cmp.rs.html -- source
Description: Source to the Rust file `libcore/cmp.rs`.
Keywords: rust, rustlang, rust-lang

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    // Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
    // file at the top-level directory of this distribution and at
    // http://rust-lang.org/COPYRIGHT.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    //! Functionality for ordering and comparison.
    //!
    //! This module defines both [`PartialOrd`] and [`PartialEq`] traits which are used
    //! by the compiler to implement comparison operators. Rust programs may
    //! implement [`PartialOrd`] to overload the `<`, `<=`, `>`, and `>=` operators,
    //! and may implement [`PartialEq`] to overload the `==` and `!=` operators.
    //!
    //! [`PartialOrd`]: trait.PartialOrd.html
    //! [`PartialEq`]: trait.PartialEq.html
    //!
    //! # Examples
    //!
    //! ```
    //! let x: u32 = 0;
    //! let y: u32 = 1;
    //!
    //! // these two lines are equivalent
    //! assert_eq!(x < y, true);
    //! assert_eq!(x.lt(&y), true);
    //!
    //! // these two lines are also equivalent
    //! assert_eq!(x == y, false);
    //! assert_eq!(x.eq(&y), false);
    //! ```

    #![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`.
    ///
    /// 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: &Book) -> 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);
    /// ```
    ///
    /// # Examples
    ///
    /// ```
    /// let x: u32 = 0;
    /// let y: u32 = 1;
    ///
    /// assert_eq!(x == y, false);
    /// assert_eq!(x.eq(&y), false);
    /// ```
    #[lang = "eq"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_on_unimplemented = "can't compare `{Self}` with `{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) }
    }

    /// 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: &Book) -> bool {
    ///         self.isbn == other.isbn
    ///     }
    /// }
    /// impl Eq for Book {}
    /// ```
    #[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) {}
    }

    // 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 = "0")]
    pub struct AssertParamIsEq<T: Eq + ?Sized> { _field: ::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 mut 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]
        #[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]
        #[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]
        #[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.
    ///
    /// Example usage:
    ///
    /// ```
    /// 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)]
    #[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 ge(&self, other: &Self) -> bool { other.0 >= self.0 }
        #[inline]
        fn gt(&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 antisymmetric: 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. 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: &Person) -> Ordering {
    ///         self.height.cmp(&other.height)
    ///     }
    /// }
    ///
    /// impl PartialOrd for Person {
    ///     fn partial_cmp(&self, other: &Person) -> Option<Ordering> {
    ///         Some(self.cmp(other))
    ///     }
    /// }
    ///
    /// impl PartialEq for Person {
    ///     fn eq(&self, other: &Person) -> bool {
    ///         self.height == other.height
    ///     }
    /// }
    /// ```
    #[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);
        /// ```
        #[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")]
        fn max(self, other: Self) -> Self
        where Self: Sized {
            if other >= self { other } else { self }
        }

        /// 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")]
        fn min(self, other: Self) -> Self
        where Self: Sized {
            if self <= other { self } else { other }
        }
    }

    #[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`:
    ///
    /// - antisymmetry: 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: &Person) -> Option<Ordering> {
    ///         self.height.partial_cmp(&other.height)
    ///     }
    /// }
    ///
    /// impl PartialEq for Person {
    ///     fn eq(&self, other: &Person) -> 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);
    /// ```
    #[lang = "ord"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_on_unimplemented = "can't compare `{Self}` with `{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 = std::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 {
            match self.partial_cmp(other) {
                Some(Less) => true,
                _ => false,
            }
        }

        /// 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 {
            match self.partial_cmp(other) {
                Some(Less) | Some(Equal) => true,
                _ => false,
            }
        }

        /// 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 {
            match self.partial_cmp(other) {
                Some(Greater) => true,
                _ => false,
            }
        }

        /// 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 {
            match self.partial_cmp(other) {
                Some(Greater) | Some(Equal) => true,
                _ => false,
            }
        }
    }

    /// 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]
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn min<T: Ord>(v1: T, v2: T) -> T {
        v1.min(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]
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn max<T: Ord>(v1: T, v2: T) -> T {
        v1.max(v2)
    }

    // Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
    mod impls {
        use cmp::Ordering::{self, Less, Greater, Equal};

        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 {
                        if *self == *other { Equal }
                        else if *self < *other { Less }
                        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 {
                (*self as u8).cmp(&(*other as u8))
            }
        }

        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, 'b, A: ?Sized, B: ?Sized> PartialEq<&'b B> for &'a A where A: PartialEq<B> {
            #[inline]
            fn eq(&self, other: & &'b B) -> bool { PartialEq::eq(*self, *other) }
            #[inline]
            fn ne(&self, other: & &'b B) -> bool { PartialEq::ne(*self, *other) }
        }
        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, 'b, A: ?Sized, B: ?Sized> PartialOrd<&'b B> for &'a A where A: PartialOrd<B> {
            #[inline]
            fn partial_cmp(&self, other: &&'b B) -> Option<Ordering> {
                PartialOrd::partial_cmp(*self, *other)
            }
            #[inline]
            fn lt(&self, other: & &'b B) -> bool { PartialOrd::lt(*self, *other) }
            #[inline]
            fn le(&self, other: & &'b B) -> bool { PartialOrd::le(*self, *other) }
            #[inline]
            fn ge(&self, other: & &'b B) -> bool { PartialOrd::ge(*self, *other) }
            #[inline]
            fn gt(&self, other: & &'b B) -> bool { PartialOrd::gt(*self, *other) }
        }
        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, A: ?Sized> Ord for &'a A where A: Ord {
            #[inline]
            fn cmp(&self, other: & &'a A) -> Ordering { Ord::cmp(*self, *other) }
        }
        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, A: ?Sized> Eq for &'a A where A: Eq {}

        // &mut pointers

        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, 'b, A: ?Sized, B: ?Sized> PartialEq<&'b mut B> for &'a mut A where A: PartialEq<B> {
            #[inline]
            fn eq(&self, other: &&'b mut B) -> bool { PartialEq::eq(*self, *other) }
            #[inline]
            fn ne(&self, other: &&'b mut B) -> bool { PartialEq::ne(*self, *other) }
        }
        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, 'b, A: ?Sized, B: ?Sized> PartialOrd<&'b mut B> for &'a mut A where A: PartialOrd<B> {
            #[inline]
            fn partial_cmp(&self, other: &&'b mut B) -> Option<Ordering> {
                PartialOrd::partial_cmp(*self, *other)
            }
            #[inline]
            fn lt(&self, other: &&'b mut B) -> bool { PartialOrd::lt(*self, *other) }
            #[inline]
            fn le(&self, other: &&'b mut B) -> bool { PartialOrd::le(*self, *other) }
            #[inline]
            fn ge(&self, other: &&'b mut B) -> bool { PartialOrd::ge(*self, *other) }
            #[inline]
            fn gt(&self, other: &&'b mut B) -> bool { PartialOrd::gt(*self, *other) }
        }
        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, A: ?Sized> Ord for &'a mut A where A: Ord {
            #[inline]
            fn cmp(&self, other: &&'a mut A) -> Ordering { Ord::cmp(*self, *other) }
        }
        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, A: ?Sized> Eq for &'a mut A where A: Eq {}

        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, 'b, A: ?Sized, B: ?Sized> PartialEq<&'b mut B> for &'a A where A: PartialEq<B> {
            #[inline]
            fn eq(&self, other: &&'b mut B) -> bool { PartialEq::eq(*self, *other) }
            #[inline]
            fn ne(&self, other: &&'b mut B) -> bool { PartialEq::ne(*self, *other) }
        }

        #[stable(feature = "rust1", since = "1.0.0")]
        impl<'a, 'b, A: ?Sized, B: ?Sized> PartialEq<&'b B> for &'a mut A where A: PartialEq<B> {
            #[inline]
            fn eq(&self, other: &&'b B) -> bool { PartialEq::eq(*self, *other) }
            #[inline]
            fn ne(&self, other: &&'b B) -> bool { PartialEq::ne(*self, *other) }
        }
    }

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