src/libcore/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 //! [`Eq`]: trait.Eq.html
  21 //! [`PartialEq`]: trait.PartialEq.html
  22 //! [`Ord`]: trait.Ord.html
  23 //! [`PartialOrd`]: trait.PartialOrd.html
  24 //! [`Ordering`]: enum.Ordering.html
  25 //! [`Reverse`]: struct.Reverse.html
  26 //! [`max`]: fn.max.html
  27 //! [`min`]: fn.min.html
  28
  29 #![stable(feature = "rust1", since = "1.0.0")]
  30
  31 use self::Ordering::*;
  32
  33 /// Trait for equality comparisons which are [partial equivalence
  34 /// relations](http://en.wikipedia.org/wiki/Partial_equivalence_relation).
  35 ///
  36 /// This trait allows for partial equality, for types that do not have a full
  37 /// equivalence relation. For example, in floating point numbers `NaN != NaN`,
  38 /// so floating point types implement `PartialEq` but not [`Eq`].
  39 ///
  40 /// Formally, the equality must be (for all `a`, `b` and `c`):
  41 ///
  42 /// - symmetric: `a == b` implies `b == a`; and
  43 /// - transitive: `a == b` and `b == c` implies `a == c`.
  44 ///
  45 /// Note that these requirements mean that the trait itself must be implemented
  46 /// symmetrically and transitively: if `T: PartialEq<U>` and `U: PartialEq<V>`
  47 /// then `U: PartialEq<T>` and `T: PartialEq<V>`.
  48 ///
  49 /// ## Derivable
  50 ///
  51 /// This trait can be used with `#[derive]`. When `derive`d on structs, two
  52 /// instances are equal if all fields are equal, and not equal if any fields
  53 /// are not equal. When `derive`d on enums, each variant is equal to itself
  54 /// and not equal to the other variants.
  55 ///
  56 /// ## How can I implement `PartialEq`?
  57 ///
  58 /// `PartialEq` only requires the [`eq`] method to be implemented; [`ne`] is defined
  59 /// in terms of it by default. Any manual implementation of [`ne`] *must* respect
  60 /// the rule that [`eq`] is a strict inverse of [`ne`]; that is, `!(a == b)` if and
  61 /// only if `a != b`.
  62 ///
  63 /// Implementations of `PartialEq`, [`PartialOrd`], and [`Ord`] *must* agree with
  64 /// each other. It's easy to accidentally make them disagree by deriving some
  65 /// of the traits and manually implementing others.
  66 ///
  67 /// An example implementation for a domain in which two books are considered
  68 /// the same book if their ISBN matches, even if the formats differ:
  69 ///
  70 /// ```
  71 /// enum BookFormat {
  72 ///     Paperback,
  73 ///     Hardback,
  74 ///     Ebook,
  75 /// }
  76 ///
  77 /// struct Book {
  78 ///     isbn: i32,
  79 ///     format: BookFormat,
  80 /// }
  81 ///
  82 /// impl PartialEq for Book {
  83 ///     fn eq(&self, other: &Self) -> bool {
  84 ///         self.isbn == other.isbn
  85 ///     }
  86 /// }
  87 ///
  88 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
  89 /// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
  90 /// let b3 = Book { isbn: 10, format: BookFormat::Paperback };
  91 ///
  92 /// assert!(b1 == b2);
  93 /// assert!(b1 != b3);
  94 /// ```
  95 ///
  96 /// ## How can I compare two different types?
  97 ///
  98 /// The type you can compare with is controlled by `PartialEq`'s type parameter.
  99 /// For example, let's tweak our previous code a bit:
 100 ///
 101 /// ```
 102 /// // The derive implements <BookFormat> == <BookFormat> comparisons
 103 /// #[derive(PartialEq)]
 104 /// enum BookFormat {
 105 ///     Paperback,
 106 ///     Hardback,
 107 ///     Ebook,
 108 /// }
 109 ///
 110 /// struct Book {
 111 ///     isbn: i32,
 112 ///     format: BookFormat,
 113 /// }
 114 ///
 115 /// // Implement <Book> == <BookFormat> comparisons
 116 /// impl PartialEq<BookFormat> for Book {
 117 ///     fn eq(&self, other: &BookFormat) -> bool {
 118 ///         self.format == *other
 119 ///     }
 120 /// }
 121 ///
 122 /// // Implement <BookFormat> == <Book> comparisons
 123 /// impl PartialEq<Book> for BookFormat {
 124 ///     fn eq(&self, other: &Book) -> bool {
 125 ///         *self == other.format
 126 ///     }
 127 /// }
 128 ///
 129 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
 130 ///
 131 /// assert!(b1 == BookFormat::Paperback);
 132 /// assert!(BookFormat::Ebook != b1);
 133 /// ```
 134 ///
 135 /// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
 136 /// we allow `BookFormat`s to be compared with `Book`s.
 137 ///
 138 /// A comparison like the one above, which ignores some fields of the struct,
 139 /// can be dangerous. It can easily lead to an unintended violation of the
 140 /// requirements for a partial equivalence relation. For example, if we kept
 141 /// the above implementation of `PartialEq<Book>` for `BookFormat` and added an
 142 /// implementation of `PartialEq<Book>` for `Book` (either via a `#[derive]` or
 143 /// via the manual implementation from the first example) then the result would
 144 /// violate transitivity:
 145 ///
 146 /// ```should_panic
 147 /// #[derive(PartialEq)]
 148 /// enum BookFormat {
 149 ///     Paperback,
 150 ///     Hardback,
 151 ///     Ebook,
 152 /// }
 153 ///
 154 /// #[derive(PartialEq)]
 155 /// struct Book {
 156 ///     isbn: i32,
 157 ///     format: BookFormat,
 158 /// }
 159 ///
 160 /// impl PartialEq<BookFormat> for Book {
 161 ///     fn eq(&self, other: &BookFormat) -> bool {
 162 ///         self.format == *other
 163 ///     }
 164 /// }
 165 ///
 166 /// impl PartialEq<Book> for BookFormat {
 167 ///     fn eq(&self, other: &Book) -> bool {
 168 ///         *self == other.format
 169 ///     }
 170 /// }
 171 ///
 172 /// fn main() {
 173 ///     let b1 = Book { isbn: 1, format: BookFormat::Paperback };
 174 ///     let b2 = Book { isbn: 2, format: BookFormat::Paperback };
 175 ///
 176 ///     assert!(b1 == BookFormat::Paperback);
 177 ///     assert!(BookFormat::Paperback == b2);
 178 ///
 179 ///     // The following should hold by transitivity but doesn't.
 180 ///     assert!(b1 == b2); // <-- PANICS
 181 /// }
 182 /// ```
 183 ///
 184 /// # Examples
 185 ///
 186 /// ```
 187 /// let x: u32 = 0;
 188 /// let y: u32 = 1;
 189 ///
 190 /// assert_eq!(x == y, false);
 191 /// assert_eq!(x.eq(&y), false);
 192 /// ```
 193 ///
 194 /// [`eq`]: PartialEq::eq
 195 /// [`ne`]: PartialEq::ne
 196 #[lang = "eq"]
 197 #[stable(feature = "rust1", since = "1.0.0")]
 198 #[doc(alias = "==")]
 199 #[doc(alias = "!=")]
 200 #[rustc_on_unimplemented(
 201     message = "can't compare `{Self}` with `{Rhs}`",
 202     label = "no implementation for `{Self} == {Rhs}`"
 203 )]
 204 pub trait PartialEq<Rhs: ?Sized = Self> {
 205     /// This method tests for `self` and `other` values to be equal, and is used
 206     /// by `==`.
 207     #[must_use]
 208     #[stable(feature = "rust1", since = "1.0.0")]
 209     fn eq(&self, other: &Rhs) -> bool;
 210
 211     /// This method tests for `!=`.
 212     #[inline]
 213     #[must_use]
 214     #[stable(feature = "rust1", since = "1.0.0")]
 215     fn ne(&self, other: &Rhs) -> bool {
 216         !self.eq(other)
 217     }
 218 }
 219
 220 /// Derive macro generating an impl of the trait `PartialEq`.
 221 #[rustc_builtin_macro]
 222 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 223 #[allow_internal_unstable(core_intrinsics, structural_match)]
 224 pub macro PartialEq($item:item) {
 225     /* compiler built-in */
 226 }
 227
 228 /// Trait for equality comparisons which are [equivalence relations](
 229 /// https://en.wikipedia.org/wiki/Equivalence_relation).
 230 ///
 231 /// This means, that in addition to `a == b` and `a != b` being strict inverses, the equality must
 232 /// be (for all `a`, `b` and `c`):
 233 ///
 234 /// - reflexive: `a == a`;
 235 /// - symmetric: `a == b` implies `b == a`; and
 236 /// - transitive: `a == b` and `b == c` implies `a == c`.
 237 ///
 238 /// This property cannot be checked by the compiler, and therefore `Eq` implies
 239 /// [`PartialEq`], and has no extra methods.
 240 ///
 241 /// ## Derivable
 242 ///
 243 /// This trait can be used with `#[derive]`. When `derive`d, because `Eq` has
 244 /// no extra methods, it is only informing the compiler that this is an
 245 /// equivalence relation rather than a partial equivalence relation. Note that
 246 /// the `derive` strategy requires all fields are `Eq`, which isn't
 247 /// always desired.
 248 ///
 249 /// ## How can I implement `Eq`?
 250 ///
 251 /// If you cannot use the `derive` strategy, specify that your type implements
 252 /// `Eq`, which has no methods:
 253 ///
 254 /// ```
 255 /// enum BookFormat { Paperback, Hardback, Ebook }
 256 /// struct Book {
 257 ///     isbn: i32,
 258 ///     format: BookFormat,
 259 /// }
 260 /// impl PartialEq for Book {
 261 ///     fn eq(&self, other: &Self) -> bool {
 262 ///         self.isbn == other.isbn
 263 ///     }
 264 /// }
 265 /// impl Eq for Book {}
 266 /// ```
 267 #[doc(alias = "==")]
 268 #[doc(alias = "!=")]
 269 #[stable(feature = "rust1", since = "1.0.0")]
 270 pub trait Eq: PartialEq<Self> {
 271     // this method is used solely by #[deriving] to assert
 272     // that every component of a type implements #[deriving]
 273     // itself, the current deriving infrastructure means doing this
 274     // assertion without using a method on this trait is nearly
 275     // impossible.
 276     //
 277     // This should never be implemented by hand.
 278     #[doc(hidden)]
 279     #[inline]
 280     #[stable(feature = "rust1", since = "1.0.0")]
 281     fn assert_receiver_is_total_eq(&self) {}
 282 }
 283
 284 /// Derive macro generating an impl of the trait `Eq`.
 285 #[rustc_builtin_macro]
 286 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 287 #[allow_internal_unstable(core_intrinsics, derive_eq, structural_match)]
 288 pub macro Eq($item:item) {
 289     /* compiler built-in */
 290 }
 291
 292 // FIXME: this struct is used solely by #[derive] to
 293 // assert that every component of a type implements Eq.
 294 //
 295 // This struct should never appear in user code.
 296 #[doc(hidden)]
 297 #[allow(missing_debug_implementations)]
 298 #[unstable(feature = "derive_eq", reason = "deriving hack, should not be public", issue = "none")]
 299 pub struct AssertParamIsEq<T: Eq + ?Sized> {
 300     _field: crate::marker::PhantomData<T>,
 301 }
 302
 303 /// An `Ordering` is the result of a comparison between two values.
 304 ///
 305 /// # Examples
 306 ///
 307 /// ```
 308 /// use std::cmp::Ordering;
 309 ///
 310 /// let result = 1.cmp(&2);
 311 /// assert_eq!(Ordering::Less, result);
 312 ///
 313 /// let result = 1.cmp(&1);
 314 /// assert_eq!(Ordering::Equal, result);
 315 ///
 316 /// let result = 2.cmp(&1);
 317 /// assert_eq!(Ordering::Greater, result);
 318 /// ```
 319 #[derive(Clone, Copy, PartialEq, Debug, Hash)]
 320 #[stable(feature = "rust1", since = "1.0.0")]
 321 pub enum Ordering {
 322     /// An ordering where a compared value is less than another.
 323     #[stable(feature = "rust1", since = "1.0.0")]
 324     Less = -1,
 325     /// An ordering where a compared value is equal to another.
 326     #[stable(feature = "rust1", since = "1.0.0")]
 327     Equal = 0,
 328     /// An ordering where a compared value is greater than another.
 329     #[stable(feature = "rust1", since = "1.0.0")]
 330     Greater = 1,
 331 }
 332
 333 impl Ordering {
 334     /// Reverses the `Ordering`.
 335     ///
 336     /// * `Less` becomes `Greater`.
 337     /// * `Greater` becomes `Less`.
 338     /// * `Equal` becomes `Equal`.
 339     ///
 340     /// # Examples
 341     ///
 342     /// Basic behavior:
 343     ///
 344     /// ```
 345     /// use std::cmp::Ordering;
 346     ///
 347     /// assert_eq!(Ordering::Less.reverse(), Ordering::Greater);
 348     /// assert_eq!(Ordering::Equal.reverse(), Ordering::Equal);
 349     /// assert_eq!(Ordering::Greater.reverse(), Ordering::Less);
 350     /// ```
 351     ///
 352     /// This method can be used to reverse a comparison:
 353     ///
 354     /// ```
 355     /// let data: &mut [_] = &mut [2, 10, 5, 8];
 356     ///
 357     /// // sort the array from largest to smallest.
 358     /// data.sort_by(|a, b| a.cmp(b).reverse());
 359     ///
 360     /// let b: &mut [_] = &mut [10, 8, 5, 2];
 361     /// assert!(data == b);
 362     /// ```
 363     #[inline]
 364     #[must_use]
 365     #[stable(feature = "rust1", since = "1.0.0")]
 366     pub fn reverse(self) -> Ordering {
 367         match self {
 368             Less => Greater,
 369             Equal => Equal,
 370             Greater => Less,
 371         }
 372     }
 373
 374     /// Chains two orderings.
 375     ///
 376     /// Returns `self` when it's not `Equal`. Otherwise returns `other`.
 377     ///
 378     /// # Examples
 379     ///
 380     /// ```
 381     /// use std::cmp::Ordering;
 382     ///
 383     /// let result = Ordering::Equal.then(Ordering::Less);
 384     /// assert_eq!(result, Ordering::Less);
 385     ///
 386     /// let result = Ordering::Less.then(Ordering::Equal);
 387     /// assert_eq!(result, Ordering::Less);
 388     ///
 389     /// let result = Ordering::Less.then(Ordering::Greater);
 390     /// assert_eq!(result, Ordering::Less);
 391     ///
 392     /// let result = Ordering::Equal.then(Ordering::Equal);
 393     /// assert_eq!(result, Ordering::Equal);
 394     ///
 395     /// let x: (i64, i64, i64) = (1, 2, 7);
 396     /// let y: (i64, i64, i64) = (1, 5, 3);
 397     /// let result = x.0.cmp(&y.0).then(x.1.cmp(&y.1)).then(x.2.cmp(&y.2));
 398     ///
 399     /// assert_eq!(result, Ordering::Less);
 400     /// ```
 401     #[inline]
 402     #[must_use]
 403     #[stable(feature = "ordering_chaining", since = "1.17.0")]
 404     pub fn then(self, other: Ordering) -> Ordering {
 405         match self {
 406             Equal => other,
 407             _ => self,
 408         }
 409     }
 410
 411     /// Chains the ordering with the given function.
 412     ///
 413     /// Returns `self` when it's not `Equal`. Otherwise calls `f` and returns
 414     /// the result.
 415     ///
 416     /// # Examples
 417     ///
 418     /// ```
 419     /// use std::cmp::Ordering;
 420     ///
 421     /// let result = Ordering::Equal.then_with(|| Ordering::Less);
 422     /// assert_eq!(result, Ordering::Less);
 423     ///
 424     /// let result = Ordering::Less.then_with(|| Ordering::Equal);
 425     /// assert_eq!(result, Ordering::Less);
 426     ///
 427     /// let result = Ordering::Less.then_with(|| Ordering::Greater);
 428     /// assert_eq!(result, Ordering::Less);
 429     ///
 430     /// let result = Ordering::Equal.then_with(|| Ordering::Equal);
 431     /// assert_eq!(result, Ordering::Equal);
 432     ///
 433     /// let x: (i64, i64, i64) = (1, 2, 7);
 434     /// let y: (i64, i64, i64)  = (1, 5, 3);
 435     /// let result = x.0.cmp(&y.0).then_with(|| x.1.cmp(&y.1)).then_with(|| x.2.cmp(&y.2));
 436     ///
 437     /// assert_eq!(result, Ordering::Less);
 438     /// ```
 439     #[inline]
 440     #[must_use]
 441     #[stable(feature = "ordering_chaining", since = "1.17.0")]
 442     pub fn then_with<F: FnOnce() -> Ordering>(self, f: F) -> Ordering {
 443         match self {
 444             Equal => f(),
 445             _ => self,
 446         }
 447     }
 448 }
 449
 450 /// A helper struct for reverse ordering.
 451 ///
 452 /// This struct is a helper to be used with functions like [`Vec::sort_by_key`] and
 453 /// can be used to reverse order a part of a key.
 454 ///
 455 /// [`Vec::sort_by_key`]: ../../std/vec/struct.Vec.html#method.sort_by_key
 456 ///
 457 /// # Examples
 458 ///
 459 /// ```
 460 /// use std::cmp::Reverse;
 461 ///
 462 /// let mut v = vec![1, 2, 3, 4, 5, 6];
 463 /// v.sort_by_key(|&num| (num > 3, Reverse(num)));
 464 /// assert_eq!(v, vec![3, 2, 1, 6, 5, 4]);
 465 /// ```
 466 #[derive(PartialEq, Eq, Debug, Copy, Clone, Default, Hash)]
 467 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 468 pub struct Reverse<T>(#[stable(feature = "reverse_cmp_key", since = "1.19.0")] pub T);
 469
 470 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 471 impl<T: PartialOrd> PartialOrd for Reverse<T> {
 472     #[inline]
 473     fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
 474         other.0.partial_cmp(&self.0)
 475     }
 476
 477     #[inline]
 478     fn lt(&self, other: &Self) -> bool {
 479         other.0 < self.0
 480     }
 481     #[inline]
 482     fn le(&self, other: &Self) -> bool {
 483         other.0 <= self.0
 484     }
 485     #[inline]
 486     fn gt(&self, other: &Self) -> bool {
 487         other.0 > self.0
 488     }
 489     #[inline]
 490     fn ge(&self, other: &Self) -> bool {
 491         other.0 >= self.0
 492     }
 493 }
 494
 495 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 496 impl<T: Ord> Ord for Reverse<T> {
 497     #[inline]
 498     fn cmp(&self, other: &Reverse<T>) -> Ordering {
 499         other.0.cmp(&self.0)
 500     }
 501 }
 502
 503 /// Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order).
 504 ///
 505 /// An order is a total order if it is (for all `a`, `b` and `c`):
 506 ///
 507 /// - total and asymmetric: exactly one of `a < b`, `a == b` or `a > b` is true; and
 508 /// - transitive, `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
 509 ///
 510 /// ## Derivable
 511 ///
 512 /// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
 513 /// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
 514 /// When `derive`d on enums, variants are ordered by their top-to-bottom declaration order.
 515 ///
 516 /// ## How can I implement `Ord`?
 517 ///
 518 /// `Ord` requires that the type also be [`PartialOrd`] and [`Eq`] (which requires [`PartialEq`]).
 519 ///
 520 /// Then you must define an implementation for [`cmp`]. You may find it useful to use
 521 /// [`cmp`] on your type's fields.
 522 ///
 523 /// Implementations of [`PartialEq`], [`PartialOrd`], and `Ord` *must*
 524 /// agree with each other. That is, `a.cmp(b) == Ordering::Equal` if
 525 /// and only if `a == b` and `Some(a.cmp(b)) == a.partial_cmp(b)` for
 526 /// all `a` and `b`. It's easy to accidentally make them disagree by
 527 /// deriving some of the traits and manually implementing others.
 528 ///
 529 /// Here's an example where you want to sort people by height only, disregarding `id`
 530 /// and `name`:
 531 ///
 532 /// ```
 533 /// use std::cmp::Ordering;
 534 ///
 535 /// #[derive(Eq)]
 536 /// struct Person {
 537 ///     id: u32,
 538 ///     name: String,
 539 ///     height: u32,
 540 /// }
 541 ///
 542 /// impl Ord for Person {
 543 ///     fn cmp(&self, other: &Self) -> Ordering {
 544 ///         self.height.cmp(&other.height)
 545 ///     }
 546 /// }
 547 ///
 548 /// impl PartialOrd for Person {
 549 ///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 550 ///         Some(self.cmp(other))
 551 ///     }
 552 /// }
 553 ///
 554 /// impl PartialEq for Person {
 555 ///     fn eq(&self, other: &Self) -> bool {
 556 ///         self.height == other.height
 557 ///     }
 558 /// }
 559 /// ```
 560 ///
 561 /// [`cmp`]: Ord::cmp
 562 #[doc(alias = "<")]
 563 #[doc(alias = ">")]
 564 #[doc(alias = "<=")]
 565 #[doc(alias = ">=")]
 566 #[stable(feature = "rust1", since = "1.0.0")]
 567 pub trait Ord: Eq + PartialOrd<Self> {
 568     /// This method returns an [`Ordering`] between `self` and `other`.
 569     ///
 570     /// By convention, `self.cmp(&other)` returns the ordering matching the expression
 571     /// `self <operator> other` if true.
 572     ///
 573     /// # Examples
 574     ///
 575     /// ```
 576     /// use std::cmp::Ordering;
 577     ///
 578     /// assert_eq!(5.cmp(&10), Ordering::Less);
 579     /// assert_eq!(10.cmp(&5), Ordering::Greater);
 580     /// assert_eq!(5.cmp(&5), Ordering::Equal);
 581     /// ```
 582     #[must_use]
 583     #[stable(feature = "rust1", since = "1.0.0")]
 584     fn cmp(&self, other: &Self) -> Ordering;
 585
 586     /// Compares and returns the maximum of two values.
 587     ///
 588     /// Returns the second argument if the comparison determines them to be equal.
 589     ///
 590     /// # Examples
 591     ///
 592     /// ```
 593     /// assert_eq!(2, 1.max(2));
 594     /// assert_eq!(2, 2.max(2));
 595     /// ```
 596     #[stable(feature = "ord_max_min", since = "1.21.0")]
 597     #[inline]
 598     #[must_use]
 599     fn max(self, other: Self) -> Self
 600     where
 601         Self: Sized,
 602     {
 603         max_by(self, other, Ord::cmp)
 604     }
 605
 606     /// Compares and returns the minimum of two values.
 607     ///
 608     /// Returns the first argument if the comparison determines them to be equal.
 609     ///
 610     /// # Examples
 611     ///
 612     /// ```
 613     /// assert_eq!(1, 1.min(2));
 614     /// assert_eq!(2, 2.min(2));
 615     /// ```
 616     #[stable(feature = "ord_max_min", since = "1.21.0")]
 617     #[inline]
 618     #[must_use]
 619     fn min(self, other: Self) -> Self
 620     where
 621         Self: Sized,
 622     {
 623         min_by(self, other, Ord::cmp)
 624     }
 625
 626     /// Restrict a value to a certain interval.
 627     ///
 628     /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
 629     /// less than `min`. Otherwise this returns `self`.
 630     ///
 631     /// # Panics
 632     ///
 633     /// Panics if `min > max`.
 634     ///
 635     /// # Examples
 636     ///
 637     /// ```
 638     /// #![feature(clamp)]
 639     ///
 640     /// assert!((-3).clamp(-2, 1) == -2);
 641     /// assert!(0.clamp(-2, 1) == 0);
 642     /// assert!(2.clamp(-2, 1) == 1);
 643     /// ```
 644     #[must_use]
 645     #[unstable(feature = "clamp", issue = "44095")]
 646     fn clamp(self, min: Self, max: Self) -> Self
 647     where
 648         Self: Sized,
 649     {
 650         assert!(min <= max);
 651         if self < min {
 652             min
 653         } else if self > max {
 654             max
 655         } else {
 656             self
 657         }
 658     }
 659 }
 660
 661 /// Derive macro generating an impl of the trait `Ord`.
 662 #[rustc_builtin_macro]
 663 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 664 #[allow_internal_unstable(core_intrinsics)]
 665 pub macro Ord($item:item) {
 666     /* compiler built-in */
 667 }
 668
 669 #[stable(feature = "rust1", since = "1.0.0")]
 670 impl Eq for Ordering {}
 671
 672 #[stable(feature = "rust1", since = "1.0.0")]
 673 impl Ord for Ordering {
 674     #[inline]
 675     fn cmp(&self, other: &Ordering) -> Ordering {
 676         (*self as i32).cmp(&(*other as i32))
 677     }
 678 }
 679
 680 #[stable(feature = "rust1", since = "1.0.0")]
 681 impl PartialOrd for Ordering {
 682     #[inline]
 683     fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
 684         (*self as i32).partial_cmp(&(*other as i32))
 685     }
 686 }
 687
 688 /// Trait for values that can be compared for a sort-order.
 689 ///
 690 /// The comparison must satisfy, for all `a`, `b` and `c`:
 691 ///
 692 /// - asymmetry: if `a < b` then `!(a > b)`, as well as `a > b` implying `!(a < b)`; and
 693 /// - transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
 694 ///
 695 /// Note that these requirements mean that the trait itself must be implemented symmetrically and
 696 /// transitively: if `T: PartialOrd<U>` and `U: PartialOrd<V>` then `U: PartialOrd<T>` and `T:
 697 /// PartialOrd<V>`.
 698 ///
 699 /// ## Derivable
 700 ///
 701 /// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
 702 /// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
 703 /// When `derive`d on enums, variants are ordered by their top-to-bottom declaration order.
 704 ///
 705 /// ## How can I implement `PartialOrd`?
 706 ///
 707 /// `PartialOrd` only requires implementation of the [`partial_cmp`] method, with the others
 708 /// generated from default implementations.
 709 ///
 710 /// However it remains possible to implement the others separately for types which do not have a
 711 /// total order. For example, for floating point numbers, `NaN < 0 == false` and `NaN >= 0 ==
 712 /// false` (cf. IEEE 754-2008 section 5.11).
 713 ///
 714 /// `PartialOrd` requires your type to be [`PartialEq`].
 715 ///
 716 /// Implementations of [`PartialEq`], `PartialOrd`, and [`Ord`] *must* agree with each other. It's
 717 /// easy to accidentally make them disagree by deriving some of the traits and manually
 718 /// implementing others.
 719 ///
 720 /// If your type is [`Ord`], you can implement [`partial_cmp`] by using [`cmp`]:
 721 ///
 722 /// ```
 723 /// use std::cmp::Ordering;
 724 ///
 725 /// #[derive(Eq)]
 726 /// struct Person {
 727 ///     id: u32,
 728 ///     name: String,
 729 ///     height: u32,
 730 /// }
 731 ///
 732 /// impl PartialOrd for Person {
 733 ///     fn partial_cmp(&self, other: &Person) -> Option<Ordering> {
 734 ///         Some(self.cmp(other))
 735 ///     }
 736 /// }
 737 ///
 738 /// impl Ord for Person {
 739 ///     fn cmp(&self, other: &Person) -> Ordering {
 740 ///         self.height.cmp(&other.height)
 741 ///     }
 742 /// }
 743 ///
 744 /// impl PartialEq for Person {
 745 ///     fn eq(&self, other: &Person) -> bool {
 746 ///         self.height == other.height
 747 ///     }
 748 /// }
 749 /// ```
 750 ///
 751 /// You may also find it useful to use [`partial_cmp`] on your type's fields. Here
 752 /// is an example of `Person` types who have a floating-point `height` field that
 753 /// is the only field to be used for sorting:
 754 ///
 755 /// ```
 756 /// use std::cmp::Ordering;
 757 ///
 758 /// struct Person {
 759 ///     id: u32,
 760 ///     name: String,
 761 ///     height: f64,
 762 /// }
 763 ///
 764 /// impl PartialOrd for Person {
 765 ///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 766 ///         self.height.partial_cmp(&other.height)
 767 ///     }
 768 /// }
 769 ///
 770 /// impl PartialEq for Person {
 771 ///     fn eq(&self, other: &Self) -> bool {
 772 ///         self.height == other.height
 773 ///     }
 774 /// }
 775 /// ```
 776 ///
 777 /// # Examples
 778 ///
 779 /// ```
 780 /// let x : u32 = 0;
 781 /// let y : u32 = 1;
 782 ///
 783 /// assert_eq!(x < y, true);
 784 /// assert_eq!(x.lt(&y), true);
 785 /// ```
 786 ///
 787 /// [`partial_cmp`]: PartialOrd::partial_cmp
 788 /// [`cmp`]: Ord::cmp
 789 #[lang = "partial_ord"]
 790 #[stable(feature = "rust1", since = "1.0.0")]
 791 #[doc(alias = ">")]
 792 #[doc(alias = "<")]
 793 #[doc(alias = "<=")]
 794 #[doc(alias = ">=")]
 795 #[rustc_on_unimplemented(
 796     message = "can't compare `{Self}` with `{Rhs}`",
 797     label = "no implementation for `{Self} < {Rhs}` and `{Self} > {Rhs}`"
 798 )]
 799 pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
 800     /// This method returns an ordering between `self` and `other` values if one exists.
 801     ///
 802     /// # Examples
 803     ///
 804     /// ```
 805     /// use std::cmp::Ordering;
 806     ///
 807     /// let result = 1.0.partial_cmp(&2.0);
 808     /// assert_eq!(result, Some(Ordering::Less));
 809     ///
 810     /// let result = 1.0.partial_cmp(&1.0);
 811     /// assert_eq!(result, Some(Ordering::Equal));
 812     ///
 813     /// let result = 2.0.partial_cmp(&1.0);
 814     /// assert_eq!(result, Some(Ordering::Greater));
 815     /// ```
 816     ///
 817     /// When comparison is impossible:
 818     ///
 819     /// ```
 820     /// let result = f64::NAN.partial_cmp(&1.0);
 821     /// assert_eq!(result, None);
 822     /// ```
 823     #[must_use]
 824     #[stable(feature = "rust1", since = "1.0.0")]
 825     fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;
 826
 827     /// This method tests less than (for `self` and `other`) and is used by the `<` operator.
 828     ///
 829     /// # Examples
 830     ///
 831     /// ```
 832     /// let result = 1.0 < 2.0;
 833     /// assert_eq!(result, true);
 834     ///
 835     /// let result = 2.0 < 1.0;
 836     /// assert_eq!(result, false);
 837     /// ```
 838     #[inline]
 839     #[must_use]
 840     #[stable(feature = "rust1", since = "1.0.0")]
 841     fn lt(&self, other: &Rhs) -> bool {
 842         matches!(self.partial_cmp(other), Some(Less))
 843     }
 844
 845     /// This method tests less than or equal to (for `self` and `other`) and is used by the `<=`
 846     /// operator.
 847     ///
 848     /// # Examples
 849     ///
 850     /// ```
 851     /// let result = 1.0 <= 2.0;
 852     /// assert_eq!(result, true);
 853     ///
 854     /// let result = 2.0 <= 2.0;
 855     /// assert_eq!(result, true);
 856     /// ```
 857     #[inline]
 858     #[must_use]
 859     #[stable(feature = "rust1", since = "1.0.0")]
 860     fn le(&self, other: &Rhs) -> bool {
 861         matches!(self.partial_cmp(other), Some(Less | Equal))
 862     }
 863
 864     /// This method tests greater than (for `self` and `other`) and is used by the `>` operator.
 865     ///
 866     /// # Examples
 867     ///
 868     /// ```
 869     /// let result = 1.0 > 2.0;
 870     /// assert_eq!(result, false);
 871     ///
 872     /// let result = 2.0 > 2.0;
 873     /// assert_eq!(result, false);
 874     /// ```
 875     #[inline]
 876     #[must_use]
 877     #[stable(feature = "rust1", since = "1.0.0")]
 878     fn gt(&self, other: &Rhs) -> bool {
 879         matches!(self.partial_cmp(other), Some(Greater))
 880     }
 881
 882     /// This method tests greater than or equal to (for `self` and `other`) and is used by the `>=`
 883     /// operator.
 884     ///
 885     /// # Examples
 886     ///
 887     /// ```
 888     /// let result = 2.0 >= 1.0;
 889     /// assert_eq!(result, true);
 890     ///
 891     /// let result = 2.0 >= 2.0;
 892     /// assert_eq!(result, true);
 893     /// ```
 894     #[inline]
 895     #[must_use]
 896     #[stable(feature = "rust1", since = "1.0.0")]
 897     fn ge(&self, other: &Rhs) -> bool {
 898         matches!(self.partial_cmp(other), Some(Greater | Equal))
 899     }
 900 }
 901
 902 /// Derive macro generating an impl of the trait `PartialOrd`.
 903 #[rustc_builtin_macro]
 904 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 905 #[allow_internal_unstable(core_intrinsics)]
 906 pub macro PartialOrd($item:item) {
 907     /* compiler built-in */
 908 }
 909
 910 /// Compares and returns the minimum of two values.
 911 ///
 912 /// Returns the first argument if the comparison determines them to be equal.
 913 ///
 914 /// Internally uses an alias to [`Ord::min`].
 915 ///
 916 /// # Examples
 917 ///
 918 /// ```
 919 /// use std::cmp;
 920 ///
 921 /// assert_eq!(1, cmp::min(1, 2));
 922 /// assert_eq!(2, cmp::min(2, 2));
 923 /// ```
 924 #[inline]
 925 #[must_use]
 926 #[stable(feature = "rust1", since = "1.0.0")]
 927 pub fn min<T: Ord>(v1: T, v2: T) -> T {
 928     v1.min(v2)
 929 }
 930
 931 /// Returns the minimum of two values with respect to the specified comparison function.
 932 ///
 933 /// Returns the first argument if the comparison determines them to be equal.
 934 ///
 935 /// # Examples
 936 ///
 937 /// ```
 938 /// #![feature(cmp_min_max_by)]
 939 ///
 940 /// use std::cmp;
 941 ///
 942 /// assert_eq!(cmp::min_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 1);
 943 /// assert_eq!(cmp::min_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
 944 /// ```
 945 #[inline]
 946 #[must_use]
 947 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
 948 pub fn min_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
 949     match compare(&v1, &v2) {
 950         Ordering::Less | Ordering::Equal => v1,
 951         Ordering::Greater => v2,
 952     }
 953 }
 954
 955 /// Returns the element that gives the minimum value from the specified function.
 956 ///
 957 /// Returns the first argument if the comparison determines them to be equal.
 958 ///
 959 /// # Examples
 960 ///
 961 /// ```
 962 /// #![feature(cmp_min_max_by)]
 963 ///
 964 /// use std::cmp;
 965 ///
 966 /// assert_eq!(cmp::min_by_key(-2, 1, |x: &i32| x.abs()), 1);
 967 /// assert_eq!(cmp::min_by_key(-2, 2, |x: &i32| x.abs()), -2);
 968 /// ```
 969 #[inline]
 970 #[must_use]
 971 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
 972 pub fn min_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
 973     min_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
 974 }
 975
 976 /// Compares and returns the maximum of two values.
 977 ///
 978 /// Returns the second argument if the comparison determines them to be equal.
 979 ///
 980 /// Internally uses an alias to [`Ord::max`].
 981 ///
 982 /// # Examples
 983 ///
 984 /// ```
 985 /// use std::cmp;
 986 ///
 987 /// assert_eq!(2, cmp::max(1, 2));
 988 /// assert_eq!(2, cmp::max(2, 2));
 989 /// ```
 990 #[inline]
 991 #[must_use]
 992 #[stable(feature = "rust1", since = "1.0.0")]
 993 pub fn max<T: Ord>(v1: T, v2: T) -> T {
 994     v1.max(v2)
 995 }
 996
 997 /// Returns the maximum of two values with respect to the specified comparison function.
 998 ///
 999 /// Returns the second argument if the comparison determines them to be equal.
1000 ///
1001 /// # Examples
1002 ///
1003 /// ```
1004 /// #![feature(cmp_min_max_by)]
1005 ///
1006 /// use std::cmp;
1007 ///
1008 /// assert_eq!(cmp::max_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
1009 /// assert_eq!(cmp::max_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 2);
1010 /// ```
1011 #[inline]
1012 #[must_use]
1013 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
1014 pub fn max_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
1015     match compare(&v1, &v2) {
1016         Ordering::Less | Ordering::Equal => v2,
1017         Ordering::Greater => v1,
1018     }
1019 }
1020
1021 /// Returns the element that gives the maximum value from the specified function.
1022 ///
1023 /// Returns the second argument if the comparison determines them to be equal.
1024 ///
1025 /// # Examples
1026 ///
1027 /// ```
1028 /// #![feature(cmp_min_max_by)]
1029 ///
1030 /// use std::cmp;
1031 ///
1032 /// assert_eq!(cmp::max_by_key(-2, 1, |x: &i32| x.abs()), -2);
1033 /// assert_eq!(cmp::max_by_key(-2, 2, |x: &i32| x.abs()), 2);
1034 /// ```
1035 #[inline]
1036 #[must_use]
1037 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
1038 pub fn max_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
1039     max_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
1040 }
1041
1042 // Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
1043 mod impls {
1044     use crate::cmp::Ordering::{self, Equal, Greater, Less};
1045     use crate::hint::unreachable_unchecked;
1046
1047     macro_rules! partial_eq_impl {
1048         ($($t:ty)*) => ($(
1049             #[stable(feature = "rust1", since = "1.0.0")]
1050             impl PartialEq for $t {
1051                 #[inline]
1052                 fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
1053                 #[inline]
1054                 fn ne(&self, other: &$t) -> bool { (*self) != (*other) }
1055             }
1056         )*)
1057     }
1058
1059     #[stable(feature = "rust1", since = "1.0.0")]
1060     impl PartialEq for () {
1061         #[inline]
1062         fn eq(&self, _other: &()) -> bool {
1063             true
1064         }
1065         #[inline]
1066         fn ne(&self, _other: &()) -> bool {
1067             false
1068         }
1069     }
1070
1071     partial_eq_impl! {
1072         bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f32 f64
1073     }
1074
1075     macro_rules! eq_impl {
1076         ($($t:ty)*) => ($(
1077             #[stable(feature = "rust1", since = "1.0.0")]
1078             impl Eq for $t {}
1079         )*)
1080     }
1081
1082     eq_impl! { () bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1083
1084     macro_rules! partial_ord_impl {
1085         ($($t:ty)*) => ($(
1086             #[stable(feature = "rust1", since = "1.0.0")]
1087             impl PartialOrd for $t {
1088                 #[inline]
1089                 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1090                     match (self <= other, self >= other) {
1091                         (false, false) => None,
1092                         (false, true) => Some(Greater),
1093                         (true, false) => Some(Less),
1094                         (true, true) => Some(Equal),
1095                     }
1096                 }
1097                 #[inline]
1098                 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1099                 #[inline]
1100                 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1101                 #[inline]
1102                 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1103                 #[inline]
1104                 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1105             }
1106         )*)
1107     }
1108
1109     #[stable(feature = "rust1", since = "1.0.0")]
1110     impl PartialOrd for () {
1111         #[inline]
1112         fn partial_cmp(&self, _: &()) -> Option<Ordering> {
1113             Some(Equal)
1114         }
1115     }
1116
1117     #[stable(feature = "rust1", since = "1.0.0")]
1118     impl PartialOrd for bool {
1119         #[inline]
1120         fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
1121             (*self as u8).partial_cmp(&(*other as u8))
1122         }
1123     }
1124
1125     partial_ord_impl! { f32 f64 }
1126
1127     macro_rules! ord_impl {
1128         ($($t:ty)*) => ($(
1129             #[stable(feature = "rust1", since = "1.0.0")]
1130             impl PartialOrd for $t {
1131                 #[inline]
1132                 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1133                     Some(self.cmp(other))
1134                 }
1135                 #[inline]
1136                 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1137                 #[inline]
1138                 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1139                 #[inline]
1140                 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1141                 #[inline]
1142                 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1143             }
1144
1145             #[stable(feature = "rust1", since = "1.0.0")]
1146             impl Ord for $t {
1147                 #[inline]
1148                 fn cmp(&self, other: &$t) -> Ordering {
1149                     // The order here is important to generate more optimal assembly.
1150                     // See <https://github.com/rust-lang/rust/issues/63758> for more info.
1151                     if *self < *other { Less }
1152                     else if *self == *other { Equal }
1153                     else { Greater }
1154                 }
1155             }
1156         )*)
1157     }
1158
1159     #[stable(feature = "rust1", since = "1.0.0")]
1160     impl Ord for () {
1161         #[inline]
1162         fn cmp(&self, _other: &()) -> Ordering {
1163             Equal
1164         }
1165     }
1166
1167     #[stable(feature = "rust1", since = "1.0.0")]
1168     impl Ord for bool {
1169         #[inline]
1170         fn cmp(&self, other: &bool) -> Ordering {
1171             // Casting to i8's and converting the difference to an Ordering generates
1172             // more optimal assembly.
1173             // See <https://github.com/rust-lang/rust/issues/66780> for more info.
1174             match (*self as i8) - (*other as i8) {
1175                 -1 => Less,
1176                 0 => Equal,
1177                 1 => Greater,
1178                 // SAFETY: bool as i8 returns 0 or 1, so the difference can't be anything else
1179                 _ => unsafe { unreachable_unchecked() },
1180             }
1181         }
1182     }
1183
1184     ord_impl! { char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1185
1186     #[unstable(feature = "never_type", issue = "35121")]
1187     impl PartialEq for ! {
1188         fn eq(&self, _: &!) -> bool {
1189             *self
1190         }
1191     }
1192
1193     #[unstable(feature = "never_type", issue = "35121")]
1194     impl Eq for ! {}
1195
1196     #[unstable(feature = "never_type", issue = "35121")]
1197     impl PartialOrd for ! {
1198         fn partial_cmp(&self, _: &!) -> Option<Ordering> {
1199             *self
1200         }
1201     }
1202
1203     #[unstable(feature = "never_type", issue = "35121")]
1204     impl Ord for ! {
1205         fn cmp(&self, _: &!) -> Ordering {
1206             *self
1207         }
1208     }
1209
1210     // & pointers
1211
1212     #[stable(feature = "rust1", since = "1.0.0")]
1213     impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &A
1214     where
1215         A: PartialEq<B>,
1216     {
1217         #[inline]
1218         fn eq(&self, other: &&B) -> bool {
1219             PartialEq::eq(*self, *other)
1220         }
1221         #[inline]
1222         fn ne(&self, other: &&B) -> bool {
1223             PartialEq::ne(*self, *other)
1224         }
1225     }
1226     #[stable(feature = "rust1", since = "1.0.0")]
1227     impl<A: ?Sized, B: ?Sized> PartialOrd<&B> for &A
1228     where
1229         A: PartialOrd<B>,
1230     {
1231         #[inline]
1232         fn partial_cmp(&self, other: &&B) -> Option<Ordering> {
1233             PartialOrd::partial_cmp(*self, *other)
1234         }
1235         #[inline]
1236         fn lt(&self, other: &&B) -> bool {
1237             PartialOrd::lt(*self, *other)
1238         }
1239         #[inline]
1240         fn le(&self, other: &&B) -> bool {
1241             PartialOrd::le(*self, *other)
1242         }
1243         #[inline]
1244         fn gt(&self, other: &&B) -> bool {
1245             PartialOrd::gt(*self, *other)
1246         }
1247         #[inline]
1248         fn ge(&self, other: &&B) -> bool {
1249             PartialOrd::ge(*self, *other)
1250         }
1251     }
1252     #[stable(feature = "rust1", since = "1.0.0")]
1253     impl<A: ?Sized> Ord for &A
1254     where
1255         A: Ord,
1256     {
1257         #[inline]
1258         fn cmp(&self, other: &Self) -> Ordering {
1259             Ord::cmp(*self, *other)
1260         }
1261     }
1262     #[stable(feature = "rust1", since = "1.0.0")]
1263     impl<A: ?Sized> Eq for &A where A: Eq {}
1264
1265     // &mut pointers
1266
1267     #[stable(feature = "rust1", since = "1.0.0")]
1268     impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &mut A
1269     where
1270         A: PartialEq<B>,
1271     {
1272         #[inline]
1273         fn eq(&self, other: &&mut B) -> bool {
1274             PartialEq::eq(*self, *other)
1275         }
1276         #[inline]
1277         fn ne(&self, other: &&mut B) -> bool {
1278             PartialEq::ne(*self, *other)
1279         }
1280     }
1281     #[stable(feature = "rust1", since = "1.0.0")]
1282     impl<A: ?Sized, B: ?Sized> PartialOrd<&mut B> for &mut A
1283     where
1284         A: PartialOrd<B>,
1285     {
1286         #[inline]
1287         fn partial_cmp(&self, other: &&mut B) -> Option<Ordering> {
1288             PartialOrd::partial_cmp(*self, *other)
1289         }
1290         #[inline]
1291         fn lt(&self, other: &&mut B) -> bool {
1292             PartialOrd::lt(*self, *other)
1293         }
1294         #[inline]
1295         fn le(&self, other: &&mut B) -> bool {
1296             PartialOrd::le(*self, *other)
1297         }
1298         #[inline]
1299         fn gt(&self, other: &&mut B) -> bool {
1300             PartialOrd::gt(*self, *other)
1301         }
1302         #[inline]
1303         fn ge(&self, other: &&mut B) -> bool {
1304             PartialOrd::ge(*self, *other)
1305         }
1306     }
1307     #[stable(feature = "rust1", since = "1.0.0")]
1308     impl<A: ?Sized> Ord for &mut A
1309     where
1310         A: Ord,
1311     {
1312         #[inline]
1313         fn cmp(&self, other: &Self) -> Ordering {
1314             Ord::cmp(*self, *other)
1315         }
1316     }
1317     #[stable(feature = "rust1", since = "1.0.0")]
1318     impl<A: ?Sized> Eq for &mut A where A: Eq {}
1319
1320     #[stable(feature = "rust1", since = "1.0.0")]
1321     impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &A
1322     where
1323         A: PartialEq<B>,
1324     {
1325         #[inline]
1326         fn eq(&self, other: &&mut B) -> bool {
1327             PartialEq::eq(*self, *other)
1328         }
1329         #[inline]
1330         fn ne(&self, other: &&mut B) -> bool {
1331             PartialEq::ne(*self, *other)
1332         }
1333     }
1334
1335     #[stable(feature = "rust1", since = "1.0.0")]
1336     impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &mut A
1337     where
1338         A: PartialEq<B>,
1339     {
1340         #[inline]
1341         fn eq(&self, other: &&B) -> bool {
1342             PartialEq::eq(*self, *other)
1343         }
1344         #[inline]
1345         fn ne(&self, other: &&B) -> bool {
1346             PartialEq::ne(*self, *other)
1347         }
1348     }
1349 }