       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
    1091
    1092
    1093
    1094
    1095
    1096
    1097
    1098
    1099
    1100
    1101
    1102
    1103
    1104
    1105
    1106
    1107
    1108
    1109
    1110
    1111
    1112
    1113
    1114
    1115
    1116
    1117
    1118
    1119
    1120
    1121
    1122
    1123
    1124
    1125
    1126
    1127
    1128
    1129
    1130
    1131
    1132
    1133
    1134
    1135
    1136
    1137
    1138
    1139
    1140
    1141
    1142
    1143
    1144
    1145
    1146
    1147
    1148
    1149
    1150
    1151
    1152
    1153
    1154
    1155
    1156
    1157
    1158
    1159
    1160
    1161
    1162
    1163
    1164
    1165
    1166
    1167
    1168
    1169
    1170
    1171
    1172
    1173
    1174
    1175
    1176
    1177
    1178
    1179
    1180
    1181
    1182
    1183
    1184
    1185
    1186
    1187
    1188
    1189
    1190
    1191
    1192
    1193
    1194
    1195
    1196
    1197
    1198
    1199
    1200
    1201
    1202
    1203
    1204
    1205
    1206
    1207
    1208
    1209
    1210
    1211
    1212
    1213
    1214
    1215
    1216
    1217
    1218
    1219
    1220
    1221
    1222
    1223
    1224
    1225
    1226
    1227
    1228
    1229
    1230
    1231
    1232
    1233
    1234
    1235
    1236
    1237
    1238
    1239
    1240
    1241
    1242
    1243
    1244
    1245
    1246
    1247
    1248
    1249
    1250
    1251
    1252
    1253
    1254
    1255
    1256
    1257
    1258
    1259
    1260
    1261
    1262
    1263
    1264
    1265
    1266
    1267
    1268
    1269
    1270
    1271
    1272
    1273
    1274
    1275
    1276
    1277
    1278
    1279
    1280
    1281
    1282
    1283
    1284
    1285
    1286
    1287
    1288
    1289
    1290
    1291
    1292
    1293
    1294
    1295
    1296
    1297
    1298
    1299
    1300
    1301
    1302
    1303
    1304
    1305
    1306
    1307
    1308
    1309
    1310
    1311
    1312
    1313
    1314
    1315
    1316
    1317
    1318
    1319
    1320
    1321
    1322
    1323
    1324
    1325
    1326
    1327
    1328
    1329
    1330
    1331
    1332
    1333
    1334
    1335
    1336
    1337
    1338
    1339
    1340
    1341
    1342
    1343
    1344
    1345
    1346
    1347
    1348
    1349
    1350
    1351
    1352
    1353
    1354
    1355
    1356
    1357
    1358
    1359
    1360
    1361
    1362
    1363
    1364
    1365
    1366
    1367
    1368
    1369
    1370
    1371
    1372
    1373
    1374
    1375
    1376
    1377
    1378
    1379
    1380
    1381
    1382
    1383
    1384
    1385
    1386
    1387
    1388
    1389
    1390
    1391
    1392
    1393
    1394
    1395
    1396
    1397
    1398
    1399
    1400
    1401
    1402
    1403
    1404
    1405
    1406
    1407
    1408
    1409
    1410
    1411
    1412
    1413
    1414
    1415
    1416
    1417
    1418
    1419
    1420
    1421
    1422
    1423
    1424
    1425
    1426
    1427
    1428
    1429
    1430
    1431
    1432
    1433
    1434
    1435
    1436
    1437
    1438
    1439
    1440
    1441
    1442
    1443
    1444
    1445
    1446
    1447
    1448
    1449
    1450
    1451
    1452
    1453
    1454
    1455
    1456
    1457
    1458
    1459
    1460
    1461
    1462
    1463
    1464
    1465
    1466
    1467
    1468
    1469
    1470
    1471
    1472
    1473
    1474
    1475
    1476
    1477
    1478
    1479
    1480
    1481
    1482
    1483
    1484
    1485
    1486
    1487
    1488
    1489
    1490
    1491
    1492
    1493
    1494
    1495
    1496
    1497
    1498
    1499
    1500
    1501
    1502
    1503
    1504
    1505
    1506
    1507
    1508
    1509
    1510
    1511
    1512
    1513
    1514
    1515
    1516
    1517
    1518
    1519
    1520
    1521
    1522
    1523
    1524
    1525
    1526
    1527
    1528
    1529
    1530
    1531
    1532
    1533
    1534
    1535
    1536
    1537
    1538
    1539
    1540
    1541
    1542
    1543
    1544
    1545
    1546
    1547
    1548
    1549
    1550
    1551
    1552
    1553
    1554
    1555
    1556
    1557
    1558
    1559
    1560
    1561
    1562
    1563
    1564
    1565
    1566
    1567
    1568
    1569
    1570
    1571
    1572
    1573
    1574
    1575
    1576
    1577
    1578
    1579
    1580
    1581
    1582
    1583
    1584
    1585
    1586
    1587
    1588
    1589
    1590
    1591
    1592
    1593
    1594
    1595
    1596
    1597
    1598
    1599
    1600
    1601
    1602
    1603
    1604
    1605
    1606
    1607
    1608
    1609
    1610
    1611
    1612
    1613
    1614
    1615
    1616
    1617
    1618
    1619
    1620
    1621
    1622

    // Copyright 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.

    // This is an attempt at an implementation following the ideal
    //
    // ```
    // struct BTreeMap<K, V> {
    //     height: usize,
    //     root: Option<Box<Node<K, V, height>>>
    // }
    //
    // struct Node<K, V, height: usize> {
    //     keys: [K; 2 * B - 1],
    //     vals: [V; 2 * B - 1],
    //     edges: if height > 0 {
    //         [Box<Node<K, V, height - 1>>; 2 * B]
    //     } else { () },
    //     parent: *const Node<K, V, height + 1>,
    //     parent_idx: u16,
    //     len: u16,
    // }
    // ```
    //
    // Since Rust doesn't actually have dependent types and polymorphic recursion,
    // we make do with lots of unsafety.

    // A major goal of this module is to avoid complexity by treating the tree as a generic (if
    // weirdly shaped) container and avoiding dealing with most of the B-Tree invariants. As such,
    // this module doesn't care whether the entries are sorted, which nodes can be underfull, or
    // even what underfull means. However, we do rely on a few invariants:
    //
    // - Trees must have uniform depth/height. This means that every path down to a leaf from a
    //   given node has exactly the same length.
    // - A node of length `n` has `n` keys, `n` values, and (in an internal node) `n + 1` edges.
    //   This implies that even an empty internal node has at least one edge.

    use core::marker::PhantomData;
    use core::mem;
    use core::ptr::{self, Unique, NonNull};
    use core::slice;

    use alloc::{Global, Alloc, Layout};
    use boxed::Box;

    const B: usize = 6;
    pub const MIN_LEN: usize = B - 1;
    pub const CAPACITY: usize = 2 * B - 1;

    /// The underlying representation of leaf nodes. Note that it is often unsafe to actually store
    /// these, since only the first `len` keys and values are assumed to be initialized. As such,
    /// these should always be put behind pointers, and specifically behind `BoxedNode` in the owned
    /// case.
    ///
    /// See also rust-lang/rfcs#197, which would make this structure significantly more safe by
    /// avoiding accidentally dropping unused and uninitialized keys and values.
    ///
    /// We put the metadata first so that its position is the same for every `K` and `V`, in order
    /// to statically allocate a single dummy node to avoid allocations. This struct is `repr(C)` to
    /// prevent them from being reordered.
    #[repr(C)]
    struct LeafNode<K, V> {
        /// We use `*const` as opposed to `*mut` so as to be covariant in `K` and `V`.
        /// This either points to an actual node or is null.
        parent: *const InternalNode<K, V>,

        /// This node's index into the parent node's `edges` array.
        /// `*node.parent.edges[node.parent_idx]` should be the same thing as `node`.
        /// This is only guaranteed to be initialized when `parent` is nonnull.
        parent_idx: u16,

        /// The number of keys and values this node stores.
        ///
        /// This next to `parent_idx` to encourage the compiler to join `len` and
        /// `parent_idx` into the same 32-bit word, reducing space overhead.
        len: u16,

        /// The arrays storing the actual data of the node. Only the first `len` elements of each
        /// array are initialized and valid.
        keys: [K; CAPACITY],
        vals: [V; CAPACITY],
    }

    impl<K, V> LeafNode<K, V> {
        /// Creates a new `LeafNode`. Unsafe because all nodes should really be hidden behind
        /// `BoxedNode`, preventing accidental dropping of uninitialized keys and values.
        unsafe fn new() -> Self {
            LeafNode {
                // As a general policy, we leave fields uninitialized if they can be, as this should
                // be both slightly faster and easier to track in Valgrind.
                keys: mem::uninitialized(),
                vals: mem::uninitialized(),
                parent: ptr::null(),
                parent_idx: mem::uninitialized(),
                len: 0
            }
        }

        fn is_shared_root(&self) -> bool {
            ptr::eq(self, &EMPTY_ROOT_NODE as *const _ as *const _)
        }
    }

    // We need to implement Sync here in order to make a static instance.
    unsafe impl Sync for LeafNode<(), ()> {}

    // An empty node used as a placeholder for the root node, to avoid allocations.
    // We use () in order to save space, since no operation on an empty tree will
    // ever take a pointer past the first key.
    static EMPTY_ROOT_NODE: LeafNode<(), ()> = LeafNode {
        parent: ptr::null(),
        parent_idx: 0,
        len: 0,
        keys: [(); CAPACITY],
        vals: [(); CAPACITY],
    };

    /// The underlying representation of internal nodes. As with `LeafNode`s, these should be hidden
    /// behind `BoxedNode`s to prevent dropping uninitialized keys and values. Any pointer to an
    /// `InternalNode` can be directly casted to a pointer to the underlying `LeafNode` portion of the
    /// node, allowing code to act on leaf and internal nodes generically without having to even check
    /// which of the two a pointer is pointing at. This property is enabled by the use of `repr(C)`.
    #[repr(C)]
    struct InternalNode<K, V> {
        data: LeafNode<K, V>,

        /// The pointers to the children of this node. `len + 1` of these are considered
        /// initialized and valid.
        edges: [BoxedNode<K, V>; 2 * B],
    }

    impl<K, V> InternalNode<K, V> {
        /// Creates a new `InternalNode`.
        ///
        /// This is unsafe for two reasons. First, it returns an `InternalNode` by value, risking
        /// dropping of uninitialized fields. Second, an invariant of internal nodes is that `len + 1`
        /// edges are initialized and valid, meaning that even when the node is empty (having a
        /// `len` of 0), there must be one initialized and valid edge. This function does not set up
        /// such an edge.
        unsafe fn new() -> Self {
            InternalNode {
                data: LeafNode::new(),
                edges: mem::uninitialized()
            }
        }
    }

    /// An owned pointer to a node. This basically is either `Box<LeafNode<K, V>>` or
    /// `Box<InternalNode<K, V>>`. However, it contains no information as to which of the two types
    /// of nodes is actually behind the box, and, partially due to this lack of information, has no
    /// destructor.
    struct BoxedNode<K, V> {
        ptr: Unique<LeafNode<K, V>>
    }

    impl<K, V> BoxedNode<K, V> {
        fn from_leaf(node: Box<LeafNode<K, V>>) -> Self {
            BoxedNode { ptr: Box::into_unique(node) }
        }

        fn from_internal(node: Box<InternalNode<K, V>>) -> Self {
            unsafe {
                BoxedNode { ptr: Unique::new_unchecked(Box::into_raw(node) as *mut LeafNode<K, V>) }
            }
        }

        unsafe fn from_ptr(ptr: NonNull<LeafNode<K, V>>) -> Self {
            BoxedNode { ptr: Unique::from(ptr) }
        }

        fn as_ptr(&self) -> NonNull<LeafNode<K, V>> {
            NonNull::from(self.ptr)
        }
    }

    /// An owned tree. Note that despite being owned, this does not have a destructor,
    /// and must be cleaned up manually.
    pub struct Root<K, V> {
        node: BoxedNode<K, V>,
        height: usize
    }

    unsafe impl<K: Sync, V: Sync> Sync for Root<K, V> { }
    unsafe impl<K: Send, V: Send> Send for Root<K, V> { }

    impl<K, V> Root<K, V> {
        pub fn is_shared_root(&self) -> bool {
            self.as_ref().is_shared_root()
        }

        pub fn shared_empty_root() -> Self {
            Root {
                node: unsafe {
                    BoxedNode::from_ptr(NonNull::new_unchecked(
                        &EMPTY_ROOT_NODE as *const _ as *const LeafNode<K, V> as *mut _
                    ))
                },
                height: 0,
            }
        }

        pub fn new_leaf() -> Self {
            Root {
                node: BoxedNode::from_leaf(Box::new(unsafe { LeafNode::new() })),
                height: 0
            }
        }

        pub fn as_ref(&self)
                -> NodeRef<marker::Immut, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.height,
                node: self.node.as_ptr(),
                root: self as *const _ as *mut _,
                _marker: PhantomData,
            }
        }

        pub fn as_mut(&mut self)
                -> NodeRef<marker::Mut, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.height,
                node: self.node.as_ptr(),
                root: self as *mut _,
                _marker: PhantomData,
            }
        }

        pub fn into_ref(self)
                -> NodeRef<marker::Owned, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.height,
                node: self.node.as_ptr(),
                root: ptr::null_mut(), // FIXME: Is there anything better to do here?
                _marker: PhantomData,
            }
        }

        /// Adds a new internal node with a single edge, pointing to the previous root, and make that
        /// new node the root. This increases the height by 1 and is the opposite of `pop_level`.
        pub fn push_level(&mut self)
                -> NodeRef<marker::Mut, K, V, marker::Internal> {
            debug_assert!(!self.is_shared_root());
            let mut new_node = Box::new(unsafe { InternalNode::new() });
            new_node.edges[0] = unsafe { BoxedNode::from_ptr(self.node.as_ptr()) };

            self.node = BoxedNode::from_internal(new_node);
            self.height += 1;

            let mut ret = NodeRef {
                height: self.height,
                node: self.node.as_ptr(),
                root: self as *mut _,
                _marker: PhantomData
            };

            unsafe {
                ret.reborrow_mut().first_edge().correct_parent_link();
            }

            ret
        }

        /// Removes the root node, using its first child as the new root. This cannot be called when
        /// the tree consists only of a leaf node. As it is intended only to be called when the root
        /// has only one edge, no cleanup is done on any of the other children are elements of the root.
        /// This decreases the height by 1 and is the opposite of `push_level`.
        pub fn pop_level(&mut self) {
            debug_assert!(self.height > 0);

            let top = self.node.ptr;

            self.node = unsafe {
                BoxedNode::from_ptr(self.as_mut()
                                        .cast_unchecked::<marker::Internal>()
                                        .first_edge()
                                        .descend()
                                        .node)
            };
            self.height -= 1;
            self.as_mut().as_leaf_mut().parent = ptr::null();

            unsafe {
                Global.dealloc(NonNull::from(top).cast(), Layout::new::<InternalNode<K, V>>());
            }
        }
    }

    // N.B. `NodeRef` is always covariant in `K` and `V`, even when the `BorrowType`
    // is `Mut`. This is technically wrong, but cannot result in any unsafety due to
    // internal use of `NodeRef` because we stay completely generic over `K` and `V`.
    // However, whenever a public type wraps `NodeRef`, make sure that it has the
    // correct variance.
    /// A reference to a node.
    ///
    /// This type has a number of parameters that controls how it acts:
    /// - `BorrowType`: This can be `Immut<'a>` or `Mut<'a>` for some `'a` or `Owned`.
    ///    When this is `Immut<'a>`, the `NodeRef` acts roughly like `&'a Node`,
    ///    when this is `Mut<'a>`, the `NodeRef` acts roughly like `&'a mut Node`,
    ///    and when this is `Owned`, the `NodeRef` acts roughly like `Box<Node>`.
    /// - `K` and `V`: These control what types of things are stored in the nodes.
    /// - `Type`: This can be `Leaf`, `Internal`, or `LeafOrInternal`. When this is
    ///   `Leaf`, the `NodeRef` points to a leaf node, when this is `Internal` the
    ///   `NodeRef` points to an internal node, and when this is `LeafOrInternal` the
    ///   `NodeRef` could be pointing to either type of node.
    pub struct NodeRef<BorrowType, K, V, Type> {
        height: usize,
        node: NonNull<LeafNode<K, V>>,
        // This is null unless the borrow type is `Mut`
        root: *const Root<K, V>,
        _marker: PhantomData<(BorrowType, Type)>
    }

    impl<'a, K: 'a, V: 'a, Type> Copy for NodeRef<marker::Immut<'a>, K, V, Type> { }
    impl<'a, K: 'a, V: 'a, Type> Clone for NodeRef<marker::Immut<'a>, K, V, Type> {
        fn clone(&self) -> Self {
            *self
        }
    }

    unsafe impl<BorrowType, K: Sync, V: Sync, Type> Sync
        for NodeRef<BorrowType, K, V, Type> { }

    unsafe impl<'a, K: Sync + 'a, V: Sync + 'a, Type> Send
       for NodeRef<marker::Immut<'a>, K, V, Type> { }
    unsafe impl<'a, K: Send + 'a, V: Send + 'a, Type> Send
       for NodeRef<marker::Mut<'a>, K, V, Type> { }
    unsafe impl<K: Send, V: Send, Type> Send
       for NodeRef<marker::Owned, K, V, Type> { }

    impl<BorrowType, K, V> NodeRef<BorrowType, K, V, marker::Internal> {
        fn as_internal(&self) -> &InternalNode<K, V> {
            unsafe {
                &*(self.node.as_ptr() as *mut InternalNode<K, V>)
            }
        }
    }

    impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Internal> {
        fn as_internal_mut(&mut self) -> &mut InternalNode<K, V> {
            unsafe {
                &mut *(self.node.as_ptr() as *mut InternalNode<K, V>)
            }
        }
    }

    impl<BorrowType, K, V, Type> NodeRef<BorrowType, K, V, Type> {
        /// Finds the length of the node. This is the number of keys or values. In an
        /// internal node, the number of edges is `len() + 1`.
        pub fn len(&self) -> usize {
            self.as_leaf().len as usize
        }

        /// Returns the height of this node in the whole tree. Zero height denotes the
        /// leaf level.
        pub fn height(&self) -> usize {
            self.height
        }

        /// Removes any static information about whether this node is a `Leaf` or an
        /// `Internal` node.
        pub fn forget_type(self) -> NodeRef<BorrowType, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.height,
                node: self.node,
                root: self.root,
                _marker: PhantomData
            }
        }

        /// Temporarily takes out another, immutable reference to the same node.
        fn reborrow<'a>(&'a self) -> NodeRef<marker::Immut<'a>, K, V, Type> {
            NodeRef {
                height: self.height,
                node: self.node,
                root: self.root,
                _marker: PhantomData
            }
        }

        fn as_leaf(&self) -> &LeafNode<K, V> {
            unsafe {
                self.node.as_ref()
            }
        }

        pub fn is_shared_root(&self) -> bool {
            self.as_leaf().is_shared_root()
        }

        pub fn keys(&self) -> &[K] {
            self.reborrow().into_key_slice()
        }

        fn vals(&self) -> &[V] {
            self.reborrow().into_val_slice()
        }

        /// Finds the parent of the current node. Returns `Ok(handle)` if the current
        /// node actually has a parent, where `handle` points to the edge of the parent
        /// that points to the current node. Returns `Err(self)` if the current node has
        /// no parent, giving back the original `NodeRef`.
        ///
        /// `edge.descend().ascend().unwrap()` and `node.ascend().unwrap().descend()` should
        /// both, upon success, do nothing.
        pub fn ascend(self) -> Result<
            Handle<
                NodeRef<
                    BorrowType,
                    K, V,
                    marker::Internal
                >,
                marker::Edge
            >,
            Self
        > {
            let parent_as_leaf = self.as_leaf().parent as *const LeafNode<K, V>;
            if let Some(non_zero) = NonNull::new(parent_as_leaf as *mut _) {
                Ok(Handle {
                    node: NodeRef {
                        height: self.height + 1,
                        node: non_zero,
                        root: self.root,
                        _marker: PhantomData
                    },
                    idx: self.as_leaf().parent_idx as usize,
                    _marker: PhantomData
                })
            } else {
                Err(self)
            }
        }

        pub fn first_edge(self) -> Handle<Self, marker::Edge> {
            Handle::new_edge(self, 0)
        }

        pub fn last_edge(self) -> Handle<Self, marker::Edge> {
            let len = self.len();
            Handle::new_edge(self, len)
        }

        /// Note that `self` must be nonempty.
        pub fn first_kv(self) -> Handle<Self, marker::KV> {
            debug_assert!(self.len() > 0);
            Handle::new_kv(self, 0)
        }

        /// Note that `self` must be nonempty.
        pub fn last_kv(self) -> Handle<Self, marker::KV> {
            let len = self.len();
            debug_assert!(len > 0);
            Handle::new_kv(self, len - 1)
        }
    }

    impl<K, V> NodeRef<marker::Owned, K, V, marker::Leaf> {
        /// Similar to `ascend`, gets a reference to a node's parent node, but also
        /// deallocate the current node in the process. This is unsafe because the
        /// current node will still be accessible despite being deallocated.
        pub unsafe fn deallocate_and_ascend(self) -> Option<
            Handle<
                NodeRef<
                    marker::Owned,
                    K, V,
                    marker::Internal
                >,
                marker::Edge
            >
        > {
            debug_assert!(!self.is_shared_root());
            let node = self.node;
            let ret = self.ascend().ok();
            Global.dealloc(node.cast(), Layout::new::<LeafNode<K, V>>());
            ret
        }
    }

    impl<K, V> NodeRef<marker::Owned, K, V, marker::Internal> {
        /// Similar to `ascend`, gets a reference to a node's parent node, but also
        /// deallocate the current node in the process. This is unsafe because the
        /// current node will still be accessible despite being deallocated.
        pub unsafe fn deallocate_and_ascend(self) -> Option<
            Handle<
                NodeRef<
                    marker::Owned,
                    K, V,
                    marker::Internal
                >,
                marker::Edge
            >
        > {
            let node = self.node;
            let ret = self.ascend().ok();
            Global.dealloc(node.cast(), Layout::new::<InternalNode<K, V>>());
            ret
        }
    }

    impl<'a, K, V, Type> NodeRef<marker::Mut<'a>, K, V, Type> {
        /// Unsafely asserts to the compiler some static information about whether this
        /// node is a `Leaf`.
        unsafe fn cast_unchecked<NewType>(&mut self)
                -> NodeRef<marker::Mut, K, V, NewType> {

            NodeRef {
                height: self.height,
                node: self.node,
                root: self.root,
                _marker: PhantomData
            }
        }

        /// Temporarily takes out another, mutable reference to the same node. Beware, as
        /// this method is very dangerous, doubly so since it may not immediately appear
        /// dangerous.
        ///
        /// Because mutable pointers can roam anywhere around the tree and can even (through
        /// `into_root_mut`) mess with the root of the tree, the result of `reborrow_mut`
        /// can easily be used to make the original mutable pointer dangling, or, in the case
        /// of a reborrowed handle, out of bounds.
        // FIXME(@gereeter) consider adding yet another type parameter to `NodeRef` that restricts
        // the use of `ascend` and `into_root_mut` on reborrowed pointers, preventing this unsafety.
        unsafe fn reborrow_mut(&mut self) -> NodeRef<marker::Mut, K, V, Type> {
            NodeRef {
                height: self.height,
                node: self.node,
                root: self.root,
                _marker: PhantomData
            }
        }

        fn as_leaf_mut(&mut self) -> &mut LeafNode<K, V> {
            unsafe {
                self.node.as_mut()
            }
        }

        fn keys_mut(&mut self) -> &mut [K] {
            unsafe { self.reborrow_mut().into_key_slice_mut() }
        }

        fn vals_mut(&mut self) -> &mut [V] {
            unsafe { self.reborrow_mut().into_val_slice_mut() }
        }
    }

    impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Immut<'a>, K, V, Type> {
        fn into_key_slice(self) -> &'a [K] {
            // When taking a pointer to the keys, if our key has a stricter
            // alignment requirement than the shared root does, then the pointer
            // would be out of bounds, which LLVM assumes will not happen. If the
            // alignment is more strict, we need to make an empty slice that doesn't
            // use an out of bounds pointer.
            if mem::align_of::<K>() > mem::align_of::<LeafNode<(), ()>>() && self.is_shared_root() {
                &[]
            } else {
                // Here either it's not the root, or the alignment is less strict,
                // in which case the keys pointer will point "one-past-the-end" of
                // the node, which is allowed by LLVM.
                unsafe {
                    slice::from_raw_parts(
                        self.as_leaf().keys.as_ptr(),
                        self.len()
                    )
                }
            }
        }

        fn into_val_slice(self) -> &'a [V] {
            debug_assert!(!self.is_shared_root());
            unsafe {
                slice::from_raw_parts(
                    self.as_leaf().vals.as_ptr(),
                    self.len()
                )
            }
        }

        fn into_slices(self) -> (&'a [K], &'a [V]) {
            let k = unsafe { ptr::read(&self) };
            (k.into_key_slice(), self.into_val_slice())
        }
    }

    impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Mut<'a>, K, V, Type> {
        /// Gets a mutable reference to the root itself. This is useful primarily when the
        /// height of the tree needs to be adjusted. Never call this on a reborrowed pointer.
        pub fn into_root_mut(self) -> &'a mut Root<K, V> {
            unsafe {
                &mut *(self.root as *mut Root<K, V>)
            }
        }

        fn into_key_slice_mut(mut self) -> &'a mut [K] {
            if mem::align_of::<K>() > mem::align_of::<LeafNode<(), ()>>() && self.is_shared_root() {
                &mut []
            } else {
                unsafe {
                    slice::from_raw_parts_mut(
                        &mut self.as_leaf_mut().keys as *mut [K] as *mut K,
                        self.len()
                    )
                }
            }
        }

        fn into_val_slice_mut(mut self) -> &'a mut [V] {
            debug_assert!(!self.is_shared_root());
            unsafe {
                slice::from_raw_parts_mut(
                    &mut self.as_leaf_mut().vals as *mut [V] as *mut V,
                    self.len()
                )
            }
        }

        fn into_slices_mut(self) -> (&'a mut [K], &'a mut [V]) {
            let k = unsafe { ptr::read(&self) };
            (k.into_key_slice_mut(), self.into_val_slice_mut())
        }
    }

    impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Leaf> {
        /// Adds a key/value pair the end of the node.
        pub fn push(&mut self, key: K, val: V) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(self.len() < CAPACITY);
            debug_assert!(!self.is_shared_root());

            let idx = self.len();

            unsafe {
                ptr::write(self.keys_mut().get_unchecked_mut(idx), key);
                ptr::write(self.vals_mut().get_unchecked_mut(idx), val);
            }

            self.as_leaf_mut().len += 1;
        }

        /// Adds a key/value pair to the beginning of the node.
        pub fn push_front(&mut self, key: K, val: V) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(self.len() < CAPACITY);
            debug_assert!(!self.is_shared_root());

            unsafe {
                slice_insert(self.keys_mut(), 0, key);
                slice_insert(self.vals_mut(), 0, val);
            }

            self.as_leaf_mut().len += 1;
        }
    }

    impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Internal> {
        /// Adds a key/value pair and an edge to go to the right of that pair to
        /// the end of the node.
        pub fn push(&mut self, key: K, val: V, edge: Root<K, V>) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(edge.height == self.height - 1);
            debug_assert!(self.len() < CAPACITY);

            let idx = self.len();

            unsafe {
                ptr::write(self.keys_mut().get_unchecked_mut(idx), key);
                ptr::write(self.vals_mut().get_unchecked_mut(idx), val);
                ptr::write(self.as_internal_mut().edges.get_unchecked_mut(idx + 1), edge.node);

                self.as_leaf_mut().len += 1;

                Handle::new_edge(self.reborrow_mut(), idx + 1).correct_parent_link();
            }
        }

        fn correct_childrens_parent_links(&mut self, first: usize, after_last: usize) {
            for i in first..after_last {
                Handle::new_edge(unsafe { self.reborrow_mut() }, i).correct_parent_link();
            }
        }

        fn correct_all_childrens_parent_links(&mut self) {
            let len = self.len();
            self.correct_childrens_parent_links(0, len + 1);
        }

        /// Adds a key/value pair and an edge to go to the left of that pair to
        /// the beginning of the node.
        pub fn push_front(&mut self, key: K, val: V, edge: Root<K, V>) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(edge.height == self.height - 1);
            debug_assert!(self.len() < CAPACITY);

            unsafe {
                slice_insert(self.keys_mut(), 0, key);
                slice_insert(self.vals_mut(), 0, val);
                slice_insert(
                    slice::from_raw_parts_mut(
                        self.as_internal_mut().edges.as_mut_ptr(),
                        self.len()+1
                    ),
                    0,
                    edge.node
                );

                self.as_leaf_mut().len += 1;

                self.correct_all_childrens_parent_links();
            }
        }
    }

    impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> {
        /// Removes a key/value pair from the end of this node. If this is an internal node,
        /// also removes the edge that was to the right of that pair.
        pub fn pop(&mut self) -> (K, V, Option<Root<K, V>>) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(self.len() > 0);

            let idx = self.len() - 1;

            unsafe {
                let key = ptr::read(self.keys().get_unchecked(idx));
                let val = ptr::read(self.vals().get_unchecked(idx));
                let edge = match self.reborrow_mut().force() {
                    ForceResult::Leaf(_) => None,
                    ForceResult::Internal(internal) => {
                        let edge = ptr::read(internal.as_internal().edges.get_unchecked(idx + 1));
                        let mut new_root = Root { node: edge, height: internal.height - 1 };
                        new_root.as_mut().as_leaf_mut().parent = ptr::null();
                        Some(new_root)
                    }
                };

                self.as_leaf_mut().len -= 1;
                (key, val, edge)
            }
        }

        /// Removes a key/value pair from the beginning of this node. If this is an internal node,
        /// also removes the edge that was to the left of that pair.
        pub fn pop_front(&mut self) -> (K, V, Option<Root<K, V>>) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(self.len() > 0);

            let old_len = self.len();

            unsafe {
                let key = slice_remove(self.keys_mut(), 0);
                let val = slice_remove(self.vals_mut(), 0);
                let edge = match self.reborrow_mut().force() {
                    ForceResult::Leaf(_) => None,
                    ForceResult::Internal(mut internal) => {
                        let edge = slice_remove(
                            slice::from_raw_parts_mut(
                                internal.as_internal_mut().edges.as_mut_ptr(),
                                old_len+1
                            ),
                            0
                        );

                        let mut new_root = Root { node: edge, height: internal.height - 1 };
                        new_root.as_mut().as_leaf_mut().parent = ptr::null();

                        for i in 0..old_len {
                            Handle::new_edge(internal.reborrow_mut(), i).correct_parent_link();
                        }

                        Some(new_root)
                    }
                };

                self.as_leaf_mut().len -= 1;

                (key, val, edge)
            }
        }

        fn into_kv_pointers_mut(mut self) -> (*mut K, *mut V) {
            (
                self.keys_mut().as_mut_ptr(),
                self.vals_mut().as_mut_ptr()
            )
        }
    }

    impl<BorrowType, K, V> NodeRef<BorrowType, K, V, marker::LeafOrInternal> {
        /// Checks whether a node is an `Internal` node or a `Leaf` node.
        pub fn force(self) -> ForceResult<
            NodeRef<BorrowType, K, V, marker::Leaf>,
            NodeRef<BorrowType, K, V, marker::Internal>
        > {
            if self.height == 0 {
                ForceResult::Leaf(NodeRef {
                    height: self.height,
                    node: self.node,
                    root: self.root,
                    _marker: PhantomData
                })
            } else {
                ForceResult::Internal(NodeRef {
                    height: self.height,
                    node: self.node,
                    root: self.root,
                    _marker: PhantomData
                })
            }
        }
    }

    /// A reference to a specific key/value pair or edge within a node. The `Node` parameter
    /// must be a `NodeRef`, while the `Type` can either be `KV` (signifying a handle on a key/value
    /// pair) or `Edge` (signifying a handle on an edge).
    ///
    /// Note that even `Leaf` nodes can have `Edge` handles. Instead of representing a pointer to
    /// a child node, these represent the spaces where child pointers would go between the key/value
    /// pairs. For example, in a node with length 2, there would be 3 possible edge locations - one
    /// to the left of the node, one between the two pairs, and one at the right of the node.
    pub struct Handle<Node, Type> {
        node: Node,
        idx: usize,
        _marker: PhantomData<Type>
    }

    impl<Node: Copy, Type> Copy for Handle<Node, Type> { }
    // We don't need the full generality of `#[derive(Clone)]`, as the only time `Node` will be
    // `Clone`able is when it is an immutable reference and therefore `Copy`.
    impl<Node: Copy, Type> Clone for Handle<Node, Type> {
        fn clone(&self) -> Self {
            *self
        }
    }

    impl<Node, Type> Handle<Node, Type> {
        /// Retrieves the node that contains the edge of key/value pair this handle points to.
        pub fn into_node(self) -> Node {
            self.node
        }
    }

    impl<BorrowType, K, V, NodeType> Handle<NodeRef<BorrowType, K, V, NodeType>, marker::KV> {
        /// Creates a new handle to a key/value pair in `node`. `idx` must be less than `node.len()`.
        pub fn new_kv(node: NodeRef<BorrowType, K, V, NodeType>, idx: usize) -> Self {
            // Necessary for correctness, but in a private module
            debug_assert!(idx < node.len());

            Handle {
                node,
                idx,
                _marker: PhantomData
            }
        }

        pub fn left_edge(self) -> Handle<NodeRef<BorrowType, K, V, NodeType>, marker::Edge> {
            Handle::new_edge(self.node, self.idx)
        }

        pub fn right_edge(self) -> Handle<NodeRef<BorrowType, K, V, NodeType>, marker::Edge> {
            Handle::new_edge(self.node, self.idx + 1)
        }
    }

    impl<BorrowType, K, V, NodeType, HandleType> PartialEq
            for Handle<NodeRef<BorrowType, K, V, NodeType>, HandleType> {

        fn eq(&self, other: &Self) -> bool {
            self.node.node == other.node.node && self.idx == other.idx
        }
    }

    impl<BorrowType, K, V, NodeType, HandleType>
            Handle<NodeRef<BorrowType, K, V, NodeType>, HandleType> {

        /// Temporarily takes out another, immutable handle on the same location.
        pub fn reborrow(&self)
                -> Handle<NodeRef<marker::Immut, K, V, NodeType>, HandleType> {

            // We can't use Handle::new_kv or Handle::new_edge because we don't know our type
            Handle {
                node: self.node.reborrow(),
                idx: self.idx,
                _marker: PhantomData
            }
        }
    }

    impl<'a, K, V, NodeType, HandleType>
            Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, HandleType> {

        /// Temporarily takes out another, mutable handle on the same location. Beware, as
        /// this method is very dangerous, doubly so since it may not immediately appear
        /// dangerous.
        ///
        /// Because mutable pointers can roam anywhere around the tree and can even (through
        /// `into_root_mut`) mess with the root of the tree, the result of `reborrow_mut`
        /// can easily be used to make the original mutable pointer dangling, or, in the case
        /// of a reborrowed handle, out of bounds.
        // FIXME(@gereeter) consider adding yet another type parameter to `NodeRef` that restricts
        // the use of `ascend` and `into_root_mut` on reborrowed pointers, preventing this unsafety.
        pub unsafe fn reborrow_mut(&mut self)
                -> Handle<NodeRef<marker::Mut, K, V, NodeType>, HandleType> {

            // We can't use Handle::new_kv or Handle::new_edge because we don't know our type
            Handle {
                node: self.node.reborrow_mut(),
                idx: self.idx,
                _marker: PhantomData
            }
        }
    }

    impl<BorrowType, K, V, NodeType>
            Handle<NodeRef<BorrowType, K, V, NodeType>, marker::Edge> {

        /// Creates a new handle to an edge in `node`. `idx` must be less than or equal to
        /// `node.len()`.
        pub fn new_edge(node: NodeRef<BorrowType, K, V, NodeType>, idx: usize) -> Self {
            // Necessary for correctness, but in a private module
            debug_assert!(idx <= node.len());

            Handle {
                node,
                idx,
                _marker: PhantomData
            }
        }

        pub fn left_kv(self)
                -> Result<Handle<NodeRef<BorrowType, K, V, NodeType>, marker::KV>, Self> {

            if self.idx > 0 {
                Ok(Handle::new_kv(self.node, self.idx - 1))
            } else {
                Err(self)
            }
        }

        pub fn right_kv(self)
                -> Result<Handle<NodeRef<BorrowType, K, V, NodeType>, marker::KV>, Self> {

            if self.idx < self.node.len() {
                Ok(Handle::new_kv(self.node, self.idx))
            } else {
                Err(self)
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge> {
        /// Inserts a new key/value pair between the key/value pairs to the right and left of
        /// this edge. This method assumes that there is enough space in the node for the new
        /// pair to fit.
        ///
        /// The returned pointer points to the inserted value.
        fn insert_fit(&mut self, key: K, val: V) -> *mut V {
            // Necessary for correctness, but in a private module
            debug_assert!(self.node.len() < CAPACITY);
            debug_assert!(!self.node.is_shared_root());

            unsafe {
                slice_insert(self.node.keys_mut(), self.idx, key);
                slice_insert(self.node.vals_mut(), self.idx, val);

                self.node.as_leaf_mut().len += 1;

                self.node.vals_mut().get_unchecked_mut(self.idx)
            }
        }

        /// Inserts a new key/value pair between the key/value pairs to the right and left of
        /// this edge. This method splits the node if there isn't enough room.
        ///
        /// The returned pointer points to the inserted value.
        pub fn insert(mut self, key: K, val: V)
                -> (InsertResult<'a, K, V, marker::Leaf>, *mut V) {

            if self.node.len() < CAPACITY {
                let ptr = self.insert_fit(key, val);
                (InsertResult::Fit(Handle::new_kv(self.node, self.idx)), ptr)
            } else {
                let middle = Handle::new_kv(self.node, B);
                let (mut left, k, v, mut right) = middle.split();
                let ptr = if self.idx <= B {
                    unsafe {
                        Handle::new_edge(left.reborrow_mut(), self.idx).insert_fit(key, val)
                    }
                } else {
                    unsafe {
                        Handle::new_edge(
                            right.as_mut().cast_unchecked::<marker::Leaf>(),
                            self.idx - (B + 1)
                        ).insert_fit(key, val)
                    }
                };
                (InsertResult::Split(left, k, v, right), ptr)
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::Edge> {
        /// Fixes the parent pointer and index in the child node below this edge. This is useful
        /// when the ordering of edges has been changed, such as in the various `insert` methods.
        fn correct_parent_link(mut self) {
            let idx = self.idx as u16;
            let ptr = self.node.as_internal_mut() as *mut _;
            let mut child = self.descend();
            child.as_leaf_mut().parent = ptr;
            child.as_leaf_mut().parent_idx = idx;
        }

        /// Unsafely asserts to the compiler some static information about whether the underlying
        /// node of this handle is a `Leaf`.
        unsafe fn cast_unchecked<NewType>(&mut self)
                -> Handle<NodeRef<marker::Mut, K, V, NewType>, marker::Edge> {

            Handle::new_edge(self.node.cast_unchecked(), self.idx)
        }

        /// Inserts a new key/value pair and an edge that will go to the right of that new pair
        /// between this edge and the key/value pair to the right of this edge. This method assumes
        /// that there is enough space in the node for the new pair to fit.
        fn insert_fit(&mut self, key: K, val: V, edge: Root<K, V>) {
            // Necessary for correctness, but in an internal module
            debug_assert!(self.node.len() < CAPACITY);
            debug_assert!(edge.height == self.node.height - 1);

            unsafe {
                // This cast is a lie, but it allows us to reuse the key/value insertion logic.
                self.cast_unchecked::<marker::Leaf>().insert_fit(key, val);

                slice_insert(
                    slice::from_raw_parts_mut(
                        self.node.as_internal_mut().edges.as_mut_ptr(),
                        self.node.len()
                    ),
                    self.idx + 1,
                    edge.node
                );

                for i in (self.idx+1)..(self.node.len()+1) {
                    Handle::new_edge(self.node.reborrow_mut(), i).correct_parent_link();
                }
            }
        }

        /// Inserts a new key/value pair and an edge that will go to the right of that new pair
        /// between this edge and the key/value pair to the right of this edge. This method splits
        /// the node if there isn't enough room.
        pub fn insert(mut self, key: K, val: V, edge: Root<K, V>)
                -> InsertResult<'a, K, V, marker::Internal> {

            // Necessary for correctness, but this is an internal module
            debug_assert!(edge.height == self.node.height - 1);

            if self.node.len() < CAPACITY {
                self.insert_fit(key, val, edge);
                InsertResult::Fit(Handle::new_kv(self.node, self.idx))
            } else {
                let middle = Handle::new_kv(self.node, B);
                let (mut left, k, v, mut right) = middle.split();
                if self.idx <= B {
                    unsafe {
                        Handle::new_edge(left.reborrow_mut(), self.idx).insert_fit(key, val, edge);
                    }
                } else {
                    unsafe {
                        Handle::new_edge(
                            right.as_mut().cast_unchecked::<marker::Internal>(),
                            self.idx - (B + 1)
                        ).insert_fit(key, val, edge);
                    }
                }
                InsertResult::Split(left, k, v, right)
            }
        }
    }

    impl<BorrowType, K, V>
            Handle<NodeRef<BorrowType, K, V, marker::Internal>, marker::Edge> {

        /// Finds the node pointed to by this edge.
        ///
        /// `edge.descend().ascend().unwrap()` and `node.ascend().unwrap().descend()` should
        /// both, upon success, do nothing.
        pub fn descend(self) -> NodeRef<BorrowType, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.node.height - 1,
                node: unsafe { self.node.as_internal().edges.get_unchecked(self.idx).as_ptr() },
                root: self.node.root,
                _marker: PhantomData
            }
        }
    }

    impl<'a, K: 'a, V: 'a, NodeType>
            Handle<NodeRef<marker::Immut<'a>, K, V, NodeType>, marker::KV> {

        pub fn into_kv(self) -> (&'a K, &'a V) {
            let (keys, vals) = self.node.into_slices();
            unsafe {
                (keys.get_unchecked(self.idx), vals.get_unchecked(self.idx))
            }
        }
    }

    impl<'a, K: 'a, V: 'a, NodeType>
            Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::KV> {

        pub fn into_kv_mut(self) -> (&'a mut K, &'a mut V) {
            let (keys, vals) = self.node.into_slices_mut();
            unsafe {
                (keys.get_unchecked_mut(self.idx), vals.get_unchecked_mut(self.idx))
            }
        }
    }

    impl<'a, K, V, NodeType> Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::KV> {
        pub fn kv_mut(&mut self) -> (&mut K, &mut V) {
            unsafe {
                let (keys, vals) = self.node.reborrow_mut().into_slices_mut();
                (keys.get_unchecked_mut(self.idx), vals.get_unchecked_mut(self.idx))
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::KV> {
        /// Splits the underlying node into three parts:
        ///
        /// - The node is truncated to only contain the key/value pairs to the right of
        ///   this handle.
        /// - The key and value pointed to by this handle and extracted.
        /// - All the key/value pairs to the right of this handle are put into a newly
        ///   allocated node.
        pub fn split(mut self)
                -> (NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, K, V, Root<K, V>) {
            debug_assert!(!self.node.is_shared_root());
            unsafe {
                let mut new_node = Box::new(LeafNode::new());

                let k = ptr::read(self.node.keys().get_unchecked(self.idx));
                let v = ptr::read(self.node.vals().get_unchecked(self.idx));

                let new_len = self.node.len() - self.idx - 1;

                ptr::copy_nonoverlapping(
                    self.node.keys().as_ptr().offset(self.idx as isize + 1),
                    new_node.keys.as_mut_ptr(),
                    new_len
                );
                ptr::copy_nonoverlapping(
                    self.node.vals().as_ptr().offset(self.idx as isize + 1),
                    new_node.vals.as_mut_ptr(),
                    new_len
                );

                self.node.as_leaf_mut().len = self.idx as u16;
                new_node.len = new_len as u16;

                (
                    self.node,
                    k, v,
                    Root {
                        node: BoxedNode::from_leaf(new_node),
                        height: 0
                    }
                )
            }
        }

        /// Removes the key/value pair pointed to by this handle, returning the edge between the
        /// now adjacent key/value pairs to the left and right of this handle.
        pub fn remove(mut self)
                -> (Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>, K, V) {
            debug_assert!(!self.node.is_shared_root());
            unsafe {
                let k = slice_remove(self.node.keys_mut(), self.idx);
                let v = slice_remove(self.node.vals_mut(), self.idx);
                self.node.as_leaf_mut().len -= 1;
                (self.left_edge(), k, v)
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::KV> {
        /// Splits the underlying node into three parts:
        ///
        /// - The node is truncated to only contain the edges and key/value pairs to the
        ///   right of this handle.
        /// - The key and value pointed to by this handle and extracted.
        /// - All the edges and key/value pairs to the right of this handle are put into
        ///   a newly allocated node.
        pub fn split(mut self)
                -> (NodeRef<marker::Mut<'a>, K, V, marker::Internal>, K, V, Root<K, V>) {
            unsafe {
                let mut new_node = Box::new(InternalNode::new());

                let k = ptr::read(self.node.keys().get_unchecked(self.idx));
                let v = ptr::read(self.node.vals().get_unchecked(self.idx));

                let height = self.node.height;
                let new_len = self.node.len() - self.idx - 1;

                ptr::copy_nonoverlapping(
                    self.node.keys().as_ptr().offset(self.idx as isize + 1),
                    new_node.data.keys.as_mut_ptr(),
                    new_len
                );
                ptr::copy_nonoverlapping(
                    self.node.vals().as_ptr().offset(self.idx as isize + 1),
                    new_node.data.vals.as_mut_ptr(),
                    new_len
                );
                ptr::copy_nonoverlapping(
                    self.node.as_internal().edges.as_ptr().offset(self.idx as isize + 1),
                    new_node.edges.as_mut_ptr(),
                    new_len + 1
                );

                self.node.as_leaf_mut().len = self.idx as u16;
                new_node.data.len = new_len as u16;

                let mut new_root = Root {
                    node: BoxedNode::from_internal(new_node),
                    height,
                };

                for i in 0..(new_len+1) {
                    Handle::new_edge(new_root.as_mut().cast_unchecked(), i).correct_parent_link();
                }

                (
                    self.node,
                    k, v,
                    new_root
                )
            }
        }

        /// Returns whether it is valid to call `.merge()`, i.e., whether there is enough room in
        /// a node to hold the combination of the nodes to the left and right of this handle along
        /// with the key/value pair at this handle.
        pub fn can_merge(&self) -> bool {
            (
                self.reborrow()
                    .left_edge()
                    .descend()
                    .len()
              + self.reborrow()
                    .right_edge()
                    .descend()
                    .len()
              + 1
            ) <= CAPACITY
        }

        /// Combines the node immediately to the left of this handle, the key/value pair pointed
        /// to by this handle, and the node immediately to the right of this handle into one new
        /// child of the underlying node, returning an edge referencing that new child.
        ///
        /// Assumes that this edge `.can_merge()`.
        pub fn merge(mut self)
                -> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::Edge> {
            let self1 = unsafe { ptr::read(&self) };
            let self2 = unsafe { ptr::read(&self) };
            let mut left_node = self1.left_edge().descend();
            let left_len = left_node.len();
            let mut right_node = self2.right_edge().descend();
            let right_len = right_node.len();

            // necessary for correctness, but in a private module
            debug_assert!(left_len + right_len + 1 <= CAPACITY);

            unsafe {
                ptr::write(left_node.keys_mut().get_unchecked_mut(left_len),
                           slice_remove(self.node.keys_mut(), self.idx));
                ptr::copy_nonoverlapping(
                    right_node.keys().as_ptr(),
                    left_node.keys_mut().as_mut_ptr().offset(left_len as isize + 1),
                    right_len
                );
                ptr::write(left_node.vals_mut().get_unchecked_mut(left_len),
                           slice_remove(self.node.vals_mut(), self.idx));
                ptr::copy_nonoverlapping(
                    right_node.vals().as_ptr(),
                    left_node.vals_mut().as_mut_ptr().offset(left_len as isize + 1),
                    right_len
                );

                slice_remove(&mut self.node.as_internal_mut().edges, self.idx + 1);
                for i in self.idx+1..self.node.len() {
                    Handle::new_edge(self.node.reborrow_mut(), i).correct_parent_link();
                }
                self.node.as_leaf_mut().len -= 1;

                left_node.as_leaf_mut().len += right_len as u16 + 1;

                if self.node.height > 1 {
                    ptr::copy_nonoverlapping(
                        right_node.cast_unchecked().as_internal().edges.as_ptr(),
                        left_node.cast_unchecked()
                                 .as_internal_mut()
                                 .edges
                                 .as_mut_ptr()
                                 .offset(left_len as isize + 1),
                        right_len + 1
                    );

                    for i in left_len+1..left_len+right_len+2 {
                        Handle::new_edge(
                            left_node.cast_unchecked().reborrow_mut(),
                            i
                        ).correct_parent_link();
                    }

                    Global.dealloc(
                        right_node.node.cast(),
                        Layout::new::<InternalNode<K, V>>(),
                    );
                } else {
                    Global.dealloc(
                        right_node.node.cast(),
                        Layout::new::<LeafNode<K, V>>(),
                    );
                }

                Handle::new_edge(self.node, self.idx)
            }
        }

        /// This removes a key/value pair from the left child and replaces it with the key/value pair
        /// pointed to by this handle while pushing the old key/value pair of this handle into the right
        /// child.
        pub fn steal_left(&mut self) {
            unsafe {
                let (k, v, edge) = self.reborrow_mut().left_edge().descend().pop();

                let k = mem::replace(self.reborrow_mut().into_kv_mut().0, k);
                let v = mem::replace(self.reborrow_mut().into_kv_mut().1, v);

                match self.reborrow_mut().right_edge().descend().force() {
                    ForceResult::Leaf(mut leaf) => leaf.push_front(k, v),
                    ForceResult::Internal(mut internal) => internal.push_front(k, v, edge.unwrap())
                }
            }
        }

        /// This removes a key/value pair from the right child and replaces it with the key/value pair
        /// pointed to by this handle while pushing the old key/value pair of this handle into the left
        /// child.
        pub fn steal_right(&mut self) {
            unsafe {
                let (k, v, edge) = self.reborrow_mut().right_edge().descend().pop_front();

                let k = mem::replace(self.reborrow_mut().into_kv_mut().0, k);
                let v = mem::replace(self.reborrow_mut().into_kv_mut().1, v);

                match self.reborrow_mut().left_edge().descend().force() {
                    ForceResult::Leaf(mut leaf) => leaf.push(k, v),
                    ForceResult::Internal(mut internal) => internal.push(k, v, edge.unwrap())
                }
            }
        }

        /// This does stealing similar to `steal_left` but steals multiple elements at once.
        pub fn bulk_steal_left(&mut self, count: usize) {
            unsafe {
                let mut left_node = ptr::read(self).left_edge().descend();
                let left_len = left_node.len();
                let mut right_node = ptr::read(self).right_edge().descend();
                let right_len = right_node.len();

                // Make sure that we may steal safely.
                debug_assert!(right_len + count <= CAPACITY);
                debug_assert!(left_len >= count);

                let new_left_len = left_len - count;

                // Move data.
                {
                    let left_kv = left_node.reborrow_mut().into_kv_pointers_mut();
                    let right_kv = right_node.reborrow_mut().into_kv_pointers_mut();
                    let parent_kv = {
                        let kv = self.reborrow_mut().into_kv_mut();
                        (kv.0 as *mut K, kv.1 as *mut V)
                    };

                    // Make room for stolen elements in the right child.
                    ptr::copy(right_kv.0,
                              right_kv.0.offset(count as isize),
                              right_len);
                    ptr::copy(right_kv.1,
                              right_kv.1.offset(count as isize),
                              right_len);

                    // Move elements from the left child to the right one.
                    move_kv(left_kv, new_left_len + 1, right_kv, 0, count - 1);

                    // Move parent's key/value pair to the right child.
                    move_kv(parent_kv, 0, right_kv, count - 1, 1);

                    // Move the left-most stolen pair to the parent.
                    move_kv(left_kv, new_left_len, parent_kv, 0, 1);
                }

                left_node.reborrow_mut().as_leaf_mut().len -= count as u16;
                right_node.reborrow_mut().as_leaf_mut().len += count as u16;

                match (left_node.force(), right_node.force()) {
                    (ForceResult::Internal(left), ForceResult::Internal(mut right)) => {
                        // Make room for stolen edges.
                        let right_edges = right.reborrow_mut().as_internal_mut().edges.as_mut_ptr();
                        ptr::copy(right_edges,
                                  right_edges.offset(count as isize),
                                  right_len + 1);
                        right.correct_childrens_parent_links(count, count + right_len + 1);

                        move_edges(left, new_left_len + 1, right, 0, count);
                    },
                    (ForceResult::Leaf(_), ForceResult::Leaf(_)) => { }
                    _ => { unreachable!(); }
                }
            }
        }

        /// The symmetric clone of `bulk_steal_left`.
        pub fn bulk_steal_right(&mut self, count: usize) {
            unsafe {
                let mut left_node = ptr::read(self).left_edge().descend();
                let left_len = left_node.len();
                let mut right_node = ptr::read(self).right_edge().descend();
                let right_len = right_node.len();

                // Make sure that we may steal safely.
                debug_assert!(left_len + count <= CAPACITY);
                debug_assert!(right_len >= count);

                let new_right_len = right_len - count;

                // Move data.
                {
                    let left_kv = left_node.reborrow_mut().into_kv_pointers_mut();
                    let right_kv = right_node.reborrow_mut().into_kv_pointers_mut();
                    let parent_kv = {
                        let kv = self.reborrow_mut().into_kv_mut();
                        (kv.0 as *mut K, kv.1 as *mut V)
                    };

                    // Move parent's key/value pair to the left child.
                    move_kv(parent_kv, 0, left_kv, left_len, 1);

                    // Move elements from the right child to the left one.
                    move_kv(right_kv, 0, left_kv, left_len + 1, count - 1);

                    // Move the right-most stolen pair to the parent.
                    move_kv(right_kv, count - 1, parent_kv, 0, 1);

                    // Fix right indexing
                    ptr::copy(right_kv.0.offset(count as isize),
                              right_kv.0,
                              new_right_len);
                    ptr::copy(right_kv.1.offset(count as isize),
                              right_kv.1,
                              new_right_len);
                }

                left_node.reborrow_mut().as_leaf_mut().len += count as u16;
                right_node.reborrow_mut().as_leaf_mut().len -= count as u16;

                match (left_node.force(), right_node.force()) {
                    (ForceResult::Internal(left), ForceResult::Internal(mut right)) => {
                        move_edges(right.reborrow_mut(), 0, left, left_len + 1, count);

                        // Fix right indexing.
                        let right_edges = right.reborrow_mut().as_internal_mut().edges.as_mut_ptr();
                        ptr::copy(right_edges.offset(count as isize),
                                  right_edges,
                                  new_right_len + 1);
                        right.correct_childrens_parent_links(0, new_right_len + 1);
                    },
                    (ForceResult::Leaf(_), ForceResult::Leaf(_)) => { }
                    _ => { unreachable!(); }
                }
            }
        }
    }

    unsafe fn move_kv<K, V>(
        source: (*mut K, *mut V), source_offset: usize,
        dest: (*mut K, *mut V), dest_offset: usize,
        count: usize)
    {
        ptr::copy_nonoverlapping(source.0.offset(source_offset as isize),
                                 dest.0.offset(dest_offset as isize),
                                 count);
        ptr::copy_nonoverlapping(source.1.offset(source_offset as isize),
                                 dest.1.offset(dest_offset as isize),
                                 count);
    }

    // Source and destination must have the same height.
    unsafe fn move_edges<K, V>(
        mut source: NodeRef<marker::Mut, K, V, marker::Internal>, source_offset: usize,
        mut dest: NodeRef<marker::Mut, K, V, marker::Internal>, dest_offset: usize,
        count: usize)
    {
        let source_ptr = source.as_internal_mut().edges.as_mut_ptr();
        let dest_ptr = dest.as_internal_mut().edges.as_mut_ptr();
        ptr::copy_nonoverlapping(source_ptr.offset(source_offset as isize),
                                 dest_ptr.offset(dest_offset as isize),
                                 count);
        dest.correct_childrens_parent_links(dest_offset, dest_offset + count);
    }

    impl<BorrowType, K, V, HandleType>
            Handle<NodeRef<BorrowType, K, V, marker::LeafOrInternal>, HandleType> {

        /// Check whether the underlying node is an `Internal` node or a `Leaf` node.
        pub fn force(self) -> ForceResult<
            Handle<NodeRef<BorrowType, K, V, marker::Leaf>, HandleType>,
            Handle<NodeRef<BorrowType, K, V, marker::Internal>, HandleType>
        > {
            match self.node.force() {
                ForceResult::Leaf(node) => ForceResult::Leaf(Handle {
                    node,
                    idx: self.idx,
                    _marker: PhantomData
                }),
                ForceResult::Internal(node) => ForceResult::Internal(Handle {
                    node,
                    idx: self.idx,
                    _marker: PhantomData
                })
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, marker::Edge> {
        /// Move the suffix after `self` from one node to another one. `right` must be empty.
        /// The first edge of `right` remains unchanged.
        pub fn move_suffix(&mut self,
                right: &mut NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>) {
            unsafe {
                let left_new_len = self.idx;
                let mut left_node = self.reborrow_mut().into_node();

                let right_new_len = left_node.len() - left_new_len;
                let mut right_node = right.reborrow_mut();

                debug_assert!(right_node.len() == 0);
                debug_assert!(left_node.height == right_node.height);

                let left_kv = left_node.reborrow_mut().into_kv_pointers_mut();
                let right_kv = right_node.reborrow_mut().into_kv_pointers_mut();

                move_kv(left_kv, left_new_len, right_kv, 0, right_new_len);

                left_node.reborrow_mut().as_leaf_mut().len = left_new_len as u16;
                right_node.reborrow_mut().as_leaf_mut().len = right_new_len as u16;

                match (left_node.force(), right_node.force()) {
                    (ForceResult::Internal(left), ForceResult::Internal(right)) => {
                        move_edges(left, left_new_len + 1, right, 1, right_new_len);
                    },
                    (ForceResult::Leaf(_), ForceResult::Leaf(_)) => { }
                    _ => { unreachable!(); }
                }
            }
        }
    }

    pub enum ForceResult<Leaf, Internal> {
        Leaf(Leaf),
        Internal(Internal)
    }

    pub enum InsertResult<'a, K, V, Type> {
        Fit(Handle<NodeRef<marker::Mut<'a>, K, V, Type>, marker::KV>),
        Split(NodeRef<marker::Mut<'a>, K, V, Type>, K, V, Root<K, V>)
    }

    pub mod marker {
        use core::marker::PhantomData;

        pub enum Leaf { }
        pub enum Internal { }
        pub enum LeafOrInternal { }

        pub enum Owned { }
        pub struct Immut<'a>(PhantomData<&'a ()>);
        pub struct Mut<'a>(PhantomData<&'a mut ()>);

        pub enum KV { }
        pub enum Edge { }
    }

    unsafe fn slice_insert<T>(slice: &mut [T], idx: usize, val: T) {
        ptr::copy(
            slice.as_ptr().offset(idx as isize),
            slice.as_mut_ptr().offset(idx as isize + 1),
            slice.len() - idx
        );
        ptr::write(slice.get_unchecked_mut(idx), val);
    }

    unsafe fn slice_remove<T>(slice: &mut [T], idx: usize) -> T {
        let ret = ptr::read(slice.get_unchecked(idx));
        ptr::copy(
            slice.as_ptr().offset(idx as isize + 1),
            slice.as_mut_ptr().offset(idx as isize),
            slice.len() - idx - 1
        );
        ret
    }

# Help

## Keyboard Shortcuts

`?`
  Show this help dialog
`S`
  Focus the search field
`↑`
  Move up in search results
`↓`
  Move down in search results
`↹`
  Switch tab
`⏎`
  Go to active search result
`+`
  Expand all sections
`-`
  Collapse all sections

## Search Tricks

Prefix searches with a type followed by a colon (e.g. `fn:`) to restrict the search to a given type.

Accepted types are: `fn`, `mod`, `struct`, `enum`, `trait`, `type`, `macro`, and `const`.

Search functions by type signature (e.g. `vec -> usize` or `* -> vec`)

Search multiple things at once by splitting your query with comma (e.g. `str,u8` or `String,struct:Vec,test`)