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 [`trait@Eq`].
  33 ///
  34 /// Formally, the equality must be (for all `a`, `b`, `c` of type `A`, `B`,
  35 /// `C`):
  36 ///
  37 /// - **Symmetric**: if `A: PartialEq<B>` and `B: PartialEq<A>`, then **`a == b`
  38 ///   implies `b == a`**; and
  39 ///
  40 /// - **Transitive**: if `A: PartialEq<B>` and `B: PartialEq<C>` and `A:
  41 ///   PartialEq<C>`, then **`a == b` and `b == c` implies `a == c`**.
  42 ///
  43 /// Note that the `B: PartialEq<A>` (symmetric) and `A: PartialEq<C>`
  44 /// (transitive) impls are not forced to exist, but these requirements apply
  45 /// whenever they do exist.
  46 ///
  47 /// ## Derivable
  48 ///
  49 /// This trait can be used with `#[derive]`. When `derive`d on structs, two
  50 /// instances are equal if all fields are equal, and not equal if any fields
  51 /// are not equal. When `derive`d on enums, each variant is equal to itself
  52 /// and not equal to the other variants.
  53 ///
  54 /// ## How can I implement `PartialEq`?
  55 ///
  56 /// `PartialEq` only requires the [`eq`] method to be implemented; [`ne`] is defined
  57 /// in terms of it by default. Any manual implementation of [`ne`] *must* respect
  58 /// the rule that [`eq`] is a strict inverse of [`ne`]; that is, `!(a == b)` if and
  59 /// only if `a != b`.
  60 ///
  61 /// Implementations of `PartialEq`, [`PartialOrd`], and [`Ord`] *must* agree with
  62 /// each other. It's easy to accidentally make them disagree by deriving some
  63 /// of the traits and manually implementing others.
  64 ///
  65 /// An example implementation for a domain in which two books are considered
  66 /// the same book if their ISBN matches, even if the formats differ:
  67 ///
  68 /// ```
  69 /// enum BookFormat {
  70 ///     Paperback,
  71 ///     Hardback,
  72 ///     Ebook,
  73 /// }
  74 ///
  75 /// struct Book {
  76 ///     isbn: i32,
  77 ///     format: BookFormat,
  78 /// }
  79 ///
  80 /// impl PartialEq for Book {
  81 ///     fn eq(&self, other: &Self) -> bool {
  82 ///         self.isbn == other.isbn
  83 ///     }
  84 /// }
  85 ///
  86 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
  87 /// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
  88 /// let b3 = Book { isbn: 10, format: BookFormat::Paperback };
  89 ///
  90 /// assert!(b1 == b2);
  91 /// assert!(b1 != b3);
  92 /// ```
  93 ///
  94 /// ## How can I compare two different types?
  95 ///
  96 /// The type you can compare with is controlled by `PartialEq`'s type parameter.
  97 /// For example, let's tweak our previous code a bit:
  98 ///
  99 /// ```
 100 /// // The derive implements <BookFormat> == <BookFormat> comparisons
 101 /// #[derive(PartialEq)]
 102 /// enum BookFormat {
 103 ///     Paperback,
 104 ///     Hardback,
 105 ///     Ebook,
 106 /// }
 107 ///
 108 /// struct Book {
 109 ///     isbn: i32,
 110 ///     format: BookFormat,
 111 /// }
 112 ///
 113 /// // Implement <Book> == <BookFormat> comparisons
 114 /// impl PartialEq<BookFormat> for Book {
 115 ///     fn eq(&self, other: &BookFormat) -> bool {
 116 ///         self.format == *other
 117 ///     }
 118 /// }
 119 ///
 120 /// // Implement <BookFormat> == <Book> comparisons
 121 /// impl PartialEq<Book> for BookFormat {
 122 ///     fn eq(&self, other: &Book) -> bool {
 123 ///         *self == other.format
 124 ///     }
 125 /// }
 126 ///
 127 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
 128 ///
 129 /// assert!(b1 == BookFormat::Paperback);
 130 /// assert!(BookFormat::Ebook != b1);
 131 /// ```
 132 ///
 133 /// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
 134 /// we allow `BookFormat`s to be compared with `Book`s.
 135 ///
 136 /// A comparison like the one above, which ignores some fields of the struct,
 137 /// can be dangerous. It can easily lead to an unintended violation of the
 138 /// requirements for a partial equivalence relation. For example, if we kept
 139 /// the above implementation of `PartialEq<Book>` for `BookFormat` and added an
 140 /// implementation of `PartialEq<Book>` for `Book` (either via a `#[derive]` or
 141 /// via the manual implementation from the first example) then the result would
 142 /// violate transitivity:
 143 ///
 144 /// ```should_panic
 145 /// #[derive(PartialEq)]
 146 /// enum BookFormat {
 147 ///     Paperback,
 148 ///     Hardback,
 149 ///     Ebook,
 150 /// }
 151 ///
 152 /// #[derive(PartialEq)]
 153 /// struct Book {
 154 ///     isbn: i32,
 155 ///     format: BookFormat,
 156 /// }
 157 ///
 158 /// impl PartialEq<BookFormat> for Book {
 159 ///     fn eq(&self, other: &BookFormat) -> bool {
 160 ///         self.format == *other
 161 ///     }
 162 /// }
 163 ///
 164 /// impl PartialEq<Book> for BookFormat {
 165 ///     fn eq(&self, other: &Book) -> bool {
 166 ///         *self == other.format
 167 ///     }
 168 /// }
 169 ///
 170 /// fn main() {
 171 ///     let b1 = Book { isbn: 1, format: BookFormat::Paperback };
 172 ///     let b2 = Book { isbn: 2, format: BookFormat::Paperback };
 173 ///
 174 ///     assert!(b1 == BookFormat::Paperback);
 175 ///     assert!(BookFormat::Paperback == b2);
 176 ///
 177 ///     // The following should hold by transitivity but doesn't.
 178 ///     assert!(b1 == b2); // <-- PANICS
 179 /// }
 180 /// ```
 181 ///
 182 /// # Examples
 183 ///
 184 /// ```
 185 /// let x: u32 = 0;
 186 /// let y: u32 = 1;
 187 ///
 188 /// assert_eq!(x == y, false);
 189 /// assert_eq!(x.eq(&y), false);
 190 /// ```
 191 ///
 192 /// [`eq`]: PartialEq::eq
 193 /// [`ne`]: PartialEq::ne
 194 #[lang = "eq"]
 195 #[stable(feature = "rust1", since = "1.0.0")]
 196 #[doc(alias = "==")]
 197 #[doc(alias = "!=")]
 198 #[rustc_on_unimplemented(
 199     message = "can't compare `{Self}` with `{Rhs}`",
 200     label = "no implementation for `{Self} == {Rhs}`"
 201 )]
 202 pub trait PartialEq<Rhs: ?Sized = Self> {
 203     /// This method tests for `self` and `other` values to be equal, and is used
 204     /// by `==`.
 205     #[must_use]
 206     #[stable(feature = "rust1", since = "1.0.0")]
 207     fn eq(&self, other: &Rhs) -> bool;
 208
 209     /// This method tests for `!=`.
 210     #[inline]
 211     #[must_use]
 212     #[stable(feature = "rust1", since = "1.0.0")]
 213     fn ne(&self, other: &Rhs) -> bool {
 214         !self.eq(other)
 215     }
 216 }
 217
 218 /// Derive macro generating an impl of the trait `PartialEq`.
 219 #[rustc_builtin_macro]
 220 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 221 #[allow_internal_unstable(core_intrinsics, structural_match)]
 222 pub macro PartialEq($item:item) {
 223     /* compiler built-in */
 224 }
 225
 226 /// Trait for equality comparisons which are [equivalence relations](
 227 /// https://en.wikipedia.org/wiki/Equivalence_relation).
 228 ///
 229 /// This means, that in addition to `a == b` and `a != b` being strict inverses, the equality must
 230 /// be (for all `a`, `b` and `c`):
 231 ///
 232 /// - reflexive: `a == a`;
 233 /// - symmetric: `a == b` implies `b == a`; and
 234 /// - transitive: `a == b` and `b == c` implies `a == c`.
 235 ///
 236 /// This property cannot be checked by the compiler, and therefore `Eq` implies
 237 /// [`PartialEq`], and has no extra methods.
 238 ///
 239 /// ## Derivable
 240 ///
 241 /// This trait can be used with `#[derive]`. When `derive`d, because `Eq` has
 242 /// no extra methods, it is only informing the compiler that this is an
 243 /// equivalence relation rather than a partial equivalence relation. Note that
 244 /// the `derive` strategy requires all fields are `Eq`, which isn't
 245 /// always desired.
 246 ///
 247 /// ## How can I implement `Eq`?
 248 ///
 249 /// If you cannot use the `derive` strategy, specify that your type implements
 250 /// `Eq`, which has no methods:
 251 ///
 252 /// ```
 253 /// enum BookFormat { Paperback, Hardback, Ebook }
 254 /// struct Book {
 255 ///     isbn: i32,
 256 ///     format: BookFormat,
 257 /// }
 258 /// impl PartialEq for Book {
 259 ///     fn eq(&self, other: &Self) -> bool {
 260 ///         self.isbn == other.isbn
 261 ///     }
 262 /// }
 263 /// impl Eq for Book {}
 264 /// ```
 265 #[doc(alias = "==")]
 266 #[doc(alias = "!=")]
 267 #[stable(feature = "rust1", since = "1.0.0")]
 268 pub trait Eq: PartialEq<Self> {
 269     // this method is used solely by #[deriving] to assert
 270     // that every component of a type implements #[deriving]
 271     // itself, the current deriving infrastructure means doing this
 272     // assertion without using a method on this trait is nearly
 273     // impossible.
 274     //
 275     // This should never be implemented by hand.
 276     #[doc(hidden)]
 277     #[inline]
 278     #[stable(feature = "rust1", since = "1.0.0")]
 279     fn assert_receiver_is_total_eq(&self) {}
 280 }
 281
 282 /// Derive macro generating an impl of the trait `Eq`.
 283 #[rustc_builtin_macro]
 284 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 285 #[allow_internal_unstable(core_intrinsics, derive_eq, structural_match)]
 286 pub macro Eq($item:item) {
 287     /* compiler built-in */
 288 }
 289
 290 // FIXME: this struct is used solely by #[derive] to
 291 // assert that every component of a type implements Eq.
 292 //
 293 // This struct should never appear in user code.
 294 #[doc(hidden)]
 295 #[allow(missing_debug_implementations)]
 296 #[unstable(feature = "derive_eq", reason = "deriving hack, should not be public", issue = "none")]
 297 pub struct AssertParamIsEq<T: Eq + ?Sized> {
 298     _field: crate::marker::PhantomData<T>,
 299 }
 300
 301 /// An `Ordering` is the result of a comparison between two values.
 302 ///
 303 /// # Examples
 304 ///
 305 /// ```
 306 /// use std::cmp::Ordering;
 307 ///
 308 /// let result = 1.cmp(&2);
 309 /// assert_eq!(Ordering::Less, result);
 310 ///
 311 /// let result = 1.cmp(&1);
 312 /// assert_eq!(Ordering::Equal, result);
 313 ///
 314 /// let result = 2.cmp(&1);
 315 /// assert_eq!(Ordering::Greater, result);
 316 /// ```
 317 #[derive(Clone, Copy, PartialEq, Debug, Hash)]
 318 #[stable(feature = "rust1", since = "1.0.0")]
 319 pub enum Ordering {
 320     /// An ordering where a compared value is less than another.
 321     #[stable(feature = "rust1", since = "1.0.0")]
 322     Less = -1,
 323     /// An ordering where a compared value is equal to another.
 324     #[stable(feature = "rust1", since = "1.0.0")]
 325     Equal = 0,
 326     /// An ordering where a compared value is greater than another.
 327     #[stable(feature = "rust1", since = "1.0.0")]
 328     Greater = 1,
 329 }
 330
 331 impl Ordering {
 332     /// Returns `true` if the ordering is the `Equal` variant.
 333     ///
 334     /// # Examples
 335     ///
 336     /// ```
 337     /// #![feature(ordering_helpers)]
 338     /// use std::cmp::Ordering;
 339     ///
 340     /// assert_eq!(Ordering::Less.is_eq(), false);
 341     /// assert_eq!(Ordering::Equal.is_eq(), true);
 342     /// assert_eq!(Ordering::Greater.is_eq(), false);
 343     /// ```
 344     #[inline]
 345     #[must_use]
 346     #[unstable(feature = "ordering_helpers", issue = "79885")]
 347     pub const fn is_eq(self) -> bool {
 348         matches!(self, Equal)
 349     }
 350
 351     /// Returns `true` if the ordering is not the `Equal` variant.
 352     ///
 353     /// # Examples
 354     ///
 355     /// ```
 356     /// #![feature(ordering_helpers)]
 357     /// use std::cmp::Ordering;
 358     ///
 359     /// assert_eq!(Ordering::Less.is_ne(), true);
 360     /// assert_eq!(Ordering::Equal.is_ne(), false);
 361     /// assert_eq!(Ordering::Greater.is_ne(), true);
 362     /// ```
 363     #[inline]
 364     #[must_use]
 365     #[unstable(feature = "ordering_helpers", issue = "79885")]
 366     pub const fn is_ne(self) -> bool {
 367         !matches!(self, Equal)
 368     }
 369
 370     /// Returns `true` if the ordering is the `Less` variant.
 371     ///
 372     /// # Examples
 373     ///
 374     /// ```
 375     /// #![feature(ordering_helpers)]
 376     /// use std::cmp::Ordering;
 377     ///
 378     /// assert_eq!(Ordering::Less.is_lt(), true);
 379     /// assert_eq!(Ordering::Equal.is_lt(), false);
 380     /// assert_eq!(Ordering::Greater.is_lt(), false);
 381     /// ```
 382     #[inline]
 383     #[must_use]
 384     #[unstable(feature = "ordering_helpers", issue = "79885")]
 385     pub const fn is_lt(self) -> bool {
 386         matches!(self, Less)
 387     }
 388
 389     /// Returns `true` if the ordering is the `Greater` variant.
 390     ///
 391     /// # Examples
 392     ///
 393     /// ```
 394     /// #![feature(ordering_helpers)]
 395     /// use std::cmp::Ordering;
 396     ///
 397     /// assert_eq!(Ordering::Less.is_gt(), false);
 398     /// assert_eq!(Ordering::Equal.is_gt(), false);
 399     /// assert_eq!(Ordering::Greater.is_gt(), true);
 400     /// ```
 401     #[inline]
 402     #[must_use]
 403     #[unstable(feature = "ordering_helpers", issue = "79885")]
 404     pub const fn is_gt(self) -> bool {
 405         matches!(self, Greater)
 406     }
 407
 408     /// Returns `true` if the ordering is either the `Less` or `Equal` variant.
 409     ///
 410     /// # Examples
 411     ///
 412     /// ```
 413     /// #![feature(ordering_helpers)]
 414     /// use std::cmp::Ordering;
 415     ///
 416     /// assert_eq!(Ordering::Less.is_le(), true);
 417     /// assert_eq!(Ordering::Equal.is_le(), true);
 418     /// assert_eq!(Ordering::Greater.is_le(), false);
 419     /// ```
 420     #[inline]
 421     #[must_use]
 422     #[unstable(feature = "ordering_helpers", issue = "79885")]
 423     pub const fn is_le(self) -> bool {
 424         !matches!(self, Greater)
 425     }
 426
 427     /// Returns `true` if the ordering is either the `Greater` or `Equal` variant.
 428     ///
 429     /// # Examples
 430     ///
 431     /// ```
 432     /// #![feature(ordering_helpers)]
 433     /// use std::cmp::Ordering;
 434     ///
 435     /// assert_eq!(Ordering::Less.is_ge(), false);
 436     /// assert_eq!(Ordering::Equal.is_ge(), true);
 437     /// assert_eq!(Ordering::Greater.is_ge(), true);
 438     /// ```
 439     #[inline]
 440     #[must_use]
 441     #[unstable(feature = "ordering_helpers", issue = "79885")]
 442     pub const fn is_ge(self) -> bool {
 443         !matches!(self, Less)
 444     }
 445
 446     /// Reverses the `Ordering`.
 447     ///
 448     /// * `Less` becomes `Greater`.
 449     /// * `Greater` becomes `Less`.
 450     /// * `Equal` becomes `Equal`.
 451     ///
 452     /// # Examples
 453     ///
 454     /// Basic behavior:
 455     ///
 456     /// ```
 457     /// use std::cmp::Ordering;
 458     ///
 459     /// assert_eq!(Ordering::Less.reverse(), Ordering::Greater);
 460     /// assert_eq!(Ordering::Equal.reverse(), Ordering::Equal);
 461     /// assert_eq!(Ordering::Greater.reverse(), Ordering::Less);
 462     /// ```
 463     ///
 464     /// This method can be used to reverse a comparison:
 465     ///
 466     /// ```
 467     /// let data: &mut [_] = &mut [2, 10, 5, 8];
 468     ///
 469     /// // sort the array from largest to smallest.
 470     /// data.sort_by(|a, b| a.cmp(b).reverse());
 471     ///
 472     /// let b: &mut [_] = &mut [10, 8, 5, 2];
 473     /// assert!(data == b);
 474     /// ```
 475     #[inline]
 476     #[must_use]
 477     #[rustc_const_stable(feature = "const_ordering", since = "1.48.0")]
 478     #[stable(feature = "rust1", since = "1.0.0")]
 479     pub const fn reverse(self) -> Ordering {
 480         match self {
 481             Less => Greater,
 482             Equal => Equal,
 483             Greater => Less,
 484         }
 485     }
 486
 487     /// Chains two orderings.
 488     ///
 489     /// Returns `self` when it's not `Equal`. Otherwise returns `other`.
 490     ///
 491     /// # Examples
 492     ///
 493     /// ```
 494     /// use std::cmp::Ordering;
 495     ///
 496     /// let result = Ordering::Equal.then(Ordering::Less);
 497     /// assert_eq!(result, Ordering::Less);
 498     ///
 499     /// let result = Ordering::Less.then(Ordering::Equal);
 500     /// assert_eq!(result, Ordering::Less);
 501     ///
 502     /// let result = Ordering::Less.then(Ordering::Greater);
 503     /// assert_eq!(result, Ordering::Less);
 504     ///
 505     /// let result = Ordering::Equal.then(Ordering::Equal);
 506     /// assert_eq!(result, Ordering::Equal);
 507     ///
 508     /// let x: (i64, i64, i64) = (1, 2, 7);
 509     /// let y: (i64, i64, i64) = (1, 5, 3);
 510     /// let result = x.0.cmp(&y.0).then(x.1.cmp(&y.1)).then(x.2.cmp(&y.2));
 511     ///
 512     /// assert_eq!(result, Ordering::Less);
 513     /// ```
 514     #[inline]
 515     #[must_use]
 516     #[rustc_const_stable(feature = "const_ordering", since = "1.48.0")]
 517     #[stable(feature = "ordering_chaining", since = "1.17.0")]
 518     pub const fn then(self, other: Ordering) -> Ordering {
 519         match self {
 520             Equal => other,
 521             _ => self,
 522         }
 523     }
 524
 525     /// Chains the ordering with the given function.
 526     ///
 527     /// Returns `self` when it's not `Equal`. Otherwise calls `f` and returns
 528     /// the result.
 529     ///
 530     /// # Examples
 531     ///
 532     /// ```
 533     /// use std::cmp::Ordering;
 534     ///
 535     /// let result = Ordering::Equal.then_with(|| Ordering::Less);
 536     /// assert_eq!(result, Ordering::Less);
 537     ///
 538     /// let result = Ordering::Less.then_with(|| Ordering::Equal);
 539     /// assert_eq!(result, Ordering::Less);
 540     ///
 541     /// let result = Ordering::Less.then_with(|| Ordering::Greater);
 542     /// assert_eq!(result, Ordering::Less);
 543     ///
 544     /// let result = Ordering::Equal.then_with(|| Ordering::Equal);
 545     /// assert_eq!(result, Ordering::Equal);
 546     ///
 547     /// let x: (i64, i64, i64) = (1, 2, 7);
 548     /// let y: (i64, i64, i64) = (1, 5, 3);
 549     /// let result = x.0.cmp(&y.0).then_with(|| x.1.cmp(&y.1)).then_with(|| x.2.cmp(&y.2));
 550     ///
 551     /// assert_eq!(result, Ordering::Less);
 552     /// ```
 553     #[inline]
 554     #[must_use]
 555     #[stable(feature = "ordering_chaining", since = "1.17.0")]
 556     pub fn then_with<F: FnOnce() -> Ordering>(self, f: F) -> Ordering {
 557         match self {
 558             Equal => f(),
 559             _ => self,
 560         }
 561     }
 562 }
 563
 564 /// A helper struct for reverse ordering.
 565 ///
 566 /// This struct is a helper to be used with functions like [`Vec::sort_by_key`] and
 567 /// can be used to reverse order a part of a key.
 568 ///
 569 /// [`Vec::sort_by_key`]: ../../std/vec/struct.Vec.html#method.sort_by_key
 570 ///
 571 /// # Examples
 572 ///
 573 /// ```
 574 /// use std::cmp::Reverse;
 575 ///
 576 /// let mut v = vec![1, 2, 3, 4, 5, 6];
 577 /// v.sort_by_key(|&num| (num > 3, Reverse(num)));
 578 /// assert_eq!(v, vec![3, 2, 1, 6, 5, 4]);
 579 /// ```
 580 #[derive(PartialEq, Eq, Debug, Copy, Clone, Default, Hash)]
 581 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 582 pub struct Reverse<T>(#[stable(feature = "reverse_cmp_key", since = "1.19.0")] pub T);
 583
 584 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 585 impl<T: PartialOrd> PartialOrd for Reverse<T> {
 586     #[inline]
 587     fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
 588         other.0.partial_cmp(&self.0)
 589     }
 590
 591     #[inline]
 592     fn lt(&self, other: &Self) -> bool {
 593         other.0 < self.0
 594     }
 595     #[inline]
 596     fn le(&self, other: &Self) -> bool {
 597         other.0 <= self.0
 598     }
 599     #[inline]
 600     fn gt(&self, other: &Self) -> bool {
 601         other.0 > self.0
 602     }
 603     #[inline]
 604     fn ge(&self, other: &Self) -> bool {
 605         other.0 >= self.0
 606     }
 607 }
 608
 609 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
 610 impl<T: Ord> Ord for Reverse<T> {
 611     #[inline]
 612     fn cmp(&self, other: &Reverse<T>) -> Ordering {
 613         other.0.cmp(&self.0)
 614     }
 615 }
 616
 617 /// Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order).
 618 ///
 619 /// An order is a total order if it is (for all `a`, `b` and `c`):
 620 ///
 621 /// - total and asymmetric: exactly one of `a < b`, `a == b` or `a > b` is true; and
 622 /// - transitive, `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
 623 ///
 624 /// ## Derivable
 625 ///
 626 /// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
 627 /// [lexicographic](https://en.wikipedia.org/wiki/Lexicographic_order) ordering based on the top-to-bottom declaration order of the struct's members.
 628 /// When `derive`d on enums, variants are ordered by their top-to-bottom discriminant order.
 629 ///
 630 /// ## Lexicographical comparison
 631 ///
 632 /// Lexicographical comparison is an operation with the following properties:
 633 ///  - Two sequences are compared element by element.
 634 ///  - The first mismatching element defines which sequence is lexicographically less or greater than the other.
 635 ///  - If one sequence is a prefix of another, the shorter sequence is lexicographically less than the other.
 636 ///  - If two sequence have equivalent elements and are of the same length, then the sequences are lexicographically equal.
 637 ///  - An empty sequence is lexicographically less than any non-empty sequence.
 638 ///  - Two empty sequences are lexicographically equal.
 639 ///
 640 /// ## How can I implement `Ord`?
 641 ///
 642 /// `Ord` requires that the type also be [`PartialOrd`] and [`Eq`] (which requires [`PartialEq`]).
 643 ///
 644 /// Then you must define an implementation for [`cmp`]. You may find it useful to use
 645 /// [`cmp`] on your type's fields.
 646 ///
 647 /// Implementations of [`PartialEq`], [`PartialOrd`], and `Ord` *must*
 648 /// agree with each other. That is, `a.cmp(b) == Ordering::Equal` if
 649 /// and only if `a == b` and `Some(a.cmp(b)) == a.partial_cmp(b)` for
 650 /// all `a` and `b`. It's easy to accidentally make them disagree by
 651 /// deriving some of the traits and manually implementing others.
 652 ///
 653 /// Here's an example where you want to sort people by height only, disregarding `id`
 654 /// and `name`:
 655 ///
 656 /// ```
 657 /// use std::cmp::Ordering;
 658 ///
 659 /// #[derive(Eq)]
 660 /// struct Person {
 661 ///     id: u32,
 662 ///     name: String,
 663 ///     height: u32,
 664 /// }
 665 ///
 666 /// impl Ord for Person {
 667 ///     fn cmp(&self, other: &Self) -> Ordering {
 668 ///         self.height.cmp(&other.height)
 669 ///     }
 670 /// }
 671 ///
 672 /// impl PartialOrd for Person {
 673 ///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 674 ///         Some(self.cmp(other))
 675 ///     }
 676 /// }
 677 ///
 678 /// impl PartialEq for Person {
 679 ///     fn eq(&self, other: &Self) -> bool {
 680 ///         self.height == other.height
 681 ///     }
 682 /// }
 683 /// ```
 684 ///
 685 /// [`cmp`]: Ord::cmp
 686 #[doc(alias = "<")]
 687 #[doc(alias = ">")]
 688 #[doc(alias = "<=")]
 689 #[doc(alias = ">=")]
 690 #[stable(feature = "rust1", since = "1.0.0")]
 691 pub trait Ord: Eq + PartialOrd<Self> {
 692     /// This method returns an [`Ordering`] between `self` and `other`.
 693     ///
 694     /// By convention, `self.cmp(&other)` returns the ordering matching the expression
 695     /// `self <operator> other` if true.
 696     ///
 697     /// # Examples
 698     ///
 699     /// ```
 700     /// use std::cmp::Ordering;
 701     ///
 702     /// assert_eq!(5.cmp(&10), Ordering::Less);
 703     /// assert_eq!(10.cmp(&5), Ordering::Greater);
 704     /// assert_eq!(5.cmp(&5), Ordering::Equal);
 705     /// ```
 706     #[must_use]
 707     #[stable(feature = "rust1", since = "1.0.0")]
 708     fn cmp(&self, other: &Self) -> Ordering;
 709
 710     /// Compares and returns the maximum of two values.
 711     ///
 712     /// Returns the second argument if the comparison determines them to be equal.
 713     ///
 714     /// # Examples
 715     ///
 716     /// ```
 717     /// assert_eq!(2, 1.max(2));
 718     /// assert_eq!(2, 2.max(2));
 719     /// ```
 720     #[stable(feature = "ord_max_min", since = "1.21.0")]
 721     #[inline]
 722     #[must_use]
 723     fn max(self, other: Self) -> Self
 724     where
 725         Self: Sized,
 726     {
 727         max_by(self, other, Ord::cmp)
 728     }
 729
 730     /// Compares and returns the minimum of two values.
 731     ///
 732     /// Returns the first argument if the comparison determines them to be equal.
 733     ///
 734     /// # Examples
 735     ///
 736     /// ```
 737     /// assert_eq!(1, 1.min(2));
 738     /// assert_eq!(2, 2.min(2));
 739     /// ```
 740     #[stable(feature = "ord_max_min", since = "1.21.0")]
 741     #[inline]
 742     #[must_use]
 743     fn min(self, other: Self) -> Self
 744     where
 745         Self: Sized,
 746     {
 747         min_by(self, other, Ord::cmp)
 748     }
 749
 750     /// Restrict a value to a certain interval.
 751     ///
 752     /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
 753     /// less than `min`. Otherwise this returns `self`.
 754     ///
 755     /// # Panics
 756     ///
 757     /// Panics if `min > max`.
 758     ///
 759     /// # Examples
 760     ///
 761     /// ```
 762     /// assert!((-3).clamp(-2, 1) == -2);
 763     /// assert!(0.clamp(-2, 1) == 0);
 764     /// assert!(2.clamp(-2, 1) == 1);
 765     /// ```
 766     #[must_use]
 767     #[stable(feature = "clamp", since = "1.50.0")]
 768     fn clamp(self, min: Self, max: Self) -> Self
 769     where
 770         Self: Sized,
 771     {
 772         assert!(min <= max);
 773         if self < min {
 774             min
 775         } else if self > max {
 776             max
 777         } else {
 778             self
 779         }
 780     }
 781 }
 782
 783 /// Derive macro generating an impl of the trait `Ord`.
 784 #[rustc_builtin_macro]
 785 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
 786 #[allow_internal_unstable(core_intrinsics)]
 787 pub macro Ord($item:item) {
 788     /* compiler built-in */
 789 }
 790
 791 #[stable(feature = "rust1", since = "1.0.0")]
 792 impl Eq for Ordering {}
 793
 794 #[stable(feature = "rust1", since = "1.0.0")]
 795 impl Ord for Ordering {
 796     #[inline]
 797     fn cmp(&self, other: &Ordering) -> Ordering {
 798         (*self as i32).cmp(&(*other as i32))
 799     }
 800 }
 801
 802 #[stable(feature = "rust1", since = "1.0.0")]
 803 impl PartialOrd for Ordering {
 804     #[inline]
 805     fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
 806         (*self as i32).partial_cmp(&(*other as i32))
 807     }
 808 }
 809
 810 /// Trait for values that can be compared for a sort-order.
 811 ///
 812 /// The comparison must satisfy, for all `a`, `b` and `c`:
 813 ///
 814 /// - asymmetry: if `a < b` then `!(a > b)`, as well as `a > b` implying `!(a < b)`; and
 815 /// - transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
 816 ///
 817 /// Note that these requirements mean that the trait itself must be implemented symmetrically and
 818 /// transitively: if `T: PartialOrd<U>` and `U: PartialOrd<V>` then `U: PartialOrd<T>` and `T:
 819 /// PartialOrd<V>`.
 820 ///
 821 /// ## Derivable
 822 ///
 823 /// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
 824 /// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
 825 /// When `derive`d on enums, variants are ordered by their top-to-bottom discriminant order.
 826 ///
 827 /// ## How can I implement `PartialOrd`?
 828 ///
 829 /// `PartialOrd` only requires implementation of the [`partial_cmp`] method, with the others
 830 /// generated from default implementations.
 831 ///
 832 /// However it remains possible to implement the others separately for types which do not have a
 833 /// total order. For example, for floating point numbers, `NaN < 0 == false` and `NaN >= 0 ==
 834 /// false` (cf. IEEE 754-2008 section 5.11).
 835 ///
 836 /// `PartialOrd` requires your type to be [`PartialEq`].
 837 ///
 838 /// Implementations of [`PartialEq`], `PartialOrd`, and [`Ord`] *must* agree with each other. It's
 839 /// easy to accidentally make them disagree by deriving some of the traits and manually
 840 /// implementing others.
 841 ///
 842 /// If your type is [`Ord`], you can implement [`partial_cmp`] by using [`cmp`]:
 843 ///
 844 /// ```
 845 /// use std::cmp::Ordering;
 846 ///
 847 /// #[derive(Eq)]
 848 /// struct Person {
 849 ///     id: u32,
 850 ///     name: String,
 851 ///     height: u32,
 852 /// }
 853 ///
 854 /// impl PartialOrd for Person {
 855 ///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 856 ///         Some(self.cmp(other))
 857 ///     }
 858 /// }
 859 ///
 860 /// impl Ord for Person {
 861 ///     fn cmp(&self, other: &Self) -> Ordering {
 862 ///         self.height.cmp(&other.height)
 863 ///     }
 864 /// }
 865 ///
 866 /// impl PartialEq for Person {
 867 ///     fn eq(&self, other: &Self) -> bool {
 868 ///         self.height == other.height
 869 ///     }
 870 /// }
 871 /// ```
 872 ///
 873 /// You may also find it useful to use [`partial_cmp`] on your type's fields. Here
 874 /// is an example of `Person` types who have a floating-point `height` field that
 875 /// is the only field to be used for sorting:
 876 ///
 877 /// ```
 878 /// use std::cmp::Ordering;
 879 ///
 880 /// struct Person {
 881 ///     id: u32,
 882 ///     name: String,
 883 ///     height: f64,
 884 /// }
 885 ///
 886 /// impl PartialOrd for Person {
 887 ///     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 888 ///         self.height.partial_cmp(&other.height)
 889 ///     }
 890 /// }
 891 ///
 892 /// impl PartialEq for Person {
 893 ///     fn eq(&self, other: &Self) -> bool {
 894 ///         self.height == other.height
 895 ///     }
 896 /// }
 897 /// ```
 898 ///
 899 /// # Examples
 900 ///
 901 /// ```
 902 /// let x : u32 = 0;
 903 /// let y : u32 = 1;
 904 ///
 905 /// assert_eq!(x < y, true);
 906 /// assert_eq!(x.lt(&y), true);
 907 /// ```
 908 ///
 909 /// [`partial_cmp`]: PartialOrd::partial_cmp
 910 /// [`cmp`]: Ord::cmp
 911 #[lang = "partial_ord"]
 912 #[stable(feature = "rust1", since = "1.0.0")]
 913 #[doc(alias = ">")]
 914 #[doc(alias = "<")]
 915 #[doc(alias = "<=")]
 916 #[doc(alias = ">=")]
 917 #[rustc_on_unimplemented(
 918     message = "can't compare `{Self}` with `{Rhs}`",
 919     label = "no implementation for `{Self} < {Rhs}` and `{Self} > {Rhs}`"
 920 )]
 921 pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
 922     /// This method returns an ordering between `self` and `other` values if one exists.
 923     ///
 924     /// # Examples
 925     ///
 926     /// ```
 927     /// use std::cmp::Ordering;
 928     ///
 929     /// let result = 1.0.partial_cmp(&2.0);
 930     /// assert_eq!(result, Some(Ordering::Less));
 931     ///
 932     /// let result = 1.0.partial_cmp(&1.0);
 933     /// assert_eq!(result, Some(Ordering::Equal));
 934     ///
 935     /// let result = 2.0.partial_cmp(&1.0);
 936     /// assert_eq!(result, Some(Ordering::Greater));
 937     /// ```
 938     ///
 939     /// When comparison is impossible:
 940     ///
 941     /// ```
 942     /// let result = f64::NAN.partial_cmp(&1.0);
 943     /// assert_eq!(result, None);
 944     /// ```
 945     #[must_use]
 946     #[stable(feature = "rust1", since = "1.0.0")]
 947     fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;
 948
 949     /// This method tests less than (for `self` and `other`) and is used by the `<` operator.
 950     ///
 951     /// # Examples
 952     ///
 953     /// ```
 954     /// let result = 1.0 < 2.0;
 955     /// assert_eq!(result, true);
 956     ///
 957     /// let result = 2.0 < 1.0;
 958     /// assert_eq!(result, false);
 959     /// ```
 960     #[inline]
 961     #[must_use]
 962     #[stable(feature = "rust1", since = "1.0.0")]
 963     fn lt(&self, other: &Rhs) -> bool {
 964         matches!(self.partial_cmp(other), Some(Less))
 965     }
 966
 967     /// This method tests less than or equal to (for `self` and `other`) and is used by the `<=`
 968     /// operator.
 969     ///
 970     /// # Examples
 971     ///
 972     /// ```
 973     /// let result = 1.0 <= 2.0;
 974     /// assert_eq!(result, true);
 975     ///
 976     /// let result = 2.0 <= 2.0;
 977     /// assert_eq!(result, true);
 978     /// ```
 979     #[inline]
 980     #[must_use]
 981     #[stable(feature = "rust1", since = "1.0.0")]
 982     fn le(&self, other: &Rhs) -> bool {
 983         matches!(self.partial_cmp(other), Some(Less | Equal))
 984     }
 985
 986     /// This method tests greater than (for `self` and `other`) and is used by the `>` operator.
 987     ///
 988     /// # Examples
 989     ///
 990     /// ```
 991     /// let result = 1.0 > 2.0;
 992     /// assert_eq!(result, false);
 993     ///
 994     /// let result = 2.0 > 2.0;
 995     /// assert_eq!(result, false);
 996     /// ```
 997     #[inline]
 998     #[must_use]
 999     #[stable(feature = "rust1", since = "1.0.0")]
1000     fn gt(&self, other: &Rhs) -> bool {
1001         matches!(self.partial_cmp(other), Some(Greater))
1002     }
1003
1004     /// This method tests greater than or equal to (for `self` and `other`) and is used by the `>=`
1005     /// operator.
1006     ///
1007     /// # Examples
1008     ///
1009     /// ```
1010     /// let result = 2.0 >= 1.0;
1011     /// assert_eq!(result, true);
1012     ///
1013     /// let result = 2.0 >= 2.0;
1014     /// assert_eq!(result, true);
1015     /// ```
1016     #[inline]
1017     #[must_use]
1018     #[stable(feature = "rust1", since = "1.0.0")]
1019     fn ge(&self, other: &Rhs) -> bool {
1020         matches!(self.partial_cmp(other), Some(Greater | Equal))
1021     }
1022 }
1023
1024 /// Derive macro generating an impl of the trait `PartialOrd`.
1025 #[rustc_builtin_macro]
1026 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
1027 #[allow_internal_unstable(core_intrinsics)]
1028 pub macro PartialOrd($item:item) {
1029     /* compiler built-in */
1030 }
1031
1032 /// Compares and returns the minimum of two values.
1033 ///
1034 /// Returns the first argument if the comparison determines them to be equal.
1035 ///
1036 /// Internally uses an alias to [`Ord::min`].
1037 ///
1038 /// # Examples
1039 ///
1040 /// ```
1041 /// use std::cmp;
1042 ///
1043 /// assert_eq!(1, cmp::min(1, 2));
1044 /// assert_eq!(2, cmp::min(2, 2));
1045 /// ```
1046 #[inline]
1047 #[must_use]
1048 #[stable(feature = "rust1", since = "1.0.0")]
1049 pub fn min<T: Ord>(v1: T, v2: T) -> T {
1050     v1.min(v2)
1051 }
1052
1053 /// Returns the minimum of two values with respect to the specified comparison function.
1054 ///
1055 /// Returns the first argument if the comparison determines them to be equal.
1056 ///
1057 /// # Examples
1058 ///
1059 /// ```
1060 /// #![feature(cmp_min_max_by)]
1061 ///
1062 /// use std::cmp;
1063 ///
1064 /// assert_eq!(cmp::min_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 1);
1065 /// assert_eq!(cmp::min_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
1066 /// ```
1067 #[inline]
1068 #[must_use]
1069 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
1070 pub fn min_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
1071     match compare(&v1, &v2) {
1072         Ordering::Less | Ordering::Equal => v1,
1073         Ordering::Greater => v2,
1074     }
1075 }
1076
1077 /// Returns the element that gives the minimum value from the specified function.
1078 ///
1079 /// Returns the first argument if the comparison determines them to be equal.
1080 ///
1081 /// # Examples
1082 ///
1083 /// ```
1084 /// #![feature(cmp_min_max_by)]
1085 ///
1086 /// use std::cmp;
1087 ///
1088 /// assert_eq!(cmp::min_by_key(-2, 1, |x: &i32| x.abs()), 1);
1089 /// assert_eq!(cmp::min_by_key(-2, 2, |x: &i32| x.abs()), -2);
1090 /// ```
1091 #[inline]
1092 #[must_use]
1093 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
1094 pub fn min_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
1095     min_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
1096 }
1097
1098 /// Compares and returns the maximum of two values.
1099 ///
1100 /// Returns the second argument if the comparison determines them to be equal.
1101 ///
1102 /// Internally uses an alias to [`Ord::max`].
1103 ///
1104 /// # Examples
1105 ///
1106 /// ```
1107 /// use std::cmp;
1108 ///
1109 /// assert_eq!(2, cmp::max(1, 2));
1110 /// assert_eq!(2, cmp::max(2, 2));
1111 /// ```
1112 #[inline]
1113 #[must_use]
1114 #[stable(feature = "rust1", since = "1.0.0")]
1115 pub fn max<T: Ord>(v1: T, v2: T) -> T {
1116     v1.max(v2)
1117 }
1118
1119 /// Returns the maximum of two values with respect to the specified comparison function.
1120 ///
1121 /// Returns the second argument if the comparison determines them to be equal.
1122 ///
1123 /// # Examples
1124 ///
1125 /// ```
1126 /// #![feature(cmp_min_max_by)]
1127 ///
1128 /// use std::cmp;
1129 ///
1130 /// assert_eq!(cmp::max_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
1131 /// assert_eq!(cmp::max_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 2);
1132 /// ```
1133 #[inline]
1134 #[must_use]
1135 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
1136 pub fn max_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
1137     match compare(&v1, &v2) {
1138         Ordering::Less | Ordering::Equal => v2,
1139         Ordering::Greater => v1,
1140     }
1141 }
1142
1143 /// Returns the element that gives the maximum value from the specified function.
1144 ///
1145 /// Returns the second argument if the comparison determines them to be equal.
1146 ///
1147 /// # Examples
1148 ///
1149 /// ```
1150 /// #![feature(cmp_min_max_by)]
1151 ///
1152 /// use std::cmp;
1153 ///
1154 /// assert_eq!(cmp::max_by_key(-2, 1, |x: &i32| x.abs()), -2);
1155 /// assert_eq!(cmp::max_by_key(-2, 2, |x: &i32| x.abs()), 2);
1156 /// ```
1157 #[inline]
1158 #[must_use]
1159 #[unstable(feature = "cmp_min_max_by", issue = "64460")]
1160 pub fn max_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
1161     max_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
1162 }
1163
1164 // Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
1165 mod impls {
1166     use crate::cmp::Ordering::{self, Equal, Greater, Less};
1167     use crate::hint::unreachable_unchecked;
1168
1169     macro_rules! partial_eq_impl {
1170         ($($t:ty)*) => ($(
1171             #[stable(feature = "rust1", since = "1.0.0")]
1172             impl PartialEq for $t {
1173                 #[inline]
1174                 fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
1175                 #[inline]
1176                 fn ne(&self, other: &$t) -> bool { (*self) != (*other) }
1177             }
1178         )*)
1179     }
1180
1181     #[stable(feature = "rust1", since = "1.0.0")]
1182     impl PartialEq for () {
1183         #[inline]
1184         fn eq(&self, _other: &()) -> bool {
1185             true
1186         }
1187         #[inline]
1188         fn ne(&self, _other: &()) -> bool {
1189             false
1190         }
1191     }
1192
1193     partial_eq_impl! {
1194         bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f32 f64
1195     }
1196
1197     macro_rules! eq_impl {
1198         ($($t:ty)*) => ($(
1199             #[stable(feature = "rust1", since = "1.0.0")]
1200             impl Eq for $t {}
1201         )*)
1202     }
1203
1204     eq_impl! { () bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1205
1206     macro_rules! partial_ord_impl {
1207         ($($t:ty)*) => ($(
1208             #[stable(feature = "rust1", since = "1.0.0")]
1209             impl PartialOrd for $t {
1210                 #[inline]
1211                 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1212                     match (self <= other, self >= other) {
1213                         (false, false) => None,
1214                         (false, true) => Some(Greater),
1215                         (true, false) => Some(Less),
1216                         (true, true) => Some(Equal),
1217                     }
1218                 }
1219                 #[inline]
1220                 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1221                 #[inline]
1222                 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1223                 #[inline]
1224                 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1225                 #[inline]
1226                 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1227             }
1228         )*)
1229     }
1230
1231     #[stable(feature = "rust1", since = "1.0.0")]
1232     impl PartialOrd for () {
1233         #[inline]
1234         fn partial_cmp(&self, _: &()) -> Option<Ordering> {
1235             Some(Equal)
1236         }
1237     }
1238
1239     #[stable(feature = "rust1", since = "1.0.0")]
1240     impl PartialOrd for bool {
1241         #[inline]
1242         fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
1243             Some(self.cmp(other))
1244         }
1245     }
1246
1247     partial_ord_impl! { f32 f64 }
1248
1249     macro_rules! ord_impl {
1250         ($($t:ty)*) => ($(
1251             #[stable(feature = "rust1", since = "1.0.0")]
1252             impl PartialOrd for $t {
1253                 #[inline]
1254                 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1255                     Some(self.cmp(other))
1256                 }
1257                 #[inline]
1258                 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1259                 #[inline]
1260                 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1261                 #[inline]
1262                 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1263                 #[inline]
1264                 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1265             }
1266
1267             #[stable(feature = "rust1", since = "1.0.0")]
1268             impl Ord for $t {
1269                 #[inline]
1270                 fn cmp(&self, other: &$t) -> Ordering {
1271                     // The order here is important to generate more optimal assembly.
1272                     // See <https://github.com/rust-lang/rust/issues/63758> for more info.
1273                     if *self < *other { Less }
1274                     else if *self == *other { Equal }
1275                     else { Greater }
1276                 }
1277             }
1278         )*)
1279     }
1280
1281     #[stable(feature = "rust1", since = "1.0.0")]
1282     impl Ord for () {
1283         #[inline]
1284         fn cmp(&self, _other: &()) -> Ordering {
1285             Equal
1286         }
1287     }
1288
1289     #[stable(feature = "rust1", since = "1.0.0")]
1290     impl Ord for bool {
1291         #[inline]
1292         fn cmp(&self, other: &bool) -> Ordering {
1293             // Casting to i8's and converting the difference to an Ordering generates
1294             // more optimal assembly.
1295             // See <https://github.com/rust-lang/rust/issues/66780> for more info.
1296             match (*self as i8) - (*other as i8) {
1297                 -1 => Less,
1298                 0 => Equal,
1299                 1 => Greater,
1300                 // SAFETY: bool as i8 returns 0 or 1, so the difference can't be anything else
1301                 _ => unsafe { unreachable_unchecked() },
1302             }
1303         }
1304     }
1305
1306     ord_impl! { char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1307
1308     #[unstable(feature = "never_type", issue = "35121")]
1309     impl PartialEq for ! {
1310         fn eq(&self, _: &!) -> bool {
1311             *self
1312         }
1313     }
1314
1315     #[unstable(feature = "never_type", issue = "35121")]
1316     impl Eq for ! {}
1317
1318     #[unstable(feature = "never_type", issue = "35121")]
1319     impl PartialOrd for ! {
1320         fn partial_cmp(&self, _: &!) -> Option<Ordering> {
1321             *self
1322         }
1323     }
1324
1325     #[unstable(feature = "never_type", issue = "35121")]
1326     impl Ord for ! {
1327         fn cmp(&self, _: &!) -> Ordering {
1328             *self
1329         }
1330     }
1331
1332     // & pointers
1333
1334     #[stable(feature = "rust1", since = "1.0.0")]
1335     impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &A
1336     where
1337         A: PartialEq<B>,
1338     {
1339         #[inline]
1340         fn eq(&self, other: &&B) -> bool {
1341             PartialEq::eq(*self, *other)
1342         }
1343         #[inline]
1344         fn ne(&self, other: &&B) -> bool {
1345             PartialEq::ne(*self, *other)
1346         }
1347     }
1348     #[stable(feature = "rust1", since = "1.0.0")]
1349     impl<A: ?Sized, B: ?Sized> PartialOrd<&B> for &A
1350     where
1351         A: PartialOrd<B>,
1352     {
1353         #[inline]
1354         fn partial_cmp(&self, other: &&B) -> Option<Ordering> {
1355             PartialOrd::partial_cmp(*self, *other)
1356         }
1357         #[inline]
1358         fn lt(&self, other: &&B) -> bool {
1359             PartialOrd::lt(*self, *other)
1360         }
1361         #[inline]
1362         fn le(&self, other: &&B) -> bool {
1363             PartialOrd::le(*self, *other)
1364         }
1365         #[inline]
1366         fn gt(&self, other: &&B) -> bool {
1367             PartialOrd::gt(*self, *other)
1368         }
1369         #[inline]
1370         fn ge(&self, other: &&B) -> bool {
1371             PartialOrd::ge(*self, *other)
1372         }
1373     }
1374     #[stable(feature = "rust1", since = "1.0.0")]
1375     impl<A: ?Sized> Ord for &A
1376     where
1377         A: Ord,
1378     {
1379         #[inline]
1380         fn cmp(&self, other: &Self) -> Ordering {
1381             Ord::cmp(*self, *other)
1382         }
1383     }
1384     #[stable(feature = "rust1", since = "1.0.0")]
1385     impl<A: ?Sized> Eq for &A where A: Eq {}
1386
1387     // &mut pointers
1388
1389     #[stable(feature = "rust1", since = "1.0.0")]
1390     impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &mut A
1391     where
1392         A: PartialEq<B>,
1393     {
1394         #[inline]
1395         fn eq(&self, other: &&mut B) -> bool {
1396             PartialEq::eq(*self, *other)
1397         }
1398         #[inline]
1399         fn ne(&self, other: &&mut B) -> bool {
1400             PartialEq::ne(*self, *other)
1401         }
1402     }
1403     #[stable(feature = "rust1", since = "1.0.0")]
1404     impl<A: ?Sized, B: ?Sized> PartialOrd<&mut B> for &mut A
1405     where
1406         A: PartialOrd<B>,
1407     {
1408         #[inline]
1409         fn partial_cmp(&self, other: &&mut B) -> Option<Ordering> {
1410             PartialOrd::partial_cmp(*self, *other)
1411         }
1412         #[inline]
1413         fn lt(&self, other: &&mut B) -> bool {
1414             PartialOrd::lt(*self, *other)
1415         }
1416         #[inline]
1417         fn le(&self, other: &&mut B) -> bool {
1418             PartialOrd::le(*self, *other)
1419         }
1420         #[inline]
1421         fn gt(&self, other: &&mut B) -> bool {
1422             PartialOrd::gt(*self, *other)
1423         }
1424         #[inline]
1425         fn ge(&self, other: &&mut B) -> bool {
1426             PartialOrd::ge(*self, *other)
1427         }
1428     }
1429     #[stable(feature = "rust1", since = "1.0.0")]
1430     impl<A: ?Sized> Ord for &mut A
1431     where
1432         A: Ord,
1433     {
1434         #[inline]
1435         fn cmp(&self, other: &Self) -> Ordering {
1436             Ord::cmp(*self, *other)
1437         }
1438     }
1439     #[stable(feature = "rust1", since = "1.0.0")]
1440     impl<A: ?Sized> Eq for &mut A where A: Eq {}
1441
1442     #[stable(feature = "rust1", since = "1.0.0")]
1443     impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &A
1444     where
1445         A: PartialEq<B>,
1446     {
1447         #[inline]
1448         fn eq(&self, other: &&mut B) -> bool {
1449             PartialEq::eq(*self, *other)
1450         }
1451         #[inline]
1452         fn ne(&self, other: &&mut B) -> bool {
1453             PartialEq::ne(*self, *other)
1454         }
1455     }
1456
1457     #[stable(feature = "rust1", since = "1.0.0")]
1458     impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &mut A
1459     where
1460         A: PartialEq<B>,
1461     {
1462         #[inline]
1463         fn eq(&self, other: &&B) -> bool {
1464             PartialEq::eq(*self, *other)
1465         }
1466         #[inline]
1467         fn ne(&self, other: &&B) -> bool {
1468             PartialEq::ne(*self, *other)
1469         }
1470     }
1471 }