library/core/src/cmp.rs

   1 //! Functionality for ordering and comparison.
   2 //!
   3 //! This module contains various tools for ordering and comparing values. In
   4 //! summary:
   5 //!
   6 //! * [`Eq`] and [`PartialEq`] are traits that allow you to define total and
   7 //!   partial equality between values, respectively. Implementing them overloads
   8 //!   the `==` and `!=` operators.
   9 //! * [`Ord`] and [`PartialOrd`] are traits that allow you to define total and
  10 //!   partial orderings between values, respectively. Implementing them overloads
  11 //!   the `<`, `<=`, `>`, and `>=` operators.
  12 //! * [`Ordering`] is an enum returned by the main functions of [`Ord`] and
  13 //!   [`PartialOrd`], and describes an ordering.
  14 //! * [`Reverse`] is a struct that allows you to easily reverse an ordering.
  15 //! * [`max`] and [`min`] are functions that build off of [`Ord`] and allow you
  16 //!   to find the maximum or minimum of two values.
  17 //!
  18 //! For more details, see the respective documentation of each item in the list.
  19 //!
  20 //! [`max`]: Ord::max
  21 //! [`min`]: Ord::min
  22
  23 #![stable(feature = "rust1", since = "1.0.0")]
  24
  25 use self::Ordering::*;
  26
  27 /// Trait for equality comparisons which are [partial equivalence
  28 /// relations](https://en.wikipedia.org/wiki/Partial_equivalence_relation).
  29 ///
  30 /// This trait allows for partial equality, for types that do not have a full
  31 /// equivalence relation. For example, in floating point numbers `NaN != NaN`,
  32 /// so floating point types implement `PartialEq` but not [`Eq`](Eq).
  33 ///
  34 /// Formally, the equality must be (for all `a`, `b` and `c`):
  35 ///
  36 /// - symmetric: `a == b` implies `b == a`; and
  37 /// - transitive: `a == b` and `b == c` implies `a == c`.
  38 ///
  39 /// Note that these requirements mean that the trait itself must be implemented
  40 /// symmetrically and transitively: if `T: PartialEq<U>` and `U: PartialEq<V>`
  41 /// then `U: PartialEq<T>` and `T: PartialEq<V>`.
  42 ///
  43 /// ## Derivable
  44 ///
  45 /// This trait can be used with `#[derive]`. When `derive`d on structs, two
  46 /// instances are equal if all fields are equal, and not equal if any fields
  47 /// are not equal. When `derive`d on enums, each variant is equal to itself
  48 /// and not equal to the other variants.
  49 ///
  50 /// ## How can I implement `PartialEq`?
  51 ///
  52 /// `PartialEq` only requires the [`eq`] method to be implemented; [`ne`] is defined
  53 /// in terms of it by default. Any manual implementation of [`ne`] *must* respect
  54 /// the rule that [`eq`] is a strict inverse of [`ne`]; that is, `!(a == b)` if and
  55 /// only if `a != b`.
  56 ///
  57 /// Implementations of `PartialEq`, [`PartialOrd`], and [`Ord`] *must* agree with
  58 /// each other. It's easy to accidentally make them disagree by deriving some
  59 /// of the traits and manually implementing others.
  60 ///
  61 /// An example implementation for a domain in which two books are considered
  62 /// the same book if their ISBN matches, even if the formats differ:
  63 ///
  64 /// ```
  65 /// enum BookFormat {
  66 ///     Paperback,
  67 ///     Hardback,
  68 ///     Ebook,
  69 /// }
  70 ///
  71 /// struct Book {
  72 ///     isbn: i32,
  73 ///     format: BookFormat,
  74 /// }
  75 ///
  76 /// impl PartialEq for Book {
  77 ///     fn eq(&self, other: &Self) -> bool {
  78 ///         self.isbn == other.isbn
  79 ///     }
  80 /// }
  81 ///
  82 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
  83 /// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
  84 /// let b3 = Book { isbn: 10, format: BookFormat::Paperback };
  85 ///
  86 /// assert!(b1 == b2);
  87 /// assert!(b1 != b3);
  88 /// ```
  89 ///
  90 /// ## How can I compare two different types?
  91 ///
  92 /// The type you can compare with is controlled by `PartialEq`'s type parameter.
  93 /// For example, let's tweak our previous code a bit:
  94 ///
  95 /// ```
  96 /// // The derive implements <BookFormat> == <BookFormat> comparisons
  97 /// #[derive(PartialEq)]
  98 /// enum BookFormat {
  99 ///     Paperback,
 100 ///     Hardback,
 101 ///     Ebook,
 102 /// }
 103 ///
 104 /// struct Book {
 105 ///     isbn: i32,
 106 ///     format: BookFormat,
 107 /// }
 108 ///
 109 /// // Implement <Book> == <BookFormat> comparisons
 110 /// impl PartialEq<BookFormat> for Book {
 111 ///     fn eq(&self, other: &BookFormat) -> bool {
 112 ///         self.format == *other
 113 ///     }
 114 /// }
 115 ///
 116 /// // Implement <BookFormat> == <Book> comparisons
 117 /// impl PartialEq<Book> for BookFormat {
 118 ///     fn eq(&self, other: &Book) -> bool {
 119 ///         *self == other.format
 120 ///     }
 121 /// }
 122 ///
 123 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
 124 ///
 125 /// assert!(b1 == BookFormat::Paperback);
 126 /// assert!(BookFormat::Ebook != b1);
 127 /// ```
 128 ///
 129 /// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
 130 /// we allow `BookFormat`s to be compared with `Book`s.
 131 ///
 132 /// A comparison like the one above, which ignores some fields of the struct,
 133 /// can be dangerous. It can easily lead to an unintended violation of the
 134 /// requirements for a partial equivalence relation. For example, if we kept
 135 /// the above implementation of `PartialEq<Book>` for `BookFormat` and added an
 136 /// implementation of `PartialEq<Book>` for `Book` (either via a `#[derive]` or
 137 /// via the manual implementation from the first example) then the result would
 138 /// violate transitivity:
 139 ///
 140 /// ```should_panic
 141 /// #[derive(PartialEq)]
 142 /// enum BookFormat {
 143 ///     Paperback,
 144 ///     Hardback,
 145 ///     Ebook,
 146 /// }
 147 ///
 148 /// #[derive(PartialEq)]
 149 /// struct Book {
 150 ///     isbn: i32,
 151 ///     format: BookFormat,
 152 /// }
 153 ///
 154 /// impl PartialEq<BookFormat> for Book {
 155 ///     fn eq(&self, other: &BookFormat) -> bool {
 156 ///         self.format == *other
 157 ///     }
 158 /// }
 159 ///
 160 /// impl PartialEq<Book> for BookFormat {
 161 ///     fn eq(&self, other: &Book) -> bool {
 162 ///         *self == other.format
 163 ///     }
 164 /// }
 165 ///
 166 /// fn main() {
 167 ///     let b1 = Book { isbn: 1, format: BookFormat::Paperback };
 168 ///     let b2 = Book { isbn: 2, format: BookFormat::Paperback };
 169 ///
 170 ///     assert!(b1 == BookFormat::Paperback);
 171 ///     assert!(BookFormat::Paperback == b2);
 172 ///
 173 ///     // The following should hold by transitivity but doesn't.
 174 ///     assert!(b1 == b2); // <-- PANICS
 175 /// }
 176 /// ```
 177 ///
 178 /// # Examples
 179 ///
 180 /// ```
 181 /// let x: u32 = 0;
 182 /// let y: u32 = 1;
 183 ///
 184 /// assert_eq!(x == y, false);
 185 /// assert_eq!(x.eq(&y), false);
 186 /// ```
 187 ///
 188 /// [`eq`]: PartialEq::eq
 189 /// [`ne`]: PartialEq::ne
 190 #[lang = "eq"]
 191 #[stable(feature = "rust1", since = "1.0.0")]
 192 #[doc(alias = "==")]
 193 #[doc(alias = "!=")]
 194 #[rustc_on_unimplemented(
 195     message = "can't compare `{Self}` with `{Rhs}`",
 196     label = "no implementation for `{Self} == {Rhs}`"
 197 )]
 198 pub trait PartialEq<Rhs: ?Sized = Self> {
 199     /// This method tests for `self` and `other` values to be equal, and is used
 200     /// by `==`.
 201     #[must_use]
 202     #[stable(feature = "rust1", since = "1.0.0")]
 203     fn eq(&self, other: &Rhs) -> bool;
 204
 205     /// This method tests for `!=`.
 206     #[inline]
 207     #[must_use]
 208     #[stable(feature = "rust1", since = "1.0.0")]
 209     fn ne(&self, other: &Rhs) -> bool {
 210         !self.eq(other)
 211     }
 212 }
 213
 214 /// Derive macro generating an impl of the trait `PartialEq`.
 215 #[rustc_builtin_macro]
 216 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 217 #[allow_internal_unstable(core_intrinsics, structural_match)]
 218 pub macro PartialEq($item:item) {
 219     /* compiler built-in */
 220 }
 221
 222 /// Trait for equality comparisons which are [equivalence relations](
 223 /// https://en.wikipedia.org/wiki/Equivalence_relation).
 224 ///
 225 /// This means, that in addition to `a == b` and `a != b` being strict inverses, the equality must
 226 /// be (for all `a`, `b` and `c`):
 227 ///
 228 /// - reflexive: `a == a`;
 229 /// - symmetric: `a == b` implies `b == a`; and
 230 /// - transitive: `a == b` and `b == c` implies `a == c`.
 231 ///
 232 /// This property cannot be checked by the compiler, and therefore `Eq` implies
 233 /// [`PartialEq`], and has no extra methods.
 234 ///
 235 /// ## Derivable
 236 ///
 237 /// This trait can be used with `#[derive]`. When `derive`d, because `Eq` has
 238 /// no extra methods, it is only informing the compiler that this is an
 239 /// equivalence relation rather than a partial equivalence relation. Note that
 240 /// the `derive` strategy requires all fields are `Eq`, which isn't
 241 /// always desired.
 242 ///
 243 /// ## How can I implement `Eq`?
 244 ///
 245 /// If you cannot use the `derive` strategy, specify that your type implements
 246 /// `Eq`, which has no methods:
 247 ///
 248 /// ```
 249 /// enum BookFormat { Paperback, Hardback, Ebook }
 250 /// struct Book {
 251 ///     isbn: i32,
 252 ///     format: BookFormat,
 253 /// }
 254 /// impl PartialEq for Book {
 255 ///     fn eq(&self, other: &Self) -> bool {
 256 ///         self.isbn == other.isbn
 257 ///     }
 258 /// }
 259 /// impl Eq for Book {}
 260 /// ```
 261 #[doc(alias = "==")]
 262 #[doc(alias = "!=")]
 263 #[stable(feature = "rust1", since = "1.0.0")]
 264 pub trait Eq: PartialEq<Self> {
 265     // this method is used solely by #[deriving] to assert
 266     // that every component of a type implements #[deriving]
 267     // itself, the current deriving infrastructure means doing this
 268     // assertion without using a method on this trait is nearly
 269     // impossible.
 270     //
 271     // This should never be implemented by hand.
 272     #[doc(hidden)]
 273     #[inline]
 274     #[stable(feature = "rust1", since = "1.0.0")]
 275     fn assert_receiver_is_total_eq(&self) {}
 276 }
 277
 278 /// Derive macro generating an impl of the trait `Eq`.
 279 #[rustc_builtin_macro]
 280 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 281 #[allow_internal_unstable(core_intrinsics, derive_eq, structural_match)]
 282 pub macro Eq($item:item) {
 283     /* compiler built-in */
 284 }
 285
 286 // FIXME: this struct is used solely by #[derive] to
 287 // assert that every component of a type implements Eq.
 288 //
 289 // This struct should never appear in user code.
 290 #[doc(hidden)]
 291 #[allow(missing_debug_implementations)]
 292 #[unstable(feature = "derive_eq", reason = "deriving hack, should not be public", issue = "none")]
 293 pub struct AssertParamIsEq<T: Eq + ?Sized> {
 294     _field: crate::marker::PhantomData<T>,
 295 }
 296
 297 /// An `Ordering` is the result of a comparison between two values.
 298 ///
 299 /// # Examples
 300 ///
 301 /// ```
 302 /// use std::cmp::Ordering;
 303 ///
 304 /// let result = 1.cmp(&2);
 305 /// assert_eq!(Ordering::Less, result);
 306 ///
 307 /// let result = 1.cmp(&1);
 308 /// assert_eq!(Ordering::Equal, result);
 309 ///
 310 /// let result = 2.cmp(&1);
 311 /// assert_eq!(Ordering::Greater, result);
 312 /// ```
 313 #[derive(Clone, Copy, PartialEq, Debug, Hash)]
 314 #[stable(feature = "rust1", since = "1.0.0")]
 315 pub enum Ordering {
 316     /// An ordering where a compared value is less than another.
 317     #[stable(feature = "rust1", since = "1.0.0")]
 318     Less = -1,
 319     /// An ordering where a compared value is equal to another.
 320     #[stable(feature = "rust1", since = "1.0.0")]
 321     Equal = 0,
 322     /// An ordering where a compared value is greater than another.
 323     #[stable(feature = "rust1", since = "1.0.0")]
 324     Greater = 1,
 325 }
 326
 327 impl Ordering {
 328     /// Reverses the `Ordering`.
 329     ///
 330     /// * `Less` becomes `Greater`.
 331     /// * `Greater` becomes `Less`.
 332     /// * `Equal` becomes `Equal`.
 333     ///
 334     /// # Examples
 335     ///
 336     /// Basic behavior:
 337     ///
 338     /// ```
 339     /// use std::cmp::Ordering;
 340     ///
 341     /// assert_eq!(Ordering::Less.reverse(), Ordering::Greater);
 342     /// assert_eq!(Ordering::Equal.reverse(), Ordering::Equal);
 343     /// assert_eq!(Ordering::Greater.reverse(), Ordering::Less);
 344     /// ```
 345     ///
 346     /// This method can be used to reverse a comparison:
 347     ///
 348     /// ```
 349     /// let data: &mut [_] = &mut [2, 10, 5, 8];
 350     ///
 351     /// // sort the array from largest to smallest.
 352     /// data.sort_by(|a, b| a.cmp(b).reverse());
 353     ///
 354     /// let b: &mut [_] = &mut [10, 8, 5, 2];
 355     /// assert!(data == b);
 356     /// ```
 357     #[inline]
 358     #[must_use]
 359     #[rustc_const_stable(feature = "const_ordering", since = "1.48.0")]
 360     #[stable(feature = "rust1", since = "1.0.0")]
 361     pub const fn reverse(self) -> Ordering {
 362         match self {
 363             Less => Greater,
 364             Equal => Equal,
 365             Greater => Less,
 366         }
 367     }
 368
 369     /// Chains two orderings.
 370     ///
 371     /// Returns `self` when it's not `Equal`. Otherwise returns `other`.
 372     ///
 373     /// # Examples
 374     ///
 375     /// ```
 376     /// use std::cmp::Ordering;
 377     ///
 378     /// let result = Ordering::Equal.then(Ordering::Less);
 379     /// assert_eq!(result, Ordering::Less);
 380     ///
 381     /// let result = Ordering::Less.then(Ordering::Equal);
 382     /// assert_eq!(result, Ordering::Less);
 383     ///
 384     /// let result = Ordering::Less.then(Ordering::Greater);
 385     /// assert_eq!(result, Ordering::Less);
 386     ///
 387     /// let result = Ordering::Equal.then(Ordering::Equal);
 388     /// assert_eq!(result, Ordering::Equal);
 389     ///
 390     /// let x: (i64, i64, i64) = (1, 2, 7);
 391     /// let y: (i64, i64, i64) = (1, 5, 3);
 392     /// let result = x.0.cmp(&y.0).then(x.1.cmp(&y.1)).then(x.2.cmp(&y.2));
 393     ///
 394     /// assert_eq!(result, Ordering::Less);
 395     /// ```
 396     #[inline]
 397     #[must_use]
 398     #[rustc_const_stable(feature = "const_ordering", since = "1.48.0")]
 399     #[stable(feature = "ordering_chaining", since = "1.17.0")]
 400     pub const fn then(self, other: Ordering) -> Ordering {
 401         match self {
 402             Equal => other,
 403             _ => self,
 404         }
 405     }
 406
 407     /// Chains the ordering with the given function.
 408     ///
 409     /// Returns `self` when it's not `Equal`. Otherwise calls `f` and returns
 410     /// the result.
 411     ///
 412     /// # Examples
 413     ///
 414     /// ```
 415     /// use std::cmp::Ordering;
 416     ///
 417     /// let result = Ordering::Equal.then_with(|| Ordering::Less);
 418     /// assert_eq!(result, Ordering::Less);
 419     ///
 420     /// let result = Ordering::Less.then_with(|| Ordering::Equal);
 421     /// assert_eq!(result, Ordering::Less);
 422     ///
 423     /// let result = Ordering::Less.then_with(|| Ordering::Greater);
 424     /// assert_eq!(result, Ordering::Less);
 425     ///
 426     /// let result = Ordering::Equal.then_with(|| Ordering::Equal);
 427     /// assert_eq!(result, Ordering::Equal);
 428     ///
 429     /// let x: (i64, i64, i64) = (1, 2, 7);
 430     /// let y: (i64, i64, i64)  = (1, 5, 3);
 431     /// let result = x.0.cmp(&y.0).then_with(|| x.1.cmp(&y.1)).then_with(|| x.2.cmp(&y.2));
 432     ///
 433     /// assert_eq!(result, Ordering::Less);
 434     /// ```
 435     #[inline]
 436     #[must_use]
 437     #[stable(feature = "ordering_chaining", since = "1.17.0")]
 438     pub fn then_with<F: FnOnce() -> Ordering>(self, f: F) -> Ordering {
 439         match self {
 440             Equal => f(),
 441             _ => self,
 442         }
 443     }
 444 }
 445
 446 /// A helper struct for reverse ordering.
 447 ///
 448 /// This struct is a helper to be used with functions like [`Vec::sort_by_key`] and
 449 /// can be used to reverse order a part of a key.
 450 ///
 451 /// [`Vec::sort_by_key`]: ../../std/vec/struct.Vec.html#method.sort_by_key
 452 ///
 453 /// # Examples
 454 ///
 455 /// ```
 456 /// use std::cmp::Reverse;
 457 ///
 458 /// let mut v = vec![1, 2, 3, 4, 5, 6];
 459 /// v.sort_by_key(|&num| (num > 3, Reverse(num)));
 460 /// assert_eq!(v, vec![3, 2, 1, 6, 5, 4]);
 461 /// ```
 462 #[derive(PartialEq, Eq, Debug, Copy, Clone, Default, Hash)]
 463 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 464 pub struct Reverse<T>(#[stable(feature = "reverse_cmp_key", since = "1.19.0")] pub T);
 465
 466 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 467 impl<T: PartialOrd> PartialOrd for Reverse<T> {
 468     #[inline]
 469     fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
 470         other.0.partial_cmp(&self.0)
 471     }
 472
 473     #[inline]
 474     fn lt(&self, other: &Self) -> bool {
 475         other.0 < self.0
 476     }
 477     #[inline]
 478     fn le(&self, other: &Self) -> bool {
 479         other.0 <= self.0
 480     }
 481     #[inline]
 482     fn gt(&self, other: &Self) -> bool {
 483         other.0 > self.0
 484     }
 485     #[inline]
 486     fn ge(&self, other: &Self) -> bool {
 487         other.0 >= self.0
 488     }
 489 }
 490
 491 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 492 impl<T: Ord> Ord for Reverse<T> {
 493     #[inline]
 494     fn cmp(&self, other: &Reverse<T>) -> Ordering {
 495         other.0.cmp(&self.0)
 496     }
 497 }
 498
 499 /// Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order).
 500 ///
 501 /// An order is a total order if it is (for all `a`, `b` and `c`):
 502 ///
 503 /// - total and asymmetric: exactly one of `a < b`, `a == b` or `a > b` is true; and
 504 /// - transitive, `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
 505 ///
 506 /// ## Derivable
 507 ///
 508 /// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
 509 /// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
 510 /// When `derive`d on enums, variants are ordered by their top-to-bottom discriminant order.
 511 ///
 512 /// ## How can I implement `Ord`?
 513 ///
 514 /// `Ord` requires that the type also be [`PartialOrd`] and [`Eq`] (which requires [`PartialEq`]).
 515 ///
 516 /// Then you must define an implementation for [`cmp`]. You may find it useful to use
 517 /// [`cmp`] on your type's fields.
 518 ///
 519 /// Implementations of [`PartialEq`], [`PartialOrd`], and `Ord` *must*
 520 /// agree with each other. That is, `a.cmp(b) == Ordering::Equal` if
 521 /// and only if `a == b` and `Some(a.cmp(b)) == a.partial_cmp(b)` for
 522 /// all `a` and `b`. It's easy to accidentally make them disagree by
 523 /// deriving some of the traits and manually implementing others.
 524 ///
 525 /// Here's an example where you want to sort people by height only, disregarding `id`
 526 /// and `name`:
 527 ///
 528 /// ```
 529 /// use std::cmp::Ordering;
 530 ///
 531 /// #[derive(Eq)]
 532 /// struct Person {
 533 ///     id: u32,
 534 ///     name: String,
 535 ///     height: u32,
 536 /// }
 537 ///
 538 /// impl Ord for Person {
 539 ///     fn cmp(&self, other: &Self) -> Ordering {
 540 ///         self.height.cmp(&other.height)
 541 ///     }
 542 /// }
 543 ///
 544 /// impl PartialOrd for Person {
 545 ///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 546 ///         Some(self.cmp(other))
 547 ///     }
 548 /// }
 549 ///
 550 /// impl PartialEq for Person {
 551 ///     fn eq(&self, other: &Self) -> bool {
 552 ///         self.height == other.height
 553 ///     }
 554 /// }
 555 /// ```
 556 ///
 557 /// [`cmp`]: Ord::cmp
 558 #[doc(alias = "<")]
 559 #[doc(alias = ">")]
 560 #[doc(alias = "<=")]
 561 #[doc(alias = ">=")]
 562 #[stable(feature = "rust1", since = "1.0.0")]
 563 pub trait Ord: Eq + PartialOrd<Self> {
 564     /// This method returns an [`Ordering`] between `self` and `other`.
 565     ///
 566     /// By convention, `self.cmp(&other)` returns the ordering matching the expression
 567     /// `self <operator> other` if true.
 568     ///
 569     /// # Examples
 570     ///
 571     /// ```
 572     /// use std::cmp::Ordering;
 573     ///
 574     /// assert_eq!(5.cmp(&10), Ordering::Less);
 575     /// assert_eq!(10.cmp(&5), Ordering::Greater);
 576     /// assert_eq!(5.cmp(&5), Ordering::Equal);
 577     /// ```
 578     #[must_use]
 579     #[stable(feature = "rust1", since = "1.0.0")]
 580     fn cmp(&self, other: &Self) -> Ordering;
 581
 582     /// Compares and returns the maximum of two values.
 583     ///
 584     /// Returns the second argument if the comparison determines them to be equal.
 585     ///
 586     /// # Examples
 587     ///
 588     /// ```
 589     /// assert_eq!(2, 1.max(2));
 590     /// assert_eq!(2, 2.max(2));
 591     /// ```
 592     #[stable(feature = "ord_max_min", since = "1.21.0")]
 593     #[inline]
 594     #[must_use]
 595     fn max(self, other: Self) -> Self
 596     where
 597         Self: Sized,
 598     {
 599         max_by(self, other, Ord::cmp)
 600     }
 601
 602     /// Compares and returns the minimum of two values.
 603     ///
 604     /// Returns the first argument if the comparison determines them to be equal.
 605     ///
 606     /// # Examples
 607     ///
 608     /// ```
 609     /// assert_eq!(1, 1.min(2));
 610     /// assert_eq!(2, 2.min(2));
 611     /// ```
 612     #[stable(feature = "ord_max_min", since = "1.21.0")]
 613     #[inline]
 614     #[must_use]
 615     fn min(self, other: Self) -> Self
 616     where
 617         Self: Sized,
 618     {
 619         min_by(self, other, Ord::cmp)
 620     }
 621
 622     /// Restrict a value to a certain interval.
 623     ///
 624     /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
 625     /// less than `min`. Otherwise this returns `self`.
 626     ///
 627     /// # Panics
 628     ///
 629     /// Panics if `min > max`.
 630     ///
 631     /// # Examples
 632     ///
 633     /// ```
 634     /// #![feature(clamp)]
 635     ///
 636     /// assert!((-3).clamp(-2, 1) == -2);
 637     /// assert!(0.clamp(-2, 1) == 0);
 638     /// assert!(2.clamp(-2, 1) == 1);
 639     /// ```
 640     #[must_use]
 641     #[unstable(feature = "clamp", issue = "44095")]
 642     fn clamp(self, min: Self, max: Self) -> Self
 643     where
 644         Self: Sized,
 645     {
 646         assert!(min <= max);
 647         if self < min {
 648             min
 649         } else if self > max {
 650             max
 651         } else {
 652             self
 653         }
 654     }
 655 }
 656
 657 /// Derive macro generating an impl of the trait `Ord`.
 658 #[rustc_builtin_macro]
 659 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 660 #[allow_internal_unstable(core_intrinsics)]
 661 pub macro Ord($item:item) {
 662     /* compiler built-in */
 663 }
 664
 665 #[stable(feature = "rust1", since = "1.0.0")]
 666 impl Eq for Ordering {}
 667
 668 #[stable(feature = "rust1", since = "1.0.0")]
 669 impl Ord for Ordering {
 670     #[inline]
 671     fn cmp(&self, other: &Ordering) -> Ordering {
 672         (*self as i32).cmp(&(*other as i32))
 673     }
 674 }
 675
 676 #[stable(feature = "rust1", since = "1.0.0")]
 677 impl PartialOrd for Ordering {
 678     #[inline]
 679     fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
 680         (*self as i32).partial_cmp(&(*other as i32))
 681     }
 682 }
 683
 684 /// Trait for values that can be compared for a sort-order.
 685 ///
 686 /// The comparison must satisfy, for all `a`, `b` and `c`:
 687 ///
 688 /// - asymmetry: if `a < b` then `!(a > b)`, as well as `a > b` implying `!(a < b)`; and
 689 /// - transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
 690 ///
 691 /// Note that these requirements mean that the trait itself must be implemented symmetrically and
 692 /// transitively: if `T: PartialOrd<U>` and `U: PartialOrd<V>` then `U: PartialOrd<T>` and `T:
 693 /// PartialOrd<V>`.
 694 ///
 695 /// ## Derivable
 696 ///
 697 /// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
 698 /// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
 699 /// When `derive`d on enums, variants are ordered by their top-to-bottom discriminant order.
 700 ///
 701 /// ## How can I implement `PartialOrd`?
 702 ///
 703 /// `PartialOrd` only requires implementation of the [`partial_cmp`] method, with the others
 704 /// generated from default implementations.
 705 ///
 706 /// However it remains possible to implement the others separately for types which do not have a
 707 /// total order. For example, for floating point numbers, `NaN < 0 == false` and `NaN >= 0 ==
 708 /// false` (cf. IEEE 754-2008 section 5.11).
 709 ///
 710 /// `PartialOrd` requires your type to be [`PartialEq`].
 711 ///
 712 /// Implementations of [`PartialEq`], `PartialOrd`, and [`Ord`] *must* agree with each other. It's
 713 /// easy to accidentally make them disagree by deriving some of the traits and manually
 714 /// implementing others.
 715 ///
 716 /// If your type is [`Ord`], you can implement [`partial_cmp`] by using [`cmp`]:
 717 ///
 718 /// ```
 719 /// use std::cmp::Ordering;
 720 ///
 721 /// #[derive(Eq)]
 722 /// struct Person {
 723 ///     id: u32,
 724 ///     name: String,
 725 ///     height: u32,
 726 /// }
 727 ///
 728 /// impl PartialOrd for Person {
 729 ///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 730 ///         Some(self.cmp(other))
 731 ///     }
 732 /// }
 733 ///
 734 /// impl Ord for Person {
 735 ///     fn cmp(&self, other: &Self) -> Ordering {
 736 ///         self.height.cmp(&other.height)
 737 ///     }
 738 /// }
 739 ///
 740 /// impl PartialEq for Person {
 741 ///     fn eq(&self, other: &Self) -> bool {
 742 ///         self.height == other.height
 743 ///     }
 744 /// }
 745 /// ```
 746 ///
 747 /// You may also find it useful to use [`partial_cmp`] on your type's fields. Here
 748 /// is an example of `Person` types who have a floating-point `height` field that
 749 /// is the only field to be used for sorting:
 750 ///
 751 /// ```
 752 /// use std::cmp::Ordering;
 753 ///
 754 /// struct Person {
 755 ///     id: u32,
 756 ///     name: String,
 757 ///     height: f64,
 758 /// }
 759 ///
 760 /// impl PartialOrd for Person {
 761 ///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 762 ///         self.height.partial_cmp(&other.height)
 763 ///     }
 764 /// }
 765 ///
 766 /// impl PartialEq for Person {
 767 ///     fn eq(&self, other: &Self) -> bool {
 768 ///         self.height == other.height
 769 ///     }
 770 /// }
 771 /// ```
 772 ///
 773 /// # Examples
 774 ///
 775 /// ```
 776 /// let x : u32 = 0;
 777 /// let y : u32 = 1;
 778 ///
 779 /// assert_eq!(x < y, true);
 780 /// assert_eq!(x.lt(&y), true);
 781 /// ```
 782 ///
 783 /// [`partial_cmp`]: PartialOrd::partial_cmp
 784 /// [`cmp`]: Ord::cmp
 785 #[lang = "partial_ord"]
 786 #[stable(feature = "rust1", since = "1.0.0")]
 787 #[doc(alias = ">")]
 788 #[doc(alias = "<")]
 789 #[doc(alias = "<=")]
 790 #[doc(alias = ">=")]
 791 #[rustc_on_unimplemented(
 792     message = "can't compare `{Self}` with `{Rhs}`",
 793     label = "no implementation for `{Self} < {Rhs}` and `{Self} > {Rhs}`"
 794 )]
 795 pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
 796     /// This method returns an ordering between `self` and `other` values if one exists.
 797     ///
 798     /// # Examples
 799     ///
 800     /// ```
 801     /// use std::cmp::Ordering;
 802     ///
 803     /// let result = 1.0.partial_cmp(&2.0);
 804     /// assert_eq!(result, Some(Ordering::Less));
 805     ///
 806     /// let result = 1.0.partial_cmp(&1.0);
 807     /// assert_eq!(result, Some(Ordering::Equal));
 808     ///
 809     /// let result = 2.0.partial_cmp(&1.0);
 810     /// assert_eq!(result, Some(Ordering::Greater));
 811     /// ```
 812     ///
 813     /// When comparison is impossible:
 814     ///
 815     /// ```
 816     /// let result = f64::NAN.partial_cmp(&1.0);
 817     /// assert_eq!(result, None);
 818     /// ```
 819     #[must_use]
 820     #[stable(feature = "rust1", since = "1.0.0")]
 821     fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;
 822
 823     /// This method tests less than (for `self` and `other`) and is used by the `<` operator.
 824     ///
 825     /// # Examples
 826     ///
 827     /// ```
 828     /// let result = 1.0 < 2.0;
 829     /// assert_eq!(result, true);
 830     ///
 831     /// let result = 2.0 < 1.0;
 832     /// assert_eq!(result, false);
 833     /// ```
 834     #[inline]
 835     #[must_use]
 836     #[stable(feature = "rust1", since = "1.0.0")]
 837     fn lt(&self, other: &Rhs) -> bool {
 838         matches!(self.partial_cmp(other), Some(Less))
 839     }
 840
 841     /// This method tests less than or equal to (for `self` and `other`) and is used by the `<=`
 842     /// operator.
 843     ///
 844     /// # Examples
 845     ///
 846     /// ```
 847     /// let result = 1.0 <= 2.0;
 848     /// assert_eq!(result, true);
 849     ///
 850     /// let result = 2.0 <= 2.0;
 851     /// assert_eq!(result, true);
 852     /// ```
 853     #[inline]
 854     #[must_use]
 855     #[stable(feature = "rust1", since = "1.0.0")]
 856     fn le(&self, other: &Rhs) -> bool {
 857         matches!(self.partial_cmp(other), Some(Less | Equal))
 858     }
 859
 860     /// This method tests greater than (for `self` and `other`) and is used by the `>` operator.
 861     ///
 862     /// # Examples
 863     ///
 864     /// ```
 865     /// let result = 1.0 > 2.0;
 866     /// assert_eq!(result, false);
 867     ///
 868     /// let result = 2.0 > 2.0;
 869     /// assert_eq!(result, false);
 870     /// ```
 871     #[inline]
 872     #[must_use]
 873     #[stable(feature = "rust1", since = "1.0.0")]
 874     fn gt(&self, other: &Rhs) -> bool {
 875         matches!(self.partial_cmp(other), Some(Greater))
 876     }
 877
 878     /// This method tests greater than or equal to (for `self` and `other`) and is used by the `>=`
 879     /// operator.
 880     ///
 881     /// # Examples
 882     ///
 883     /// ```
 884     /// let result = 2.0 >= 1.0;
 885     /// assert_eq!(result, true);
 886     ///
 887     /// let result = 2.0 >= 2.0;
 888     /// assert_eq!(result, true);
 889     /// ```
 890     #[inline]
 891     #[must_use]
 892     #[stable(feature = "rust1", since = "1.0.0")]
 893     fn ge(&self, other: &Rhs) -> bool {
 894         matches!(self.partial_cmp(other), Some(Greater | Equal))
 895     }
 896 }
 897
 898 /// Derive macro generating an impl of the trait `PartialOrd`.
 899 #[rustc_builtin_macro]
 900 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 901 #[allow_internal_unstable(core_intrinsics)]
 902 pub macro PartialOrd($item:item) {
 903     /* compiler built-in */
 904 }
 905
 906 /// Compares and returns the minimum of two values.
 907 ///
 908 /// Returns the first argument if the comparison determines them to be equal.
 909 ///
 910 /// Internally uses an alias to [`Ord::min`].
 911 ///
 912 /// # Examples
 913 ///
 914 /// ```
 915 /// use std::cmp;
 916 ///
 917 /// assert_eq!(1, cmp::min(1, 2));
 918 /// assert_eq!(2, cmp::min(2, 2));
 919 /// ```
 920 #[inline]
 921 #[must_use]
 922 #[stable(feature = "rust1", since = "1.0.0")]
 923 pub fn min<T: Ord>(v1: T, v2: T) -> T {
 924     v1.min(v2)
 925 }
 926
 927 /// Returns the minimum of two values with respect to the specified comparison function.
 928 ///
 929 /// Returns the first argument if the comparison determines them to be equal.
 930 ///
 931 /// # Examples
 932 ///
 933 /// ```
 934 /// #![feature(cmp_min_max_by)]
 935 ///
 936 /// use std::cmp;
 937 ///
 938 /// assert_eq!(cmp::min_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 1);
 939 /// assert_eq!(cmp::min_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
 940 /// ```
 941 #[inline]
 942 #[must_use]
 943 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
 944 pub fn min_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
 945     match compare(&v1, &v2) {
 946         Ordering::Less | Ordering::Equal => v1,
 947         Ordering::Greater => v2,
 948     }
 949 }
 950
 951 /// Returns the element that gives the minimum value from the specified function.
 952 ///
 953 /// Returns the first argument if the comparison determines them to be equal.
 954 ///
 955 /// # Examples
 956 ///
 957 /// ```
 958 /// #![feature(cmp_min_max_by)]
 959 ///
 960 /// use std::cmp;
 961 ///
 962 /// assert_eq!(cmp::min_by_key(-2, 1, |x: &i32| x.abs()), 1);
 963 /// assert_eq!(cmp::min_by_key(-2, 2, |x: &i32| x.abs()), -2);
 964 /// ```
 965 #[inline]
 966 #[must_use]
 967 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
 968 pub fn min_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
 969     min_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
 970 }
 971
 972 /// Compares and returns the maximum of two values.
 973 ///
 974 /// Returns the second argument if the comparison determines them to be equal.
 975 ///
 976 /// Internally uses an alias to [`Ord::max`].
 977 ///
 978 /// # Examples
 979 ///
 980 /// ```
 981 /// use std::cmp;
 982 ///
 983 /// assert_eq!(2, cmp::max(1, 2));
 984 /// assert_eq!(2, cmp::max(2, 2));
 985 /// ```
 986 #[inline]
 987 #[must_use]
 988 #[stable(feature = "rust1", since = "1.0.0")]
 989 pub fn max<T: Ord>(v1: T, v2: T) -> T {
 990     v1.max(v2)
 991 }
 992
 993 /// Returns the maximum of two values with respect to the specified comparison function.
 994 ///
 995 /// Returns the second argument if the comparison determines them to be equal.
 996 ///
 997 /// # Examples
 998 ///
 999 /// ```
1000 /// #![feature(cmp_min_max_by)]
1001 ///
1002 /// use std::cmp;
1003 ///
1004 /// assert_eq!(cmp::max_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
1005 /// assert_eq!(cmp::max_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 2);
1006 /// ```
1007 #[inline]
1008 #[must_use]
1009 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
1010 pub fn max_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
1011     match compare(&v1, &v2) {
1012         Ordering::Less | Ordering::Equal => v2,
1013         Ordering::Greater => v1,
1014     }
1015 }
1016
1017 /// Returns the element that gives the maximum value from the specified function.
1018 ///
1019 /// Returns the second argument if the comparison determines them to be equal.
1020 ///
1021 /// # Examples
1022 ///
1023 /// ```
1024 /// #![feature(cmp_min_max_by)]
1025 ///
1026 /// use std::cmp;
1027 ///
1028 /// assert_eq!(cmp::max_by_key(-2, 1, |x: &i32| x.abs()), -2);
1029 /// assert_eq!(cmp::max_by_key(-2, 2, |x: &i32| x.abs()), 2);
1030 /// ```
1031 #[inline]
1032 #[must_use]
1033 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
1034 pub fn max_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
1035     max_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
1036 }
1037
1038 // Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
1039 mod impls {
1040     use crate::cmp::Ordering::{self, Equal, Greater, Less};
1041     use crate::hint::unreachable_unchecked;
1042
1043     macro_rules! partial_eq_impl {
1044         ($($t:ty)*) => ($(
1045             #[stable(feature = "rust1", since = "1.0.0")]
1046             impl PartialEq for $t {
1047                 #[inline]
1048                 fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
1049                 #[inline]
1050                 fn ne(&self, other: &$t) -> bool { (*self) != (*other) }
1051             }
1052         )*)
1053     }
1054
1055     #[stable(feature = "rust1", since = "1.0.0")]
1056     impl PartialEq for () {
1057         #[inline]
1058         fn eq(&self, _other: &()) -> bool {
1059             true
1060         }
1061         #[inline]
1062         fn ne(&self, _other: &()) -> bool {
1063             false
1064         }
1065     }
1066
1067     partial_eq_impl! {
1068         bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f32 f64
1069     }
1070
1071     macro_rules! eq_impl {
1072         ($($t:ty)*) => ($(
1073             #[stable(feature = "rust1", since = "1.0.0")]
1074             impl Eq for $t {}
1075         )*)
1076     }
1077
1078     eq_impl! { () bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1079
1080     macro_rules! partial_ord_impl {
1081         ($($t:ty)*) => ($(
1082             #[stable(feature = "rust1", since = "1.0.0")]
1083             impl PartialOrd for $t {
1084                 #[inline]
1085                 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1086                     match (self <= other, self >= other) {
1087                         (false, false) => None,
1088                         (false, true) => Some(Greater),
1089                         (true, false) => Some(Less),
1090                         (true, true) => Some(Equal),
1091                     }
1092                 }
1093                 #[inline]
1094                 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1095                 #[inline]
1096                 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1097                 #[inline]
1098                 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1099                 #[inline]
1100                 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1101             }
1102         )*)
1103     }
1104
1105     #[stable(feature = "rust1", since = "1.0.0")]
1106     impl PartialOrd for () {
1107         #[inline]
1108         fn partial_cmp(&self, _: &()) -> Option<Ordering> {
1109             Some(Equal)
1110         }
1111     }
1112
1113     #[stable(feature = "rust1", since = "1.0.0")]
1114     impl PartialOrd for bool {
1115         #[inline]
1116         fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
1117             (*self as u8).partial_cmp(&(*other as u8))
1118         }
1119     }
1120
1121     partial_ord_impl! { f32 f64 }
1122
1123     macro_rules! ord_impl {
1124         ($($t:ty)*) => ($(
1125             #[stable(feature = "rust1", since = "1.0.0")]
1126             impl PartialOrd for $t {
1127                 #[inline]
1128                 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1129                     Some(self.cmp(other))
1130                 }
1131                 #[inline]
1132                 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1133                 #[inline]
1134                 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1135                 #[inline]
1136                 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1137                 #[inline]
1138                 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1139             }
1140
1141             #[stable(feature = "rust1", since = "1.0.0")]
1142             impl Ord for $t {
1143                 #[inline]
1144                 fn cmp(&self, other: &$t) -> Ordering {
1145                     // The order here is important to generate more optimal assembly.
1146                     // See <https://github.com/rust-lang/rust/issues/63758> for more info.
1147                     if *self < *other { Less }
1148                     else if *self == *other { Equal }
1149                     else { Greater }
1150                 }
1151             }
1152         )*)
1153     }
1154
1155     #[stable(feature = "rust1", since = "1.0.0")]
1156     impl Ord for () {
1157         #[inline]
1158         fn cmp(&self, _other: &()) -> Ordering {
1159             Equal
1160         }
1161     }
1162
1163     #[stable(feature = "rust1", since = "1.0.0")]
1164     impl Ord for bool {
1165         #[inline]
1166         fn cmp(&self, other: &bool) -> Ordering {
1167             // Casting to i8's and converting the difference to an Ordering generates
1168             // more optimal assembly.
1169             // See <https://github.com/rust-lang/rust/issues/66780> for more info.
1170             match (*self as i8) - (*other as i8) {
1171                 -1 => Less,
1172                 0 => Equal,
1173                 1 => Greater,
1174                 // SAFETY: bool as i8 returns 0 or 1, so the difference can't be anything else
1175                 _ => unsafe { unreachable_unchecked() },
1176             }
1177         }
1178     }
1179
1180     ord_impl! { char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1181
1182     #[unstable(feature = "never_type", issue = "35121")]
1183     impl PartialEq for ! {
1184         fn eq(&self, _: &!) -> bool {
1185             *self
1186         }
1187     }
1188
1189     #[unstable(feature = "never_type", issue = "35121")]
1190     impl Eq for ! {}
1191
1192     #[unstable(feature = "never_type", issue = "35121")]
1193     impl PartialOrd for ! {
1194         fn partial_cmp(&self, _: &!) -> Option<Ordering> {
1195             *self
1196         }
1197     }
1198
1199     #[unstable(feature = "never_type", issue = "35121")]
1200     impl Ord for ! {
1201         fn cmp(&self, _: &!) -> Ordering {
1202             *self
1203         }
1204     }
1205
1206     // & pointers
1207
1208     #[stable(feature = "rust1", since = "1.0.0")]
1209     impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &A
1210     where
1211         A: PartialEq<B>,
1212     {
1213         #[inline]
1214         fn eq(&self, other: &&B) -> bool {
1215             PartialEq::eq(*self, *other)
1216         }
1217         #[inline]
1218         fn ne(&self, other: &&B) -> bool {
1219             PartialEq::ne(*self, *other)
1220         }
1221     }
1222     #[stable(feature = "rust1", since = "1.0.0")]
1223     impl<A: ?Sized, B: ?Sized> PartialOrd<&B> for &A
1224     where
1225         A: PartialOrd<B>,
1226     {
1227         #[inline]
1228         fn partial_cmp(&self, other: &&B) -> Option<Ordering> {
1229             PartialOrd::partial_cmp(*self, *other)
1230         }
1231         #[inline]
1232         fn lt(&self, other: &&B) -> bool {
1233             PartialOrd::lt(*self, *other)
1234         }
1235         #[inline]
1236         fn le(&self, other: &&B) -> bool {
1237             PartialOrd::le(*self, *other)
1238         }
1239         #[inline]
1240         fn gt(&self, other: &&B) -> bool {
1241             PartialOrd::gt(*self, *other)
1242         }
1243         #[inline]
1244         fn ge(&self, other: &&B) -> bool {
1245             PartialOrd::ge(*self, *other)
1246         }
1247     }
1248     #[stable(feature = "rust1", since = "1.0.0")]
1249     impl<A: ?Sized> Ord for &A
1250     where
1251         A: Ord,
1252     {
1253         #[inline]
1254         fn cmp(&self, other: &Self) -> Ordering {
1255             Ord::cmp(*self, *other)
1256         }
1257     }
1258     #[stable(feature = "rust1", since = "1.0.0")]
1259     impl<A: ?Sized> Eq for &A where A: Eq {}
1260
1261     // &mut pointers
1262
1263     #[stable(feature = "rust1", since = "1.0.0")]
1264     impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &mut A
1265     where
1266         A: PartialEq<B>,
1267     {
1268         #[inline]
1269         fn eq(&self, other: &&mut B) -> bool {
1270             PartialEq::eq(*self, *other)
1271         }
1272         #[inline]
1273         fn ne(&self, other: &&mut B) -> bool {
1274             PartialEq::ne(*self, *other)
1275         }
1276     }
1277     #[stable(feature = "rust1", since = "1.0.0")]
1278     impl<A: ?Sized, B: ?Sized> PartialOrd<&mut B> for &mut A
1279     where
1280         A: PartialOrd<B>,
1281     {
1282         #[inline]
1283         fn partial_cmp(&self, other: &&mut B) -> Option<Ordering> {
1284             PartialOrd::partial_cmp(*self, *other)
1285         }
1286         #[inline]
1287         fn lt(&self, other: &&mut B) -> bool {
1288             PartialOrd::lt(*self, *other)
1289         }
1290         #[inline]
1291         fn le(&self, other: &&mut B) -> bool {
1292             PartialOrd::le(*self, *other)
1293         }
1294         #[inline]
1295         fn gt(&self, other: &&mut B) -> bool {
1296             PartialOrd::gt(*self, *other)
1297         }
1298         #[inline]
1299         fn ge(&self, other: &&mut B) -> bool {
1300             PartialOrd::ge(*self, *other)
1301         }
1302     }
1303     #[stable(feature = "rust1", since = "1.0.0")]
1304     impl<A: ?Sized> Ord for &mut A
1305     where
1306         A: Ord,
1307     {
1308         #[inline]
1309         fn cmp(&self, other: &Self) -> Ordering {
1310             Ord::cmp(*self, *other)
1311         }
1312     }
1313     #[stable(feature = "rust1", since = "1.0.0")]
1314     impl<A: ?Sized> Eq for &mut A where A: Eq {}
1315
1316     #[stable(feature = "rust1", since = "1.0.0")]
1317     impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &A
1318     where
1319         A: PartialEq<B>,
1320     {
1321         #[inline]
1322         fn eq(&self, other: &&mut B) -> bool {
1323             PartialEq::eq(*self, *other)
1324         }
1325         #[inline]
1326         fn ne(&self, other: &&mut B) -> bool {
1327             PartialEq::ne(*self, *other)
1328         }
1329     }
1330
1331     #[stable(feature = "rust1", since = "1.0.0")]
1332     impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &mut A
1333     where
1334         A: PartialEq<B>,
1335     {
1336         #[inline]
1337         fn eq(&self, other: &&B) -> bool {
1338             PartialEq::eq(*self, *other)
1339         }
1340         #[inline]
1341         fn ne(&self, other: &&B) -> bool {
1342             PartialEq::ne(*self, *other)
1343         }
1344     }
1345 }