*self, *other)
-        }
-    }
-
-    #[stable(feature = "rust1", since = "1.0.0")]
-    impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &mut A
-    where
-        A: PartialEq<B>,
-    {
-        #[inline]
-        fn eq(&self, other: &&B) -> bool {
-            PartialEq::eq(*self, *other)
-        }
-        #[inline]
-        fn ne(&self, other: &&B) -> bool {
-            PartialEq::ne(*self, *other)
-        }
-    }
-}