src/libcore/cmp.rs - rust - Git at Google

 // 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.

 //! Defines the `PartialOrd` and `PartialEq` comparison traits.
 //!
 //! 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.
 //!
 //! For example, to define a type with a customized definition for the PartialEq
 //! operators, you could do the following:
 //!
 //! ```rust
 //! use core::num::SignedInt;
 //!
 //! // Our type.
 //! struct SketchyNum {
 //!     num : int
 //! }
 //!
 //! // Our implementation of `PartialEq` to support `==` and `!=`.
 //! impl PartialEq for SketchyNum {
 //!     // Our custom eq allows numbers which are near each other to be equal! :D
 //!     fn eq(&self, other: &SketchyNum) -> bool {
 //!         (self.num - other.num).abs() < 5
 //!     }
 //! }
 //!
 //! // Now these binary operators will work when applied!
 //! assert!(SketchyNum {num: 37} == SketchyNum {num: 34});
 //! assert!(SketchyNum {num: 25} != SketchyNum {num: 57});
 //! ```

 #![stable]

 use self::Ordering::*;

 use marker::Sized;
 use option::Option::{self, Some, None};

 /// 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>`.
 ///
 /// 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`.
 #[lang="eq"]
 #[stable]
 #[old_orphan_check]
 pub trait PartialEq<Rhs: ?Sized = Self> {
     /// This method tests for `self` and `other` values to be equal, and is used by `==`.
     #[stable]
     fn eq(&self, other: &Rhs) -> bool;

     /// This method tests for `!=`.
     #[inline]
     #[stable]
     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`.
 #[stable]
 pub trait Eq: PartialEq<Self> {
     // FIXME #13101: 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(always)]
     fn assert_receiver_is_total_eq(&self) {}
 }

 /// An ordering is, e.g, a result of a comparison between two values.
 #[derive(Clone, Copy, PartialEq, Show)]
 #[stable]
 pub enum Ordering {
     /// An ordering where a compared value is less [than another].
     #[stable]
     Less = -1i,
     /// An ordering where a compared value is equal [to another].
     #[stable]
     Equal = 0i,
     /// An ordering where a compared value is greater [than another].
     #[stable]
     Greater = 1i,
 }

 impl Ordering {
     /// Reverse the `Ordering`, so that `Less` becomes `Greater` and
     /// vice versa.
     ///
     /// # Example
     ///
     /// ```rust
     /// use std::cmp::Ordering::{Less, Equal, Greater};
     ///
     /// assert_eq!(Less.reverse(), Greater);
     /// assert_eq!(Equal.reverse(), Equal);
     /// assert_eq!(Greater.reverse(), Less);
     ///
     /// let mut data: &mut [_] = &mut [2u, 10, 5, 8];
     ///
     /// // sort the array from largest to smallest.
     /// data.sort_by(|a, b| a.cmp(b).reverse());
     ///
     /// let b: &mut [_] = &mut [10u, 8, 5, 2];
     /// assert!(data == b);
     /// ```
     #[inline]
     #[stable]
     pub fn reverse(self) -> Ordering {
         unsafe {
             // this compiles really nicely (to a single instruction);
             // an explicit match has a pile of branches and
             // comparisons.
             //
             // NB. it is safe because of the explicit discriminants
             // given above.
             ::mem::transmute::<_, Ordering>(-(self as i8))
         }
     }
 }

 /// 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 `>`.
 #[stable]
 pub trait Ord: Eq + PartialOrd<Self> {
     /// This method returns an ordering between `self` and `other` values.
     ///
     /// By convention, `self.cmp(&other)` returns the ordering matching
     /// the expression `self <operator> other` if true.  For example:
     ///
     /// ```
     /// use std::cmp::Ordering::{Less, Equal, Greater};
     ///
     /// assert_eq!( 5u.cmp(&10), Less);     // because 5 < 10
     /// assert_eq!(10u.cmp(&5),  Greater);  // because 10 > 5
     /// assert_eq!( 5u.cmp(&5),  Equal);    // because 5 == 5
     /// ```
     #[stable]
     fn cmp(&self, other: &Self) -> Ordering;
 }

 #[stable]
 impl Eq for Ordering {}

 #[stable]
 impl Ord for Ordering {
     #[inline]
     #[stable]
     fn cmp(&self, other: &Ordering) -> Ordering {
         (*self as int).cmp(&(*other as int))
     }
 }

 #[stable]
 impl PartialOrd for Ordering {
     #[inline]
     #[stable]
     fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
         (*self as int).partial_cmp(&(*other as int))
     }
 }

 /// 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)` and vice versa; 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>`.
 ///
 /// 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).
 #[lang="ord"]
 #[stable]
 pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
     /// This method returns an ordering between `self` and `other` values
     /// if one exists.
     #[stable]
     fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;

     /// This method tests less than (for `self` and `other`) and is used by the `<` operator.
     #[inline]
     #[stable]
     fn lt(&self, other: &Rhs) -> bool {
         match self.partial_cmp(other) {
             Some(Less) => true,
             _ => false,
         }
     }

     /// This method tests less than or equal to (`<=`).
     #[inline]
     #[stable]
     fn le(&self, other: &Rhs) -> bool {
         match self.partial_cmp(other) {
             Some(Less) | Some(Equal) => true,
             _ => false,
         }
     }

     /// This method tests greater than (`>`).
     #[inline]
     #[stable]
     fn gt(&self, other: &Rhs) -> bool {
         match self.partial_cmp(other) {
             Some(Greater) => true,
             _ => false,
         }
     }

     /// This method tests greater than or equal to (`>=`).
     #[inline]
     #[stable]
     fn ge(&self, other: &Rhs) -> bool {
         match self.partial_cmp(other) {
             Some(Greater) | Some(Equal) => true,
             _ => false,
         }
     }
 }

 /// Compare and return the minimum of two values.
 #[inline]
 #[stable]
 pub fn min<T: Ord>(v1: T, v2: T) -> T {
     if v1 < v2 { v1 } else { v2 }
 }

 /// Compare and return the maximum of two values.
 #[inline]
 #[stable]
 pub fn max<T: Ord>(v1: T, v2: T) -> T {
     if v1 > v2 { v1 } else { v2 }
 }

 /// Compare and return the minimum of two values if there is one.
 ///
 /// Returns the first argument if the comparison determines them to be equal.
 #[inline]
 #[unstable]
 pub fn partial_min<T: PartialOrd>(v1: T, v2: T) -> Option<T> {
     match v1.partial_cmp(&v2) {
         Some(Less) | Some(Equal) => Some(v1),
         Some(Greater) => Some(v2),
         None => None
     }
 }

 /// Compare and return the maximum of two values if there is one.
 ///
 /// Returns the first argument if the comparison determines them to be equal.
 #[inline]
 #[unstable]
 pub fn partial_max<T: PartialOrd>(v1: T, v2: T) -> Option<T> {
     match v1.partial_cmp(&v2) {
         Some(Less) => Some(v2),
         Some(Equal) | Some(Greater) => Some(v1),
         None => None
     }
 }

 // Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
 mod impls {
     use cmp::{PartialOrd, Ord, PartialEq, Eq, Ordering};
     use cmp::Ordering::{Less, Greater, Equal};
     use marker::Sized;
     use option::Option;
     use option::Option::{Some, None};

     macro_rules! partial_eq_impl {
         ($($t:ty)*) => ($(
             #[stable]
             impl PartialEq for $t {
                 #[inline]
                 fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
                 #[inline]
                 fn ne(&self, other: &$t) -> bool { (*self) != (*other) }
             }
         )*)
     }

     #[stable]
     impl PartialEq for () {
         #[inline]
         fn eq(&self, _other: &()) -> bool { true }
         #[inline]
         fn ne(&self, _other: &()) -> bool { false }
     }

     partial_eq_impl! {
         bool char uint u8 u16 u32 u64 int i8 i16 i32 i64 f32 f64
     }

     macro_rules! eq_impl {
         ($($t:ty)*) => ($(
             #[stable]
             impl Eq for $t {}
         )*)
     }

     eq_impl! { () bool char uint u8 u16 u32 u64 int i8 i16 i32 i64 }

     macro_rules! partial_ord_impl {
         ($($t:ty)*) => ($(
             #[stable]
             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]
     impl PartialOrd for () {
         #[inline]
         fn partial_cmp(&self, _: &()) -> Option<Ordering> {
             Some(Equal)
         }
     }

     #[stable]
     impl PartialOrd for bool {
         #[inline]
         fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
             (*self as u8).partial_cmp(&(*other as u8))
         }
     }

     partial_ord_impl! { char uint u8 u16 u32 u64 int i8 i16 i32 i64 f32 f64 }

     macro_rules! ord_impl {
         ($($t:ty)*) => ($(
             #[stable]
             impl Ord for $t {
                 #[inline]
                 fn cmp(&self, other: &$t) -> Ordering {
                     if *self < *other { Less }
                     else if *self > *other { Greater }
                     else { Equal }
                 }
             }
         )*)
     }

     #[stable]
     impl Ord for () {
         #[inline]
         fn cmp(&self, _other: &()) -> Ordering { Equal }
     }

     #[stable]
     impl Ord for bool {
         #[inline]
         fn cmp(&self, other: &bool) -> Ordering {
             (*self as u8).cmp(&(*other as u8))
         }
     }

     ord_impl! { char uint u8 u16 u32 u64 int i8 i16 i32 i64 }

     // & pointers

     #[stable]
     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]
     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]
     impl<'a, A: ?Sized> Ord for &'a A where A: Ord {
         #[inline]
         fn cmp(&self, other: & &'a A) -> Ordering { Ord::cmp(*self, *other) }
     }
     #[stable]
     impl<'a, A: ?Sized> Eq for &'a A where A: Eq {}

     // &mut pointers

     #[stable]
     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]
     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]
     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]
     impl<'a, A: ?Sized> Eq for &'a mut A where A: Eq {}

     #[stable]
     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]
     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) }
     }
 }
	// 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.

	//! Defines the `PartialOrd` and `PartialEq` comparison traits.
	//!
	//! 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.
	//!
	//! For example, to define a type with a customized definition for the PartialEq
	//! operators, you could do the following:
	//!
	//! ```rust
	//! use core::num::SignedInt;
	//!
	//! // Our type.
	//! struct SketchyNum {
	//! num : int
	//! }
	//!
	//! // Our implementation of `PartialEq` to support `==` and `!=`.
	//! impl PartialEq for SketchyNum {
	//! // Our custom eq allows numbers which are near each other to be equal! :D
	//! fn eq(&self, other: &SketchyNum) -> bool {
	//! (self.num - other.num).abs() < 5
	//! }
	//! }
	//!
	//! // Now these binary operators will work when applied!
	//! assert!(SketchyNum {num: 37} == SketchyNum {num: 34});
	//! assert!(SketchyNum {num: 25} != SketchyNum {num: 57});
	//! ```

	#![stable]

	use self::Ordering::*;

	use marker::Sized;
	use option::Option::{self, Some, None};

	/// 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>`.
	///
	/// 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`.
	#[lang="eq"]
	#[stable]
	#[old_orphan_check]
	pub trait PartialEq<Rhs: ?Sized = Self> {
	/// This method tests for `self` and `other` values to be equal, and is used by `==`.
	#[stable]
	fn eq(&self, other: &Rhs) -> bool;

	/// This method tests for `!=`.
	#[inline]
	#[stable]
	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`.
	#[stable]
	pub trait Eq: PartialEq<Self> {
	// FIXME #13101: 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(always)]
	fn assert_receiver_is_total_eq(&self) {}
	}

	/// An ordering is, e.g, a result of a comparison between two values.
	#[derive(Clone, Copy, PartialEq, Show)]
	#[stable]
	pub enum Ordering {
	/// An ordering where a compared value is less [than another].
	#[stable]
	Less = -1i,
	/// An ordering where a compared value is equal [to another].
	#[stable]
	Equal = 0i,
	/// An ordering where a compared value is greater [than another].
	#[stable]
	Greater = 1i,
	}

	impl Ordering {
	/// Reverse the `Ordering`, so that `Less` becomes `Greater` and
	/// vice versa.
	///
	/// # Example
	///
	/// ```rust
	/// use std::cmp::Ordering::{Less, Equal, Greater};
	///
	/// assert_eq!(Less.reverse(), Greater);
	/// assert_eq!(Equal.reverse(), Equal);
	/// assert_eq!(Greater.reverse(), Less);
	///
	/// let mut data: &mut [_] = &mut [2u, 10, 5, 8];
	///
	/// // sort the array from largest to smallest.
	/// data.sort_by(\|a, b\| a.cmp(b).reverse());
	///
	/// let b: &mut [_] = &mut [10u, 8, 5, 2];
	/// assert!(data == b);
	/// ```
	#[inline]
	#[stable]
	pub fn reverse(self) -> Ordering {
	unsafe {
	// this compiles really nicely (to a single instruction);
	// an explicit match has a pile of branches and
	// comparisons.
	//
	// NB. it is safe because of the explicit discriminants
	// given above.
	::mem::transmute::<_, Ordering>(-(self as i8))
	}
	}
	}

	/// 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 `>`.
	#[stable]
	pub trait Ord: Eq + PartialOrd<Self> {
	/// This method returns an ordering between `self` and `other` values.
	///
	/// By convention, `self.cmp(&other)` returns the ordering matching
	/// the expression `self <operator> other` if true. For example:
	///
	/// ```
	/// use std::cmp::Ordering::{Less, Equal, Greater};
	///
	/// assert_eq!( 5u.cmp(&10), Less); // because 5 < 10
	/// assert_eq!(10u.cmp(&5), Greater); // because 10 > 5
	/// assert_eq!( 5u.cmp(&5), Equal); // because 5 == 5
	/// ```
	#[stable]
	fn cmp(&self, other: &Self) -> Ordering;
	}

	#[stable]
	impl Eq for Ordering {}

	#[stable]
	impl Ord for Ordering {
	#[inline]
	#[stable]
	fn cmp(&self, other: &Ordering) -> Ordering {
	(self as int).cmp(&(other as int))
	}
	}

	#[stable]
	impl PartialOrd for Ordering {
	#[inline]
	#[stable]
	fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
	(self as int).partial_cmp(&(other as int))
	}
	}

	/// 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)` and vice versa; 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>`.
	///
	/// 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).
	#[lang="ord"]
	#[stable]
	pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
	/// This method returns an ordering between `self` and `other` values
	/// if one exists.
	#[stable]
	fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;

	/// This method tests less than (for `self` and `other`) and is used by the `<` operator.
	#[inline]
	#[stable]
	fn lt(&self, other: &Rhs) -> bool {
	match self.partial_cmp(other) {
	Some(Less) => true,
	_ => false,
	}
	}

	/// This method tests less than or equal to (`<=`).
	#[inline]
	#[stable]
	fn le(&self, other: &Rhs) -> bool {
	match self.partial_cmp(other) {
	Some(Less) \| Some(Equal) => true,
	_ => false,
	}
	}

	/// This method tests greater than (`>`).
	#[inline]
	#[stable]
	fn gt(&self, other: &Rhs) -> bool {
	match self.partial_cmp(other) {
	Some(Greater) => true,
	_ => false,
	}
	}

	/// This method tests greater than or equal to (`>=`).
	#[inline]
	#[stable]
	fn ge(&self, other: &Rhs) -> bool {
	match self.partial_cmp(other) {
	Some(Greater) \| Some(Equal) => true,
	_ => false,
	}
	}
	}

	/// Compare and return the minimum of two values.
	#[inline]
	#[stable]
	pub fn min<T: Ord>(v1: T, v2: T) -> T {
	if v1 < v2 { v1 } else { v2 }
	}

	/// Compare and return the maximum of two values.
	#[inline]
	#[stable]
	pub fn max<T: Ord>(v1: T, v2: T) -> T {
	if v1 > v2 { v1 } else { v2 }
	}

	/// Compare and return the minimum of two values if there is one.
	///
	/// Returns the first argument if the comparison determines them to be equal.
	#[inline]
	#[unstable]
	pub fn partial_min<T: PartialOrd>(v1: T, v2: T) -> Option<T> {
	match v1.partial_cmp(&v2) {
	Some(Less) \| Some(Equal) => Some(v1),
	Some(Greater) => Some(v2),
	None => None
	}
	}

	/// Compare and return the maximum of two values if there is one.
	///
	/// Returns the first argument if the comparison determines them to be equal.
	#[inline]
	#[unstable]
	pub fn partial_max<T: PartialOrd>(v1: T, v2: T) -> Option<T> {
	match v1.partial_cmp(&v2) {
	Some(Less) => Some(v2),
	Some(Equal) \| Some(Greater) => Some(v1),
	None => None
	}
	}

	// Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
	mod impls {
	use cmp::{PartialOrd, Ord, PartialEq, Eq, Ordering};
	use cmp::Ordering::{Less, Greater, Equal};
	use marker::Sized;
	use option::Option;
	use option::Option::{Some, None};

	macro_rules! partial_eq_impl {
	($($t:ty)*) => ($(
	#[stable]
	impl PartialEq for $t {
	#[inline]
	fn eq(&self, other: &$t) -> bool { (self) == (other) }
	#[inline]
	fn ne(&self, other: &$t) -> bool { (self) != (other) }
	}
	)*)
	}

	#[stable]
	impl PartialEq for () {
	#[inline]
	fn eq(&self, _other: &()) -> bool { true }
	#[inline]
	fn ne(&self, _other: &()) -> bool { false }
	}

	partial_eq_impl! {
	bool char uint u8 u16 u32 u64 int i8 i16 i32 i64 f32 f64
	}

	macro_rules! eq_impl {
	($($t:ty)*) => ($(
	#[stable]
	impl Eq for $t {}
	)*)
	}

	eq_impl! { () bool char uint u8 u16 u32 u64 int i8 i16 i32 i64 }

	macro_rules! partial_ord_impl {
	($($t:ty)*) => ($(
	#[stable]
	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]
	impl PartialOrd for () {
	#[inline]
	fn partial_cmp(&self, _: &()) -> Option<Ordering> {
	Some(Equal)
	}
	}

	#[stable]
	impl PartialOrd for bool {
	#[inline]
	fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
	(self as u8).partial_cmp(&(other as u8))
	}
	}

	partial_ord_impl! { char uint u8 u16 u32 u64 int i8 i16 i32 i64 f32 f64 }

	macro_rules! ord_impl {
	($($t:ty)*) => ($(
	#[stable]
	impl Ord for $t {
	#[inline]
	fn cmp(&self, other: &$t) -> Ordering {
	if self < other { Less }
	else if self > other { Greater }
	else { Equal }
	}
	}
	)*)
	}

	#[stable]
	impl Ord for () {
	#[inline]
	fn cmp(&self, _other: &()) -> Ordering { Equal }
	}

	#[stable]
	impl Ord for bool {
	#[inline]
	fn cmp(&self, other: &bool) -> Ordering {
	(self as u8).cmp(&(other as u8))
	}
	}

	ord_impl! { char uint u8 u16 u32 u64 int i8 i16 i32 i64 }

	// & pointers

	#[stable]
	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]
	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]
	impl<'a, A: ?Sized> Ord for &'a A where A: Ord {
	#[inline]
	fn cmp(&self, other: & &'a A) -> Ordering { Ord::cmp(self, other) }
	}
	#[stable]
	impl<'a, A: ?Sized> Eq for &'a A where A: Eq {}

	// &mut pointers

	#[stable]
	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]
	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]
	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]
	impl<'a, A: ?Sized> Eq for &'a mut A where A: Eq {}

	#[stable]
	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]
	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) }
	}
	}