1
   2
   3
   4
   5
   6
   7
   8
   9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
// Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! Functionality for ordering and comparison.
//!
//! This module defines both [`PartialOrd`] and [`PartialEq`] traits which are used
//! by the compiler to implement comparison operators. Rust programs may
//! implement [`PartialOrd`] to overload the `<`, `<=`, `>`, and `>=` operators,
//! and may implement [`PartialEq`] to overload the `==` and `!=` operators.
//!
//! [`PartialOrd`]: trait.PartialOrd.html
//! [`PartialEq`]: trait.PartialEq.html
//!
//! # Examples
//!
//! ```
//! let x: u32 = 0;
//! let y: u32 = 1;
//!
//! // these two lines are equivalent
//! assert_eq!(x < y, true);
//! assert_eq!(x.lt(&y), true);
//!
//! // these two lines are also equivalent
//! assert_eq!(x == y, false);
//! assert_eq!(x.eq(&y), false);
//! ```

#![stable(feature = "rust1", since = "1.0.0")]

use self::Ordering::*;

/// Trait for equality comparisons which are [partial equivalence
/// relations](http://en.wikipedia.org/wiki/Partial_equivalence_relation).
///
/// This trait allows for partial equality, for types that do not have a full
/// equivalence relation.  For example, in floating point numbers `NaN != NaN`,
/// so floating point types implement `PartialEq` but not `Eq`.
///
/// Formally, the equality must be (for all `a`, `b` and `c`):
///
/// - symmetric: `a == b` implies `b == a`; and
/// - transitive: `a == b` and `b == c` implies `a == c`.
///
/// Note that these requirements mean that the trait itself must be implemented
/// symmetrically and transitively: if `T: PartialEq<U>` and `U: PartialEq<V>`
/// then `U: PartialEq<T>` and `T: PartialEq<V>`.
///
/// ## Derivable
///
/// This trait can be used with `#[derive]`. When `derive`d on structs, two
/// instances are equal if all fields are equal, and not equal if any fields
/// are not equal. When `derive`d on enums, each variant is equal to itself
/// and not equal to the other variants.
///
/// ## How can I implement `PartialEq`?
///
/// PartialEq only requires the `eq` method to be implemented; `ne` is defined
/// in terms of it by default. Any manual implementation of `ne` *must* respect
/// the rule that `eq` is a strict inverse of `ne`; that is, `!(a == b)` if and
/// only if `a != b`.
///
/// Implementations of `PartialEq`, `PartialOrd`, and `Ord` *must* agree with
/// each other. It's easy to accidentally make them disagree by deriving some
/// of the traits and manually implementing others.
///
/// An example implementation for a domain in which two books are considered
/// the same book if their ISBN matches, even if the formats differ:
///
/// ```
/// enum BookFormat {
///     Paperback,
///     Hardback,
///     Ebook,
/// }
///
/// struct Book {
///     isbn: i32,
///     format: BookFormat,
/// }
///
/// impl PartialEq for Book {
///     fn eq(&self, other: &Book) -> bool {
///         self.isbn == other.isbn
///     }
/// }
///
/// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
/// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
/// let b3 = Book { isbn: 10, format: BookFormat::Paperback };
///
/// assert!(b1 == b2);
/// assert!(b1 != b3);
/// ```
///
/// ## How can I compare two different types?
///
/// The type you can compare with is controlled by `PartialEq`'s type parameter.
/// For example, let's tweak our previous code a bit:
///
/// ```
/// enum BookFormat {
///     Paperback,
///     Hardback,
///     Ebook,
/// }
///
/// struct Book {
///     isbn: i32,
///     format: BookFormat,
/// }
///
/// impl PartialEq<BookFormat> for Book {
///     fn eq(&self, other: &BookFormat) -> bool {
///         match (&self.format, other) {
///            (BookFormat::Paperback, BookFormat::Paperback) => true,
///            (BookFormat::Hardback,  BookFormat::Hardback)  => true,
///            (BookFormat::Ebook,     BookFormat::Ebook)     => true,
///            (_, _) => false,
///         }
///     }
/// }
///
/// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
///
/// assert!(b1 == BookFormat::Paperback);
/// assert!(b1 != BookFormat::Ebook);
/// ```
///
/// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
/// we've changed what type we can use on the right side of the `==` operator.
/// This lets us use it in the `assert!` statements at the bottom.
///
/// You can also combine these implementations to let the `==` operator work with
/// two different types:
///
/// ```
/// enum BookFormat {
///     Paperback,
///     Hardback,
///     Ebook,
/// }
///
/// struct Book {
///     isbn: i32,
///     format: BookFormat,
/// }
///
/// impl PartialEq<BookFormat> for Book {
///     fn eq(&self, other: &BookFormat) -> bool {
///         match (&self.format, other) {
///            (&BookFormat::Paperback, &BookFormat::Paperback) => true,
///            (&BookFormat::Hardback,  &BookFormat::Hardback)  => true,
///            (&BookFormat::Ebook,     &BookFormat::Ebook)     => true,
///            (_, _) => false,
///         }
///     }
/// }
///
/// impl PartialEq for Book {
///     fn eq(&self, other: &Book) -> bool {
///         self.isbn == other.isbn
///     }
/// }
///
/// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
/// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
///
/// assert!(b1 == BookFormat::Paperback);
/// assert!(b1 != BookFormat::Ebook);
/// assert!(b1 == b2);
/// ```
///
/// # Examples
///
/// ```
/// let x: u32 = 0;
/// let y: u32 = 1;
///
/// assert_eq!(x == y, false);
/// assert_eq!(x.eq(&y), false);
/// ```
#[lang = "eq"]
#[stable(feature = "rust1", since = "1.0.0")]
#[doc(alias = "==")]
#[doc(alias = "!=")]
#[rustc_on_unimplemented(
    message="can't compare `{Self}` with `{Rhs}`",
    label="no implementation for `{Self} == {Rhs}`",
)]
pub trait PartialEq<Rhs: ?Sized = Self> {
    /// This method tests for `self` and `other` values to be equal, and is used
    /// by `==`.
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    fn eq(&self, other: &Rhs) -> bool;

    /// This method tests for `!=`.
    #[inline]
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    fn ne(&self, other: &Rhs) -> bool { !self.eq(other) }
}

/// Trait for equality comparisons which are [equivalence relations](
/// https://en.wikipedia.org/wiki/Equivalence_relation).
///
/// This means, that in addition to `a == b` and `a != b` being strict inverses, the equality must
/// be (for all `a`, `b` and `c`):
///
/// - reflexive: `a == a`;
/// - symmetric: `a == b` implies `b == a`; and
/// - transitive: `a == b` and `b == c` implies `a == c`.
///
/// This property cannot be checked by the compiler, and therefore `Eq` implies
/// `PartialEq`, and has no extra methods.
///
/// ## Derivable
///
/// This trait can be used with `#[derive]`. When `derive`d, because `Eq` has
/// no extra methods, it is only informing the compiler that this is an
/// equivalence relation rather than a partial equivalence relation. Note that
/// the `derive` strategy requires all fields are `Eq`, which isn't
/// always desired.
///
/// ## How can I implement `Eq`?
///
/// If you cannot use the `derive` strategy, specify that your type implements
/// `Eq`, which has no methods:
///
/// ```
/// enum BookFormat { Paperback, Hardback, Ebook }
/// struct Book {
///     isbn: i32,
///     format: BookFormat,
/// }
/// impl PartialEq for Book {
///     fn eq(&self, other: &Book) -> bool {
///         self.isbn == other.isbn
///     }
/// }
/// impl Eq for Book {}
/// ```
#[doc(alias = "==")]
#[doc(alias = "!=")]
#[stable(feature = "rust1", since = "1.0.0")]
pub trait Eq: PartialEq<Self> {
    // this method is used solely by #[deriving] to assert
    // that every component of a type implements #[deriving]
    // itself, the current deriving infrastructure means doing this
    // assertion without using a method on this trait is nearly
    // impossible.
    //
    // This should never be implemented by hand.
    #[doc(hidden)]
    #[inline]
    #[stable(feature = "rust1", since = "1.0.0")]
    fn assert_receiver_is_total_eq(&self) {}
}

// FIXME: this struct is used solely by #[derive] to
// assert that every component of a type implements Eq.
//
// This struct should never appear in user code.
#[doc(hidden)]
#[allow(missing_debug_implementations)]
#[unstable(feature = "derive_eq",
           reason = "deriving hack, should not be public",
           issue = "0")]
pub struct AssertParamIsEq<T: Eq + ?Sized> { _field: ::marker::PhantomData<T> }

/// An `Ordering` is the result of a comparison between two values.
///
/// # Examples
///
/// ```
/// use std::cmp::Ordering;
///
/// let result = 1.cmp(&2);
/// assert_eq!(Ordering::Less, result);
///
/// let result = 1.cmp(&1);
/// assert_eq!(Ordering::Equal, result);
///
/// let result = 2.cmp(&1);
/// assert_eq!(Ordering::Greater, result);
/// ```
#[derive(Clone, Copy, PartialEq, Debug, Hash)]
#[stable(feature = "rust1", since = "1.0.0")]
pub enum Ordering {
    /// An ordering where a compared value is less [than another].
    #[stable(feature = "rust1", since = "1.0.0")]
    Less = -1,
    /// An ordering where a compared value is equal [to another].
    #[stable(feature = "rust1", since = "1.0.0")]
    Equal = 0,
    /// An ordering where a compared value is greater [than another].
    #[stable(feature = "rust1", since = "1.0.0")]
    Greater = 1,
}

impl Ordering {
    /// Reverses the `Ordering`.
    ///
    /// * `Less` becomes `Greater`.
    /// * `Greater` becomes `Less`.
    /// * `Equal` becomes `Equal`.
    ///
    /// # Examples
    ///
    /// Basic behavior:
    ///
    /// ```
    /// use std::cmp::Ordering;
    ///
    /// assert_eq!(Ordering::Less.reverse(), Ordering::Greater);
    /// assert_eq!(Ordering::Equal.reverse(), Ordering::Equal);
    /// assert_eq!(Ordering::Greater.reverse(), Ordering::Less);
    /// ```
    ///
    /// This method can be used to reverse a comparison:
    ///
    /// ```
    /// let mut data: &mut [_] = &mut [2, 10, 5, 8];
    ///
    /// // sort the array from largest to smallest.
    /// data.sort_by(|a, b| a.cmp(b).reverse());
    ///
    /// let b: &mut [_] = &mut [10, 8, 5, 2];
    /// assert!(data == b);
    /// ```
    #[inline]
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn reverse(self) -> Ordering {
        match self {
            Less => Greater,
            Equal => Equal,
            Greater => Less,
        }
    }

    /// Chains two orderings.
    ///
    /// Returns `self` when it's not `Equal`. Otherwise returns `other`.
    /// # Examples
    ///
    /// ```
    /// use std::cmp::Ordering;
    ///
    /// let result = Ordering::Equal.then(Ordering::Less);
    /// assert_eq!(result, Ordering::Less);
    ///
    /// let result = Ordering::Less.then(Ordering::Equal);
    /// assert_eq!(result, Ordering::Less);
    ///
    /// let result = Ordering::Less.then(Ordering::Greater);
    /// assert_eq!(result, Ordering::Less);
    ///
    /// let result = Ordering::Equal.then(Ordering::Equal);
    /// assert_eq!(result, Ordering::Equal);
    ///
    /// let x: (i64, i64, i64) = (1, 2, 7);
    /// let y: (i64, i64, i64) = (1, 5, 3);
    /// let result = x.0.cmp(&y.0).then(x.1.cmp(&y.1)).then(x.2.cmp(&y.2));
    ///
    /// assert_eq!(result, Ordering::Less);
    /// ```
    #[inline]
    #[stable(feature = "ordering_chaining", since = "1.17.0")]
    pub fn then(self, other: Ordering) -> Ordering {
        match self {
            Equal => other,
            _ => self,
        }
    }

    /// Chains the ordering with the given function.
    ///
    /// Returns `self` when it's not `Equal`. Otherwise calls `f` and returns
    /// the result.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::cmp::Ordering;
    ///
    /// let result = Ordering::Equal.then_with(|| Ordering::Less);
    /// assert_eq!(result, Ordering::Less);
    ///
    /// let result = Ordering::Less.then_with(|| Ordering::Equal);
    /// assert_eq!(result, Ordering::Less);
    ///
    /// let result = Ordering::Less.then_with(|| Ordering::Greater);
    /// assert_eq!(result, Ordering::Less);
    ///
    /// let result = Ordering::Equal.then_with(|| Ordering::Equal);
    /// assert_eq!(result, Ordering::Equal);
    ///
    /// let x: (i64, i64, i64) = (1, 2, 7);
    /// let y: (i64, i64, i64)  = (1, 5, 3);
    /// let result = x.0.cmp(&y.0).then_with(|| x.1.cmp(&y.1)).then_with(|| x.2.cmp(&y.2));
    ///
    /// assert_eq!(result, Ordering::Less);
    /// ```
    #[inline]
    #[stable(feature = "ordering_chaining", since = "1.17.0")]
    pub fn then_with<F: FnOnce() -> Ordering>(self, f: F) -> Ordering {
        match self {
            Equal => f(),
            _ => self,
        }
    }
}

/// A helper struct for reverse ordering.
///
/// This struct is a helper to be used with functions like `Vec::sort_by_key` and
/// can be used to reverse order a part of a key.
///
/// Example usage:
///
/// ```
/// use std::cmp::Reverse;
///
/// let mut v = vec![1, 2, 3, 4, 5, 6];
/// v.sort_by_key(|&num| (num > 3, Reverse(num)));
/// assert_eq!(v, vec![3, 2, 1, 6, 5, 4]);
/// ```
#[derive(PartialEq, Eq, Debug, Copy, Clone, Default, Hash)]
#[stable(feature = "reverse_cmp_key", since = "1.19.0")]
pub struct Reverse<T>(#[stable(feature = "reverse_cmp_key", since = "1.19.0")] pub T);

#[stable(feature = "reverse_cmp_key", since = "1.19.0")]
impl<T: PartialOrd> PartialOrd for Reverse<T> {
    #[inline]
    fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }

    #[inline]
    fn lt(&self, other: &Self) -> bool { other.0 < self.0 }
    #[inline]
    fn le(&self, other: &Self) -> bool { other.0 <= self.0 }
    #[inline]
    fn ge(&self, other: &Self) -> bool { other.0 >= self.0 }
    #[inline]
    fn gt(&self, other: &Self) -> bool { other.0 > self.0 }
}

#[stable(feature = "reverse_cmp_key", since = "1.19.0")]
impl<T: Ord> Ord for Reverse<T> {
    #[inline]
    fn cmp(&self, other: &Reverse<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

/// Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order).
///
/// An order is a total order if it is (for all `a`, `b` and `c`):
///
/// - total and antisymmetric: exactly one of `a < b`, `a == b` or `a > b` is true; and
/// - transitive, `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
///
/// ## Derivable
///
/// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
/// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
/// When `derive`d on enums, variants are ordered by their top-to-bottom declaration order.
///
/// ## How can I implement `Ord`?
///
/// `Ord` requires that the type also be `PartialOrd` and `Eq` (which requires `PartialEq`).
///
/// Then you must define an implementation for `cmp()`. You may find it useful to use
/// `cmp()` on your type's fields.
///
/// Implementations of `PartialEq`, `PartialOrd`, and `Ord` *must* agree with each other. It's
/// easy to accidentally make them disagree by deriving some of the traits and manually
/// implementing others.
///
/// Here's an example where you want to sort people by height only, disregarding `id`
/// and `name`:
///
/// ```
/// use std::cmp::Ordering;
///
/// #[derive(Eq)]
/// struct Person {
///     id: u32,
///     name: String,
///     height: u32,
/// }
///
/// impl Ord for Person {
///     fn cmp(&self, other: &Person) -> Ordering {
///         self.height.cmp(&other.height)
///     }
/// }
///
/// impl PartialOrd for Person {
///     fn partial_cmp(&self, other: &Person) -> Option<Ordering> {
///         Some(self.cmp(other))
///     }
/// }
///
/// impl PartialEq for Person {
///     fn eq(&self, other: &Person) -> bool {
///         self.height == other.height
///     }
/// }
/// ```
#[lang = "ord"]
#[doc(alias = "<")]
#[doc(alias = ">")]
#[doc(alias = "<=")]
#[doc(alias = ">=")]
#[stable(feature = "rust1", since = "1.0.0")]
pub trait Ord: Eq + PartialOrd<Self> {
    /// This method returns an `Ordering` between `self` and `other`.
    ///
    /// By convention, `self.cmp(&other)` returns the ordering matching the expression
    /// `self <operator> other` if true.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::cmp::Ordering;
    ///
    /// assert_eq!(5.cmp(&10), Ordering::Less);
    /// assert_eq!(10.cmp(&5), Ordering::Greater);
    /// assert_eq!(5.cmp(&5), Ordering::Equal);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    fn cmp(&self, other: &Self) -> Ordering;

    /// Compares and returns the maximum of two values.
    ///
    /// Returns the second argument if the comparison determines them to be equal.
    ///
    /// # Examples
    ///
    /// ```
    /// assert_eq!(2, 1.max(2));
    /// assert_eq!(2, 2.max(2));
    /// ```
    #[stable(feature = "ord_max_min", since = "1.21.0")]
    #[inline]
    fn max(self, other: Self) -> Self
    where Self: Sized {
        if other >= self { other } else { self }
    }

    /// Compares and returns the minimum of two values.
    ///
    /// Returns the first argument if the comparison determines them to be equal.
    ///
    /// # Examples
    ///
    /// ```
    /// assert_eq!(1, 1.min(2));
    /// assert_eq!(2, 2.min(2));
    /// ```
    #[stable(feature = "ord_max_min", since = "1.21.0")]
    #[inline]
    fn min(self, other: Self) -> Self
    where Self: Sized {
        if self <= other { self } else { other }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl Eq for Ordering {}

#[stable(feature = "rust1", since = "1.0.0")]
impl Ord for Ordering {
    #[inline]
    fn cmp(&self, other: &Ordering) -> Ordering {
        (*self as i32).cmp(&(*other as i32))
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl PartialOrd for Ordering {
    #[inline]
    fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
        (*self as i32).partial_cmp(&(*other as i32))
    }
}

/// Trait for values that can be compared for a sort-order.
///
/// The comparison must satisfy, for all `a`, `b` and `c`:
///
/// - antisymmetry: if `a < b` then `!(a > b)`, as well as `a > b` implying `!(a < b)`; and
/// - transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
///
/// Note that these requirements mean that the trait itself must be implemented symmetrically and
/// transitively: if `T: PartialOrd<U>` and `U: PartialOrd<V>` then `U: PartialOrd<T>` and `T:
/// PartialOrd<V>`.
///
/// ## Derivable
///
/// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
/// lexicographic ordering based on the top-to-bottom declaration order of the struct's members.
/// When `derive`d on enums, variants are ordered by their top-to-bottom declaration order.
///
/// ## How can I implement `PartialOrd`?
///
/// `PartialOrd` only requires implementation of the `partial_cmp` method, with the others
/// generated from default implementations.
///
/// However it remains possible to implement the others separately for types which do not have a
/// total order. For example, for floating point numbers, `NaN < 0 == false` and `NaN >= 0 ==
/// false` (cf. IEEE 754-2008 section 5.11).
///
/// `PartialOrd` requires your type to be `PartialEq`.
///
/// Implementations of `PartialEq`, `PartialOrd`, and `Ord` *must* agree with each other. It's
/// easy to accidentally make them disagree by deriving some of the traits and manually
/// implementing others.
///
/// If your type is `Ord`, you can implement `partial_cmp()` by using `cmp()`:
///
/// ```
/// use std::cmp::Ordering;
///
/// #[derive(Eq)]
/// struct Person {
///     id: u32,
///     name: String,
///     height: u32,
/// }
///
/// impl PartialOrd for Person {
///     fn partial_cmp(&self, other: &Person) -> Option<Ordering> {
///         Some(self.cmp(other))
///     }
/// }
///
/// impl Ord for Person {
///     fn cmp(&self, other: &Person) -> Ordering {
///         self.height.cmp(&other.height)
///     }
/// }
///
/// impl PartialEq for Person {
///     fn eq(&self, other: &Person) -> bool {
///         self.height == other.height
///     }
/// }
/// ```
///
/// You may also find it useful to use `partial_cmp()` on your type's fields. Here
/// is an example of `Person` types who have a floating-point `height` field that
/// is the only field to be used for sorting:
///
/// ```
/// use std::cmp::Ordering;
///
/// struct Person {
///     id: u32,
///     name: String,
///     height: f64,
/// }
///
/// impl PartialOrd for Person {
///     fn partial_cmp(&self, other: &Person) -> Option<Ordering> {
///         self.height.partial_cmp(&other.height)
///     }
/// }
///
/// impl PartialEq for Person {
///     fn eq(&self, other: &Person) -> bool {
///         self.height == other.height
///     }
/// }
/// ```
///
/// # Examples
///
/// ```
/// let x : u32 = 0;
/// let y : u32 = 1;
///
/// assert_eq!(x < y, true);
/// assert_eq!(x.lt(&y), true);
/// ```
#[lang = "partial_ord"]
#[stable(feature = "rust1", since = "1.0.0")]
#[doc(alias = ">")]
#[doc(alias = "<")]
#[doc(alias = "<=")]
#[doc(alias = ">=")]
#[rustc_on_unimplemented(
    message="can't compare `{Self}` with `{Rhs}`",
    label="no implementation for `{Self} < {Rhs}` and `{Self} > {Rhs}`",
)]
pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
    /// This method returns an ordering between `self` and `other` values if one exists.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::cmp::Ordering;
    ///
    /// let result = 1.0.partial_cmp(&2.0);
    /// assert_eq!(result, Some(Ordering::Less));
    ///
    /// let result = 1.0.partial_cmp(&1.0);
    /// assert_eq!(result, Some(Ordering::Equal));
    ///
    /// let result = 2.0.partial_cmp(&1.0);
    /// assert_eq!(result, Some(Ordering::Greater));
    /// ```
    ///
    /// When comparison is impossible:
    ///
    /// ```
    /// let result = std::f64::NAN.partial_cmp(&1.0);
    /// assert_eq!(result, None);
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    fn partial_cmp(&self, other: &Rhs) -> Option<Ordering>;

    /// This method tests less than (for `self` and `other`) and is used by the `<` operator.
    ///
    /// # Examples
    ///
    /// ```
    /// let result = 1.0 < 2.0;
    /// assert_eq!(result, true);
    ///
    /// let result = 2.0 < 1.0;
    /// assert_eq!(result, false);
    /// ```
    #[inline]
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    fn lt(&self, other: &Rhs) -> bool {
        match self.partial_cmp(other) {
            Some(Less) => true,
            _ => false,
        }
    }

    /// This method tests less than or equal to (for `self` and `other`) and is used by the `<=`
    /// operator.
    ///
    /// # Examples
    ///
    /// ```
    /// let result = 1.0 <= 2.0;
    /// assert_eq!(result, true);
    ///
    /// let result = 2.0 <= 2.0;
    /// assert_eq!(result, true);
    /// ```
    #[inline]
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    fn le(&self, other: &Rhs) -> bool {
        match self.partial_cmp(other) {
            Some(Less) | Some(Equal) => true,
            _ => false,
        }
    }

    /// This method tests greater than (for `self` and `other`) and is used by the `>` operator.
    ///
    /// # Examples
    ///
    /// ```
    /// let result = 1.0 > 2.0;
    /// assert_eq!(result, false);
    ///
    /// let result = 2.0 > 2.0;
    /// assert_eq!(result, false);
    /// ```
    #[inline]
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    fn gt(&self, other: &Rhs) -> bool {
        match self.partial_cmp(other) {
            Some(Greater) => true,
            _ => false,
        }
    }

    /// This method tests greater than or equal to (for `self` and `other`) and is used by the `>=`
    /// operator.
    ///
    /// # Examples
    ///
    /// ```
    /// let result = 2.0 >= 1.0;
    /// assert_eq!(result, true);
    ///
    /// let result = 2.0 >= 2.0;
    /// assert_eq!(result, true);
    /// ```
    #[inline]
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    fn ge(&self, other: &Rhs) -> bool {
        match self.partial_cmp(other) {
            Some(Greater) | Some(Equal) => true,
            _ => false,
        }
    }
}

/// Compares and returns the minimum of two values.
///
/// Returns the first argument if the comparison determines them to be equal.
///
/// Internally uses an alias to `Ord::min`.
///
/// # Examples
///
/// ```
/// use std::cmp;
///
/// assert_eq!(1, cmp::min(1, 2));
/// assert_eq!(2, cmp::min(2, 2));
/// ```
#[inline]
#[stable(feature = "rust1", since = "1.0.0")]
pub fn min<T: Ord>(v1: T, v2: T) -> T {
    v1.min(v2)
}

/// Compares and returns the maximum of two values.
///
/// Returns the second argument if the comparison determines them to be equal.
///
/// Internally uses an alias to `Ord::max`.
///
/// # Examples
///
/// ```
/// use std::cmp;
///
/// assert_eq!(2, cmp::max(1, 2));
/// assert_eq!(2, cmp::max(2, 2));
/// ```
#[inline]
#[stable(feature = "rust1", since = "1.0.0")]
pub fn max<T: Ord>(v1: T, v2: T) -> T {
    v1.max(v2)
}

// Implementation of PartialEq, Eq, PartialOrd and Ord for primitive types
mod impls {
    use cmp::Ordering::{self, Less, Greater, Equal};

    macro_rules! partial_eq_impl {
        ($($t:ty)*) => ($(
            #[stable(feature = "rust1", since = "1.0.0")]
            impl PartialEq for $t {
                #[inline]
                fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
                #[inline]
                fn ne(&self, other: &$t) -> bool { (*self) != (*other) }
            }
        )*)
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl PartialEq for () {
        #[inline]
        fn eq(&self, _other: &()) -> bool { true }
        #[inline]
        fn ne(&self, _other: &()) -> bool { false }
    }

    partial_eq_impl! {
        bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f32 f64
    }

    macro_rules! eq_impl {
        ($($t:ty)*) => ($(
            #[stable(feature = "rust1", since = "1.0.0")]
            impl Eq for $t {}
        )*)
    }

    eq_impl! { () bool char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }

    macro_rules! partial_ord_impl {
        ($($t:ty)*) => ($(
            #[stable(feature = "rust1", since = "1.0.0")]
            impl PartialOrd for $t {
                #[inline]
                fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
                    match (self <= other, self >= other) {
                        (false, false) => None,
                        (false, true) => Some(Greater),
                        (true, false) => Some(Less),
                        (true, true) => Some(Equal),
                    }
                }
                #[inline]
                fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
                #[inline]
                fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
                #[inline]
                fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
                #[inline]
                fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
            }
        )*)
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl PartialOrd for () {
        #[inline]
        fn partial_cmp(&self, _: &()) -> Option<Ordering> {
            Some(Equal)
        }
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl PartialOrd for bool {
        #[inline]
        fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
            (*self as u8).partial_cmp(&(*other as u8))
        }
    }

    partial_ord_impl! { f32 f64 }

    macro_rules! ord_impl {
        ($($t:ty)*) => ($(
            #[stable(feature = "rust1", since = "1.0.0")]
            impl PartialOrd for $t {
                #[inline]
                fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
                    Some(self.cmp(other))
                }
                #[inline]
                fn lt(&self, other: &$t) -> bool { (*self) < (*other) }
                #[inline]
                fn le(&self, other: &$t) -> bool { (*self) <= (*other) }
                #[inline]
                fn ge(&self, other: &$t) -> bool { (*self) >= (*other) }
                #[inline]
                fn gt(&self, other: &$t) -> bool { (*self) > (*other) }
            }

            #[stable(feature = "rust1", since = "1.0.0")]
            impl Ord for $t {
                #[inline]
                fn cmp(&self, other: &$t) -> Ordering {
                    if *self == *other { Equal }
                    else if *self < *other { Less }
                    else { Greater }
                }
            }
        )*)
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl Ord for () {
        #[inline]
        fn cmp(&self, _other: &()) -> Ordering { Equal }
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl Ord for bool {
        #[inline]
        fn cmp(&self, other: &bool) -> Ordering {
            (*self as u8).cmp(&(*other as u8))
        }
    }

    ord_impl! { char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }

    #[unstable(feature = "never_type", issue = "35121")]
    impl PartialEq for ! {
        fn eq(&self, _: &!) -> bool {
            *self
        }
    }

    #[unstable(feature = "never_type", issue = "35121")]
    impl Eq for ! {}

    #[unstable(feature = "never_type", issue = "35121")]
    impl PartialOrd for ! {
        fn partial_cmp(&self, _: &!) -> Option<Ordering> {
            *self
        }
    }

    #[unstable(feature = "never_type", issue = "35121")]
    impl Ord for ! {
        fn cmp(&self, _: &!) -> Ordering {
            *self
        }
    }

    // & pointers

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, 'b, A: ?Sized, B: ?Sized> PartialEq<&'b B> for &'a A where A: PartialEq<B> {
        #[inline]
        fn eq(&self, other: & &'b B) -> bool { PartialEq::eq(*self, *other) }
        #[inline]
        fn ne(&self, other: & &'b B) -> bool { PartialEq::ne(*self, *other) }
    }
    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, 'b, A: ?Sized, B: ?Sized> PartialOrd<&'b B> for &'a A where A: PartialOrd<B> {
        #[inline]
        fn partial_cmp(&self, other: &&'b B) -> Option<Ordering> {
            PartialOrd::partial_cmp(*self, *other)
        }
        #[inline]
        fn lt(&self, other: & &'b B) -> bool { PartialOrd::lt(*self, *other) }
        #[inline]
        fn le(&self, other: & &'b B) -> bool { PartialOrd::le(*self, *other) }
        #[inline]
        fn ge(&self, other: & &'b B) -> bool { PartialOrd::ge(*self, *other) }
        #[inline]
        fn gt(&self, other: & &'b B) -> bool { PartialOrd::gt(*self, *other) }
    }
    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, A: ?Sized> Ord for &'a A where A: Ord {
        #[inline]
        fn cmp(&self, other: & &'a A) -> Ordering { Ord::cmp(*self, *other) }
    }
    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, A: ?Sized> Eq for &'a A where A: Eq {}

    // &mut pointers

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, 'b, A: ?Sized, B: ?Sized> PartialEq<&'b mut B> for &'a mut A where A: PartialEq<B> {
        #[inline]
        fn eq(&self, other: &&'b mut B) -> bool { PartialEq::eq(*self, *other) }
        #[inline]
        fn ne(&self, other: &&'b mut B) -> bool { PartialEq::ne(*self, *other) }
    }
    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, 'b, A: ?Sized, B: ?Sized> PartialOrd<&'b mut B> for &'a mut A where A: PartialOrd<B> {
        #[inline]
        fn partial_cmp(&self, other: &&'b mut B) -> Option<Ordering> {
            PartialOrd::partial_cmp(*self, *other)
        }
        #[inline]
        fn lt(&self, other: &&'b mut B) -> bool { PartialOrd::lt(*self, *other) }
        #[inline]
        fn le(&self, other: &&'b mut B) -> bool { PartialOrd::le(*self, *other) }
        #[inline]
        fn ge(&self, other: &&'b mut B) -> bool { PartialOrd::ge(*self, *other) }
        #[inline]
        fn gt(&self, other: &&'b mut B) -> bool { PartialOrd::gt(*self, *other) }
    }
    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, A: ?Sized> Ord for &'a mut A where A: Ord {
        #[inline]
        fn cmp(&self, other: &&'a mut A) -> Ordering { Ord::cmp(*self, *other) }
    }
    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, A: ?Sized> Eq for &'a mut A where A: Eq {}

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, 'b, A: ?Sized, B: ?Sized> PartialEq<&'b mut B> for &'a A where A: PartialEq<B> {
        #[inline]
        fn eq(&self, other: &&'b mut B) -> bool { PartialEq::eq(*self, *other) }
        #[inline]
        fn ne(&self, other: &&'b mut B) -> bool { PartialEq::ne(*self, *other) }
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, 'b, A: ?Sized, B: ?Sized> PartialEq<&'b B> for &'a mut A where A: PartialEq<B> {
        #[inline]
        fn eq(&self, other: &&'b B) -> bool { PartialEq::eq(*self, *other) }
        #[inline]
        fn ne(&self, other: &&'b B) -> bool { PartialEq::ne(*self, *other) }
    }
}