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
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
use crate::{Rectangle, Size};
use euclid::{vec2, point2, size2};

use std::num::Wrapping;

const LARGE_BUCKET: usize = 2;
const MEDIUM_BUCKET: usize = 1;
const SMALL_BUCKET: usize = 0;
const NUM_BUCKETS: usize = 3;

fn free_list_for_size(small_threshold: i32, large_threshold: i32, size: &Size) -> usize {
    if size.width >= large_threshold || size.height >= large_threshold {
        LARGE_BUCKET
    } else if size.width >= small_threshold || size.height >= small_threshold {
        MEDIUM_BUCKET
    } else {
        SMALL_BUCKET
    }
}

#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
struct AllocIndex(u32);
impl AllocIndex {
    const NONE: AllocIndex = AllocIndex(std::u32::MAX);

    fn index(self) -> usize {
        self.0 as usize
    }

    fn is_none(self) -> bool {
        self == AllocIndex::NONE
    }

    fn is_some(self) -> bool {
        self != AllocIndex::NONE
    }
}

/// ID referring to an allocated rectangle.
#[repr(C)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
pub struct AllocId(pub(crate) u32);

impl AllocId {
    pub fn serialize(&self) -> u32 {
        self.0
    }

    pub fn deserialize(bytes: u32) -> Self {
        AllocId(bytes)
    }
}

const GEN_MASK: u32 = 0xFF000000;
const IDX_MASK: u32 = 0x00FFFFFF;

#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
enum Orientation {
    Vertical,
    Horizontal,
}

impl Orientation {
    fn flipped(self) -> Self {
        match self {
            Orientation::Vertical => Orientation::Horizontal,
            Orientation::Horizontal => Orientation::Vertical,
        }
    }
}

#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
pub enum NodeKind {
    Container,
    Alloc,
    Free,
    Unused,
}

#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone, Debug)]
struct Node {
    parent: AllocIndex,
    next_sibling: AllocIndex,
    prev_sibling: AllocIndex,
    kind: NodeKind,
    orientation: Orientation,
    rect: Rectangle,
}

/// Options to tweak the behavior of the atlas allocator.
#[repr(C)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
pub struct AllocatorOptions {
    /// Round the rectangle sizes up to a multiple of this value.
    ///
    /// Width and height alignments must be superior to zero.
    ///
    /// Default value: (1, 1),
    pub alignment: Size,

    /// Value below which a size is considered small.
    ///
    /// This is value is used to speed up the storage and lookup of free rectangles.
    /// This value must be inferior or equal to `large_size_threshold`
    ///
    /// Default value: 32,
    pub small_size_threshold: i32,

    /// Value above which a size is considered large.
    ///
    /// This is value is used to speed up the storage and lookup of free rectangles.
    /// This value must be inferior or equal to `large_size_threshold`
    ///
    /// Default value: 256,
    pub large_size_threshold: i32,
}

pub const DEFAULT_OPTIONS: AllocatorOptions = AllocatorOptions {
    alignment: size2(1,  1),
    large_size_threshold: 256,
    small_size_threshold: 32,
};

impl Default for AllocatorOptions {
    fn default() -> Self {
        DEFAULT_OPTIONS
    }
}

/// A dynamic texture atlas allocator using the guillotine algorithm.
///
/// The guillotine algorithm is assisted by a data structure that keeps track of
/// neighboring rectangles to provide fast deallocation and coalescing.
///
/// ## Goals
///
/// Coalescing free rectangles, in the context of dynamic atlas allocation can be
/// prohibitively expensive under real-time constraints if the algorithm needs to
/// visit a large amount of free rectangles to find merge candidates.
///
/// This implementation proposes a compromise with fast (constant time) search
/// for merge candidates at the expense of some (constant time) bookkeeping overhead
/// when allocating and removing rectangles and imperfect defragmentation (see the
/// "Limitations" section below.
///
/// The subdivision scheme uses the worst fit variant of the guillotine algorithm
/// for its simplicity and CPU efficiency.
///
/// ## The data structure
///
/// We maintain a tree with allocated and free rectangles as leaf nodes and
/// containers as non-leaf nodes.
///
/// The direct children of a Containers's form an ordered horizontal or vertical
/// sequence of rectangles that cover exactly their parent container's area.
///
/// For example, a subdivision such as this one:
///
/// ```ascii
/// +-----------+----------+---+---+--+---------+---+
/// |           |          | C | D |E | F       | G |
/// |           |          +---+---+--+---------+---+
/// |     A     |    B     |                        |
/// |           |          |           H            |
/// |           |          |                        |
/// +------+----+----------+-+----------------------+
/// |      |        J        |                      |
/// |  I   +-----------------+          L           |
/// |      |        K        |                      |
/// +------+-----------------+----------------------+
/// ```
///
/// Would have a tree of the form:
///
/// ```ascii
///
///  Tree                | Layout
/// ---------------------+------------
///                      |
///           #          |
///           |          |
///      +----+----+. . .|. vertical
///      |         |     |
///      #         #     |
///      |         |     |
///    +-+-+ . . +-+-+. .|. horizontal
///    | | |     | | |   |
///    A B #     I # L   |
///        |       |     |
///      +-+-+ . +-+-+. .|. vertical
///      |   |   |   |   |
///      #   H   J   K   |
///      |               |
///  +-+-+-+-+. . . . . .|. horizontal
///  | | | | |           |
///  C D E F G           |
/// ```
///
/// Where container nodes are represented with "#".
///
/// Note that if a horizontal container is the direct child of another
/// horizontal container, we can merge the two into a single horizontal
/// sequence.
/// We use this property to always keep the tree in its simplest form.
/// In practice this means that the orientation of a container is always
/// the opposite of the orientation of its parent, if any.
///
/// The goal of this data structure is to quickly find neighboring free
/// rectangles that can be coalesced into fewer rectangles.
/// This structure guarantees that two consecutive children of the same
/// container, if both rectangles are free, can be coalesced into a single
/// one.
///
/// An important thing to note about this tree structure is that we only
/// use it to visit neighbor and parent nodes. As a result we don't care
/// about whether the tree is balanced, although flat sequences of children
/// tend to offer more opportunity for coalescing than deeply nested structures
/// Either way, the cost of finding potential merges is the same because
/// each node stores the indices of their siblings, and we never have to
/// traverse any global list of free rectangle nodes.
///
/// ### Merging siblings
///
/// As soon as two consecutive sibling nodes are marked as "free", they are coalesced
/// into a single node.
///
/// In the example below, we just deallocated the rectangle `B`, which is a sibling of
/// `A` which is free and `C` which is still allocated. `A` and `B` are merged and this
/// change is reflected on the tree as shown below:
///
/// ```ascii
/// +---+---+---+         #               +-------+---+         #
/// |   |   |///|         |               |       |///|         |
/// | A | B |/C/|     +---+---+           | AB    |/C/|     +---+---+
/// |   |   |///|     |       |           |       |///|     |       |
/// +---+---+---+     #       D           +-------+---+     #       D
/// | D         |     |            ->     | D         |     |
/// |           |   +-+-+                 |           |   +-+-+
/// |           |   | | |                 |           |   |   |
/// +-----------+   A B C                 +-----------+   AB  C
/// ```
///
/// ### Merging unique children with their parents
///
/// In the previous example `C` was an allocated slot. Let's now deallocate it:
///
/// ```ascii
/// +-------+---+         #               +-----------+         #                 #
/// |       |   |         |               |           |         |                 |
/// | AB    | C |     +---+---+           | ABC       |     +---+---+         +---+---+
/// |       |   |     |       |           |           |     |       |         |       |
/// +-------+---+     #       D           +-----------+     #       D        ABC      D
/// | D         |     |            ->     | D         |     |           ->
/// |           |   +-+-+                 |           |     +
/// |           |   |   |                 |           |     |
/// +-----------+   AB  C                 +-----------+    ABC
/// ```
///
/// Deallocating `C` allowed it to merge with the free rectangle `AB`, making the
/// resulting node `ABC` the only child of its parent container. As a result the
/// node `ABC` was lifted up the tree to replace its parent.
///
/// In this example, assuming `D` to also be a free rectangle, `ABC` and `D` would
/// be immediately merged and the resulting node `ABCD`, also being only child of
/// its parent container, would replace its parent, turning the tree into a single
/// node `ABCD`.
///
/// ### Limitations
///
/// This strategy can miss some opportunities for coalescing free rectangles
/// when the two sibling containers are split exactly the same way.
///
/// For example:
///
/// ```ascii
/// +---------+------+
/// |    A    |  B   |
/// |         |      |
/// +---------+------+
/// |    C    |  D   |
/// |         |      |
/// +---------+------+
/// ```
///
/// Could be the result of either a vertical followed with two horizontal splits,
/// or an horizontal then two vertical splits.
///
/// ```ascii
///  Tree            | Layout             Tree            | Layout
/// -----------------+------------       -----------------+------------
///         #        |                           #        |
///         |        |                           |        |
///     +---+---+ . .|. Vertical             +---+---+ . .|. Horizontal
///     |       |    |                       |       |    |
///     #       #    |               or      #       #    |
///     |       |    |                       |       |    |
///   +-+-+ . +-+-+ .|. Horizontal         +-+-+ . +-+-+ .|. Vertical
///   |   |   |   |  |                     |   |   |   |  |
///   A   B   C   D  |                     A   C   B   D  |
/// ```
///
/// In the former case A can't be merged with C nor B with D because they are not siblings.
///
/// For a lot of workloads it is rather rare for two consecutive sibling containers to be
/// subdivided exactly the same way. In this situation losing the ability to merge rectangles
/// that aren't under the same container is good compromise between the CPU cost of coalescing
/// and the fragmentation of the atlas.
///
/// This algorithm is, however, not the best solution for very "structured" grid-like
/// subdivision patterns where the ability to merge across containers would have provided
/// frequent defragmentation opportunities.
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone)]
pub struct AtlasAllocator {
    nodes: Vec<Node>,
    /// Free lists are split into a small a medium and a large bucket for faster lookups.
    free_lists: [Vec<AllocIndex>; NUM_BUCKETS],

    /// Index of the first element of an intrusive linked list of unused nodes.
    /// The `next_sibling` member of unused node serves as the linked list link.
    unused_nodes: AllocIndex,

    /// We keep a per-node generation counter to reduce the likelihood of ID reuse bugs
    /// going unnoticed.
    generations: Vec<Wrapping<u8>>,

    /// See `AllocatorOptions`.
    alignment: Size,

    /// See `AllocatorOptions`.
    small_size_threshold: i32,

    /// See `AllocatorOptions`.
    large_size_threshold: i32,

    /// Total size of the atlas.
    size: Size,

    /// Index of one of the top-level nodes in the tree.
    root_node: AllocIndex,
}

// Some notes about the atlas's tree data structure:
//
//      (AllocIndex::NONE)                (AllocIndex::NONE)
//              ^                                 ^
//              | parent                          | parent
//           +---------+ next sibling         +---------+ next sibling
// ... ------|Container|---------------------->|Free     |---> (AllocIndex::NONE)
//     ----->|         |<----------------------|         |
//           +---------+     previous sibling +---------+
//              ^ ^
//              |  \____________________________
//              |                               \
//              | parent                         \ parent
//           +---------+ next sibling         +---------+ next sibling
// ... ------|Alloc    |---------------------->|Container|---> (AllocIndex::NONE)
//     ----->|         |<----------------------|         |
//           +---------+     previous sibling +---------+
//                                               ^ ^ ^
//                                              /  |  \
//                                                ...
//
// - Nodes are stored in a contiguous vector.
// - Links between the nodes are indices in the vector (AllocIndex), with a magic value
//   AllocIndex::NONE that means no link.
// - Nodes have a link to their parent, but parents do not have a link to any of its children because
//   we never need to traverse the structure from parent to child.
// - All nodes with the same parent are "siblings". An intrusive linked list allows traversing siblings
//   in order. Consecutive siblings share an edge and can be merged if they are both "free".
// - There isn't necessarily a single root node. The top-most level of the tree can have several siblings
//   and their parent index is equal to AllocIndex::NONE. AtlasAllocator::root_node only needs to refer
//   to one of these top-level nodes.
// - After a rectangle has been deallocated, the slot for its node in the vector is not part of the
//   tree anymore in the sense that no node from the tree points to it with its sibling list or parent
//   index. This unused node is available for reuse in a future allocation, and is placed in another
//   linked list (also using AllocIndex), a singly linked list this time, which reuses the next_sibling
//   member of the node. So depending on whether the node kind is Unused or not, the next_sibling
//   member is used different things.
// - We reuse nodes aggressively to avoid growing the vector whenever possible. This is important because
//   the memory footprint of this data structure depends on the capacity of its vectors which don't
//   get deallocated during the lifetime of the atlas.
// - Because nodes are aggressively reused, the same node indices will come up often. To avoid id reuse
//   bugs, a parallel vector of generation counters is maintained.
// - The difference between AllocIndex and AllocId is that the latter embeds a generation ID to help
//   finding id reuse bugs. AllocIndex however only contains the node offset. Internal links in the
//   data structure use AllocIndex, and external users of the data structure only get to see AllocId.

impl AtlasAllocator {
    /// Create an atlas allocator.
    pub fn new(size: Size) -> Self {
        AtlasAllocator::with_options(size, &DEFAULT_OPTIONS)
    }

    /// Create an atlas allocator with the provided options.
    pub fn with_options(size: Size, options: &AllocatorOptions) -> Self {
        assert!(options.alignment.width > 0);
        assert!(options.alignment.height > 0);
        assert!(size.width > 0);
        assert!(size.height > 0);
        assert!(options.large_size_threshold >= options.small_size_threshold);

        let mut free_lists = [Vec::new(), Vec::new(), Vec::new()];
        let bucket = free_list_for_size(
            options.small_size_threshold,
            options.large_size_threshold,
            &size,
        );
        free_lists[bucket].push(AllocIndex(0));

        AtlasAllocator {
            nodes: vec![Node {
                parent: AllocIndex::NONE,
                next_sibling: AllocIndex::NONE,
                prev_sibling: AllocIndex::NONE,
                rect: size.into(),
                kind: NodeKind::Free,
                orientation: Orientation::Vertical,
            }],
            free_lists,
            generations: vec![Wrapping(0)],
            unused_nodes: AllocIndex::NONE,
            alignment: options.alignment,
            small_size_threshold: options.small_size_threshold,
            large_size_threshold: options.large_size_threshold,
            size,
            root_node: AllocIndex(0),
        }
    }

    /// The total size of the atlas.
    pub fn size(&self) -> Size {
        self.size
    }

    /// Allocate a rectangle in the atlas.
    pub fn allocate(&mut self, mut requested_size: Size) -> Option<Allocation> {
        if requested_size.is_empty() {
            return None;
        }

        adjust_size(self.alignment.width, &mut requested_size.width);
        adjust_size(self.alignment.height, &mut requested_size.height);

        // Find a suitable free rect.
        let chosen_id = self.find_suitable_rect(&requested_size);

        if chosen_id.is_none() {
            //println!("failed to allocate {:?}", requested_size);
            //self.print_free_rects();

            // No suitable free rect!
            return None;
        }

        let chosen_node = self.nodes[chosen_id.index()].clone();
        let chosen_rect = chosen_node.rect;
        let allocated_rect = Rectangle {
            min: chosen_rect.min,
            max: chosen_rect.min + requested_size.to_vector(),
        };
        let current_orientation = chosen_node.orientation;
        assert_eq!(chosen_node.kind, NodeKind::Free);

        let (split_rect, leftover_rect, orientation) =
            guillotine_rect(&chosen_node.rect, requested_size, current_orientation);

        // Update the tree.

        let allocated_id;
        let split_id;
        let leftover_id;

        //println!("{:?} -> {:?}", current_orientation, orientation);
        if orientation == current_orientation {
            if !split_rect.is_empty() {
                let next_sibling = chosen_node.next_sibling;

                split_id = self.new_node();
                self.nodes[split_id.index()] = Node {
                    parent: chosen_node.parent,
                    next_sibling,
                    prev_sibling: chosen_id,
                    rect: split_rect,
                    kind: NodeKind::Free,
                    orientation: current_orientation,
                };

                self.nodes[chosen_id.index()].next_sibling = split_id;
                if next_sibling.is_some() {
                    self.nodes[next_sibling.index()].prev_sibling = split_id;
                }
            } else {
                split_id = AllocIndex::NONE;
            }

            if !leftover_rect.is_empty() {
                self.nodes[chosen_id.index()].kind = NodeKind::Container;

                allocated_id = self.new_node();
                leftover_id = self.new_node();

                self.nodes[allocated_id.index()] = Node {
                    parent: chosen_id,
                    next_sibling: leftover_id,
                    prev_sibling: AllocIndex::NONE,
                    rect: allocated_rect,
                    kind: NodeKind::Alloc,
                    orientation: current_orientation.flipped(),
                };

                self.nodes[leftover_id.index()] = Node {
                    parent: chosen_id,
                    next_sibling: AllocIndex::NONE,
                    prev_sibling: allocated_id,
                    rect: leftover_rect,
                    kind: NodeKind::Free,
                    orientation: current_orientation.flipped(),
                };
            } else {
                // No need to split for the leftover area, we can allocate directly in the chosen node.
                allocated_id = chosen_id;
                let node = &mut self.nodes[chosen_id.index()];
                node.kind = NodeKind::Alloc;
                node.rect = allocated_rect;

                leftover_id = AllocIndex::NONE
            }
        } else {
            self.nodes[chosen_id.index()].kind = NodeKind::Container;

            if !split_rect.is_empty() {
                split_id = self.new_node();
                self.nodes[split_id.index()] = Node {
                    parent: chosen_id,
                    next_sibling: AllocIndex::NONE,
                    prev_sibling: AllocIndex::NONE,
                    rect: split_rect,
                    kind: NodeKind::Free,
                    orientation: current_orientation.flipped(),
                };
            } else {
                split_id = AllocIndex::NONE;
            }

            if !leftover_rect.is_empty() {
                let container_id = self.new_node();
                self.nodes[container_id.index()] = Node {
                    parent: chosen_id,
                    next_sibling: split_id,
                    prev_sibling: AllocIndex::NONE,
                    rect: Rectangle::zero(),
                    kind: NodeKind::Container,
                    orientation: current_orientation.flipped(),
                };

                self.nodes[split_id.index()].prev_sibling = container_id;

                allocated_id = self.new_node();
                leftover_id = self.new_node();

                self.nodes[allocated_id.index()] = Node {
                    parent: container_id,
                    next_sibling: leftover_id,
                    prev_sibling: AllocIndex::NONE,
                    rect: allocated_rect,
                    kind: NodeKind::Alloc,
                    orientation: current_orientation,
                };

                self.nodes[leftover_id.index()] = Node {
                    parent: container_id,
                    next_sibling: AllocIndex::NONE,
                    prev_sibling: allocated_id,
                    rect: leftover_rect,
                    kind: NodeKind::Free,
                    orientation: current_orientation,
                };
            } else {
                allocated_id = self.new_node();
                self.nodes[allocated_id.index()] = Node {
                    parent: chosen_id,
                    next_sibling: split_id,
                    prev_sibling: AllocIndex::NONE,
                    rect: allocated_rect,
                    kind: NodeKind::Alloc,
                    orientation: current_orientation.flipped(),
                };

                self.nodes[split_id.index()].prev_sibling = allocated_id;

                leftover_id = AllocIndex::NONE;
            }
        }

        assert_eq!(self.nodes[allocated_id.index()].kind, NodeKind::Alloc);

        if split_id.is_some() {
            self.add_free_rect(split_id, &split_rect.size());
        }

        if leftover_id.is_some() {
            self.add_free_rect(leftover_id, &leftover_rect.size());
        }

        //println!("allocated {:?}     split: {:?} leftover: {:?}", allocated_rect, split_rect, leftover_rect);
        //self.print_free_rects();

        #[cfg(feature = "checks")]
        self.check_tree();

        Some(Allocation {
            id: self.alloc_id(allocated_id),
            rectangle: allocated_rect,
        })
    }

    /// Deallocate a rectangle in the atlas.
    pub fn deallocate(&mut self, node_id: AllocId) {
        let mut node_id = self.get_index(node_id);

        assert!(node_id.index() < self.nodes.len());
        assert_eq!(self.nodes[node_id.index()].kind, NodeKind::Alloc);

        self.nodes[node_id.index()].kind = NodeKind::Free;

        loop {
            let orientation = self.nodes[node_id.index()].orientation;

            let next = self.nodes[node_id.index()].next_sibling;
            let prev = self.nodes[node_id.index()].prev_sibling;

            // Try to merge with the next node.
            if next.is_some() && self.nodes[next.index()].kind == NodeKind::Free {
                self.merge_siblings(node_id, next, orientation);
            }

            // Try to merge with the previous node.
            if prev.is_some() && self.nodes[prev.index()].kind == NodeKind::Free {
                self.merge_siblings(prev, node_id, orientation);
                node_id = prev;
            }

            // If this node is now a unique child. We collapse it into its parent and try to merge
            // again at the parent level.
            let parent = self.nodes[node_id.index()].parent;
            if self.nodes[node_id.index()].prev_sibling.is_none()
                && self.nodes[node_id.index()].next_sibling.is_none()
                && parent.is_some()
            {
                debug_assert_eq!(self.nodes[parent.index()].kind, NodeKind::Container);

                self.mark_node_unused(node_id);

                // Replace the parent container with a free node.
                self.nodes[parent.index()].rect = self.nodes[node_id.index()].rect;
                self.nodes[parent.index()].kind = NodeKind::Free;

                // Start again at the parent level.
                node_id = parent;
            } else {
                let size = self.nodes[node_id.index()].rect.size();
                self.add_free_rect(node_id, &size);
                break;
            }
        }

        #[cfg(feature = "checks")]
        self.check_tree();
    }

    pub fn is_empty(&self) -> bool {
        let root = &self.nodes[self.root_node.index()];

        root.kind == NodeKind::Free && root.next_sibling.is_none()
    }

    /// Drop all rectangles, clearing the atlas to its initial state.
    pub fn clear(&mut self) {
        self.nodes.clear();
        self.nodes.push(Node {
            parent: AllocIndex::NONE,
            next_sibling: AllocIndex::NONE,
            prev_sibling: AllocIndex::NONE,
            rect: self.size.into(),
            kind: NodeKind::Free,
            orientation: Orientation::Vertical,
        });

        self.root_node = AllocIndex(0);

        self.generations.clear();
        self.generations.push(Wrapping(0));

        self.unused_nodes = AllocIndex::NONE;

        let bucket = free_list_for_size(
            self.small_size_threshold,
            self.large_size_threshold,
            &self.size,
        );
        for i in 0..NUM_BUCKETS {
            self.free_lists[i].clear();
        }
        self.free_lists[bucket].push(AllocIndex(0));
    }

    /// Clear the allocator and reset its size and options.
    pub fn reset(&mut self, size: Size, options: &AllocatorOptions) {
        self.alignment = options.alignment;
        self.small_size_threshold = options.small_size_threshold;
        self.large_size_threshold = options.large_size_threshold;
        self.size = size;

        self.clear();
    }

    /// Recompute the allocations in the atlas and returns a list of the changes.
    ///
    /// Previous ids and rectangles are not valid anymore after this operation as each id/rectangle
    /// pair is assigned to new values which are communicated in the returned change list.
    /// Rearranging the atlas can help reduce fragmentation.
    pub fn rearrange(&mut self) -> ChangeList {
        let size = self.size;
        self.resize_and_rearrange(size)
    }

    /// Identical to `AtlasAllocator::rearrange`, also allowing to change the size of the atlas.
    pub fn resize_and_rearrange(&mut self, new_size: Size) -> ChangeList {
        let mut allocs = Vec::with_capacity(self.nodes.len());
        for (i, node) in self.nodes.iter().enumerate() {
            if node.kind != NodeKind::Alloc {
                continue;
            }
            let id = self.alloc_id(AllocIndex(i as u32));
            allocs.push(Allocation {
                id,
                rectangle: node.rect,
            });
        }

        allocs.sort_by_key(|alloc| safe_area(&alloc.rectangle));
        allocs.reverse();

        self.size = new_size;
        self.clear();

        let mut changes = Vec::new();
        let mut failures = Vec::new();

        for old in allocs {
            let size = old.rectangle.size();
            if let Some(new) = self.allocate(size) {
                changes.push(Change { old, new });
            } else {
                failures.push(old);
            }
        }

        ChangeList { changes, failures }
    }

    /// Resize the atlas without changing the allocations.
    ///
    /// This method is not allowed to shrink the width or height of the atlas.
    pub fn grow(&mut self, new_size: Size) {
        assert!(new_size.width >= self.size.width);
        assert!(new_size.height >= self.size.height);

        let old_size = self.size;
        self.size = new_size;

        let dx = new_size.width - old_size.width;
        let dy = new_size.height - old_size.height;

        // If there is only one node and it is free, just grow it.
        let root = &mut self.nodes[self.root_node.index()];
        if root.kind == NodeKind::Free && root.rect.size() == old_size {
            root.rect.max = root.rect.min + new_size.to_vector();
            return;
        }

        let root_orientation = root.orientation;
        let grows_in_root_orientation = match root_orientation {
            Orientation::Horizontal => dx > 0,
            Orientation::Vertical => dy > 0,
        };

        // If growing along the orientation of the root node, find the right-or-bottom-most sibling
        // and either grow it (if it is free) or append a free node next.
        if grows_in_root_orientation {
            let mut sibling = self.root_node;
            while self.nodes[sibling.index()].next_sibling != AllocIndex::NONE {
                sibling = self.nodes[sibling.index()].next_sibling;
            }
            let node = &mut self.nodes[sibling.index()];
            if node.kind == NodeKind::Free {
                node.rect.max += match root_orientation {
                    Orientation::Horizontal => vec2(dx, 0),
                    Orientation::Vertical => vec2(0, dy),
                };
            } else {
                let rect = match root_orientation {
                    Orientation::Horizontal => {
                        let min = point2(node.rect.max.x, node.rect.min.y);
                        let max = min + vec2(dx, node.rect.height());
                        Rectangle { min, max }
                    }
                    Orientation::Vertical => {
                        let min = point2(node.rect.min.x, node.rect.max.y);
                        let max = min + vec2(node.rect.width(), dy);
                        Rectangle { min, max }
                    }
                };

                let next = self.new_node();
                self.nodes[sibling.index()].next_sibling = next;
                self.nodes[next.index()] = Node {
                    kind: NodeKind::Free,
                    rect,
                    prev_sibling: sibling,
                    next_sibling: AllocIndex::NONE,
                    parent: AllocIndex::NONE,
                    orientation: root_orientation,
                };

                self.add_free_rect(next, &rect.size());
            }
        }

        let grows_in_opposite_orientation = match root_orientation {
            Orientation::Horizontal => dy > 0,
            Orientation::Vertical => dx > 0,
        };

        if grows_in_opposite_orientation {
            let free_node = self.new_node();
            let new_root = self.new_node();

            let old_root = self.root_node;
            self.root_node = new_root;

            let new_root_orientation = root_orientation.flipped();

            let min = match new_root_orientation {
                Orientation::Horizontal => point2(old_size.width, 0),
                Orientation::Vertical => point2(0, old_size.height),
            };
            let max = point2(new_size.width, new_size.height);
            let rect = Rectangle { min, max };

            self.nodes[free_node.index()] = Node {
                parent: AllocIndex::NONE,
                prev_sibling: new_root,
                next_sibling: AllocIndex::NONE,
                kind: NodeKind::Free,
                rect,
                orientation: new_root_orientation,
            };

            self.nodes[new_root.index()] = Node {
                parent: AllocIndex::NONE,
                prev_sibling: AllocIndex::NONE,
                next_sibling: free_node,
                kind: NodeKind::Container,
                rect: Rectangle::zero(),
                orientation: new_root_orientation,
            };

            self.add_free_rect(free_node, &rect.size());

            // Update the nodes that need to be re-parented to the new-root.

            let mut iter = old_root;
            while iter != AllocIndex::NONE {
                self.nodes[iter.index()].parent = new_root;
                iter = self.nodes[iter.index()].next_sibling;
            }

            // That second loop might not be necessary, I think that the root is always the first
            // sibling.
            let mut iter = self.nodes[old_root.index()].next_sibling;
            while iter != AllocIndex::NONE {
                self.nodes[iter.index()].parent = new_root;
                iter = self.nodes[iter.index()].prev_sibling;
            }
        }

        #[cfg(feature = "checks")]
        self.check_tree();
    }

    /// Invoke a callback for each free rectangle in the atlas.
    pub fn for_each_free_rectangle<F>(&self, mut callback: F)
    where
        F: FnMut(&Rectangle),
    {
        for node in &self.nodes {
            if node.kind == NodeKind::Free {
                callback(&node.rect);
            }
        }
    }

    /// Invoke a callback for each allocated rectangle in the atlas.
    pub fn for_each_allocated_rectangle<F>(&self, mut callback: F)
    where
        F: FnMut(AllocId, &Rectangle),
    {
        for (i, node) in self.nodes.iter().enumerate() {
            if node.kind != NodeKind::Alloc {
                continue;
            }

            let id = self.alloc_id(AllocIndex(i as u32));

            callback(id, &node.rect);
        }
    }

    fn find_suitable_rect(&mut self, requested_size: &Size) -> AllocIndex {
        let ideal_bucket = free_list_for_size(
            self.small_size_threshold,
            self.large_size_threshold,
            requested_size,
        );

        let use_worst_fit = ideal_bucket == LARGE_BUCKET;
        for bucket in ideal_bucket..NUM_BUCKETS {
            let mut candidate_score = if use_worst_fit { 0 } else { std::i32::MAX };
            let mut candidate = None;

            let mut freelist_idx = 0;
            while freelist_idx < self.free_lists[bucket].len() {
                let id = self.free_lists[bucket][freelist_idx];

                // During tree simplification we don't remove merged nodes from the free list, so we have
                // to handle it here.
                // This is a tad awkward, but lets us avoid having to maintain a doubly linked list for
                // the free list (which would be needed to remove nodes during tree simplification).
                if self.nodes[id.index()].kind != NodeKind::Free {
                    // remove the element from the free list
                    self.free_lists[bucket].swap_remove(freelist_idx);
                    continue;
                }

                let size = self.nodes[id.index()].rect.size();
                let dx = size.width - requested_size.width;
                let dy = size.height - requested_size.height;

                if dx >= 0 && dy >= 0 {
                    if dx == 0 || dy == 0 {
                        // Perfect fit!
                        candidate = Some((id, freelist_idx));
                        break;
                    }

                    // Favor the largest minimum dimension, except for small
                    // allocations.
                    let score = i32::min(dx, dy);
                    if (use_worst_fit && score > candidate_score)
                        || (!use_worst_fit && score < candidate_score)
                    {
                        candidate_score = score;
                        candidate = Some((id, freelist_idx));
                    }
                }

                freelist_idx += 1;
            }

            if let Some((id, freelist_idx)) = candidate {
                self.free_lists[bucket].swap_remove(freelist_idx);
                return id;
            }
        }

        AllocIndex::NONE
    }

    fn new_node(&mut self) -> AllocIndex {
        let idx = self.unused_nodes;
        if idx.index() < self.nodes.len() {
            self.unused_nodes = self.nodes[idx.index()].next_sibling;
            self.generations[idx.index()] += Wrapping(1);
            debug_assert_eq!(self.nodes[idx.index()].kind, NodeKind::Unused);
            return idx;
        }

        self.nodes.push(Node {
            parent: AllocIndex::NONE,
            next_sibling: AllocIndex::NONE,
            prev_sibling: AllocIndex::NONE,
            rect: Rectangle::zero(),
            kind: NodeKind::Unused,
            orientation: Orientation::Horizontal,
        });

        self.generations.push(Wrapping(0));

        AllocIndex(self.nodes.len() as u32 - 1)
    }

    fn mark_node_unused(&mut self, id: AllocIndex) {
        debug_assert!(self.nodes[id.index()].kind != NodeKind::Unused);
        self.nodes[id.index()].kind = NodeKind::Unused;
        self.nodes[id.index()].next_sibling = self.unused_nodes;
        self.unused_nodes = id;
    }

    #[allow(dead_code)]
    fn print_free_rects(&self) {
        println!("Large:");
        for &id in &self.free_lists[LARGE_BUCKET] {
            if self.nodes[id.index()].kind == NodeKind::Free {
                println!(" - {:?} #{:?}", self.nodes[id.index()].rect, id);
            }
        }
        println!("Medium:");
        for &id in &self.free_lists[MEDIUM_BUCKET] {
            if self.nodes[id.index()].kind == NodeKind::Free {
                println!(" - {:?} #{:?}", self.nodes[id.index()].rect, id);
            }
        }
        println!("Small:");
        for &id in &self.free_lists[SMALL_BUCKET] {
            if self.nodes[id.index()].kind == NodeKind::Free {
                println!(" - {:?} #{:?}", self.nodes[id.index()].rect, id);
            }
        }
    }

    #[cfg(feature = "checks")]
    fn check_siblings(&self, id: AllocIndex, next: AllocIndex, orientation: Orientation) {
        if next.is_none() {
            return;
        }

        if self.nodes[next.index()].prev_sibling != id {
            panic!("error: #{:?}'s next sibling #{:?} has prev sibling #{:?}", id, next, self.nodes[next.index()].prev_sibling);
        }
        assert_eq!(self.nodes[next.index()].prev_sibling, id);

        match self.nodes[id.index()].kind {
            NodeKind::Container | NodeKind::Unused => {
                return;
            }
            _ => {}
        }
        match self.nodes[next.index()].kind {
            NodeKind::Container | NodeKind::Unused => {
                return;
            }
            _ => {}
        }

        let r1 = self.nodes[id.index()].rect;
        let r2 = self.nodes[next.index()].rect;
        match orientation {
            Orientation::Horizontal => {
                assert_eq!(r1.min.y, r2.min.y);
                assert_eq!(r1.max.y, r2.max.y);
            }
            Orientation::Vertical => {
                assert_eq!(r1.min.x, r2.min.x);
                assert_eq!(r1.max.x, r2.max.x);
            }
        }
    }

    #[cfg(feature = "checks")]
    fn check_tree(&self) {
        for node_idx in 0..self.nodes.len() {
            let node = &self.nodes[node_idx];

            if node.kind == NodeKind::Unused {
                if node.next_sibling.is_some() {
                    assert_eq!(self.nodes[node.next_sibling.index()].kind, NodeKind::Unused);
                }
                continue;
            }

            let mut iter = node.next_sibling;
            while iter.is_some() {
                assert_eq!(self.nodes[iter.index()].orientation, node.orientation);
                assert_eq!(self.nodes[iter.index()].parent, node.parent);
                assert!(self.nodes[iter.index()].kind != NodeKind::Unused);
                let next = self.nodes[iter.index()].next_sibling;

                #[cfg(feature = "checks")]
                self.check_siblings(iter, next, node.orientation);

                iter = next;
            }

            if node.parent.is_some() {
                if self.nodes[node.parent.index()].kind != NodeKind::Container {
                    panic!("error: child: {:?} parent: {:?}", node_idx, node.parent);
                }
                assert_eq!(
                    self.nodes[node.parent.index()].orientation,
                    node.orientation.flipped()
                );
                assert_eq!(self.nodes[node.parent.index()].kind, NodeKind::Container);
            }
        }
    }

    fn add_free_rect(&mut self, id: AllocIndex, size: &Size) {
        debug_assert_eq!(self.nodes[id.index()].kind, NodeKind::Free);
        let bucket = free_list_for_size(self.small_size_threshold, self.large_size_threshold, size);
        //println!("add free rect #{:?} size {} bucket {}", id, size, bucket);
        self.free_lists[bucket].push(id);
    }

    // Merge `next` into `node` and append `next` to a list of available `nodes`vector slots.
    fn merge_siblings(&mut self, node: AllocIndex, next: AllocIndex, orientation: Orientation) {
        debug_assert_eq!(self.nodes[node.index()].kind, NodeKind::Free);
        debug_assert_eq!(self.nodes[next.index()].kind, NodeKind::Free);
        let r1 = self.nodes[node.index()].rect;
        let r2 = self.nodes[next.index()].rect;
        //println!("merge {} #{:?} and {} #{:?}       {:?}", r1, node, r2, next, orientation);
        let merge_size = self.nodes[next.index()].rect.size();
        match orientation {
            Orientation::Horizontal => {
                debug_assert_eq!(r1.min.y, r2.min.y);
                debug_assert_eq!(r1.max.y, r2.max.y);
                self.nodes[node.index()].rect.max.x += merge_size.width;
            }
            Orientation::Vertical => {
                debug_assert_eq!(r1.min.x, r2.min.x);
                debug_assert_eq!(r1.max.x, r2.max.x);
                self.nodes[node.index()].rect.max.y += merge_size.height;
            }
        }

        // Remove the merged node from the sibling list.
        let next_next = self.nodes[next.index()].next_sibling;
        self.nodes[node.index()].next_sibling = next_next;
        if next_next.is_some() {
            self.nodes[next_next.index()].prev_sibling = node;
        }

        // Add the merged node to the list of available slots in the nodes vector.
        self.mark_node_unused(next);
    }

    fn alloc_id(&self, index: AllocIndex) -> AllocId {
        let generation = self.generations[index.index()].0 as u32;
        debug_assert!(index.0 & IDX_MASK == index.0);
        AllocId(index.0 + (generation << 24))
    }

    fn get_index(&self, id: AllocId) -> AllocIndex {
        let idx = id.0 & IDX_MASK;
        let expected_generation = (self.generations[idx as usize].0 as u32) << 24;
        assert_eq!(id.0 & GEN_MASK, expected_generation);
        AllocIndex(idx)
    }
}

impl std::ops::Index<AllocId> for AtlasAllocator {
    type Output = Rectangle;
    fn index(&self, index: AllocId) -> &Rectangle {
        let idx = self.get_index(index);

        &self.nodes[idx.index()].rect
    }
}

/// A simpler atlas allocator implementation that can allocate rectangles but not deallocate them.
pub struct SimpleAtlasAllocator {
    free_rects: [Vec<Rectangle>; 3],
    alignment: Size,
    small_size_threshold: i32,
    large_size_threshold: i32,
    size: Size,
}

impl SimpleAtlasAllocator {
    /// Create a simple atlas allocator with default options.
    pub fn new(size: Size) -> Self {
        Self::with_options(size, &DEFAULT_OPTIONS)
    }

    /// Create a simple atlas allocator with the provided options.
    pub fn with_options(size: Size, options: &AllocatorOptions) -> Self {
        let bucket = free_list_for_size(
            options.small_size_threshold,
            options.large_size_threshold,
            &size,
        );

        let mut free_rects = [Vec::new(), Vec::new(), Vec::new()];
        free_rects[bucket].push(size.into());

        SimpleAtlasAllocator {
            free_rects,
            alignment: options.alignment,
            small_size_threshold: options.small_size_threshold,
            large_size_threshold: options.large_size_threshold,
            size,
        }
    }

    /// Drop all rectangles, clearing the atlas to its initial state.
    pub fn clear(&mut self) {

        for i in 0..NUM_BUCKETS {
            self.free_rects[i].clear();
        }

        let bucket = free_list_for_size(
            self.small_size_threshold,
            self.large_size_threshold,
            &self.size,
        );

        self.free_rects[bucket].push(self.size.into());
    }

    /// Clear the allocator and reset its size and options.
    pub fn reset(&mut self, size: Size, options: &AllocatorOptions) {
        self.alignment = options.alignment;
        self.small_size_threshold = options.small_size_threshold;
        self.large_size_threshold = options.large_size_threshold;
        self.size = size;

        self.clear();
    }

    pub fn is_empty(&self) -> bool {
        for b in 0..NUM_BUCKETS {
            for rect in &self.free_rects[b] {
                return rect.size() == self.size;
            }
        }

        // This should be unreachable.
        return false;
    }

    /// The total size of the atlas.
    pub fn size(&self) -> Size {
        self.size
    }

    /// Allocate a rectangle in the atlas.
    pub fn allocate(&mut self, mut requested_size: Size) -> Option<Rectangle> {
        if requested_size.is_empty() {
            return None;
        }

        adjust_size(self.alignment.width, &mut requested_size.width);
        adjust_size(self.alignment.height, &mut requested_size.height);

        let ideal_bucket = free_list_for_size(
            self.small_size_threshold,
            self.large_size_threshold,
            &requested_size,
        );

        let use_worst_fit = ideal_bucket == LARGE_BUCKET;

        let mut chosen_rect = None;
        for bucket in ideal_bucket..NUM_BUCKETS {
            let mut candidate_score = if use_worst_fit { 0 } else { std::i32::MAX };
            let mut candidate = None;

            for (index, rect) in self.free_rects[bucket].iter().enumerate() {
                let dx = rect.width() - requested_size.width;
                let dy = rect.height() - requested_size.height;

                if dx >= 0 && dy >= 0 {
                    if dx == 0 || dy == 0 {
                        // Perfect fit!
                        candidate = Some(index);
                        break;
                    }

                    let score = i32::min(dx, dy);
                    if (use_worst_fit && score > candidate_score)
                        || (!use_worst_fit && score < candidate_score)
                    {
                        candidate_score = score;
                        candidate = Some(index);
                    }
                }
            }

            if let Some(index) = candidate {
                let rect = self.free_rects[bucket].remove(index);
                chosen_rect = Some(rect);
                break;
            }
        }

        if let Some(rect) = chosen_rect {
            let (split_rect, leftover_rect, _) =
                guillotine_rect(&rect, requested_size, Orientation::Vertical);
            self.add_free_rect(&split_rect);
            self.add_free_rect(&leftover_rect);

            return Some(Rectangle {
                min: rect.min,
                max: rect.min + requested_size.to_vector(),
            });
        }

        None
    }

    /// Resize the atlas without changing the allocations.
    ///
    /// This method is not allowed to shrink the width or height of the atlas.
    pub fn grow(&mut self, new_size: Size) {
        assert!(new_size.width >= self.size.width);
        assert!(new_size.height >= self.size.height);

        let (split_rect, leftover_rect, _) =
            guillotine_rect(&new_size.into(), self.size, Orientation::Vertical);

        self.size = new_size;

        self.add_free_rect(&split_rect);
        self.add_free_rect(&leftover_rect);
    }

    /// Initialize this simple allocator with the content of an atlas allocator.
    pub fn init_from_allocator(&mut self, src: &AtlasAllocator) {
        self.size = src.size;
        self.small_size_threshold = src.small_size_threshold;
        self.large_size_threshold = src.large_size_threshold;

        for bucket in 0..NUM_BUCKETS {
            for id in src.free_lists[bucket].iter() {
                // During tree simplification we don't remove merged nodes from the free list, so we have
                // to handle it here.
                // This is a tad awkward, but lets us avoid having to maintain a doubly linked list for
                // the free list (which would be needed to remove nodes during tree simplification).
                if src.nodes[id.index()].kind != NodeKind::Free {
                    continue;
                }

                self.free_rects[bucket].push(src.nodes[id.index()].rect);
            }
        }
    }

    fn add_free_rect(&mut self, rect: &Rectangle) {
        if rect.width() < self.alignment.width || rect.height() < self.alignment.height {
            return;
        }

        let bucket = free_list_for_size(
            self.small_size_threshold,
            self.large_size_threshold,
            &rect.size(),
        );

        self.free_rects[bucket].push(*rect);
    }
}

fn adjust_size(alignment: i32, size: &mut i32) {
    let rem = *size % alignment;
    if rem > 0 {
        *size += alignment - rem;
    }
}

/// Compute the area, saturating at i32::MAX instead of overflowing.
fn safe_area(rect: &Rectangle) -> i32 {
    rect.width().checked_mul(rect.height()).unwrap_or(std::i32::MAX)
}

fn guillotine_rect(
    chosen_rect: &Rectangle,
    requested_size: Size,
    default_orientation: Orientation,
) -> (Rectangle, Rectangle, Orientation) {
    // Decide whether to split horizontally or vertically.
    //
    // If the chosen free rectangle is bigger than the requested size, we subdivide it
    // into an allocated rectangle, a split rectangle and a leftover rectangle:
    //
    // +-----------+-------------+
    // |///////////|             |
    // |/allocated/|             |
    // |///////////|             |
    // +-----------+             |
    // |                         |
    // |          chosen         |
    // |                         |
    // +-------------------------+
    //
    // Will be split into either:
    //
    // +-----------+-------------+
    // |///////////|             |
    // |/allocated/|  leftover   |
    // |///////////|             |
    // +-----------+-------------+
    // |                         |
    // |          split          |
    // |                         |
    // +-------------------------+
    //
    // or:
    //
    // +-----------+-------------+
    // |///////////|             |
    // |/allocated/|             |
    // |///////////|    split    |
    // +-----------+             |
    // |           |             |
    // | leftover  |             |
    // |           |             |
    // +-----------+-------------+

    let candidate_leftover_rect_to_right = Rectangle {
        min: chosen_rect.min + vec2(requested_size.width, 0),
        max: point2(chosen_rect.max.x, chosen_rect.min.y + requested_size.height),
    };
    let candidate_leftover_rect_to_bottom = Rectangle {
        min: chosen_rect.min + vec2(0, requested_size.height),
        max: point2(chosen_rect.min.x + requested_size.width, chosen_rect.max.y),
    };

    let split_rect;
    let leftover_rect;
    let orientation;
    if requested_size == chosen_rect.size() {
        // Perfect fit.
        orientation = default_orientation;
        split_rect = Rectangle::zero();
        leftover_rect = Rectangle::zero();
    } else if safe_area(&candidate_leftover_rect_to_right) > safe_area(&candidate_leftover_rect_to_bottom) {
        leftover_rect = candidate_leftover_rect_to_bottom;
        split_rect = Rectangle {
            min: candidate_leftover_rect_to_right.min,
            max: point2(candidate_leftover_rect_to_right.max.x, chosen_rect.max.y),
        };
        orientation = Orientation::Horizontal;
    } else {
        leftover_rect = candidate_leftover_rect_to_right;
        split_rect = Rectangle {
            min: candidate_leftover_rect_to_bottom.min,
            max: point2(chosen_rect.max.x, candidate_leftover_rect_to_bottom.max.y),
        };
        orientation = Orientation::Vertical;
    }

    (split_rect, leftover_rect, orientation)
}

#[repr(C)]
#[derive(Copy, Clone, Debug, PartialEq)]
pub struct Allocation {
    pub id: AllocId,
    pub rectangle: Rectangle,
}

#[repr(C)]
#[derive(Copy, Clone, Debug, PartialEq)]
pub struct Change {
    pub old: Allocation,
    pub new: Allocation,
}

#[derive(Clone, Debug, PartialEq)]
pub struct ChangeList {
    pub changes: Vec<Change>,
    pub failures: Vec<Allocation>,
}

impl ChangeList {
    pub fn empty() -> Self {
        ChangeList {
            changes: Vec::new(),
            failures: Vec::new(),
        }
    }
}

/// Dump a visual representation of the atlas in SVG format.
pub fn dump_svg(atlas: &AtlasAllocator, output: &mut dyn std::io::Write) -> std::io::Result<()> {
    use svg_fmt::*;

    writeln!(
        output,
        "{}",
        BeginSvg {
            w: atlas.size.width as f32,
            h: atlas.size.height as f32
        }
    )?;

    dump_into_svg(atlas, None, output)?;

    writeln!(output, "{}", EndSvg)
}

/// Dump a visual representation of the atlas in SVG, omitting the beginning and end of the
/// SVG document, so that it can be included in a larger document.
///
/// If a rectange is provided, translate and scale the output to fit it.
pub fn dump_into_svg(atlas: &AtlasAllocator, rect: Option<&Rectangle>, output: &mut dyn std::io::Write) -> std::io::Result<()> {
    use svg_fmt::*;

    let (sx, sy, tx, ty) = if let Some(rect) = rect {
        (
            rect.width() as f32 / atlas.size.width as f32,
            rect.height() as f32 / atlas.size.height as f32,
            rect.min.x as f32,
            rect.min.y as f32,
        )
    } else {
        (1.0, 1.0, 0.0, 0.0)
    };

    for node in &atlas.nodes {
        let color = match node.kind {
            NodeKind::Free => rgb(50, 50, 50),
            NodeKind::Alloc => rgb(70, 70, 180),
            _ => {
                continue;
            }
        };

        let (x, y) = node.rect.min.to_f32().to_tuple();
        let (w, h) = node.rect.size().to_f32().to_tuple();

        writeln!(
            output,
            r#"    {}"#,
            rectangle(tx + x * sx, ty + y * sy, w * sx, h * sy)
                .fill(color)
                .stroke(Stroke::Color(black(), 1.0))
        )?;
    }

    Ok(())
}

#[test]
fn atlas_basic() {
    let mut atlas = AtlasAllocator::new(size2(1000, 1000));

    let full = atlas.allocate(size2(1000, 1000)).unwrap().id;
    assert!(atlas.allocate(size2(1, 1)).is_none());

    atlas.deallocate(full);

    let a = atlas.allocate(size2(100, 1000)).unwrap().id;
    let b = atlas.allocate(size2(900, 200)).unwrap().id;
    let c = atlas.allocate(size2(300, 200)).unwrap().id;
    let d = atlas.allocate(size2(200, 300)).unwrap().id;
    let e = atlas.allocate(size2(100, 300)).unwrap().id;
    let f = atlas.allocate(size2(100, 300)).unwrap().id;
    let g = atlas.allocate(size2(100, 300)).unwrap().id;

    atlas.deallocate(b);
    atlas.deallocate(f);
    atlas.deallocate(c);
    atlas.deallocate(e);
    let h = atlas.allocate(size2(500, 200)).unwrap().id;
    atlas.deallocate(a);
    let i = atlas.allocate(size2(500, 200)).unwrap().id;
    atlas.deallocate(g);
    atlas.deallocate(h);
    atlas.deallocate(d);
    atlas.deallocate(i);

    let full = atlas.allocate(size2(1000, 1000)).unwrap().id;
    assert!(atlas.allocate(size2(1, 1)).is_none());
    atlas.deallocate(full);
}

#[test]
fn atlas_random_test() {
    let mut atlas = AtlasAllocator::with_options(
        size2(1000, 1000),
        &AllocatorOptions {
            alignment: size2(5, 2),
            ..DEFAULT_OPTIONS
        },
    );

    let a = 1103515245;
    let c = 12345;
    let m = usize::pow(2, 31);
    let mut seed: usize = 37;

    let mut rand = || {
        seed = (a * seed + c) % m;
        seed
    };

    let mut n: usize = 0;
    let mut misses: usize = 0;

    let mut allocated = Vec::new();
    for _ in 0..500000 {
        if rand() % 5 > 2 && !allocated.is_empty() {
            // deallocate something
            let nth = rand() % allocated.len();
            let id = allocated[nth];
            allocated.remove(nth);

            atlas.deallocate(id);
        } else {
            // allocate something
            let size = size2((rand() % 300) as i32 + 5, (rand() % 300) as i32 + 5);

            if let Some(alloc) = atlas.allocate(size) {
                allocated.push(alloc.id);
                n += 1;
            } else {
                misses += 1;
            }
        }
    }

    while let Some(id) = allocated.pop() {
        atlas.deallocate(id);
    }

    println!("added/removed {} rectangles, {} misses", n, misses);
    println!(
        "nodes.cap: {}, free_list.cap: {}/{}/{}",
        atlas.nodes.capacity(),
        atlas.free_lists[LARGE_BUCKET].capacity(),
        atlas.free_lists[MEDIUM_BUCKET].capacity(),
        atlas.free_lists[SMALL_BUCKET].capacity(),
    );

    let full = atlas.allocate(size2(1000, 1000)).unwrap().id;
    assert!(atlas.allocate(size2(1, 1)).is_none());
    atlas.deallocate(full);
}

#[test]
fn test_grow() {
    let mut atlas = AtlasAllocator::new(size2(1000, 1000));

    atlas.grow(size2(2000, 2000));

    let full = atlas.allocate(size2(2000, 2000)).unwrap().id;
    assert!(atlas.allocate(size2(1, 1)).is_none());
    atlas.deallocate(full);

    let a = atlas.allocate(size2(100, 100)).unwrap().id;

    atlas.grow(size2(3000, 3000));

    let b = atlas.allocate(size2(1000, 2900)).unwrap().id;

    atlas.grow(size2(4000, 4000));

    atlas.deallocate(b);
    atlas.deallocate(a);

    let full = atlas.allocate(size2(4000, 4000)).unwrap().id;
    assert!(atlas.allocate(size2(1, 1)).is_none());
    atlas.deallocate(full);
}

#[test]
fn clear_empty() {
    let mut atlas = AtlasAllocator::new(size2(1000, 1000));

    assert!(atlas.is_empty());

    assert!(atlas.allocate(size2(10, 10)).is_some());
    assert!(!atlas.is_empty());

    atlas.clear();
    assert!(atlas.is_empty());

    let a = atlas.allocate(size2(10, 10)).unwrap().id;
    let b = atlas.allocate(size2(20, 20)).unwrap().id;
    assert!(!atlas.is_empty());

    atlas.deallocate(b);
    atlas.deallocate(a);
    assert!(atlas.is_empty());

    atlas.clear();
    assert!(atlas.is_empty());

    atlas.clear();
    assert!(atlas.is_empty());
}

#[test]
fn simple_atlas() {
    let mut atlas = SimpleAtlasAllocator::new(size2(1000, 1000));

    assert!(atlas.allocate(size2(1, 1001)).is_none());
    assert!(atlas.allocate(size2(1001, 1)).is_none());

    let mut rectangles = Vec::new();
    rectangles.push(atlas.allocate(size2(100, 1000)).unwrap());
    rectangles.push(atlas.allocate(size2(900, 200)).unwrap());
    rectangles.push(atlas.allocate(size2(300, 200)).unwrap());
    rectangles.push(atlas.allocate(size2(200, 300)).unwrap());
    rectangles.push(atlas.allocate(size2(100, 300)).unwrap());
    rectangles.push(atlas.allocate(size2(100, 300)).unwrap());
    rectangles.push(atlas.allocate(size2(100, 300)).unwrap());
    assert!(atlas.allocate(size2(800, 800)).is_none());

    for i in 0..rectangles.len() {
        for j in 0..rectangles.len() {
            if i == j {
                continue;
            }

            assert!(!rectangles[i].intersects(&rectangles[j]));
        }
    }
}

#[test]
fn allocate_zero() {
    let mut atlas = SimpleAtlasAllocator::new(size2(1000, 1000));

    assert!(atlas.allocate(size2(0, 0)).is_none());
}

#[test]
fn allocate_negative() {
    let mut atlas = SimpleAtlasAllocator::new(size2(1000, 1000));

    assert!(atlas.allocate(size2(-1, 1)).is_none());
    assert!(atlas.allocate(size2(1, -1)).is_none());
    assert!(atlas.allocate(size2(-1, -1)).is_none());

    assert!(atlas.allocate(size2(-167114179, -718142)).is_none());
}

#[test]
fn issue_25() {
    let mut allocator = AtlasAllocator::new(Size::new(65536, 65536));
    allocator.allocate(Size::new(2,2));
    allocator.allocate(Size::new(65500,2));
    allocator.allocate(Size::new(2, 65500));
}