1 //! Functionality for ordering and comparison.
3 //! This module contains various tools for ordering and comparing values. In
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.
18 //! For more details, see the respective documentation of each item in the list.
23 #![stable(feature = "rust1", since = "1.0.0")]
25 use self::Ordering::*;
27 /// Trait for equality comparisons which are [partial equivalence
28 /// relations](https://en.wikipedia.org/wiki/Partial_equivalence_relation).
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`].
34 /// Formally, the equality must be (for all `a`, `b`, `c` of type `A`, `B`,
37 /// - **Symmetric**: if `A: PartialEq<B>` and `B: PartialEq<A>`, then **`a == b`
38 /// implies `b == a`**; and
40 /// - **Transitive**: if `A: PartialEq<B>` and `B: PartialEq<C>` and `A:
41 /// PartialEq<C>`, then **`a == b` and `b == c` implies `a == c`**.
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.
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.
54 /// ## How can I implement `PartialEq`?
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
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.
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:
77 /// format: BookFormat,
80 /// impl PartialEq for Book {
81 /// fn eq(&self, other: &Self) -> bool {
82 /// self.isbn == other.isbn
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 };
90 /// assert!(b1 == b2);
91 /// assert!(b1 != b3);
94 /// ## How can I compare two different types?
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:
100 /// // The derive implements <BookFormat> == <BookFormat> comparisons
101 /// #[derive(PartialEq)]
102 /// enum BookFormat {
110 /// format: BookFormat,
113 /// // Implement <Book> == <BookFormat> comparisons
114 /// impl PartialEq<BookFormat> for Book {
115 /// fn eq(&self, other: &BookFormat) -> bool {
116 /// self.format == *other
120 /// // Implement <BookFormat> == <Book> comparisons
121 /// impl PartialEq<Book> for BookFormat {
122 /// fn eq(&self, other: &Book) -> bool {
123 /// *self == other.format
127 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
129 /// assert!(b1 == BookFormat::Paperback);
130 /// assert!(BookFormat::Ebook != b1);
133 /// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
134 /// we allow `BookFormat`s to be compared with `Book`s.
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:
145 /// #[derive(PartialEq)]
146 /// enum BookFormat {
152 /// #[derive(PartialEq)]
155 /// format: BookFormat,
158 /// impl PartialEq<BookFormat> for Book {
159 /// fn eq(&self, other: &BookFormat) -> bool {
160 /// self.format == *other
164 /// impl PartialEq<Book> for BookFormat {
165 /// fn eq(&self, other: &Book) -> bool {
166 /// *self == other.format
171 /// let b1 = Book { isbn: 1, format: BookFormat::Paperback };
172 /// let b2 = Book { isbn: 2, format: BookFormat::Paperback };
174 /// assert!(b1 == BookFormat::Paperback);
175 /// assert!(BookFormat::Paperback == b2);
177 /// // The following should hold by transitivity but doesn't.
178 /// assert!(b1 == b2); // <-- PANICS
188 /// assert_eq!(x == y, false);
189 /// assert_eq!(x.eq(&y), false);
192 /// [`eq`]: PartialEq::eq
193 /// [`ne`]: PartialEq::ne
195 #[stable(feature = "rust1", since = "1.0.0")]
198 #[rustc_on_unimplemented(
199 message = "can't compare `{Self}` with `{Rhs}`",
200 label = "no implementation for `{Self} == {Rhs}`"
202 pub trait PartialEq<Rhs: ?Sized = Self> {
203 /// This method tests for `self` and `other` values to be equal, and is used
206 #[stable(feature = "rust1", since = "1.0.0")]
207 fn eq(&self, other: &Rhs) -> bool;
209 /// This method tests for `!=`.
212 #[stable(feature = "rust1", since = "1.0.0")]
213 fn ne(&self, other: &Rhs) -> bool {
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 */
226 /// Trait for equality comparisons which are [equivalence relations](
227 /// https://en.wikipedia.org/wiki/Equivalence_relation).
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`):
232 /// - reflexive: `a == a`;
233 /// - symmetric: `a == b` implies `b == a`; and
234 /// - transitive: `a == b` and `b == c` implies `a == c`.
236 /// This property cannot be checked by the compiler, and therefore `Eq` implies
237 /// [`PartialEq`], and has no extra methods.
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
247 /// ## How can I implement `Eq`?
249 /// If you cannot use the `derive` strategy, specify that your type implements
250 /// `Eq`, which has no methods:
253 /// enum BookFormat { Paperback, Hardback, Ebook }
256 /// format: BookFormat,
258 /// impl PartialEq for Book {
259 /// fn eq(&self, other: &Self) -> bool {
260 /// self.isbn == other.isbn
263 /// impl Eq for Book {}
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
275 // This should never be implemented by hand.
277 #[no_coverage] // rust-lang/rust#84605
279 #[stable(feature = "rust1", since = "1.0.0")]
280 fn assert_receiver_is_total_eq(&self) {}
283 /// Derive macro generating an impl of the trait `Eq`.
284 #[rustc_builtin_macro]
285 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
286 #[allow_internal_unstable(core_intrinsics, derive_eq, structural_match, no_coverage)]
287 pub macro Eq($item:item) {
288 /* compiler built-in */
291 // FIXME: this struct is used solely by #[derive] to
292 // assert that every component of a type implements Eq.
294 // This struct should never appear in user code.
296 #[allow(missing_debug_implementations)]
297 #[unstable(feature = "derive_eq", reason = "deriving hack, should not be public", issue = "none")]
298 pub struct AssertParamIsEq<T: Eq + ?Sized> {
299 _field: crate::marker::PhantomData<T>,
302 /// An `Ordering` is the result of a comparison between two values.
307 /// use std::cmp::Ordering;
309 /// let result = 1.cmp(&2);
310 /// assert_eq!(Ordering::Less, result);
312 /// let result = 1.cmp(&1);
313 /// assert_eq!(Ordering::Equal, result);
315 /// let result = 2.cmp(&1);
316 /// assert_eq!(Ordering::Greater, result);
318 #[derive(Clone, Copy, PartialEq, Debug, Hash)]
319 #[stable(feature = "rust1", since = "1.0.0")]
321 /// An ordering where a compared value is less than another.
322 #[stable(feature = "rust1", since = "1.0.0")]
324 /// An ordering where a compared value is equal to another.
325 #[stable(feature = "rust1", since = "1.0.0")]
327 /// An ordering where a compared value is greater than another.
328 #[stable(feature = "rust1", since = "1.0.0")]
333 /// Returns `true` if the ordering is the `Equal` variant.
338 /// use std::cmp::Ordering;
340 /// assert_eq!(Ordering::Less.is_eq(), false);
341 /// assert_eq!(Ordering::Equal.is_eq(), true);
342 /// assert_eq!(Ordering::Greater.is_eq(), false);
346 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
347 #[stable(feature = "ordering_helpers", since = "1.53.0")]
348 pub const fn is_eq(self) -> bool {
349 matches!(self, Equal)
352 /// Returns `true` if the ordering is not the `Equal` variant.
357 /// use std::cmp::Ordering;
359 /// assert_eq!(Ordering::Less.is_ne(), true);
360 /// assert_eq!(Ordering::Equal.is_ne(), false);
361 /// assert_eq!(Ordering::Greater.is_ne(), true);
365 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
366 #[stable(feature = "ordering_helpers", since = "1.53.0")]
367 pub const fn is_ne(self) -> bool {
368 !matches!(self, Equal)
371 /// Returns `true` if the ordering is the `Less` variant.
376 /// use std::cmp::Ordering;
378 /// assert_eq!(Ordering::Less.is_lt(), true);
379 /// assert_eq!(Ordering::Equal.is_lt(), false);
380 /// assert_eq!(Ordering::Greater.is_lt(), false);
384 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
385 #[stable(feature = "ordering_helpers", since = "1.53.0")]
386 pub const fn is_lt(self) -> bool {
390 /// Returns `true` if the ordering is the `Greater` variant.
395 /// use std::cmp::Ordering;
397 /// assert_eq!(Ordering::Less.is_gt(), false);
398 /// assert_eq!(Ordering::Equal.is_gt(), false);
399 /// assert_eq!(Ordering::Greater.is_gt(), true);
403 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
404 #[stable(feature = "ordering_helpers", since = "1.53.0")]
405 pub const fn is_gt(self) -> bool {
406 matches!(self, Greater)
409 /// Returns `true` if the ordering is either the `Less` or `Equal` variant.
414 /// use std::cmp::Ordering;
416 /// assert_eq!(Ordering::Less.is_le(), true);
417 /// assert_eq!(Ordering::Equal.is_le(), true);
418 /// assert_eq!(Ordering::Greater.is_le(), false);
422 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
423 #[stable(feature = "ordering_helpers", since = "1.53.0")]
424 pub const fn is_le(self) -> bool {
425 !matches!(self, Greater)
428 /// Returns `true` if the ordering is either the `Greater` or `Equal` variant.
433 /// use std::cmp::Ordering;
435 /// assert_eq!(Ordering::Less.is_ge(), false);
436 /// assert_eq!(Ordering::Equal.is_ge(), true);
437 /// assert_eq!(Ordering::Greater.is_ge(), true);
441 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
442 #[stable(feature = "ordering_helpers", since = "1.53.0")]
443 pub const fn is_ge(self) -> bool {
444 !matches!(self, Less)
447 /// Reverses the `Ordering`.
449 /// * `Less` becomes `Greater`.
450 /// * `Greater` becomes `Less`.
451 /// * `Equal` becomes `Equal`.
458 /// use std::cmp::Ordering;
460 /// assert_eq!(Ordering::Less.reverse(), Ordering::Greater);
461 /// assert_eq!(Ordering::Equal.reverse(), Ordering::Equal);
462 /// assert_eq!(Ordering::Greater.reverse(), Ordering::Less);
465 /// This method can be used to reverse a comparison:
468 /// let data: &mut [_] = &mut [2, 10, 5, 8];
470 /// // sort the array from largest to smallest.
471 /// data.sort_by(|a, b| a.cmp(b).reverse());
473 /// let b: &mut [_] = &mut [10, 8, 5, 2];
474 /// assert!(data == b);
478 #[rustc_const_stable(feature = "const_ordering", since = "1.48.0")]
479 #[stable(feature = "rust1", since = "1.0.0")]
480 pub const fn reverse(self) -> Ordering {
488 /// Chains two orderings.
490 /// Returns `self` when it's not `Equal`. Otherwise returns `other`.
495 /// use std::cmp::Ordering;
497 /// let result = Ordering::Equal.then(Ordering::Less);
498 /// assert_eq!(result, Ordering::Less);
500 /// let result = Ordering::Less.then(Ordering::Equal);
501 /// assert_eq!(result, Ordering::Less);
503 /// let result = Ordering::Less.then(Ordering::Greater);
504 /// assert_eq!(result, Ordering::Less);
506 /// let result = Ordering::Equal.then(Ordering::Equal);
507 /// assert_eq!(result, Ordering::Equal);
509 /// let x: (i64, i64, i64) = (1, 2, 7);
510 /// let y: (i64, i64, i64) = (1, 5, 3);
511 /// let result = x.0.cmp(&y.0).then(x.1.cmp(&y.1)).then(x.2.cmp(&y.2));
513 /// assert_eq!(result, Ordering::Less);
517 #[rustc_const_stable(feature = "const_ordering", since = "1.48.0")]
518 #[stable(feature = "ordering_chaining", since = "1.17.0")]
519 pub const fn then(self, other: Ordering) -> Ordering {
526 /// Chains the ordering with the given function.
528 /// Returns `self` when it's not `Equal`. Otherwise calls `f` and returns
534 /// use std::cmp::Ordering;
536 /// let result = Ordering::Equal.then_with(|| Ordering::Less);
537 /// assert_eq!(result, Ordering::Less);
539 /// let result = Ordering::Less.then_with(|| Ordering::Equal);
540 /// assert_eq!(result, Ordering::Less);
542 /// let result = Ordering::Less.then_with(|| Ordering::Greater);
543 /// assert_eq!(result, Ordering::Less);
545 /// let result = Ordering::Equal.then_with(|| Ordering::Equal);
546 /// assert_eq!(result, Ordering::Equal);
548 /// let x: (i64, i64, i64) = (1, 2, 7);
549 /// let y: (i64, i64, i64) = (1, 5, 3);
550 /// let result = x.0.cmp(&y.0).then_with(|| x.1.cmp(&y.1)).then_with(|| x.2.cmp(&y.2));
552 /// assert_eq!(result, Ordering::Less);
556 #[stable(feature = "ordering_chaining", since = "1.17.0")]
557 pub fn then_with<F: FnOnce() -> Ordering>(self, f: F) -> Ordering {
565 /// A helper struct for reverse ordering.
567 /// This struct is a helper to be used with functions like [`Vec::sort_by_key`] and
568 /// can be used to reverse order a part of a key.
570 /// [`Vec::sort_by_key`]: ../../std/vec/struct.Vec.html#method.sort_by_key
575 /// use std::cmp::Reverse;
577 /// let mut v = vec![1, 2, 3, 4, 5, 6];
578 /// v.sort_by_key(|&num| (num > 3, Reverse(num)));
579 /// assert_eq!(v, vec![3, 2, 1, 6, 5, 4]);
581 #[derive(PartialEq, Eq, Debug, Copy, Default, Hash)]
582 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
584 pub struct Reverse<T>(#[stable(feature = "reverse_cmp_key", since = "1.19.0")] pub T);
586 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
587 impl<T: PartialOrd> PartialOrd for Reverse<T> {
589 fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
590 other.0.partial_cmp(&self.0)
594 fn lt(&self, other: &Self) -> bool {
598 fn le(&self, other: &Self) -> bool {
602 fn gt(&self, other: &Self) -> bool {
606 fn ge(&self, other: &Self) -> bool {
611 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
612 impl<T: Ord> Ord for Reverse<T> {
614 fn cmp(&self, other: &Reverse<T>) -> Ordering {
619 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
620 impl<T: Clone> Clone for Reverse<T> {
622 fn clone(&self) -> Reverse<T> {
623 Reverse(self.0.clone())
627 fn clone_from(&mut self, other: &Self) {
628 self.0.clone_from(&other.0)
632 /// Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order).
634 /// An order is a total order if it is (for all `a`, `b` and `c`):
636 /// - total and asymmetric: exactly one of `a < b`, `a == b` or `a > b` is true; and
637 /// - transitive, `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
641 /// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
642 /// [lexicographic](https://en.wikipedia.org/wiki/Lexicographic_order) ordering based on the top-to-bottom declaration order of the struct's members.
643 /// When `derive`d on enums, variants are ordered by their top-to-bottom discriminant order.
645 /// ## Lexicographical comparison
647 /// Lexicographical comparison is an operation with the following properties:
648 /// - Two sequences are compared element by element.
649 /// - The first mismatching element defines which sequence is lexicographically less or greater than the other.
650 /// - If one sequence is a prefix of another, the shorter sequence is lexicographically less than the other.
651 /// - If two sequence have equivalent elements and are of the same length, then the sequences are lexicographically equal.
652 /// - An empty sequence is lexicographically less than any non-empty sequence.
653 /// - Two empty sequences are lexicographically equal.
655 /// ## How can I implement `Ord`?
657 /// `Ord` requires that the type also be [`PartialOrd`] and [`Eq`] (which requires [`PartialEq`]).
659 /// Then you must define an implementation for [`cmp`]. You may find it useful to use
660 /// [`cmp`] on your type's fields.
662 /// Implementations of [`PartialEq`], [`PartialOrd`], and `Ord` *must*
663 /// agree with each other. That is, `a.cmp(b) == Ordering::Equal` if
664 /// and only if `a == b` and `Some(a.cmp(b)) == a.partial_cmp(b)` for
665 /// all `a` and `b`. It's easy to accidentally make them disagree by
666 /// deriving some of the traits and manually implementing others.
668 /// Here's an example where you want to sort people by height only, disregarding `id`
672 /// use std::cmp::Ordering;
681 /// impl Ord for Person {
682 /// fn cmp(&self, other: &Self) -> Ordering {
683 /// self.height.cmp(&other.height)
687 /// impl PartialOrd for Person {
688 /// fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
689 /// Some(self.cmp(other))
693 /// impl PartialEq for Person {
694 /// fn eq(&self, other: &Self) -> bool {
695 /// self.height == other.height
700 /// [`cmp`]: Ord::cmp
705 #[stable(feature = "rust1", since = "1.0.0")]
706 pub trait Ord: Eq + PartialOrd<Self> {
707 /// This method returns an [`Ordering`] between `self` and `other`.
709 /// By convention, `self.cmp(&other)` returns the ordering matching the expression
710 /// `self <operator> other` if true.
715 /// use std::cmp::Ordering;
717 /// assert_eq!(5.cmp(&10), Ordering::Less);
718 /// assert_eq!(10.cmp(&5), Ordering::Greater);
719 /// assert_eq!(5.cmp(&5), Ordering::Equal);
722 #[stable(feature = "rust1", since = "1.0.0")]
723 fn cmp(&self, other: &Self) -> Ordering;
725 /// Compares and returns the maximum of two values.
727 /// Returns the second argument if the comparison determines them to be equal.
732 /// assert_eq!(2, 1.max(2));
733 /// assert_eq!(2, 2.max(2));
735 #[stable(feature = "ord_max_min", since = "1.21.0")]
738 fn max(self, other: Self) -> Self
742 max_by(self, other, Ord::cmp)
745 /// Compares and returns the minimum of two values.
747 /// Returns the first argument if the comparison determines them to be equal.
752 /// assert_eq!(1, 1.min(2));
753 /// assert_eq!(2, 2.min(2));
755 #[stable(feature = "ord_max_min", since = "1.21.0")]
758 fn min(self, other: Self) -> Self
762 min_by(self, other, Ord::cmp)
765 /// Restrict a value to a certain interval.
767 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
768 /// less than `min`. Otherwise this returns `self`.
772 /// Panics if `min > max`.
777 /// assert!((-3).clamp(-2, 1) == -2);
778 /// assert!(0.clamp(-2, 1) == 0);
779 /// assert!(2.clamp(-2, 1) == 1);
782 #[stable(feature = "clamp", since = "1.50.0")]
783 fn clamp(self, min: Self, max: Self) -> Self
790 } else if self > max {
798 /// Derive macro generating an impl of the trait `Ord`.
799 #[rustc_builtin_macro]
800 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
801 #[allow_internal_unstable(core_intrinsics)]
802 pub macro Ord($item:item) {
803 /* compiler built-in */
806 #[stable(feature = "rust1", since = "1.0.0")]
807 impl Eq for Ordering {}
809 #[stable(feature = "rust1", since = "1.0.0")]
810 impl Ord for Ordering {
812 fn cmp(&self, other: &Ordering) -> Ordering {
813 (*self as i32).cmp(&(*other as i32))
817 #[stable(feature = "rust1", since = "1.0.0")]
818 impl PartialOrd for Ordering {
820 fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
821 (*self as i32).partial_cmp(&(*other as i32))
825 /// Trait for values that can be compared for a sort-order.
827 /// The comparison must satisfy, for all `a`, `b` and `c`:
829 /// - asymmetry: if `a < b` then `!(a > b)`, as well as `a > b` implying `!(a < b)`; and
830 /// - transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
832 /// Note that these requirements mean that the trait itself must be implemented symmetrically and
833 /// transitively: if `T: PartialOrd<U>` and `U: PartialOrd<V>` then `U: PartialOrd<T>` and `T:
838 /// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
839 /// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
840 /// When `derive`d on enums, variants are ordered by their top-to-bottom discriminant order.
842 /// ## How can I implement `PartialOrd`?
844 /// `PartialOrd` only requires implementation of the [`partial_cmp`] method, with the others
845 /// generated from default implementations.
847 /// However it remains possible to implement the others separately for types which do not have a
848 /// total order. For example, for floating point numbers, `NaN < 0 == false` and `NaN >= 0 ==
849 /// false` (cf. IEEE 754-2008 section 5.11).
851 /// `PartialOrd` requires your type to be [`PartialEq`].
853 /// Implementations of [`PartialEq`], `PartialOrd`, and [`Ord`] *must* agree with each other. It's
854 /// easy to accidentally make them disagree by deriving some of the traits and manually
855 /// implementing others.
857 /// If your type is [`Ord`], you can implement [`partial_cmp`] by using [`cmp`]:
860 /// use std::cmp::Ordering;
869 /// impl PartialOrd for Person {
870 /// fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
871 /// Some(self.cmp(other))
875 /// impl Ord for Person {
876 /// fn cmp(&self, other: &Self) -> Ordering {
877 /// self.height.cmp(&other.height)
881 /// impl PartialEq for Person {
882 /// fn eq(&self, other: &Self) -> bool {
883 /// self.height == other.height
888 /// You may also find it useful to use [`partial_cmp`] on your type's fields. Here
889 /// is an example of `Person` types who have a floating-point `height` field that
890 /// is the only field to be used for sorting:
893 /// use std::cmp::Ordering;
901 /// impl PartialOrd for Person {
902 /// fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
903 /// self.height.partial_cmp(&other.height)
907 /// impl PartialEq for Person {
908 /// fn eq(&self, other: &Self) -> bool {
909 /// self.height == other.height
920 /// assert_eq!(x < y, true);
921 /// assert_eq!(x.lt(&y), true);
924 /// [`partial_cmp`]: PartialOrd::partial_cmp
925 /// [`cmp`]: Ord::cmp
926 #[lang = "partial_ord"]
927 #[stable(feature = "rust1", since = "1.0.0")]
932 #[rustc_on_unimplemented(
933 message = "can't compare `{Self}` with `{Rhs}`",
934 label = "no implementation for `{Self} < {Rhs}` and `{Self} > {Rhs}`"
936 pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
937 /// This method returns an ordering between `self` and `other` values if one exists.
942 /// use std::cmp::Ordering;
944 /// let result = 1.0.partial_cmp(&2.0);
945 /// assert_eq!(result, Some(Ordering::Less));
947 /// let result = 1.0.partial_cmp(&1.0);
948 /// assert_eq!(result, Some(Ordering::Equal));
950 /// let result = 2.0.partial_cmp(&1.0);
951 /// assert_eq!(result, Some(Ordering::Greater));
954 /// When comparison is impossible:
957 /// let result = f64::NAN.partial_cmp(&1.0);
958 /// assert_eq!(result, None);
961 #[stable(feature = "rust1", since = "1.0.0")]
962 fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;
964 /// This method tests less than (for `self` and `other`) and is used by the `<` operator.
969 /// let result = 1.0 < 2.0;
970 /// assert_eq!(result, true);
972 /// let result = 2.0 < 1.0;
973 /// assert_eq!(result, false);
977 #[stable(feature = "rust1", since = "1.0.0")]
978 fn lt(&self, other: &Rhs) -> bool {
979 matches!(self.partial_cmp(other), Some(Less))
982 /// This method tests less than or equal to (for `self` and `other`) and is used by the `<=`
988 /// let result = 1.0 <= 2.0;
989 /// assert_eq!(result, true);
991 /// let result = 2.0 <= 2.0;
992 /// assert_eq!(result, true);
996 #[stable(feature = "rust1", since = "1.0.0")]
997 fn le(&self, other: &Rhs) -> bool {
998 // Pattern `Some(Less | Eq)` optimizes worse than negating `None | Some(Greater)`.
999 // FIXME: The root cause was fixed upstream in LLVM with:
1000 // https://github.com/llvm/llvm-project/commit/9bad7de9a3fb844f1ca2965f35d0c2a3d1e11775
1001 // Revert this workaround once support for LLVM 12 gets dropped.
1002 !matches!(self.partial_cmp(other), None | Some(Greater))
1005 /// This method tests greater than (for `self` and `other`) and is used by the `>` operator.
1010 /// let result = 1.0 > 2.0;
1011 /// assert_eq!(result, false);
1013 /// let result = 2.0 > 2.0;
1014 /// assert_eq!(result, false);
1018 #[stable(feature = "rust1", since = "1.0.0")]
1019 fn gt(&self, other: &Rhs) -> bool {
1020 matches!(self.partial_cmp(other), Some(Greater))
1023 /// This method tests greater than or equal to (for `self` and `other`) and is used by the `>=`
1029 /// let result = 2.0 >= 1.0;
1030 /// assert_eq!(result, true);
1032 /// let result = 2.0 >= 2.0;
1033 /// assert_eq!(result, true);
1037 #[stable(feature = "rust1", since = "1.0.0")]
1038 fn ge(&self, other: &Rhs) -> bool {
1039 matches!(self.partial_cmp(other), Some(Greater | Equal))
1043 /// Derive macro generating an impl of the trait `PartialOrd`.
1044 #[rustc_builtin_macro]
1045 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
1046 #[allow_internal_unstable(core_intrinsics)]
1047 pub macro PartialOrd($item:item) {
1048 /* compiler built-in */
1051 /// Compares and returns the minimum of two values.
1053 /// Returns the first argument if the comparison determines them to be equal.
1055 /// Internally uses an alias to [`Ord::min`].
1062 /// assert_eq!(1, cmp::min(1, 2));
1063 /// assert_eq!(2, cmp::min(2, 2));
1067 #[stable(feature = "rust1", since = "1.0.0")]
1068 pub fn min<T: Ord>(v1: T, v2: T) -> T {
1072 /// Returns the minimum of two values with respect to the specified comparison function.
1074 /// Returns the first argument if the comparison determines them to be equal.
1081 /// assert_eq!(cmp::min_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 1);
1082 /// assert_eq!(cmp::min_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
1086 #[stable(feature = "cmp_min_max_by", since = "1.53.0")]
1087 pub fn min_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
1088 match compare(&v1, &v2) {
1089 Ordering::Less | Ordering::Equal => v1,
1090 Ordering::Greater => v2,
1094 /// Returns the element that gives the minimum value from the specified function.
1096 /// Returns the first argument if the comparison determines them to be equal.
1103 /// assert_eq!(cmp::min_by_key(-2, 1, |x: &i32| x.abs()), 1);
1104 /// assert_eq!(cmp::min_by_key(-2, 2, |x: &i32| x.abs()), -2);
1108 #[stable(feature = "cmp_min_max_by", since = "1.53.0")]
1109 pub fn min_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
1110 min_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
1113 /// Compares and returns the maximum of two values.
1115 /// Returns the second argument if the comparison determines them to be equal.
1117 /// Internally uses an alias to [`Ord::max`].
1124 /// assert_eq!(2, cmp::max(1, 2));
1125 /// assert_eq!(2, cmp::max(2, 2));
1129 #[stable(feature = "rust1", since = "1.0.0")]
1130 pub fn max<T: Ord>(v1: T, v2: T) -> T {
1134 /// Returns the maximum of two values with respect to the specified comparison function.
1136 /// Returns the second argument if the comparison determines them to be equal.
1143 /// assert_eq!(cmp::max_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
1144 /// assert_eq!(cmp::max_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 2);
1148 #[stable(feature = "cmp_min_max_by", since = "1.53.0")]
1149 pub fn max_by<T, F: FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T {
1150 match compare(&v1, &v2) {
1151 Ordering::Less | Ordering::Equal => v2,
1152 Ordering::Greater => v1,
1156 /// Returns the element that gives the maximum value from the specified function.
1158 /// Returns the second argument if the comparison determines them to be equal.
1165 /// assert_eq!(cmp::max_by_key(-2, 1, |x: &i32| x.abs()), -2);
1166 /// assert_eq!(cmp::max_by_key(-2, 2, |x: &i32| x.abs()), 2);
1170 #[stable(feature = "cmp_min_max_by", since = "1.53.0")]
1171 pub fn max_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
1172 max_by(v1, v2, |v1, v2| f(v1).cmp(&f(v2)))
1175 // Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
1177 use crate::cmp::Ordering::{self, Equal, Greater, Less};
1178 use crate::hint::unreachable_unchecked;
1180 macro_rules! partial_eq_impl {
1182 #[stable(feature = "rust1", since = "1.0.0")]
1183 impl PartialEq for $t {
1185 fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
1187 fn ne(&self, other: &$t) -> bool { (*self) != (*other) }
1192 #[stable(feature = "rust1", since = "1.0.0")]
1193 impl PartialEq for () {
1195 fn eq(&self, _other: &()) -> bool {
1199 fn ne(&self, _other: &()) -> bool {
1205 bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f32 f64
1208 macro_rules! eq_impl {
1210 #[stable(feature = "rust1", since = "1.0.0")]
1215 eq_impl! { () bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1217 macro_rules! partial_ord_impl {
1219 #[stable(feature = "rust1", since = "1.0.0")]
1220 impl PartialOrd for $t {
1222 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1223 match (self <= other, self >= other) {
1224 (false, false) => None,
1225 (false, true) => Some(Greater),
1226 (true, false) => Some(Less),
1227 (true, true) => Some(Equal),
1231 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1233 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1235 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1237 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1242 #[stable(feature = "rust1", since = "1.0.0")]
1243 impl PartialOrd for () {
1245 fn partial_cmp(&self, _: &()) -> Option<Ordering> {
1250 #[stable(feature = "rust1", since = "1.0.0")]
1251 impl PartialOrd for bool {
1253 fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
1254 Some(self.cmp(other))
1258 partial_ord_impl! { f32 f64 }
1260 macro_rules! ord_impl {
1262 #[stable(feature = "rust1", since = "1.0.0")]
1263 impl PartialOrd for $t {
1265 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1266 Some(self.cmp(other))
1269 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1271 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1273 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1275 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1278 #[stable(feature = "rust1", since = "1.0.0")]
1281 fn cmp(&self, other: &$t) -> Ordering {
1282 // The order here is important to generate more optimal assembly.
1283 // See <https://github.com/rust-lang/rust/issues/63758> for more info.
1284 if *self < *other { Less }
1285 else if *self == *other { Equal }
1292 #[stable(feature = "rust1", since = "1.0.0")]
1295 fn cmp(&self, _other: &()) -> Ordering {
1300 #[stable(feature = "rust1", since = "1.0.0")]
1303 fn cmp(&self, other: &bool) -> Ordering {
1304 // Casting to i8's and converting the difference to an Ordering generates
1305 // more optimal assembly.
1306 // See <https://github.com/rust-lang/rust/issues/66780> for more info.
1307 match (*self as i8) - (*other as i8) {
1311 // SAFETY: bool as i8 returns 0 or 1, so the difference can't be anything else
1312 _ => unsafe { unreachable_unchecked() },
1317 ord_impl! { char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1319 #[unstable(feature = "never_type", issue = "35121")]
1320 impl PartialEq for ! {
1321 fn eq(&self, _: &!) -> bool {
1326 #[unstable(feature = "never_type", issue = "35121")]
1329 #[unstable(feature = "never_type", issue = "35121")]
1330 impl PartialOrd for ! {
1331 fn partial_cmp(&self, _: &!) -> Option<Ordering> {
1336 #[unstable(feature = "never_type", issue = "35121")]
1338 fn cmp(&self, _: &!) -> Ordering {
1345 #[stable(feature = "rust1", since = "1.0.0")]
1346 impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &A
1351 fn eq(&self, other: &&B) -> bool {
1352 PartialEq::eq(*self, *other)
1355 fn ne(&self, other: &&B) -> bool {
1356 PartialEq::ne(*self, *other)
1359 #[stable(feature = "rust1", since = "1.0.0")]
1360 impl<A: ?Sized, B: ?Sized> PartialOrd<&B> for &A
1365 fn partial_cmp(&self, other: &&B) -> Option<Ordering> {
1366 PartialOrd::partial_cmp(*self, *other)
1369 fn lt(&self, other: &&B) -> bool {
1370 PartialOrd::lt(*self, *other)
1373 fn le(&self, other: &&B) -> bool {
1374 PartialOrd::le(*self, *other)
1377 fn gt(&self, other: &&B) -> bool {
1378 PartialOrd::gt(*self, *other)
1381 fn ge(&self, other: &&B) -> bool {
1382 PartialOrd::ge(*self, *other)
1385 #[stable(feature = "rust1", since = "1.0.0")]
1386 impl<A: ?Sized> Ord for &A
1391 fn cmp(&self, other: &Self) -> Ordering {
1392 Ord::cmp(*self, *other)
1395 #[stable(feature = "rust1", since = "1.0.0")]
1396 impl<A: ?Sized> Eq for &A where A: Eq {}
1400 #[stable(feature = "rust1", since = "1.0.0")]
1401 impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &mut A
1406 fn eq(&self, other: &&mut B) -> bool {
1407 PartialEq::eq(*self, *other)
1410 fn ne(&self, other: &&mut B) -> bool {
1411 PartialEq::ne(*self, *other)
1414 #[stable(feature = "rust1", since = "1.0.0")]
1415 impl<A: ?Sized, B: ?Sized> PartialOrd<&mut B> for &mut A
1420 fn partial_cmp(&self, other: &&mut B) -> Option<Ordering> {
1421 PartialOrd::partial_cmp(*self, *other)
1424 fn lt(&self, other: &&mut B) -> bool {
1425 PartialOrd::lt(*self, *other)
1428 fn le(&self, other: &&mut B) -> bool {
1429 PartialOrd::le(*self, *other)
1432 fn gt(&self, other: &&mut B) -> bool {
1433 PartialOrd::gt(*self, *other)
1436 fn ge(&self, other: &&mut B) -> bool {
1437 PartialOrd::ge(*self, *other)
1440 #[stable(feature = "rust1", since = "1.0.0")]
1441 impl<A: ?Sized> Ord for &mut A
1446 fn cmp(&self, other: &Self) -> Ordering {
1447 Ord::cmp(*self, *other)
1450 #[stable(feature = "rust1", since = "1.0.0")]
1451 impl<A: ?Sized> Eq for &mut A where A: Eq {}
1453 #[stable(feature = "rust1", since = "1.0.0")]
1454 impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &A
1459 fn eq(&self, other: &&mut B) -> bool {
1460 PartialEq::eq(*self, *other)
1463 fn ne(&self, other: &&mut B) -> bool {
1464 PartialEq::ne(*self, *other)
1468 #[stable(feature = "rust1", since = "1.0.0")]
1469 impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &mut A
1474 fn eq(&self, other: &&B) -> bool {
1475 PartialEq::eq(*self, *other)
1478 fn ne(&self, other: &&B) -> bool {
1479 PartialEq::ne(*self, *other)