    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

    use core::cmp;

    use crate::memmem::{prefilter::Pre, util};

    /// Two-Way search in the forward direction.
    #[derive(Clone, Copy, Debug)]
    pub(crate) struct Forward(TwoWay);

    /// Two-Way search in the reverse direction.
    #[derive(Clone, Copy, Debug)]
    pub(crate) struct Reverse(TwoWay);

    /// An implementation of the TwoWay substring search algorithm, with heuristics
    /// for accelerating search based on frequency analysis.
    ///
    /// This searcher supports forward and reverse search, although not
    /// simultaneously. It runs in O(n + m) time and O(1) space, where
    /// `n ~ len(needle)` and `m ~ len(haystack)`.
    ///
    /// The implementation here roughly matches that which was developed by
    /// Crochemore and Perrin in their 1991 paper "Two-way string-matching." The
    /// changes in this implementation are 1) the use of zero-based indices, 2) a
    /// heuristic skip table based on the last byte (borrowed from Rust's standard
    /// library) and 3) the addition of heuristics for a fast skip loop. That is,
    /// (3) this will detect bytes that are believed to be rare in the needle and
    /// use fast vectorized instructions to find their occurrences quickly. The
    /// Two-Way algorithm is then used to confirm whether a match at that location
    /// occurred.
    ///
    /// The heuristic for fast skipping is automatically shut off if it's
    /// detected to be ineffective at search time. Generally, this only occurs in
    /// pathological cases. But this is generally necessary in order to preserve
    /// a `O(n + m)` time bound.
    ///
    /// The code below is fairly complex and not obviously correct at all. It's
    /// likely necessary to read the Two-Way paper cited above in order to fully
    /// grok this code. The essence of it is:
    ///
    /// 1) Do something to detect a "critical" position in the needle.
    /// 2) For the current position in the haystack, look if needle[critical..]
    ///    matches at that position.
    /// 3) If so, look if needle[..critical] matches.
    /// 4) If a mismatch occurs, shift the search by some amount based on the
    ///    critical position and a pre-computed shift.
    ///
    /// This type is wrapped in Forward and Reverse types that expose consistent
    /// forward or reverse APIs.
    #[derive(Clone, Copy, Debug)]
    struct TwoWay {
        /// A small bitset used as a quick prefilter (in addition to the faster
        /// SIMD based prefilter). Namely, a bit 'i' is set if and only if b%64==i
        /// for any b in the needle.
        ///
        /// When used as a prefilter, if the last byte at the current candidate
        /// position is NOT in this set, then we can skip that entire candidate
        /// position (the length of the needle). This is essentially the shift
        /// trick found in Boyer-Moore, but only applied to bytes that don't appear
        /// in the needle.
        ///
        /// N.B. This trick was inspired by something similar in std's
        /// implementation of Two-Way.
        byteset: ApproximateByteSet,
        /// A critical position in needle. Specifically, this position corresponds
        /// to beginning of either the minimal or maximal suffix in needle. (N.B.
        /// See SuffixType below for why "minimal" isn't quite the correct word
        /// here.)
        ///
        /// This is the position at which every search begins. Namely, search
        /// starts by scanning text to the right of this position, and only if
        /// there's a match does the text to the left of this position get scanned.
        critical_pos: usize,
        /// The amount we shift by in the Two-Way search algorithm. This
        /// corresponds to the "small period" and "large period" cases.
        shift: Shift,
    }

    impl Forward {
        /// Create a searcher that uses the Two-Way algorithm by searching forwards
        /// through any haystack.
        pub(crate) fn new(needle: &[u8]) -> Forward {
            if needle.is_empty() {
                return Forward(TwoWay::empty());
            }

            let byteset = ApproximateByteSet::new(needle);
            let min_suffix = Suffix::forward(needle, SuffixKind::Minimal);
            let max_suffix = Suffix::forward(needle, SuffixKind::Maximal);
            let (period_lower_bound, critical_pos) =
                if min_suffix.pos > max_suffix.pos {
                    (min_suffix.period, min_suffix.pos)
                } else {
                    (max_suffix.period, max_suffix.pos)
                };
            let shift = Shift::forward(needle, period_lower_bound, critical_pos);
            Forward(TwoWay { byteset, critical_pos, shift })
        }

        /// Find the position of the first occurrence of this searcher's needle in
        /// the given haystack. If one does not exist, then return None.
        ///
        /// This accepts prefilter state that is useful when using the same
        /// searcher multiple times, such as in an iterator.
        ///
        /// Callers must guarantee that the needle is non-empty and its length is
        /// <= the haystack's length.
        #[inline(always)]
        pub(crate) fn find(
            &self,
            pre: Option<&mut Pre<'_>>,
            haystack: &[u8],
            needle: &[u8],
        ) -> Option<usize> {
            debug_assert!(!needle.is_empty(), "needle should not be empty");
            debug_assert!(needle.len() <= haystack.len(), "haystack too short");

            match self.0.shift {
                Shift::Small { period } => {
                    self.find_small_imp(pre, haystack, needle, period)
                }
                Shift::Large { shift } => {
                    self.find_large_imp(pre, haystack, needle, shift)
                }
            }
        }

        /// Like find, but handles the degenerate substring test cases. This is
        /// only useful for conveniently testing this substring implementation in
        /// isolation.
        #[cfg(test)]
        fn find_general(
            &self,
            pre: Option<&mut Pre<'_>>,
            haystack: &[u8],
            needle: &[u8],
        ) -> Option<usize> {
            if needle.is_empty() {
                Some(0)
            } else if haystack.len() < needle.len() {
                None
            } else {
                self.find(pre, haystack, needle)
            }
        }

        // Each of the two search implementations below can be accelerated by a
        // prefilter, but it is not always enabled. To avoid its overhead when
        // its disabled, we explicitly inline each search implementation based on
        // whether a prefilter will be used or not. The decision on which to use
        // is made in the parent meta searcher.

        #[inline(always)]
        fn find_small_imp(
            &self,
            mut pre: Option<&mut Pre<'_>>,
            haystack: &[u8],
            needle: &[u8],
            period: usize,
        ) -> Option<usize> {
            let last_byte = needle.len() - 1;
            let mut pos = 0;
            let mut shift = 0;
            while pos + needle.len() <= haystack.len() {
                let mut i = cmp::max(self.0.critical_pos, shift);
                if let Some(pre) = pre.as_mut() {
                    if pre.should_call() {
                        pos += pre.call(&haystack[pos..], needle)?;
                        shift = 0;
                        i = self.0.critical_pos;
                        if pos + needle.len() > haystack.len() {
                            return None;
                        }
                    }
                }
                if !self.0.byteset.contains(haystack[pos + last_byte]) {
                    pos += needle.len();
                    shift = 0;
                    continue;
                }
                while i < needle.len() && needle[i] == haystack[pos + i] {
                    i += 1;
                }
                if i < needle.len() {
                    pos += i - self.0.critical_pos + 1;
                    shift = 0;
                } else {
                    let mut j = self.0.critical_pos;
                    while j > shift && needle[j] == haystack[pos + j] {
                        j -= 1;
                    }
                    if j <= shift && needle[shift] == haystack[pos + shift] {
                        return Some(pos);
                    }
                    pos += period;
                    shift = needle.len() - period;
                }
            }
            None
        }

        #[inline(always)]
        fn find_large_imp(
            &self,
            mut pre: Option<&mut Pre<'_>>,
            haystack: &[u8],
            needle: &[u8],
            shift: usize,
        ) -> Option<usize> {
            let last_byte = needle.len() - 1;
            let mut pos = 0;
            'outer: while pos + needle.len() <= haystack.len() {
                if let Some(pre) = pre.as_mut() {
                    if pre.should_call() {
                        pos += pre.call(&haystack[pos..], needle)?;
                        if pos + needle.len() > haystack.len() {
                            return None;
                        }
                    }
                }

                if !self.0.byteset.contains(haystack[pos + last_byte]) {
                    pos += needle.len();
                    continue;
                }
                let mut i = self.0.critical_pos;
                while i < needle.len() && needle[i] == haystack[pos + i] {
                    i += 1;
                }
                if i < needle.len() {
                    pos += i - self.0.critical_pos + 1;
                } else {
                    for j in (0..self.0.critical_pos).rev() {
                        if needle[j] != haystack[pos + j] {
                            pos += shift;
                            continue 'outer;
                        }
                    }
                    return Some(pos);
                }
            }
            None
        }
    }

    impl Reverse {
        /// Create a searcher that uses the Two-Way algorithm by searching in
        /// reverse through any haystack.
        pub(crate) fn new(needle: &[u8]) -> Reverse {
            if needle.is_empty() {
                return Reverse(TwoWay::empty());
            }

            let byteset = ApproximateByteSet::new(needle);
            let min_suffix = Suffix::reverse(needle, SuffixKind::Minimal);
            let max_suffix = Suffix::reverse(needle, SuffixKind::Maximal);
            let (period_lower_bound, critical_pos) =
                if min_suffix.pos < max_suffix.pos {
                    (min_suffix.period, min_suffix.pos)
                } else {
                    (max_suffix.period, max_suffix.pos)
                };
            // let critical_pos = needle.len() - critical_pos;
            let shift = Shift::reverse(needle, period_lower_bound, critical_pos);
            Reverse(TwoWay { byteset, critical_pos, shift })
        }

        /// Find the position of the last occurrence of this searcher's needle
        /// in the given haystack. If one does not exist, then return None.
        ///
        /// This will automatically initialize prefilter state. This should only
        /// be used for one-off searches.
        ///
        /// Callers must guarantee that the needle is non-empty and its length is
        /// <= the haystack's length.
        #[inline(always)]
        pub(crate) fn rfind(
            &self,
            haystack: &[u8],
            needle: &[u8],
        ) -> Option<usize> {
            debug_assert!(!needle.is_empty(), "needle should not be empty");
            debug_assert!(needle.len() <= haystack.len(), "haystack too short");
            // For the reverse case, we don't use a prefilter. It's plausible that
            // perhaps we should, but it's a lot of additional code to do it, and
            // it's not clear that it's actually worth it. If you have a really
            // compelling use case for this, please file an issue.
            match self.0.shift {
                Shift::Small { period } => {
                    self.rfind_small_imp(haystack, needle, period)
                }
                Shift::Large { shift } => {
                    self.rfind_large_imp(haystack, needle, shift)
                }
            }
        }

        /// Like rfind, but handles the degenerate substring test cases. This is
        /// only useful for conveniently testing this substring implementation in
        /// isolation.
        #[cfg(test)]
        fn rfind_general(&self, haystack: &[u8], needle: &[u8]) -> Option<usize> {
            if needle.is_empty() {
                Some(haystack.len())
            } else if haystack.len() < needle.len() {
                None
            } else {
                self.rfind(haystack, needle)
            }
        }

        #[inline(always)]
        fn rfind_small_imp(
            &self,
            haystack: &[u8],
            needle: &[u8],
            period: usize,
        ) -> Option<usize> {
            let nlen = needle.len();
            let mut pos = haystack.len();
            let mut shift = nlen;
            while pos >= nlen {
                if !self.0.byteset.contains(haystack[pos - nlen]) {
                    pos -= nlen;
                    shift = nlen;
                    continue;
                }
                let mut i = cmp::min(self.0.critical_pos, shift);
                while i > 0 && needle[i - 1] == haystack[pos - nlen + i - 1] {
                    i -= 1;
                }
                if i > 0 || needle[0] != haystack[pos - nlen] {
                    pos -= self.0.critical_pos - i + 1;
                    shift = nlen;
                } else {
                    let mut j = self.0.critical_pos;
                    while j < shift && needle[j] == haystack[pos - nlen + j] {
                        j += 1;
                    }
                    if j >= shift {
                        return Some(pos - nlen);
                    }
                    pos -= period;
                    shift = period;
                }
            }
            None
        }

        #[inline(always)]
        fn rfind_large_imp(
            &self,
            haystack: &[u8],
            needle: &[u8],
            shift: usize,
        ) -> Option<usize> {
            let nlen = needle.len();
            let mut pos = haystack.len();
            while pos >= nlen {
                if !self.0.byteset.contains(haystack[pos - nlen]) {
                    pos -= nlen;
                    continue;
                }
                let mut i = self.0.critical_pos;
                while i > 0 && needle[i - 1] == haystack[pos - nlen + i - 1] {
                    i -= 1;
                }
                if i > 0 || needle[0] != haystack[pos - nlen] {
                    pos -= self.0.critical_pos - i + 1;
                } else {
                    let mut j = self.0.critical_pos;
                    while j < nlen && needle[j] == haystack[pos - nlen + j] {
                        j += 1;
                    }
                    if j == nlen {
                        return Some(pos - nlen);
                    }
                    pos -= shift;
                }
            }
            None
        }
    }

    impl TwoWay {
        fn empty() -> TwoWay {
            TwoWay {
                byteset: ApproximateByteSet::new(b""),
                critical_pos: 0,
                shift: Shift::Large { shift: 0 },
            }
        }
    }

    /// A representation of the amount we're allowed to shift by during Two-Way
    /// search.
    ///
    /// When computing a critical factorization of the needle, we find the position
    /// of the critical factorization by finding the needle's maximal (or minimal)
    /// suffix, along with the period of that suffix. It turns out that the period
    /// of that suffix is a lower bound on the period of the needle itself.
    ///
    /// This lower bound is equivalent to the actual period of the needle in
    /// some cases. To describe that case, we denote the needle as `x` where
    /// `x = uv` and `v` is the lexicographic maximal suffix of `v`. The lower
    /// bound given here is always the period of `v`, which is `<= period(x)`. The
    /// case where `period(v) == period(x)` occurs when `len(u) < (len(x) / 2)` and
    /// where `u` is a suffix of `v[0..period(v)]`.
    ///
    /// This case is important because the search algorithm for when the
    /// periods are equivalent is slightly different than the search algorithm
    /// for when the periods are not equivalent. In particular, when they aren't
    /// equivalent, we know that the period of the needle is no less than half its
    /// length. In this case, we shift by an amount less than or equal to the
    /// period of the needle (determined by the maximum length of the components
    /// of the critical factorization of `x`, i.e., `max(len(u), len(v))`)..
    ///
    /// The above two cases are represented by the variants below. Each entails
    /// a different instantiation of the Two-Way search algorithm.
    ///
    /// N.B. If we could find a way to compute the exact period in all cases,
    /// then we could collapse this case analysis and simplify the algorithm. The
    /// Two-Way paper suggests this is possible, but more reading is required to
    /// grok why the authors didn't pursue that path.
    #[derive(Clone, Copy, Debug)]
    enum Shift {
        Small { period: usize },
        Large { shift: usize },
    }

    impl Shift {
        /// Compute the shift for a given needle in the forward direction.
        ///
        /// This requires a lower bound on the period and a critical position.
        /// These can be computed by extracting both the minimal and maximal
        /// lexicographic suffixes, and choosing the right-most starting position.
        /// The lower bound on the period is then the period of the chosen suffix.
        fn forward(
            needle: &[u8],
            period_lower_bound: usize,
            critical_pos: usize,
        ) -> Shift {
            let large = cmp::max(critical_pos, needle.len() - critical_pos);
            if critical_pos * 2 >= needle.len() {
                return Shift::Large { shift: large };
            }

            let (u, v) = needle.split_at(critical_pos);
            if !util::is_suffix(&v[..period_lower_bound], u) {
                return Shift::Large { shift: large };
            }
            Shift::Small { period: period_lower_bound }
        }

        /// Compute the shift for a given needle in the reverse direction.
        ///
        /// This requires a lower bound on the period and a critical position.
        /// These can be computed by extracting both the minimal and maximal
        /// lexicographic suffixes, and choosing the left-most starting position.
        /// The lower bound on the period is then the period of the chosen suffix.
        fn reverse(
            needle: &[u8],
            period_lower_bound: usize,
            critical_pos: usize,
        ) -> Shift {
            let large = cmp::max(critical_pos, needle.len() - critical_pos);
            if (needle.len() - critical_pos) * 2 >= needle.len() {
                return Shift::Large { shift: large };
            }

            let (v, u) = needle.split_at(critical_pos);
            if !util::is_prefix(&v[v.len() - period_lower_bound..], u) {
                return Shift::Large { shift: large };
            }
            Shift::Small { period: period_lower_bound }
        }
    }

    /// A suffix extracted from a needle along with its period.
    #[derive(Debug)]
    struct Suffix {
        /// The starting position of this suffix.
        ///
        /// If this is a forward suffix, then `&bytes[pos..]` can be used. If this
        /// is a reverse suffix, then `&bytes[..pos]` can be used. That is, for
        /// forward suffixes, this is an inclusive starting position, where as for
        /// reverse suffixes, this is an exclusive ending position.
        pos: usize,
        /// The period of this suffix.
        ///
        /// Note that this is NOT necessarily the period of the string from which
        /// this suffix comes from. (It is always less than or equal to the period
        /// of the original string.)
        period: usize,
    }

    impl Suffix {
        fn forward(needle: &[u8], kind: SuffixKind) -> Suffix {
            debug_assert!(!needle.is_empty());

            // suffix represents our maximal (or minimal) suffix, along with
            // its period.
            let mut suffix = Suffix { pos: 0, period: 1 };
            // The start of a suffix in `needle` that we are considering as a
            // more maximal (or minimal) suffix than what's in `suffix`.
            let mut candidate_start = 1;
            // The current offset of our suffixes that we're comparing.
            //
            // When the characters at this offset are the same, then we mush on
            // to the next position since no decision is possible. When the
            // candidate's character is greater (or lesser) than the corresponding
            // character than our current maximal (or minimal) suffix, then the
            // current suffix is changed over to the candidate and we restart our
            // search. Otherwise, the candidate suffix is no good and we restart
            // our search on the next candidate.
            //
            // The three cases above correspond to the three cases in the loop
            // below.
            let mut offset = 0;

            while candidate_start + offset < needle.len() {
                let current = needle[suffix.pos + offset];
                let candidate = needle[candidate_start + offset];
                match kind.cmp(current, candidate) {
                    SuffixOrdering::Accept => {
                        suffix = Suffix { pos: candidate_start, period: 1 };
                        candidate_start += 1;
                        offset = 0;
                    }
                    SuffixOrdering::Skip => {
                        candidate_start += offset + 1;
                        offset = 0;
                        suffix.period = candidate_start - suffix.pos;
                    }
                    SuffixOrdering::Push => {
                        if offset + 1 == suffix.period {
                            candidate_start += suffix.period;
                            offset = 0;
                        } else {
                            offset += 1;
                        }
                    }
                }
            }
            suffix
        }

        fn reverse(needle: &[u8], kind: SuffixKind) -> Suffix {
            debug_assert!(!needle.is_empty());

            // See the comments in `forward` for how this works.
            let mut suffix = Suffix { pos: needle.len(), period: 1 };
            if needle.len() == 1 {
                return suffix;
            }
            let mut candidate_start = needle.len() - 1;
            let mut offset = 0;

            while offset < candidate_start {
                let current = needle[suffix.pos - offset - 1];
                let candidate = needle[candidate_start - offset - 1];
                match kind.cmp(current, candidate) {
                    SuffixOrdering::Accept => {
                        suffix = Suffix { pos: candidate_start, period: 1 };
                        candidate_start -= 1;
                        offset = 0;
                    }
                    SuffixOrdering::Skip => {
                        candidate_start -= offset + 1;
                        offset = 0;
                        suffix.period = suffix.pos - candidate_start;
                    }
                    SuffixOrdering::Push => {
                        if offset + 1 == suffix.period {
                            candidate_start -= suffix.period;
                            offset = 0;
                        } else {
                            offset += 1;
                        }
                    }
                }
            }
            suffix
        }
    }

    /// The kind of suffix to extract.
    #[derive(Clone, Copy, Debug)]
    enum SuffixKind {
        /// Extract the smallest lexicographic suffix from a string.
        ///
        /// Technically, this doesn't actually pick the smallest lexicographic
        /// suffix. e.g., Given the choice between `a` and `aa`, this will choose
        /// the latter over the former, even though `a < aa`. The reasoning for
        /// this isn't clear from the paper, but it still smells like a minimal
        /// suffix.
        Minimal,
        /// Extract the largest lexicographic suffix from a string.
        ///
        /// Unlike `Minimal`, this really does pick the maximum suffix. e.g., Given
        /// the choice between `z` and `zz`, this will choose the latter over the
        /// former.
        Maximal,
    }

    /// The result of comparing corresponding bytes between two suffixes.
    #[derive(Clone, Copy, Debug)]
    enum SuffixOrdering {
        /// This occurs when the given candidate byte indicates that the candidate
        /// suffix is better than the current maximal (or minimal) suffix. That is,
        /// the current candidate suffix should supplant the current maximal (or
        /// minimal) suffix.
        Accept,
        /// This occurs when the given candidate byte excludes the candidate suffix
        /// from being better than the current maximal (or minimal) suffix. That
        /// is, the current candidate suffix should be dropped and the next one
        /// should be considered.
        Skip,
        /// This occurs when no decision to accept or skip the candidate suffix
        /// can be made, e.g., when corresponding bytes are equivalent. In this
        /// case, the next corresponding bytes should be compared.
        Push,
    }

    impl SuffixKind {
        /// Returns true if and only if the given candidate byte indicates that
        /// it should replace the current suffix as the maximal (or minimal)
        /// suffix.
        fn cmp(self, current: u8, candidate: u8) -> SuffixOrdering {
            use self::SuffixOrdering::*;

            match self {
                SuffixKind::Minimal if candidate < current => Accept,
                SuffixKind::Minimal if candidate > current => Skip,
                SuffixKind::Minimal => Push,
                SuffixKind::Maximal if candidate > current => Accept,
                SuffixKind::Maximal if candidate < current => Skip,
                SuffixKind::Maximal => Push,
            }
        }
    }

    /// A bitset used to track whether a particular byte exists in a needle or not.
    ///
    /// Namely, bit 'i' is set if and only if byte%64==i for any byte in the
    /// needle. If a particular byte in the haystack is NOT in this set, then one
    /// can conclude that it is also not in the needle, and thus, one can advance
    /// in the haystack by needle.len() bytes.
    #[derive(Clone, Copy, Debug)]
    struct ApproximateByteSet(u64);

    impl ApproximateByteSet {
        /// Create a new set from the given needle.
        fn new(needle: &[u8]) -> ApproximateByteSet {
            let mut bits = 0;
            for &b in needle {
                bits |= 1 << (b % 64);
            }
            ApproximateByteSet(bits)
        }

        /// Return true if and only if the given byte might be in this set. This
        /// may return a false positive, but will never return a false negative.
        #[inline(always)]
        fn contains(&self, byte: u8) -> bool {
            self.0 & (1 << (byte % 64)) != 0
        }
    }

    #[cfg(all(test, feature = "std", not(miri)))]
    mod tests {
        use quickcheck::quickcheck;

        use super::*;

        define_memmem_quickcheck_tests!(
            super::simpletests::twoway_find,
            super::simpletests::twoway_rfind
        );

        /// Convenience wrapper for computing the suffix as a byte string.
        fn get_suffix_forward(needle: &[u8], kind: SuffixKind) -> (&[u8], usize) {
            let s = Suffix::forward(needle, kind);
            (&needle[s.pos..], s.period)
        }

        /// Convenience wrapper for computing the reverse suffix as a byte string.
        fn get_suffix_reverse(needle: &[u8], kind: SuffixKind) -> (&[u8], usize) {
            let s = Suffix::reverse(needle, kind);
            (&needle[..s.pos], s.period)
        }

        /// Return all of the non-empty suffixes in the given byte string.
        fn suffixes(bytes: &[u8]) -> Vec<&[u8]> {
            (0..bytes.len()).map(|i| &bytes[i..]).collect()
        }

        /// Return the lexicographically maximal suffix of the given byte string.
        fn naive_maximal_suffix_forward(needle: &[u8]) -> &[u8] {
            let mut sufs = suffixes(needle);
            sufs.sort();
            sufs.pop().unwrap()
        }

        /// Return the lexicographically maximal suffix of the reverse of the given
        /// byte string.
        fn naive_maximal_suffix_reverse(needle: &[u8]) -> Vec<u8> {
            let mut reversed = needle.to_vec();
            reversed.reverse();
            let mut got = naive_maximal_suffix_forward(&reversed).to_vec();
            got.reverse();
            got
        }

        #[test]
        fn suffix_forward() {
            macro_rules! assert_suffix_min {
                ($given:expr, $expected:expr, $period:expr) => {
                    let (got_suffix, got_period) =
                        get_suffix_forward($given.as_bytes(), SuffixKind::Minimal);
                    let got_suffix = std::str::from_utf8(got_suffix).unwrap();
                    assert_eq!(($expected, $period), (got_suffix, got_period));
                };
            }

            macro_rules! assert_suffix_max {
                ($given:expr, $expected:expr, $period:expr) => {
                    let (got_suffix, got_period) =
                        get_suffix_forward($given.as_bytes(), SuffixKind::Maximal);
                    let got_suffix = std::str::from_utf8(got_suffix).unwrap();
                    assert_eq!(($expected, $period), (got_suffix, got_period));
                };
            }

            assert_suffix_min!("a", "a", 1);
            assert_suffix_max!("a", "a", 1);

            assert_suffix_min!("ab", "ab", 2);
            assert_suffix_max!("ab", "b", 1);

            assert_suffix_min!("ba", "a", 1);
            assert_suffix_max!("ba", "ba", 2);

            assert_suffix_min!("abc", "abc", 3);
            assert_suffix_max!("abc", "c", 1);

            assert_suffix_min!("acb", "acb", 3);
            assert_suffix_max!("acb", "cb", 2);

            assert_suffix_min!("cba", "a", 1);
            assert_suffix_max!("cba", "cba", 3);

            assert_suffix_min!("abcabc", "abcabc", 3);
            assert_suffix_max!("abcabc", "cabc", 3);

            assert_suffix_min!("abcabcabc", "abcabcabc", 3);
            assert_suffix_max!("abcabcabc", "cabcabc", 3);

            assert_suffix_min!("abczz", "abczz", 5);
            assert_suffix_max!("abczz", "zz", 1);

            assert_suffix_min!("zzabc", "abc", 3);
            assert_suffix_max!("zzabc", "zzabc", 5);

            assert_suffix_min!("aaa", "aaa", 1);
            assert_suffix_max!("aaa", "aaa", 1);

            assert_suffix_min!("foobar", "ar", 2);
            assert_suffix_max!("foobar", "r", 1);
        }

        #[test]
        fn suffix_reverse() {
            macro_rules! assert_suffix_min {
                ($given:expr, $expected:expr, $period:expr) => {
                    let (got_suffix, got_period) =
                        get_suffix_reverse($given.as_bytes(), SuffixKind::Minimal);
                    let got_suffix = std::str::from_utf8(got_suffix).unwrap();
                    assert_eq!(($expected, $period), (got_suffix, got_period));
                };
            }

            macro_rules! assert_suffix_max {
                ($given:expr, $expected:expr, $period:expr) => {
                    let (got_suffix, got_period) =
                        get_suffix_reverse($given.as_bytes(), SuffixKind::Maximal);
                    let got_suffix = std::str::from_utf8(got_suffix).unwrap();
                    assert_eq!(($expected, $period), (got_suffix, got_period));
                };
            }

            assert_suffix_min!("a", "a", 1);
            assert_suffix_max!("a", "a", 1);

            assert_suffix_min!("ab", "a", 1);
            assert_suffix_max!("ab", "ab", 2);

            assert_suffix_min!("ba", "ba", 2);
            assert_suffix_max!("ba", "b", 1);

            assert_suffix_min!("abc", "a", 1);
            assert_suffix_max!("abc", "abc", 3);

            assert_suffix_min!("acb", "a", 1);
            assert_suffix_max!("acb", "ac", 2);

            assert_suffix_min!("cba", "cba", 3);
            assert_suffix_max!("cba", "c", 1);

            assert_suffix_min!("abcabc", "abca", 3);
            assert_suffix_max!("abcabc", "abcabc", 3);

            assert_suffix_min!("abcabcabc", "abcabca", 3);
            assert_suffix_max!("abcabcabc", "abcabcabc", 3);

            assert_suffix_min!("abczz", "a", 1);
            assert_suffix_max!("abczz", "abczz", 5);

            assert_suffix_min!("zzabc", "zza", 3);
            assert_suffix_max!("zzabc", "zz", 1);

            assert_suffix_min!("aaa", "aaa", 1);
            assert_suffix_max!("aaa", "aaa", 1);
        }

        quickcheck! {
            fn qc_suffix_forward_maximal(bytes: Vec<u8>) -> bool {
                if bytes.is_empty() {
                    return true;
                }

                let (got, _) = get_suffix_forward(&bytes, SuffixKind::Maximal);
                let expected = naive_maximal_suffix_forward(&bytes);
                got == expected
            }

            fn qc_suffix_reverse_maximal(bytes: Vec<u8>) -> bool {
                if bytes.is_empty() {
                    return true;
                }

                let (got, _) = get_suffix_reverse(&bytes, SuffixKind::Maximal);
                let expected = naive_maximal_suffix_reverse(&bytes);
                expected == got
            }
        }
    }

    #[cfg(test)]
    mod simpletests {
        use super::*;

        pub(crate) fn twoway_find(
            haystack: &[u8],
            needle: &[u8],
        ) -> Option<usize> {
            Forward::new(needle).find_general(None, haystack, needle)
        }

        pub(crate) fn twoway_rfind(
            haystack: &[u8],
            needle: &[u8],
        ) -> Option<usize> {
            Reverse::new(needle).rfind_general(haystack, needle)
        }

        define_memmem_simple_tests!(twoway_find, twoway_rfind);

        // This is a regression test caught by quickcheck that exercised a bug in
        // the reverse small period handling. The bug was that we were using 'if j
        // == shift' to determine if a match occurred, but the correct guard is 'if
        // j >= shift', which matches the corresponding guard in the forward impl.
        #[test]
        fn regression_rev_small_period() {
            let rfind = super::simpletests::twoway_rfind;
            let haystack = "ababaz";
            let needle = "abab";
            assert_eq!(Some(0), rfind(haystack.as_bytes(), needle.as_bytes()));
        }
    }