1 //! Utilities for comparing and ordering values.
3 //! This module contains various tools for comparing and ordering 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 crate::const_closure::ConstFnMutClosure;
26 use crate::marker::Destruct;
28 use self::Ordering::*;
30 /// Trait for equality comparisons.
32 /// `x.eq(y)` can also be written `x == y`, and `x.ne(y)` can be written `x != y`.
33 /// We use the easier-to-read infix notation in the remainder of this documentation.
35 /// This trait allows for partial equality, for types that do not have a full
36 /// equivalence relation. For example, in floating point numbers `NaN != NaN`,
37 /// so floating point types implement `PartialEq` but not [`trait@Eq`].
38 /// Formally speaking, when `Rhs == Self`, this trait corresponds to a [partial equivalence
39 /// relation](https://en.wikipedia.org/wiki/Partial_equivalence_relation).
41 /// Implementations must ensure that `eq` and `ne` are consistent with each other:
43 /// - `a != b` if and only if `!(a == b)`.
45 /// The default implementation of `ne` provides this consistency and is almost
46 /// always sufficient. It should not be overridden without very good reason.
48 /// If [`PartialOrd`] or [`Ord`] are also implemented for `Self` and `Rhs`, their methods must also
49 /// be consistent with `PartialEq` (see the documentation of those traits for the exact
50 /// requirements). It's easy to accidentally make them disagree by deriving some of the traits and
51 /// manually implementing others.
53 /// The equality relation `==` must satisfy the following conditions
54 /// (for all `a`, `b`, `c` of type `A`, `B`, `C`):
56 /// - **Symmetric**: if `A: PartialEq<B>` and `B: PartialEq<A>`, then **`a == b`
57 /// implies `b == a`**; and
59 /// - **Transitive**: if `A: PartialEq<B>` and `B: PartialEq<C>` and `A:
60 /// PartialEq<C>`, then **`a == b` and `b == c` implies `a == c`**.
62 /// Note that the `B: PartialEq<A>` (symmetric) and `A: PartialEq<C>`
63 /// (transitive) impls are not forced to exist, but these requirements apply
64 /// whenever they do exist.
68 /// This trait can be used with `#[derive]`. When `derive`d on structs, two
69 /// instances are equal if all fields are equal, and not equal if any fields
70 /// are not equal. When `derive`d on enums, two instances are equal if they
71 /// are the same variant and all fields are equal.
73 /// ## How can I implement `PartialEq`?
75 /// An example implementation for a domain in which two books are considered
76 /// the same book if their ISBN matches, even if the formats differ:
87 /// format: BookFormat,
90 /// impl PartialEq for Book {
91 /// fn eq(&self, other: &Self) -> bool {
92 /// self.isbn == other.isbn
96 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
97 /// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
98 /// let b3 = Book { isbn: 10, format: BookFormat::Paperback };
100 /// assert!(b1 == b2);
101 /// assert!(b1 != b3);
104 /// ## How can I compare two different types?
106 /// The type you can compare with is controlled by `PartialEq`'s type parameter.
107 /// For example, let's tweak our previous code a bit:
110 /// // The derive implements <BookFormat> == <BookFormat> comparisons
111 /// #[derive(PartialEq)]
112 /// enum BookFormat {
120 /// format: BookFormat,
123 /// // Implement <Book> == <BookFormat> comparisons
124 /// impl PartialEq<BookFormat> for Book {
125 /// fn eq(&self, other: &BookFormat) -> bool {
126 /// self.format == *other
130 /// // Implement <BookFormat> == <Book> comparisons
131 /// impl PartialEq<Book> for BookFormat {
132 /// fn eq(&self, other: &Book) -> bool {
133 /// *self == other.format
137 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
139 /// assert!(b1 == BookFormat::Paperback);
140 /// assert!(BookFormat::Ebook != b1);
143 /// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
144 /// we allow `BookFormat`s to be compared with `Book`s.
146 /// A comparison like the one above, which ignores some fields of the struct,
147 /// can be dangerous. It can easily lead to an unintended violation of the
148 /// requirements for a partial equivalence relation. For example, if we kept
149 /// the above implementation of `PartialEq<Book>` for `BookFormat` and added an
150 /// implementation of `PartialEq<Book>` for `Book` (either via a `#[derive]` or
151 /// via the manual implementation from the first example) then the result would
152 /// violate transitivity:
155 /// #[derive(PartialEq)]
156 /// enum BookFormat {
162 /// #[derive(PartialEq)]
165 /// format: BookFormat,
168 /// impl PartialEq<BookFormat> for Book {
169 /// fn eq(&self, other: &BookFormat) -> bool {
170 /// self.format == *other
174 /// impl PartialEq<Book> for BookFormat {
175 /// fn eq(&self, other: &Book) -> bool {
176 /// *self == other.format
181 /// let b1 = Book { isbn: 1, format: BookFormat::Paperback };
182 /// let b2 = Book { isbn: 2, format: BookFormat::Paperback };
184 /// assert!(b1 == BookFormat::Paperback);
185 /// assert!(BookFormat::Paperback == b2);
187 /// // The following should hold by transitivity but doesn't.
188 /// assert!(b1 == b2); // <-- PANICS
198 /// assert_eq!(x == y, false);
199 /// assert_eq!(x.eq(&y), false);
202 /// [`eq`]: PartialEq::eq
203 /// [`ne`]: PartialEq::ne
205 #[stable(feature = "rust1", since = "1.0.0")]
208 #[rustc_on_unimplemented(
209 message = "can't compare `{Self}` with `{Rhs}`",
210 label = "no implementation for `{Self} == {Rhs}`",
214 #[rustc_diagnostic_item = "PartialEq"]
215 pub trait PartialEq<Rhs: ?Sized = Self> {
216 /// This method tests for `self` and `other` values to be equal, and is used
219 #[stable(feature = "rust1", since = "1.0.0")]
220 fn eq(&self, other: &Rhs) -> bool;
222 /// This method tests for `!=`. The default implementation is almost always
223 /// sufficient, and should not be overridden without very good reason.
226 #[stable(feature = "rust1", since = "1.0.0")]
227 fn ne(&self, other: &Rhs) -> bool {
232 /// Derive macro generating an impl of the trait `PartialEq`.
233 #[rustc_builtin_macro]
234 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
235 #[allow_internal_unstable(core_intrinsics, structural_match)]
236 pub macro PartialEq($item:item) {
237 /* compiler built-in */
240 /// Trait for equality comparisons which are [equivalence relations](
241 /// https://en.wikipedia.org/wiki/Equivalence_relation).
243 /// This means, that in addition to `a == b` and `a != b` being strict inverses, the equality must
244 /// be (for all `a`, `b` and `c`):
246 /// - reflexive: `a == a`;
247 /// - symmetric: `a == b` implies `b == a`; and
248 /// - transitive: `a == b` and `b == c` implies `a == c`.
250 /// This property cannot be checked by the compiler, and therefore `Eq` implies
251 /// [`PartialEq`], and has no extra methods.
255 /// This trait can be used with `#[derive]`. When `derive`d, because `Eq` has
256 /// no extra methods, it is only informing the compiler that this is an
257 /// equivalence relation rather than a partial equivalence relation. Note that
258 /// the `derive` strategy requires all fields are `Eq`, which isn't
261 /// ## How can I implement `Eq`?
263 /// If you cannot use the `derive` strategy, specify that your type implements
264 /// `Eq`, which has no methods:
267 /// enum BookFormat { Paperback, Hardback, Ebook }
270 /// format: BookFormat,
272 /// impl PartialEq for Book {
273 /// fn eq(&self, other: &Self) -> bool {
274 /// self.isbn == other.isbn
277 /// impl Eq for Book {}
281 #[stable(feature = "rust1", since = "1.0.0")]
282 #[rustc_diagnostic_item = "Eq"]
283 pub trait Eq: PartialEq<Self> {
284 // this method is used solely by #[deriving] to assert
285 // that every component of a type implements #[deriving]
286 // itself, the current deriving infrastructure means doing this
287 // assertion without using a method on this trait is nearly
290 // This should never be implemented by hand.
292 #[no_coverage] // rust-lang/rust#84605
294 #[stable(feature = "rust1", since = "1.0.0")]
295 fn assert_receiver_is_total_eq(&self) {}
298 /// Derive macro generating an impl of the trait `Eq`.
299 #[rustc_builtin_macro]
300 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
301 #[allow_internal_unstable(core_intrinsics, derive_eq, structural_match, no_coverage)]
302 pub macro Eq($item:item) {
303 /* compiler built-in */
306 // FIXME: this struct is used solely by #[derive] to
307 // assert that every component of a type implements Eq.
309 // This struct should never appear in user code.
311 #[allow(missing_debug_implementations)]
312 #[unstable(feature = "derive_eq", reason = "deriving hack, should not be public", issue = "none")]
313 pub struct AssertParamIsEq<T: Eq + ?Sized> {
314 _field: crate::marker::PhantomData<T>,
317 /// An `Ordering` is the result of a comparison between two values.
322 /// use std::cmp::Ordering;
324 /// let result = 1.cmp(&2);
325 /// assert_eq!(Ordering::Less, result);
327 /// let result = 1.cmp(&1);
328 /// assert_eq!(Ordering::Equal, result);
330 /// let result = 2.cmp(&1);
331 /// assert_eq!(Ordering::Greater, result);
333 #[derive(Clone, Copy, Eq, Debug, Hash)]
334 #[derive_const(PartialOrd, Ord, PartialEq)]
335 #[stable(feature = "rust1", since = "1.0.0")]
338 /// An ordering where a compared value is less than another.
339 #[stable(feature = "rust1", since = "1.0.0")]
341 /// An ordering where a compared value is equal to another.
342 #[stable(feature = "rust1", since = "1.0.0")]
344 /// An ordering where a compared value is greater than another.
345 #[stable(feature = "rust1", since = "1.0.0")]
350 /// Returns `true` if the ordering is the `Equal` variant.
355 /// use std::cmp::Ordering;
357 /// assert_eq!(Ordering::Less.is_eq(), false);
358 /// assert_eq!(Ordering::Equal.is_eq(), true);
359 /// assert_eq!(Ordering::Greater.is_eq(), false);
363 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
364 #[stable(feature = "ordering_helpers", since = "1.53.0")]
365 pub const fn is_eq(self) -> bool {
366 matches!(self, Equal)
369 /// Returns `true` if the ordering is not the `Equal` variant.
374 /// use std::cmp::Ordering;
376 /// assert_eq!(Ordering::Less.is_ne(), true);
377 /// assert_eq!(Ordering::Equal.is_ne(), false);
378 /// assert_eq!(Ordering::Greater.is_ne(), true);
382 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
383 #[stable(feature = "ordering_helpers", since = "1.53.0")]
384 pub const fn is_ne(self) -> bool {
385 !matches!(self, Equal)
388 /// Returns `true` if the ordering is the `Less` variant.
393 /// use std::cmp::Ordering;
395 /// assert_eq!(Ordering::Less.is_lt(), true);
396 /// assert_eq!(Ordering::Equal.is_lt(), false);
397 /// assert_eq!(Ordering::Greater.is_lt(), false);
401 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
402 #[stable(feature = "ordering_helpers", since = "1.53.0")]
403 pub const fn is_lt(self) -> bool {
407 /// Returns `true` if the ordering is the `Greater` variant.
412 /// use std::cmp::Ordering;
414 /// assert_eq!(Ordering::Less.is_gt(), false);
415 /// assert_eq!(Ordering::Equal.is_gt(), false);
416 /// assert_eq!(Ordering::Greater.is_gt(), true);
420 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
421 #[stable(feature = "ordering_helpers", since = "1.53.0")]
422 pub const fn is_gt(self) -> bool {
423 matches!(self, Greater)
426 /// Returns `true` if the ordering is either the `Less` or `Equal` variant.
431 /// use std::cmp::Ordering;
433 /// assert_eq!(Ordering::Less.is_le(), true);
434 /// assert_eq!(Ordering::Equal.is_le(), true);
435 /// assert_eq!(Ordering::Greater.is_le(), false);
439 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
440 #[stable(feature = "ordering_helpers", since = "1.53.0")]
441 pub const fn is_le(self) -> bool {
442 !matches!(self, Greater)
445 /// Returns `true` if the ordering is either the `Greater` or `Equal` variant.
450 /// use std::cmp::Ordering;
452 /// assert_eq!(Ordering::Less.is_ge(), false);
453 /// assert_eq!(Ordering::Equal.is_ge(), true);
454 /// assert_eq!(Ordering::Greater.is_ge(), true);
458 #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
459 #[stable(feature = "ordering_helpers", since = "1.53.0")]
460 pub const fn is_ge(self) -> bool {
461 !matches!(self, Less)
464 /// Reverses the `Ordering`.
466 /// * `Less` becomes `Greater`.
467 /// * `Greater` becomes `Less`.
468 /// * `Equal` becomes `Equal`.
475 /// use std::cmp::Ordering;
477 /// assert_eq!(Ordering::Less.reverse(), Ordering::Greater);
478 /// assert_eq!(Ordering::Equal.reverse(), Ordering::Equal);
479 /// assert_eq!(Ordering::Greater.reverse(), Ordering::Less);
482 /// This method can be used to reverse a comparison:
485 /// let data: &mut [_] = &mut [2, 10, 5, 8];
487 /// // sort the array from largest to smallest.
488 /// data.sort_by(|a, b| a.cmp(b).reverse());
490 /// let b: &mut [_] = &mut [10, 8, 5, 2];
491 /// assert!(data == b);
495 #[rustc_const_stable(feature = "const_ordering", since = "1.48.0")]
496 #[stable(feature = "rust1", since = "1.0.0")]
497 pub const fn reverse(self) -> Ordering {
505 /// Chains two orderings.
507 /// Returns `self` when it's not `Equal`. Otherwise returns `other`.
512 /// use std::cmp::Ordering;
514 /// let result = Ordering::Equal.then(Ordering::Less);
515 /// assert_eq!(result, Ordering::Less);
517 /// let result = Ordering::Less.then(Ordering::Equal);
518 /// assert_eq!(result, Ordering::Less);
520 /// let result = Ordering::Less.then(Ordering::Greater);
521 /// assert_eq!(result, Ordering::Less);
523 /// let result = Ordering::Equal.then(Ordering::Equal);
524 /// assert_eq!(result, Ordering::Equal);
526 /// let x: (i64, i64, i64) = (1, 2, 7);
527 /// let y: (i64, i64, i64) = (1, 5, 3);
528 /// let result = x.0.cmp(&y.0).then(x.1.cmp(&y.1)).then(x.2.cmp(&y.2));
530 /// assert_eq!(result, Ordering::Less);
534 #[rustc_const_stable(feature = "const_ordering", since = "1.48.0")]
535 #[stable(feature = "ordering_chaining", since = "1.17.0")]
536 pub const fn then(self, other: Ordering) -> Ordering {
543 /// Chains the ordering with the given function.
545 /// Returns `self` when it's not `Equal`. Otherwise calls `f` and returns
551 /// use std::cmp::Ordering;
553 /// let result = Ordering::Equal.then_with(|| Ordering::Less);
554 /// assert_eq!(result, Ordering::Less);
556 /// let result = Ordering::Less.then_with(|| Ordering::Equal);
557 /// assert_eq!(result, Ordering::Less);
559 /// let result = Ordering::Less.then_with(|| Ordering::Greater);
560 /// assert_eq!(result, Ordering::Less);
562 /// let result = Ordering::Equal.then_with(|| Ordering::Equal);
563 /// assert_eq!(result, Ordering::Equal);
565 /// let x: (i64, i64, i64) = (1, 2, 7);
566 /// let y: (i64, i64, i64) = (1, 5, 3);
567 /// let result = x.0.cmp(&y.0).then_with(|| x.1.cmp(&y.1)).then_with(|| x.2.cmp(&y.2));
569 /// assert_eq!(result, Ordering::Less);
573 #[stable(feature = "ordering_chaining", since = "1.17.0")]
574 pub fn then_with<F: FnOnce() -> Ordering>(self, f: F) -> Ordering {
582 /// A helper struct for reverse ordering.
584 /// This struct is a helper to be used with functions like [`Vec::sort_by_key`] and
585 /// can be used to reverse order a part of a key.
587 /// [`Vec::sort_by_key`]: ../../std/vec/struct.Vec.html#method.sort_by_key
592 /// use std::cmp::Reverse;
594 /// let mut v = vec![1, 2, 3, 4, 5, 6];
595 /// v.sort_by_key(|&num| (num > 3, Reverse(num)));
596 /// assert_eq!(v, vec![3, 2, 1, 6, 5, 4]);
598 #[derive(PartialEq, Eq, Debug, Copy, Default, Hash)]
599 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
601 pub struct Reverse<T>(#[stable(feature = "reverse_cmp_key", since = "1.19.0")] pub T);
603 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
604 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
605 impl<T: ~const PartialOrd> const PartialOrd for Reverse<T> {
607 fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
608 other.0.partial_cmp(&self.0)
612 fn lt(&self, other: &Self) -> bool {
616 fn le(&self, other: &Self) -> bool {
620 fn gt(&self, other: &Self) -> bool {
624 fn ge(&self, other: &Self) -> bool {
629 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
630 impl<T: Ord> Ord for Reverse<T> {
632 fn cmp(&self, other: &Reverse<T>) -> Ordering {
637 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
638 impl<T: Clone> Clone for Reverse<T> {
640 fn clone(&self) -> Reverse<T> {
641 Reverse(self.0.clone())
645 fn clone_from(&mut self, other: &Self) {
646 self.0.clone_from(&other.0)
650 /// Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order).
652 /// Implementations must be consistent with the [`PartialOrd`] implementation, and ensure
653 /// `max`, `min`, and `clamp` are consistent with `cmp`:
655 /// - `partial_cmp(a, b) == Some(cmp(a, b))`.
656 /// - `max(a, b) == max_by(a, b, cmp)` (ensured by the default implementation).
657 /// - `min(a, b) == min_by(a, b, cmp)` (ensured by the default implementation).
658 /// - For `a.clamp(min, max)`, see the [method docs](#method.clamp)
659 /// (ensured by the default implementation).
661 /// It's easy to accidentally make `cmp` and `partial_cmp` disagree by
662 /// deriving some of the traits and manually implementing others.
666 /// From the above and the requirements of `PartialOrd`, it follows that `<` defines a strict total order.
667 /// This means that for all `a`, `b` and `c`:
669 /// - exactly one of `a < b`, `a == b` or `a > b` is true; and
670 /// - `<` is transitive: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
674 /// This trait can be used with `#[derive]`.
676 /// When `derive`d on structs, it will produce a
677 /// [lexicographic](https://en.wikipedia.org/wiki/Lexicographic_order) ordering
678 /// based on the top-to-bottom declaration order of the struct's members.
680 /// When `derive`d on enums, variants are ordered by their discriminants.
681 /// By default, the discriminant is smallest for variants at the top, and
682 /// largest for variants at the bottom. Here's an example:
685 /// #[derive(PartialEq, Eq, PartialOrd, Ord)]
691 /// assert!(E::Top < E::Bottom);
694 /// However, manually setting the discriminants can override this default
698 /// #[derive(PartialEq, Eq, PartialOrd, Ord)]
704 /// assert!(E::Bottom < E::Top);
707 /// ## Lexicographical comparison
709 /// Lexicographical comparison is an operation with the following properties:
710 /// - Two sequences are compared element by element.
711 /// - The first mismatching element defines which sequence is lexicographically less or greater than the other.
712 /// - If one sequence is a prefix of another, the shorter sequence is lexicographically less than the other.
713 /// - If two sequence have equivalent elements and are of the same length, then the sequences are lexicographically equal.
714 /// - An empty sequence is lexicographically less than any non-empty sequence.
715 /// - Two empty sequences are lexicographically equal.
717 /// ## How can I implement `Ord`?
719 /// `Ord` requires that the type also be [`PartialOrd`] and [`Eq`] (which requires [`PartialEq`]).
721 /// Then you must define an implementation for [`cmp`]. You may find it useful to use
722 /// [`cmp`] on your type's fields.
724 /// Here's an example where you want to sort people by height only, disregarding `id`
728 /// use std::cmp::Ordering;
737 /// impl Ord for Person {
738 /// fn cmp(&self, other: &Self) -> Ordering {
739 /// self.height.cmp(&other.height)
743 /// impl PartialOrd for Person {
744 /// fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
745 /// Some(self.cmp(other))
749 /// impl PartialEq for Person {
750 /// fn eq(&self, other: &Self) -> bool {
751 /// self.height == other.height
756 /// [`cmp`]: Ord::cmp
761 #[stable(feature = "rust1", since = "1.0.0")]
762 #[rustc_diagnostic_item = "Ord"]
764 pub trait Ord: Eq + PartialOrd<Self> {
765 /// This method returns an [`Ordering`] between `self` and `other`.
767 /// By convention, `self.cmp(&other)` returns the ordering matching the expression
768 /// `self <operator> other` if true.
773 /// use std::cmp::Ordering;
775 /// assert_eq!(5.cmp(&10), Ordering::Less);
776 /// assert_eq!(10.cmp(&5), Ordering::Greater);
777 /// assert_eq!(5.cmp(&5), Ordering::Equal);
780 #[stable(feature = "rust1", since = "1.0.0")]
781 fn cmp(&self, other: &Self) -> Ordering;
783 /// Compares and returns the maximum of two values.
785 /// Returns the second argument if the comparison determines them to be equal.
790 /// assert_eq!(2, 1.max(2));
791 /// assert_eq!(2, 2.max(2));
793 #[stable(feature = "ord_max_min", since = "1.21.0")]
796 fn max(self, other: Self) -> Self
799 Self: ~const Destruct,
801 #[cfg(not(bootstrap))]
803 max_by(self, other, Ord::cmp)
807 match self.cmp(&other) {
808 Ordering::Less | Ordering::Equal => other,
809 Ordering::Greater => self,
813 /// Compares and returns the minimum of two values.
815 /// Returns the first argument if the comparison determines them to be equal.
820 /// assert_eq!(1, 1.min(2));
821 /// assert_eq!(2, 2.min(2));
823 #[stable(feature = "ord_max_min", since = "1.21.0")]
826 fn min(self, other: Self) -> Self
829 Self: ~const Destruct,
831 #[cfg(not(bootstrap))]
833 min_by(self, other, Ord::cmp)
837 match self.cmp(&other) {
838 Ordering::Less | Ordering::Equal => self,
839 Ordering::Greater => other,
843 /// Restrict a value to a certain interval.
845 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
846 /// less than `min`. Otherwise this returns `self`.
850 /// Panics if `min > max`.
855 /// assert!((-3).clamp(-2, 1) == -2);
856 /// assert!(0.clamp(-2, 1) == 0);
857 /// assert!(2.clamp(-2, 1) == 1);
860 #[stable(feature = "clamp", since = "1.50.0")]
861 fn clamp(self, min: Self, max: Self) -> Self
864 Self: ~const Destruct,
865 Self: ~const PartialOrd,
870 } else if self > max {
878 /// Derive macro generating an impl of the trait `Ord`.
879 #[rustc_builtin_macro]
880 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
881 #[allow_internal_unstable(core_intrinsics)]
882 pub macro Ord($item:item) {
883 /* compiler built-in */
886 /// Trait for types that form a [partial order](https://en.wikipedia.org/wiki/Partial_order).
888 /// The `lt`, `le`, `gt`, and `ge` methods of this trait can be called using
889 /// the `<`, `<=`, `>`, and `>=` operators, respectively.
891 /// The methods of this trait must be consistent with each other and with those of [`PartialEq`].
892 /// The following conditions must hold:
894 /// 1. `a == b` if and only if `partial_cmp(a, b) == Some(Equal)`.
895 /// 2. `a < b` if and only if `partial_cmp(a, b) == Some(Less)`
896 /// 3. `a > b` if and only if `partial_cmp(a, b) == Some(Greater)`
897 /// 4. `a <= b` if and only if `a < b || a == b`
898 /// 5. `a >= b` if and only if `a > b || a == b`
899 /// 6. `a != b` if and only if `!(a == b)`.
901 /// Conditions 2–5 above are ensured by the default implementation.
902 /// Condition 6 is already ensured by [`PartialEq`].
904 /// If [`Ord`] is also implemented for `Self` and `Rhs`, it must also be consistent with
905 /// `partial_cmp` (see the documentation of that trait for the exact requirements). It's
906 /// easy to accidentally make them disagree by deriving some of the traits and manually
907 /// implementing others.
909 /// The comparison must satisfy, for all `a`, `b` and `c`:
911 /// - transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
912 /// - duality: `a < b` if and only if `b > a`.
914 /// Note that these requirements mean that the trait itself must be implemented symmetrically and
915 /// transitively: if `T: PartialOrd<U>` and `U: PartialOrd<V>` then `U: PartialOrd<T>` and `T:
920 /// The following corollaries follow from the above requirements:
922 /// - irreflexivity of `<` and `>`: `!(a < a)`, `!(a > a)`
923 /// - transitivity of `>`: if `a > b` and `b > c` then `a > c`
924 /// - duality of `partial_cmp`: `partial_cmp(a, b) == partial_cmp(b, a).map(Ordering::reverse)`
928 /// This trait can be used with `#[derive]`.
930 /// When `derive`d on structs, it will produce a
931 /// [lexicographic](https://en.wikipedia.org/wiki/Lexicographic_order) ordering
932 /// based on the top-to-bottom declaration order of the struct's members.
934 /// When `derive`d on enums, variants are ordered by their discriminants.
935 /// By default, the discriminant is smallest for variants at the top, and
936 /// largest for variants at the bottom. Here's an example:
939 /// #[derive(PartialEq, PartialOrd)]
945 /// assert!(E::Top < E::Bottom);
948 /// However, manually setting the discriminants can override this default
952 /// #[derive(PartialEq, PartialOrd)]
958 /// assert!(E::Bottom < E::Top);
961 /// ## How can I implement `PartialOrd`?
963 /// `PartialOrd` only requires implementation of the [`partial_cmp`] method, with the others
964 /// generated from default implementations.
966 /// However it remains possible to implement the others separately for types which do not have a
967 /// total order. For example, for floating point numbers, `NaN < 0 == false` and `NaN >= 0 ==
968 /// false` (cf. IEEE 754-2008 section 5.11).
970 /// `PartialOrd` requires your type to be [`PartialEq`].
972 /// If your type is [`Ord`], you can implement [`partial_cmp`] by using [`cmp`]:
975 /// use std::cmp::Ordering;
984 /// impl PartialOrd for Person {
985 /// fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
986 /// Some(self.cmp(other))
990 /// impl Ord for Person {
991 /// fn cmp(&self, other: &Self) -> Ordering {
992 /// self.height.cmp(&other.height)
996 /// impl PartialEq for Person {
997 /// fn eq(&self, other: &Self) -> bool {
998 /// self.height == other.height
1003 /// You may also find it useful to use [`partial_cmp`] on your type's fields. Here
1004 /// is an example of `Person` types who have a floating-point `height` field that
1005 /// is the only field to be used for sorting:
1008 /// use std::cmp::Ordering;
1016 /// impl PartialOrd for Person {
1017 /// fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
1018 /// self.height.partial_cmp(&other.height)
1022 /// impl PartialEq for Person {
1023 /// fn eq(&self, other: &Self) -> bool {
1024 /// self.height == other.height
1035 /// assert_eq!(x < y, true);
1036 /// assert_eq!(x.lt(&y), true);
1039 /// [`partial_cmp`]: PartialOrd::partial_cmp
1040 /// [`cmp`]: Ord::cmp
1041 #[lang = "partial_ord"]
1042 #[stable(feature = "rust1", since = "1.0.0")]
1045 #[doc(alias = "<=")]
1046 #[doc(alias = ">=")]
1047 #[rustc_on_unimplemented(
1048 message = "can't compare `{Self}` with `{Rhs}`",
1049 label = "no implementation for `{Self} < {Rhs}` and `{Self} > {Rhs}`",
1053 #[rustc_diagnostic_item = "PartialOrd"]
1054 pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
1055 /// This method returns an ordering between `self` and `other` values if one exists.
1060 /// use std::cmp::Ordering;
1062 /// let result = 1.0.partial_cmp(&2.0);
1063 /// assert_eq!(result, Some(Ordering::Less));
1065 /// let result = 1.0.partial_cmp(&1.0);
1066 /// assert_eq!(result, Some(Ordering::Equal));
1068 /// let result = 2.0.partial_cmp(&1.0);
1069 /// assert_eq!(result, Some(Ordering::Greater));
1072 /// When comparison is impossible:
1075 /// let result = f64::NAN.partial_cmp(&1.0);
1076 /// assert_eq!(result, None);
1079 #[stable(feature = "rust1", since = "1.0.0")]
1080 fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;
1082 /// This method tests less than (for `self` and `other`) and is used by the `<` operator.
1087 /// let result = 1.0 < 2.0;
1088 /// assert_eq!(result, true);
1090 /// let result = 2.0 < 1.0;
1091 /// assert_eq!(result, false);
1095 #[stable(feature = "rust1", since = "1.0.0")]
1096 fn lt(&self, other: &Rhs) -> bool {
1097 matches!(self.partial_cmp(other), Some(Less))
1100 /// This method tests less than or equal to (for `self` and `other`) and is used by the `<=`
1106 /// let result = 1.0 <= 2.0;
1107 /// assert_eq!(result, true);
1109 /// let result = 2.0 <= 2.0;
1110 /// assert_eq!(result, true);
1114 #[stable(feature = "rust1", since = "1.0.0")]
1115 fn le(&self, other: &Rhs) -> bool {
1116 matches!(self.partial_cmp(other), Some(Less | Equal))
1119 /// This method tests greater than (for `self` and `other`) and is used by the `>` operator.
1124 /// let result = 1.0 > 2.0;
1125 /// assert_eq!(result, false);
1127 /// let result = 2.0 > 2.0;
1128 /// assert_eq!(result, false);
1132 #[stable(feature = "rust1", since = "1.0.0")]
1133 fn gt(&self, other: &Rhs) -> bool {
1134 matches!(self.partial_cmp(other), Some(Greater))
1137 /// This method tests greater than or equal to (for `self` and `other`) and is used by the `>=`
1143 /// let result = 2.0 >= 1.0;
1144 /// assert_eq!(result, true);
1146 /// let result = 2.0 >= 2.0;
1147 /// assert_eq!(result, true);
1151 #[stable(feature = "rust1", since = "1.0.0")]
1152 fn ge(&self, other: &Rhs) -> bool {
1153 matches!(self.partial_cmp(other), Some(Greater | Equal))
1157 /// Derive macro generating an impl of the trait `PartialOrd`.
1158 #[rustc_builtin_macro]
1159 #[stable(feature = "builtin_macro_prelude", since = "1.38.0")]
1160 #[allow_internal_unstable(core_intrinsics)]
1161 pub macro PartialOrd($item:item) {
1162 /* compiler built-in */
1165 /// Compares and returns the minimum of two values.
1167 /// Returns the first argument if the comparison determines them to be equal.
1169 /// Internally uses an alias to [`Ord::min`].
1176 /// assert_eq!(1, cmp::min(1, 2));
1177 /// assert_eq!(2, cmp::min(2, 2));
1181 #[stable(feature = "rust1", since = "1.0.0")]
1182 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1183 #[cfg_attr(not(test), rustc_diagnostic_item = "cmp_min")]
1184 pub const fn min<T: ~const Ord + ~const Destruct>(v1: T, v2: T) -> T {
1188 /// Returns the minimum of two values with respect to the specified comparison function.
1190 /// Returns the first argument if the comparison determines them to be equal.
1197 /// assert_eq!(cmp::min_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 1);
1198 /// assert_eq!(cmp::min_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
1202 #[stable(feature = "cmp_min_max_by", since = "1.53.0")]
1203 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1204 pub const fn min_by<T, F: ~const FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T
1209 match compare(&v1, &v2) {
1210 Ordering::Less | Ordering::Equal => v1,
1211 Ordering::Greater => v2,
1215 /// Returns the element that gives the minimum value from the specified function.
1217 /// Returns the first argument if the comparison determines them to be equal.
1224 /// assert_eq!(cmp::min_by_key(-2, 1, |x: &i32| x.abs()), 1);
1225 /// assert_eq!(cmp::min_by_key(-2, 2, |x: &i32| x.abs()), -2);
1229 #[stable(feature = "cmp_min_max_by", since = "1.53.0")]
1230 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1231 pub const fn min_by_key<T, F: ~const FnMut(&T) -> K, K: ~const Ord>(v1: T, v2: T, mut f: F) -> T
1237 const fn imp<T, F: ~const FnMut(&T) -> K, K: ~const Ord>(
1247 min_by(v1, v2, ConstFnMutClosure::new(&mut f, imp))
1250 /// Compares and returns the maximum of two values.
1252 /// Returns the second argument if the comparison determines them to be equal.
1254 /// Internally uses an alias to [`Ord::max`].
1261 /// assert_eq!(2, cmp::max(1, 2));
1262 /// assert_eq!(2, cmp::max(2, 2));
1266 #[stable(feature = "rust1", since = "1.0.0")]
1267 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1268 #[cfg_attr(not(test), rustc_diagnostic_item = "cmp_max")]
1269 pub const fn max<T: ~const Ord + ~const Destruct>(v1: T, v2: T) -> T {
1273 /// Returns the maximum of two values with respect to the specified comparison function.
1275 /// Returns the second argument if the comparison determines them to be equal.
1282 /// assert_eq!(cmp::max_by(-2, 1, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), -2);
1283 /// assert_eq!(cmp::max_by(-2, 2, |x: &i32, y: &i32| x.abs().cmp(&y.abs())), 2);
1287 #[stable(feature = "cmp_min_max_by", since = "1.53.0")]
1288 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1289 pub const fn max_by<T, F: ~const FnOnce(&T, &T) -> Ordering>(v1: T, v2: T, compare: F) -> T
1294 match compare(&v1, &v2) {
1295 Ordering::Less | Ordering::Equal => v2,
1296 Ordering::Greater => v1,
1300 /// Returns the element that gives the maximum value from the specified function.
1302 /// Returns the second argument if the comparison determines them to be equal.
1309 /// assert_eq!(cmp::max_by_key(-2, 1, |x: &i32| x.abs()), -2);
1310 /// assert_eq!(cmp::max_by_key(-2, 2, |x: &i32| x.abs()), 2);
1314 #[stable(feature = "cmp_min_max_by", since = "1.53.0")]
1315 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1316 pub const fn max_by_key<T, F: ~const FnMut(&T) -> K, K: ~const Ord>(v1: T, v2: T, mut f: F) -> T
1322 const fn imp<T, F: ~const FnMut(&T) -> K, K: ~const Ord>(
1332 max_by(v1, v2, ConstFnMutClosure::new(&mut f, imp))
1335 // Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
1337 use crate::cmp::Ordering::{self, Equal, Greater, Less};
1338 use crate::hint::unreachable_unchecked;
1340 macro_rules! partial_eq_impl {
1342 #[stable(feature = "rust1", since = "1.0.0")]
1343 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1344 impl const PartialEq for $t {
1346 fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
1348 fn ne(&self, other: &$t) -> bool { (*self) != (*other) }
1353 #[stable(feature = "rust1", since = "1.0.0")]
1354 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1355 impl const PartialEq for () {
1357 fn eq(&self, _other: &()) -> bool {
1361 fn ne(&self, _other: &()) -> bool {
1367 bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f32 f64
1370 macro_rules! eq_impl {
1372 #[stable(feature = "rust1", since = "1.0.0")]
1377 eq_impl! { () bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1379 macro_rules! partial_ord_impl {
1381 #[stable(feature = "rust1", since = "1.0.0")]
1382 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1383 impl const PartialOrd for $t {
1385 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1386 match (*self <= *other, *self >= *other) {
1387 (false, false) => None,
1388 (false, true) => Some(Greater),
1389 (true, false) => Some(Less),
1390 (true, true) => Some(Equal),
1394 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1396 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1398 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1400 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1405 #[stable(feature = "rust1", since = "1.0.0")]
1406 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1407 impl const PartialOrd for () {
1409 fn partial_cmp(&self, _: &()) -> Option<Ordering> {
1414 #[stable(feature = "rust1", since = "1.0.0")]
1415 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1416 impl const PartialOrd for bool {
1418 fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
1419 Some(self.cmp(other))
1423 partial_ord_impl! { f32 f64 }
1425 macro_rules! ord_impl {
1427 #[stable(feature = "rust1", since = "1.0.0")]
1428 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1429 impl const PartialOrd for $t {
1431 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
1432 Some(self.cmp(other))
1435 fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
1437 fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
1439 fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
1441 fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
1444 #[stable(feature = "rust1", since = "1.0.0")]
1445 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1446 impl const Ord for $t {
1448 fn cmp(&self, other: &$t) -> Ordering {
1449 // The order here is important to generate more optimal assembly.
1450 // See <https://github.com/rust-lang/rust/issues/63758> for more info.
1451 if *self < *other { Less }
1452 else if *self == *other { Equal }
1459 #[stable(feature = "rust1", since = "1.0.0")]
1460 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1461 impl const Ord for () {
1463 fn cmp(&self, _other: &()) -> Ordering {
1468 #[stable(feature = "rust1", since = "1.0.0")]
1469 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1470 impl const Ord for bool {
1472 fn cmp(&self, other: &bool) -> Ordering {
1473 // Casting to i8's and converting the difference to an Ordering generates
1474 // more optimal assembly.
1475 // See <https://github.com/rust-lang/rust/issues/66780> for more info.
1476 match (*self as i8) - (*other as i8) {
1480 // SAFETY: bool as i8 returns 0 or 1, so the difference can't be anything else
1481 _ => unsafe { unreachable_unchecked() },
1486 ord_impl! { char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
1488 #[unstable(feature = "never_type", issue = "35121")]
1489 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1490 impl const PartialEq for ! {
1491 fn eq(&self, _: &!) -> bool {
1496 #[unstable(feature = "never_type", issue = "35121")]
1499 #[unstable(feature = "never_type", issue = "35121")]
1500 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1501 impl const PartialOrd for ! {
1502 fn partial_cmp(&self, _: &!) -> Option<Ordering> {
1507 #[unstable(feature = "never_type", issue = "35121")]
1508 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1509 impl const Ord for ! {
1510 fn cmp(&self, _: &!) -> Ordering {
1517 #[stable(feature = "rust1", since = "1.0.0")]
1518 #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
1519 impl<A: ?Sized, B: ?Sized> const PartialEq<&B> for &A
1521 A: ~const PartialEq<B>,
1524 fn eq(&self, other: &&B) -> bool {
1525 PartialEq::eq(*self, *other)
1528 fn ne(&self, other: &&B) -> bool {
1529 PartialEq::ne(*self, *other)
1532 #[stable(feature = "rust1", since = "1.0.0")]
1533 impl<A: ?Sized, B: ?Sized> PartialOrd<&B> for &A
1538 fn partial_cmp(&self, other: &&B) -> Option<Ordering> {
1539 PartialOrd::partial_cmp(*self, *other)
1542 fn lt(&self, other: &&B) -> bool {
1543 PartialOrd::lt(*self, *other)
1546 fn le(&self, other: &&B) -> bool {
1547 PartialOrd::le(*self, *other)
1550 fn gt(&self, other: &&B) -> bool {
1551 PartialOrd::gt(*self, *other)
1554 fn ge(&self, other: &&B) -> bool {
1555 PartialOrd::ge(*self, *other)
1558 #[stable(feature = "rust1", since = "1.0.0")]
1559 impl<A: ?Sized> Ord for &A
1564 fn cmp(&self, other: &Self) -> Ordering {
1565 Ord::cmp(*self, *other)
1568 #[stable(feature = "rust1", since = "1.0.0")]
1569 impl<A: ?Sized> Eq for &A where A: Eq {}
1573 #[stable(feature = "rust1", since = "1.0.0")]
1574 impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &mut A
1579 fn eq(&self, other: &&mut B) -> bool {
1580 PartialEq::eq(*self, *other)
1583 fn ne(&self, other: &&mut B) -> bool {
1584 PartialEq::ne(*self, *other)
1587 #[stable(feature = "rust1", since = "1.0.0")]
1588 impl<A: ?Sized, B: ?Sized> PartialOrd<&mut B> for &mut A
1593 fn partial_cmp(&self, other: &&mut B) -> Option<Ordering> {
1594 PartialOrd::partial_cmp(*self, *other)
1597 fn lt(&self, other: &&mut B) -> bool {
1598 PartialOrd::lt(*self, *other)
1601 fn le(&self, other: &&mut B) -> bool {
1602 PartialOrd::le(*self, *other)
1605 fn gt(&self, other: &&mut B) -> bool {
1606 PartialOrd::gt(*self, *other)
1609 fn ge(&self, other: &&mut B) -> bool {
1610 PartialOrd::ge(*self, *other)
1613 #[stable(feature = "rust1", since = "1.0.0")]
1614 impl<A: ?Sized> Ord for &mut A
1619 fn cmp(&self, other: &Self) -> Ordering {
1620 Ord::cmp(*self, *other)
1623 #[stable(feature = "rust1", since = "1.0.0")]
1624 impl<A: ?Sized> Eq for &mut A where A: Eq {}
1626 #[stable(feature = "rust1", since = "1.0.0")]
1627 impl<A: ?Sized, B: ?Sized> PartialEq<&mut B> for &A
1632 fn eq(&self, other: &&mut B) -> bool {
1633 PartialEq::eq(*self, *other)
1636 fn ne(&self, other: &&mut B) -> bool {
1637 PartialEq::ne(*self, *other)
1641 #[stable(feature = "rust1", since = "1.0.0")]
1642 impl<A: ?Sized, B: ?Sized> PartialEq<&B> for &mut A
1647 fn eq(&self, other: &&B) -> bool {
1648 PartialEq::eq(*self, *other)
1651 fn ne(&self, other: &&B) -> bool {
1652 PartialEq::ne(*self, *other)