aboutsummaryrefslogtreecommitdiffstats
path: root/include/llvm/ADT/IntervalMap.h
blob: 33569269c682d973ffac6415a26891a17ca75b58 (plain)
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
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
//===- llvm/ADT/IntervalMap.h - A sorted interval map -----------*- C++ -*-===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file implements a coalescing interval map for small objects.
//
// KeyT objects are mapped to ValT objects. Intervals of keys that map to the
// same value are represented in a compressed form.
//
// Iterators provide ordered access to the compressed intervals rather than the
// individual keys, and insert and erase operations use key intervals as well.
//
// Like SmallVector, IntervalMap will store the first N intervals in the map
// object itself without any allocations. When space is exhausted it switches to
// a B+-tree representation with very small overhead for small key and value
// objects.
//
// A Traits class specifies how keys are compared. It also allows IntervalMap to
// work with both closed and half-open intervals.
//
// Keys and values are not stored next to each other in a std::pair, so we don't
// provide such a value_type. Dereferencing iterators only returns the mapped
// value. The interval bounds are accessible through the start() and stop()
// iterator methods.
//
// IntervalMap is optimized for small key and value objects, 4 or 8 bytes each
// is the optimal size. For large objects use std::map instead.
//
//===----------------------------------------------------------------------===//
//
// Synopsis:
//
// template <typename KeyT, typename ValT, unsigned N, typename Traits>
// class IntervalMap {
// public:
//   typedef KeyT key_type;
//   typedef ValT mapped_type;
//   typedef RecyclingAllocator<...> Allocator;
//   class iterator;
//   class const_iterator;
//
//   explicit IntervalMap(Allocator&);
//   ~IntervalMap():
//
//   bool empty() const;
//   KeyT start() const;
//   KeyT stop() const;
//   ValT lookup(KeyT x, Value NotFound = Value()) const;
//
//   const_iterator begin() const;
//   const_iterator end() const;
//   iterator begin();
//   iterator end();
//   const_iterator find(KeyT x) const;
//   iterator find(KeyT x);
//
//   void insert(KeyT a, KeyT b, ValT y);
//   void clear();
// };
//
// template <typename KeyT, typename ValT, unsigned N, typename Traits>
// class IntervalMap::const_iterator :
//   public std::iterator<std::bidirectional_iterator_tag, ValT> {
// public:
//   bool operator==(const const_iterator &) const;
//   bool operator!=(const const_iterator &) const;
//   bool valid() const;
//
//   const KeyT &start() const;
//   const KeyT &stop() const;
//   const ValT &value() const;
//   const ValT &operator*() const;
//   const ValT *operator->() const;
//
//   const_iterator &operator++();
//   const_iterator &operator++(int);
//   const_iterator &operator--();
//   const_iterator &operator--(int);
//   void goToBegin();
//   void goToEnd();
//   void find(KeyT x);
//   void advanceTo(KeyT x);
// };
//
// template <typename KeyT, typename ValT, unsigned N, typename Traits>
// class IntervalMap::iterator : public const_iterator {
// public:
//   void insert(KeyT a, KeyT b, Value y);
//   void erase();
// };
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_ADT_INTERVALMAP_H
#define LLVM_ADT_INTERVALMAP_H

#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/PointerIntPair.h"
#include "llvm/Support/Allocator.h"
#include "llvm/Support/RecyclingAllocator.h"
#include <iterator>

// FIXME: Remove debugging code.
#include "llvm/Support/raw_ostream.h"

namespace llvm {


//===----------------------------------------------------------------------===//
//---                              Key traits                              ---//
//===----------------------------------------------------------------------===//
//
// The IntervalMap works with closed or half-open intervals.
// Adjacent intervals that map to the same value are coalesced.
//
// The IntervalMapInfo traits class is used to determine if a key is contained
// in an interval, and if two intervals are adjacent so they can be coalesced.
// The provided implementation works for closed integer intervals, other keys
// probably need a specialized version.
//
// The point x is contained in [a;b] when !startLess(x, a) && !stopLess(b, x).
//
// It is assumed that (a;b] half-open intervals are not used, only [a;b) is
// allowed. This is so that stopLess(a, b) can be used to determine if two
// intervals overlap.
//
//===----------------------------------------------------------------------===//

template <typename T>
struct IntervalMapInfo {

  /// startLess - Return true if x is not in [a;b].
  /// This is x < a both for closed intervals and for [a;b) half-open intervals.
  static inline bool startLess(const T &x, const T &a) {
    return x < a;
  }

  /// stopLess - Return true if x is not in [a;b].
  /// This is b < x for a closed interval, b <= x for [a;b) half-open intervals.
  static inline bool stopLess(const T &b, const T &x) {
    return b < x;
  }

  /// adjacent - Return true when the intervals [x;a] and [b;y] can coalesce.
  /// This is a+1 == b for closed intervals, a == b for half-open intervals.
  static inline bool adjacent(const T &a, const T &b) {
    return a+1 == b;
  }

};

/// IntervalMapImpl - Namespace used for IntervalMap implementation details.
/// It should be considered private to the implementation.
namespace IntervalMapImpl {

// Forward declarations.
template <typename, typename, unsigned, typename> class LeafNode;
template <typename, typename, unsigned, typename> class BranchNode;

typedef std::pair<unsigned,unsigned> IdxPair;


//===----------------------------------------------------------------------===//
//---                    IntervalMapImpl::NodeBase                         ---//
//===----------------------------------------------------------------------===//
//
// Both leaf and branch nodes store vectors of pairs.
// Leaves store ((KeyT, KeyT), ValT) pairs, branches use (NodeRef, KeyT).
//
// Keys and values are stored in separate arrays to avoid padding caused by
// different object alignments. This also helps improve locality of reference
// when searching the keys.
//
// The nodes don't know how many elements they contain - that information is
// stored elsewhere. Omitting the size field prevents padding and allows a node
// to fill the allocated cache lines completely.
//
// These are typical key and value sizes, the node branching factor (N), and
// wasted space when nodes are sized to fit in three cache lines (192 bytes):
//
//   T1  T2   N Waste  Used by
//    4   4  24   0    Branch<4> (32-bit pointers)
//    8   4  16   0    Leaf<4,4>, Branch<4>
//    8   8  12   0    Leaf<4,8>, Branch<8>
//   16   4   9  12    Leaf<8,4>
//   16   8   8   0    Leaf<8,8>
//
//===----------------------------------------------------------------------===//

template <typename T1, typename T2, unsigned N>
class NodeBase {
public:
  enum { Capacity = N };

  T1 first[N];
  T2 second[N];

  /// copy - Copy elements from another node.
  /// @param Other Node elements are copied from.
  /// @param i     Beginning of the source range in other.
  /// @param j     Beginning of the destination range in this.
  /// @param Count Number of elements to copy.
  template <unsigned M>
  void copy(const NodeBase<T1, T2, M> &Other, unsigned i,
            unsigned j, unsigned Count) {
    assert(i + Count <= M && "Invalid source range");
    assert(j + Count <= N && "Invalid dest range");
    for (unsigned e = i + Count; i != e; ++i, ++j) {
      first[j]  = Other.first[i];
      second[j] = Other.second[i];
    }
  }

  /// moveLeft - Move elements to the left.
  /// @param i     Beginning of the source range.
  /// @param j     Beginning of the destination range.
  /// @param Count Number of elements to copy.
  void moveLeft(unsigned i, unsigned j, unsigned Count) {
    assert(j <= i && "Use moveRight shift elements right");
    copy(*this, i, j, Count);
  }

  /// moveRight - Move elements to the right.
  /// @param i     Beginning of the source range.
  /// @param j     Beginning of the destination range.
  /// @param Count Number of elements to copy.
  void moveRight(unsigned i, unsigned j, unsigned Count) {
    assert(i <= j && "Use moveLeft shift elements left");
    assert(j + Count <= N && "Invalid range");
    while (Count--) {
      first[j + Count]  = first[i + Count];
      second[j + Count] = second[i + Count];
    }
  }

  /// erase - Erase elements [i;j).
  /// @param i    Beginning of the range to erase.
  /// @param j    End of the range. (Exclusive).
  /// @param Size Number of elements in node.
  void erase(unsigned i, unsigned j, unsigned Size) {
    moveLeft(j, i, Size - j);
  }

  /// erase - Erase element at i.
  /// @param i    Index of element to erase.
  /// @param Size Number of elements in node.
  void erase(unsigned i, unsigned Size) {
    erase(i, i+1, Size);
  }

  /// shift - Shift elements [i;size) 1 position to the right.
  /// @param i    Beginning of the range to move.
  /// @param Size Number of elements in node.
  void shift(unsigned i, unsigned Size) {
    moveRight(i, i + 1, Size - i);
  }

  /// transferToLeftSib - Transfer elements to a left sibling node.
  /// @param Size  Number of elements in this.
  /// @param Sib   Left sibling node.
  /// @param SSize Number of elements in sib.
  /// @param Count Number of elements to transfer.
  void transferToLeftSib(unsigned Size, NodeBase &Sib, unsigned SSize,
                         unsigned Count) {
    Sib.copy(*this, 0, SSize, Count);
    erase(0, Count, Size);
  }

  /// transferToRightSib - Transfer elements to a right sibling node.
  /// @param Size  Number of elements in this.
  /// @param Sib   Right sibling node.
  /// @param SSize Number of elements in sib.
  /// @param Count Number of elements to transfer.
  void transferToRightSib(unsigned Size, NodeBase &Sib, unsigned SSize,
                          unsigned Count) {
    Sib.moveRight(0, Count, SSize);
    Sib.copy(*this, Size-Count, 0, Count);
  }

  /// adjustFromLeftSib - Adjust the number if elements in this node by moving
  /// elements to or from a left sibling node.
  /// @param Size  Number of elements in this.
  /// @param Sib   Right sibling node.
  /// @param SSize Number of elements in sib.
  /// @param Add   The number of elements to add to this node, possibly < 0.
  /// @return      Number of elements added to this node, possibly negative.
  int adjustFromLeftSib(unsigned Size, NodeBase &Sib, unsigned SSize, int Add) {
    if (Add > 0) {
      // We want to grow, copy from sib.
      unsigned Count = std::min(std::min(unsigned(Add), SSize), N - Size);
      Sib.transferToRightSib(SSize, *this, Size, Count);
      return Count;
    } else {
      // We want to shrink, copy to sib.
      unsigned Count = std::min(std::min(unsigned(-Add), Size), N - SSize);
      transferToLeftSib(Size, Sib, SSize, Count);
      return -Count;
    }
  }
};

/// IntervalMapImpl::adjustSiblingSizes - Move elements between sibling nodes.
/// @param Node  Array of pointers to sibling nodes.
/// @param Nodes Number of nodes.
/// @param CurSize Array of current node sizes, will be overwritten.
/// @param NewSize Array of desired node sizes.
template <typename NodeT>
void adjustSiblingSizes(NodeT *Node[], unsigned Nodes,
                        unsigned CurSize[], const unsigned NewSize[]) {
  // Move elements right.
  for (int n = Nodes - 1; n; --n) {
    if (CurSize[n] == NewSize[n])
      continue;
    for (int m = n - 1; m != -1; --m) {
      int d = Node[n]->adjustFromLeftSib(CurSize[n], *Node[m], CurSize[m],
                                         NewSize[n] - CurSize[n]);
      CurSize[m] -= d;
      CurSize[n] += d;
      // Keep going if the current node was exhausted.
      if (CurSize[n] >= NewSize[n])
          break;
    }
  }

  if (Nodes == 0)
    return;

  // Move elements left.
  for (unsigned n = 0; n != Nodes - 1; ++n) {
    if (CurSize[n] == NewSize[n])
      continue;
    for (unsigned m = n + 1; m != Nodes; ++m) {
      int d = Node[m]->adjustFromLeftSib(CurSize[m], *Node[n], CurSize[n],
                                        CurSize[n] -  NewSize[n]);
      CurSize[m] += d;
      CurSize[n] -= d;
      // Keep going if the current node was exhausted.
      if (CurSize[n] >= NewSize[n])
          break;
    }
  }

#ifndef NDEBUG
  for (unsigned n = 0; n != Nodes; n++)
    assert(CurSize[n] == NewSize[n] && "Insufficient element shuffle");
#endif
}

/// IntervalMapImpl::distribute - Compute a new distribution of node elements
/// after an overflow or underflow. Reserve space for a new element at Position,
/// and compute the node that will hold Position after redistributing node
/// elements.
///
/// It is required that
///
///   Elements == sum(CurSize), and
///   Elements + Grow <= Nodes * Capacity.
///
/// NewSize[] will be filled in such that:
///
///   sum(NewSize) == Elements, and
///   NewSize[i] <= Capacity.
///
/// The returned index is the node where Position will go, so:
///
///   sum(NewSize[0..idx-1]) <= Position
///   sum(NewSize[0..idx])   >= Position
///
/// The last equality, sum(NewSize[0..idx]) == Position, can only happen when
/// Grow is set and NewSize[idx] == Capacity-1. The index points to the node
/// before the one holding the Position'th element where there is room for an
/// insertion.
///
/// @param Nodes    The number of nodes.
/// @param Elements Total elements in all nodes.
/// @param Capacity The capacity of each node.
/// @param CurSize  Array[Nodes] of current node sizes, or NULL.
/// @param NewSize  Array[Nodes] to receive the new node sizes.
/// @param Position Insert position.
/// @param Grow     Reserve space for a new element at Position.
/// @return         (node, offset) for Position.
IdxPair distribute(unsigned Nodes, unsigned Elements, unsigned Capacity,
                   const unsigned *CurSize, unsigned NewSize[],
                   unsigned Position, bool Grow);


//===----------------------------------------------------------------------===//
//---                   IntervalMapImpl::NodeSizer                         ---//
//===----------------------------------------------------------------------===//
//
// Compute node sizes from key and value types.
//
// The branching factors are chosen to make nodes fit in three cache lines.
// This may not be possible if keys or values are very large. Such large objects
// are handled correctly, but a std::map would probably give better performance.
//
//===----------------------------------------------------------------------===//

enum {
  // Cache line size. Most architectures have 32 or 64 byte cache lines.
  // We use 64 bytes here because it provides good branching factors.
  Log2CacheLine = 6,
  CacheLineBytes = 1 << Log2CacheLine,
  DesiredNodeBytes = 3 * CacheLineBytes
};

template <typename KeyT, typename ValT>
struct NodeSizer {
  enum {
    // Compute the leaf node branching factor that makes a node fit in three
    // cache lines. The branching factor must be at least 3, or some B+-tree
    // balancing algorithms won't work.
    // LeafSize can't be larger than CacheLineBytes. This is required by the
    // PointerIntPair used by NodeRef.
    DesiredLeafSize = DesiredNodeBytes /
      static_cast<unsigned>(2*sizeof(KeyT)+sizeof(ValT)),
    MinLeafSize = 3,
    LeafSize = DesiredLeafSize > MinLeafSize ? DesiredLeafSize : MinLeafSize
  };

  typedef NodeBase<std::pair<KeyT, KeyT>, ValT, LeafSize> LeafBase;

  enum {
    // Now that we have the leaf branching factor, compute the actual allocation
    // unit size by rounding up to a whole number of cache lines.
    AllocBytes = (sizeof(LeafBase) + CacheLineBytes-1) & ~(CacheLineBytes-1),

    // Determine the branching factor for branch nodes.
    BranchSize = AllocBytes /
      static_cast<unsigned>(sizeof(KeyT) + sizeof(void*))
  };

  /// Allocator - The recycling allocator used for both branch and leaf nodes.
  /// This typedef is very likely to be identical for all IntervalMaps with
  /// reasonably sized entries, so the same allocator can be shared among
  /// different kinds of maps.
  typedef RecyclingAllocator<BumpPtrAllocator, char,
                             AllocBytes, CacheLineBytes> Allocator;

};


//===----------------------------------------------------------------------===//
//---                     IntervalMapImpl::NodeRef                         ---//
//===----------------------------------------------------------------------===//
//
// B+-tree nodes can be leaves or branches, so we need a polymorphic node
// pointer that can point to both kinds.
//
// All nodes are cache line aligned and the low 6 bits of a node pointer are
// always 0. These bits are used to store the number of elements in the
// referenced node. Besides saving space, placing node sizes in the parents
// allow tree balancing algorithms to run without faulting cache lines for nodes
// that may not need to be modified.
//
// A NodeRef doesn't know whether it references a leaf node or a branch node.
// It is the responsibility of the caller to use the correct types.
//
// Nodes are never supposed to be empty, and it is invalid to store a node size
// of 0 in a NodeRef. The valid range of sizes is 1-64.
//
//===----------------------------------------------------------------------===//

class NodeRef {
  struct CacheAlignedPointerTraits {
    static inline void *getAsVoidPointer(void *P) { return P; }
    static inline void *getFromVoidPointer(void *P) { return P; }
    enum { NumLowBitsAvailable = Log2CacheLine };
  };
  PointerIntPair<void*, Log2CacheLine, unsigned, CacheAlignedPointerTraits> pip;

public:
  /// NodeRef - Create a null ref.
  NodeRef() {}

  /// operator bool - Detect a null ref.
  operator bool() const { return pip.getOpaqueValue(); }

  /// NodeRef - Create a reference to the node p with n elements.
  template <typename NodeT>
  NodeRef(NodeT *p, unsigned n) : pip(p, n - 1) {
    assert(n <= NodeT::Capacity && "Size too big for node");
  }

  /// size - Return the number of elements in the referenced node.
  unsigned size() const { return pip.getInt() + 1; }

  /// setSize - Update the node size.
  void setSize(unsigned n) { pip.setInt(n - 1); }

  /// subtree - Access the i'th subtree reference in a branch node.
  /// This depends on branch nodes storing the NodeRef array as their first
  /// member.
  NodeRef &subtree(unsigned i) const {
    return reinterpret_cast<NodeRef*>(pip.getPointer())[i];
  }

  /// get - Dereference as a NodeT reference.
  template <typename NodeT>
  NodeT &get() const {
    return *reinterpret_cast<NodeT*>(pip.getPointer());
  }

  bool operator==(const NodeRef &RHS) const {
    if (pip == RHS.pip)
      return true;
    assert(pip.getPointer() != RHS.pip.getPointer() && "Inconsistent NodeRefs");
    return false;
  }

  bool operator!=(const NodeRef &RHS) const {
    return !operator==(RHS);
  }
};

//===----------------------------------------------------------------------===//
//---                      IntervalMapImpl::LeafNode                       ---//
//===----------------------------------------------------------------------===//
//
// Leaf nodes store up to N disjoint intervals with corresponding values.
//
// The intervals are kept sorted and fully coalesced so there are no adjacent
// intervals mapping to the same value.
//
// These constraints are always satisfied:
//
// - Traits::stopLess(start(i), stop(i))    - Non-empty, sane intervals.
//
// - Traits::stopLess(stop(i), start(i + 1) - Sorted.
//
// - value(i) != value(i + 1) || !Traits::adjacent(stop(i), start(i + 1))
//                                          - Fully coalesced.
//
//===----------------------------------------------------------------------===//

template <typename KeyT, typename ValT, unsigned N, typename Traits>
class LeafNode : public NodeBase<std::pair<KeyT, KeyT>, ValT, N> {
public:
  const KeyT &start(unsigned i) const { return this->first[i].first; }
  const KeyT &stop(unsigned i) const { return this->first[i].second; }
  const ValT &value(unsigned i) const { return this->second[i]; }

  KeyT &start(unsigned i) { return this->first[i].first; }
  KeyT &stop(unsigned i) { return this->first[i].second; }
  ValT &value(unsigned i) { return this->second[i]; }

  /// findFrom - Find the first interval after i that may contain x.
  /// @param i    Starting index for the search.
  /// @param Size Number of elements in node.
  /// @param x    Key to search for.
  /// @return     First index with !stopLess(key[i].stop, x), or size.
  ///             This is the first interval that can possibly contain x.
  unsigned findFrom(unsigned i, unsigned Size, KeyT x) const {
    assert(i <= Size && Size <= N && "Bad indices");
    assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
           "Index is past the needed point");
    while (i != Size && Traits::stopLess(stop(i), x)) ++i;
    return i;
  }

  /// safeFind - Find an interval that is known to exist. This is the same as
  /// findFrom except is it assumed that x is at least within range of the last
  /// interval.
  /// @param i Starting index for the search.
  /// @param x Key to search for.
  /// @return  First index with !stopLess(key[i].stop, x), never size.
  ///          This is the first interval that can possibly contain x.
  unsigned safeFind(unsigned i, KeyT x) const {
    assert(i < N && "Bad index");
    assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
           "Index is past the needed point");
    while (Traits::stopLess(stop(i), x)) ++i;
    assert(i < N && "Unsafe intervals");
    return i;
  }

  /// safeLookup - Lookup mapped value for a safe key.
  /// It is assumed that x is within range of the last entry.
  /// @param x        Key to search for.
  /// @param NotFound Value to return if x is not in any interval.
  /// @return         The mapped value at x or NotFound.
  ValT safeLookup(KeyT x, ValT NotFound) const {
    unsigned i = safeFind(0, x);
    return Traits::startLess(x, start(i)) ? NotFound : value(i);
  }

  unsigned insertFrom(unsigned &Pos, unsigned Size, KeyT a, KeyT b, ValT y);

#ifndef NDEBUG
  void dump(raw_ostream &OS, unsigned Size) {
    OS << "  N" << this << " [shape=record label=\"{ " << Size << '/' << N;
    for (unsigned i = 0; i != Size; ++i)
      OS << " | {" << start(i) << '-' << stop(i) << "|" << value(i) << '}';
    OS << "}\"];\n";
  }
#endif

};

/// insertFrom - Add mapping of [a;b] to y if possible, coalescing as much as
/// possible. This may cause the node to grow by 1, or it may cause the node
/// to shrink because of coalescing.
/// @param i    Starting index = insertFrom(0, size, a)
/// @param Size Number of elements in node.
/// @param a    Interval start.
/// @param b    Interval stop.
/// @param y    Value be mapped.
/// @return     (insert position, new size), or (i, Capacity+1) on overflow.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
unsigned LeafNode<KeyT, ValT, N, Traits>::
insertFrom(unsigned &Pos, unsigned Size, KeyT a, KeyT b, ValT y) {
  unsigned i = Pos;
  assert(i <= Size && Size <= N && "Invalid index");
  assert(!Traits::stopLess(b, a) && "Invalid interval");

  // Verify the findFrom invariant.
  assert((i == 0 || Traits::stopLess(stop(i - 1), a)));
  assert((i == Size || !Traits::stopLess(stop(i), a)));
  assert((i == Size || Traits::stopLess(b, start(i))) && "Overlapping insert");

  // Coalesce with previous interval.
  if (i && value(i - 1) == y && Traits::adjacent(stop(i - 1), a)) {
    Pos = i - 1;
    // Also coalesce with next interval?
    if (i != Size && value(i) == y && Traits::adjacent(b, start(i))) {
      stop(i - 1) = stop(i);
      this->erase(i, Size);
      return Size - 1;
    }
    stop(i - 1) = b;
    return Size;
  }

  // Detect overflow.
  if (i == N)
    return N + 1;

  // Add new interval at end.
  if (i == Size) {
    start(i) = a;
    stop(i) = b;
    value(i) = y;
    return Size + 1;
  }

  // Try to coalesce with following interval.
  if (value(i) == y && Traits::adjacent(b, start(i))) {
    start(i) = a;
    return Size;
  }

  // We must insert before i. Detect overflow.
  if (Size == N)
    return N + 1;

  // Insert before i.
  this->shift(i, Size);
  start(i) = a;
  stop(i) = b;
  value(i) = y;
  return Size + 1;
}


//===----------------------------------------------------------------------===//
//---                   IntervalMapImpl::BranchNode                        ---//
//===----------------------------------------------------------------------===//
//
// A branch node stores references to 1--N subtrees all of the same height.
//
// The key array in a branch node holds the rightmost stop key of each subtree.
// It is redundant to store the last stop key since it can be found in the
// parent node, but doing so makes tree balancing a lot simpler.
//
// It is unusual for a branch node to only have one subtree, but it can happen
// in the root node if it is smaller than the normal nodes.
//
// When all of the leaf nodes from all the subtrees are concatenated, they must
// satisfy the same constraints as a single leaf node. They must be sorted,
// sane, and fully coalesced.
//
//===----------------------------------------------------------------------===//

template <typename KeyT, typename ValT, unsigned N, typename Traits>
class BranchNode : public NodeBase<NodeRef, KeyT, N> {
public:
  const KeyT &stop(unsigned i) const { return this->second[i]; }
  const NodeRef &subtree(unsigned i) const { return this->first[i]; }

  KeyT &stop(unsigned i) { return this->second[i]; }
  NodeRef &subtree(unsigned i) { return this->first[i]; }

  /// findFrom - Find the first subtree after i that may contain x.
  /// @param i    Starting index for the search.
  /// @param Size Number of elements in node.
  /// @param x    Key to search for.
  /// @return     First index with !stopLess(key[i], x), or size.
  ///             This is the first subtree that can possibly contain x.
  unsigned findFrom(unsigned i, unsigned Size, KeyT x) const {
    assert(i <= Size && Size <= N && "Bad indices");
    assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
           "Index to findFrom is past the needed point");
    while (i != Size && Traits::stopLess(stop(i), x)) ++i;
    return i;
  }

  /// safeFind - Find a subtree that is known to exist. This is the same as
  /// findFrom except is it assumed that x is in range.
  /// @param i Starting index for the search.
  /// @param x Key to search for.
  /// @return  First index with !stopLess(key[i], x), never size.
  ///          This is the first subtree that can possibly contain x.
  unsigned safeFind(unsigned i, KeyT x) const {
    assert(i < N && "Bad index");
    assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
           "Index is past the needed point");
    while (Traits::stopLess(stop(i), x)) ++i;
    assert(i < N && "Unsafe intervals");
    return i;
  }

  /// safeLookup - Get the subtree containing x, Assuming that x is in range.
  /// @param x Key to search for.
  /// @return  Subtree containing x
  NodeRef safeLookup(KeyT x) const {
    return subtree(safeFind(0, x));
  }

  /// insert - Insert a new (subtree, stop) pair.
  /// @param i    Insert position, following entries will be shifted.
  /// @param Size Number of elements in node.
  /// @param Node Subtree to insert.
  /// @param Stop Last key in subtree.
  void insert(unsigned i, unsigned Size, NodeRef Node, KeyT Stop) {
    assert(Size < N && "branch node overflow");
    assert(i <= Size && "Bad insert position");
    this->shift(i, Size);
    subtree(i) = Node;
    stop(i) = Stop;
  }

#ifndef NDEBUG
  void dump(raw_ostream &OS, unsigned Size) {
    OS << "  N" << this << " [shape=record label=\"" << Size << '/' << N;
    for (unsigned i = 0; i != Size; ++i)
      OS << " | <s" << i << "> " << stop(i);
    OS << "\"];\n";
    for (unsigned i = 0; i != Size; ++i)
      OS << "  N" << this << ":s" << i << " -> N"
         << &subtree(i).template get<BranchNode>() << ";\n";
  }
#endif

};

//===----------------------------------------------------------------------===//
//---                         IntervalMapImpl::Path                        ---//
//===----------------------------------------------------------------------===//
//
// A Path is used by iterators to represent a position in a B+-tree, and the
// path to get there from the root.
//
// The Path class also constains the tree navigation code that doesn't have to
// be templatized.
//
//===----------------------------------------------------------------------===//

class Path {
  /// Entry - Each step in the path is a node pointer and an offset into that
  /// node.
  struct Entry {
    void *node;
    unsigned size;
    unsigned offset;

    Entry(void *Node, unsigned Size, unsigned Offset)
      : node(Node), size(Size), offset(Offset) {}

    Entry(NodeRef Node, unsigned Offset)
      : node(&Node.subtree(0)), size(Node.size()), offset(Offset) {}

    NodeRef &subtree(unsigned i) const {
      return reinterpret_cast<NodeRef*>(node)[i];
    }
  };

  /// path - The path entries, path[0] is the root node, path.back() is a leaf.
  SmallVector<Entry, 4> path;

public:
  // Node accessors.
  template <typename NodeT> NodeT &node(unsigned Level) const {
    return *reinterpret_cast<NodeT*>(path[Level].node);
  }
  unsigned size(unsigned Level) const { return path[Level].size; }
  unsigned offset(unsigned Level) const { return path[Level].offset; }
  unsigned &offset(unsigned Level) { return path[Level].offset; }

  // Leaf accessors.
  template <typename NodeT> NodeT &leaf() const {
    return *reinterpret_cast<NodeT*>(path.back().node);
  }
  unsigned leafSize() const { return path.back().size; }
  unsigned leafOffset() const { return path.back().offset; }
  unsigned &leafOffset() { return path.back().offset; }

  /// valid - Return true if path is at a valid node, not at end().
  bool valid() const {
    return !path.empty() && path.front().offset < path.front().size;
  }

  /// height - Return the height of the tree corresponding to this path.
  /// This matches map->height in a full path.
  unsigned height() const { return path.size() - 1; }

  /// subtree - Get the subtree referenced from Level. When the path is
  /// consistent, node(Level + 1) == subtree(Level).
  /// @param Level 0..height-1. The leaves have no subtrees.
  NodeRef &subtree(unsigned Level) const {
    return path[Level].subtree(path[Level].offset);
  }

  /// reset - Reset cached information about node(Level) from subtree(Level -1).
  /// @param Level 1..height. THe node to update after parent node changed.
  void reset(unsigned Level) {
    path[Level] = Entry(subtree(Level - 1), offset(Level));
  }

  /// push - Add entry to path.
  /// @param Node Node to add, should be subtree(path.size()-1).
  /// @param Offset Offset into Node.
  void push(NodeRef Node, unsigned Offset) {
    path.push_back(Entry(Node, Offset));
  }

  /// pop - Remove the last path entry.
  void pop() {
    path.pop_back();
  }

  /// setSize - Set the size of a node both in the path and in the tree.
  /// @param Level 0..height. Note that setting the root size won't change
  ///              map->rootSize.
  /// @param Size New node size.
  void setSize(unsigned Level, unsigned Size) {
    path[Level].size = Size;
    if (Level)
      subtree(Level - 1).setSize(Size);
  }

  /// setRoot - Clear the path and set a new root node.
  /// @param Node New root node.
  /// @param Size New root size.
  /// @param Offset Offset into root node.
  void setRoot(void *Node, unsigned Size, unsigned Offset) {
    path.clear();
    path.push_back(Entry(Node, Size, Offset));
  }

  /// replaceRoot - Replace the current root node with two new entries after the
  /// tree height has increased.
  /// @param Root The new root node.
  /// @param Size Number of entries in the new root.
  /// @param Offsets Offsets into the root and first branch nodes.
  void replaceRoot(void *Root, unsigned Size, IdxPair Offsets);

  /// getLeftSibling - Get the left sibling node at Level, or a null NodeRef.
  /// @param Level Get the sibling to node(Level).
  /// @return Left sibling, or NodeRef().
  NodeRef getLeftSibling(unsigned Level) const;

  /// moveLeft - Move path to the left sibling at Level. Leave nodes below Level
  /// unaltered.
  /// @param Level Move node(Level).
  void moveLeft(unsigned Level);

  /// fillLeft - Grow path to Height by taking leftmost branches.
  /// @param Height The target height.
  void fillLeft(unsigned Height) {
    while (height() < Height)
      push(subtree(height()), 0);
  }

  /// getLeftSibling - Get the left sibling node at Level, or a null NodeRef.
  /// @param Level Get the sinbling to node(Level).
  /// @return Left sibling, or NodeRef().
  NodeRef getRightSibling(unsigned Level) const;

  /// moveRight - Move path to the left sibling at Level. Leave nodes below
  /// Level unaltered.
  /// @param Level Move node(Level).
  void moveRight(unsigned Level);

  /// atBegin - Return true if path is at begin().
  bool atBegin() const {
    for (unsigned i = 0, e = path.size(); i != e; ++i)
      if (path[i].offset != 0)
        return false;
    return true;
  }

  /// atLastEntry - Return true if the path is at the last entry of the node at
  /// Level.
  /// @param Level Node to examine.
  bool atLastEntry(unsigned Level) const {
    return path[Level].offset == path[Level].size - 1;
  }

  /// legalizeForInsert - Prepare the path for an insertion at Level. When the
  /// path is at end(), node(Level) may not be a legal node. legalizeForInsert
  /// ensures that node(Level) is real by moving back to the last node at Level,
  /// and setting offset(Level) to size(Level) if required.
  /// @param Level The level where an insertion is about to take place.
  void legalizeForInsert(unsigned Level) {
    if (valid())
      return;
    moveLeft(Level);
    ++path[Level].offset;
  }

#ifndef NDEBUG
  void dump() const {
    for (unsigned l = 0, e = path.size(); l != e; ++l)
      errs() << l << ": " << path[l].node << ' ' << path[l].size << ' '
             << path[l].offset << '\n';
  }
#endif
};

} // namespace IntervalMapImpl


//===----------------------------------------------------------------------===//
//---                          IntervalMap                                ----//
//===----------------------------------------------------------------------===//

template <typename KeyT, typename ValT,
          unsigned N = IntervalMapImpl::NodeSizer<KeyT, ValT>::LeafSize,
          typename Traits = IntervalMapInfo<KeyT> >
class IntervalMap {
  typedef IntervalMapImpl::NodeSizer<KeyT, ValT> Sizer;
  typedef IntervalMapImpl::LeafNode<KeyT, ValT, Sizer::LeafSize, Traits> Leaf;
  typedef IntervalMapImpl::BranchNode<KeyT, ValT, Sizer::BranchSize, Traits>
    Branch;
  typedef IntervalMapImpl::LeafNode<KeyT, ValT, N, Traits> RootLeaf;
  typedef IntervalMapImpl::IdxPair IdxPair;

  // The RootLeaf capacity is given as a template parameter. We must compute the
  // corresponding RootBranch capacity.
  enum {
    DesiredRootBranchCap = (sizeof(RootLeaf) - sizeof(KeyT)) /
      (sizeof(KeyT) + sizeof(IntervalMapImpl::NodeRef)),
    RootBranchCap = DesiredRootBranchCap ? DesiredRootBranchCap : 1
  };

  typedef IntervalMapImpl::BranchNode<KeyT, ValT, RootBranchCap, Traits>
    RootBranch;

  // When branched, we store a global start key as well as the branch node.
  struct RootBranchData {
    KeyT start;
    RootBranch node;
  };

  enum {
    RootDataSize = sizeof(RootBranchData) > sizeof(RootLeaf) ?
                   sizeof(RootBranchData) : sizeof(RootLeaf)
  };

public:
  typedef typename Sizer::Allocator Allocator;

private:
  // The root data is either a RootLeaf or a RootBranchData instance.
  // We can't put them in a union since C++03 doesn't allow non-trivial
  // constructors in unions.
  // Instead, we use a char array with pointer alignment. The alignment is
  // ensured by the allocator member in the class, but still verified in the
  // constructor. We don't support keys or values that are more aligned than a
  // pointer.
  char data[RootDataSize];

  // Tree height.
  // 0: Leaves in root.
  // 1: Root points to leaf.
  // 2: root->branch->leaf ...
  unsigned height;

  // Number of entries in the root node.
  unsigned rootSize;

  // Allocator used for creating external nodes.
  Allocator &allocator;

  /// dataAs - Represent data as a node type without breaking aliasing rules.
  template <typename T>
  T &dataAs() const {
    union {
      const char *d;
      T *t;
    } u;
    u.d = data;
    return *u.t;
  }

  const RootLeaf &rootLeaf() const {
    assert(!branched() && "Cannot acces leaf data in branched root");
    return dataAs<RootLeaf>();
  }
  RootLeaf &rootLeaf() {
    assert(!branched() && "Cannot acces leaf data in branched root");
    return dataAs<RootLeaf>();
  }
  RootBranchData &rootBranchData() const {
    assert(branched() && "Cannot access branch data in non-branched root");
    return dataAs<RootBranchData>();
  }
  RootBranchData &rootBranchData() {
    assert(branched() && "Cannot access branch data in non-branched root");
    return dataAs<RootBranchData>();
  }
  const RootBranch &rootBranch() const { return rootBranchData().node; }
  RootBranch &rootBranch()             { return rootBranchData().node; }
  KeyT rootBranchStart() const { return rootBranchData().start; }
  KeyT &rootBranchStart()      { return rootBranchData().start; }

  template <typename NodeT> NodeT *newNode() {
    return new(allocator.template Allocate<NodeT>()) NodeT();
  }

  template <typename NodeT> void deleteNode(NodeT *P) {
    P->~NodeT();
    allocator.Deallocate(P);
  }

  IdxPair branchRoot(unsigned Position);
  IdxPair splitRoot(unsigned Position);

  void switchRootToBranch() {
    rootLeaf().~RootLeaf();
    height = 1;
    new (&rootBranchData()) RootBranchData();
  }

  void switchRootToLeaf() {
    rootBranchData().~RootBranchData();
    height = 0;
    new(&rootLeaf()) RootLeaf();
  }

  bool branched() const { return height > 0; }

  ValT treeSafeLookup(KeyT x, ValT NotFound) const;
  void visitNodes(void (IntervalMap::*f)(IntervalMapImpl::NodeRef,
                  unsigned Level));
  void deleteNode(IntervalMapImpl::NodeRef Node, unsigned Level);

public:
  explicit IntervalMap(Allocator &a) : height(0), rootSize(0), allocator(a) {
    assert((uintptr_t(data) & (alignOf<RootLeaf>() - 1)) == 0 &&
           "Insufficient alignment");
    new(&rootLeaf()) RootLeaf();
  }

  ~IntervalMap() {
    clear();
    rootLeaf().~RootLeaf();
  }

  /// empty -  Return true when no intervals are mapped.
  bool empty() const {
    return rootSize == 0;
  }

  /// start - Return the smallest mapped key in a non-empty map.
  KeyT start() const {
    assert(!empty() && "Empty IntervalMap has no start");
    return !branched() ? rootLeaf().start(0) : rootBranchStart();
  }

  /// stop - Return the largest mapped key in a non-empty map.
  KeyT stop() const {
    assert(!empty() && "Empty IntervalMap has no stop");
    return !branched() ? rootLeaf().stop(rootSize - 1) :
                         rootBranch().stop(rootSize - 1);
  }

  /// lookup - Return the mapped value at x or NotFound.
  ValT lookup(KeyT x, ValT NotFound = ValT()) const {
    if (empty() || Traits::startLess(x, start()) || Traits::stopLess(stop(), x))
      return NotFound;
    return branched() ? treeSafeLookup(x, NotFound) :
                        rootLeaf().safeLookup(x, NotFound);
  }

  /// insert - Add a mapping of [a;b] to y, coalesce with adjacent intervals.
  /// It is assumed that no key in the interval is mapped to another value, but
  /// overlapping intervals already mapped to y will be coalesced.
  void insert(KeyT a, KeyT b, ValT y) {
    if (branched() || rootSize == RootLeaf::Capacity)
      return find(a).insert(a, b, y);

    // Easy insert into root leaf.
    unsigned p = rootLeaf().findFrom(0, rootSize, a);
    rootSize = rootLeaf().insertFrom(p, rootSize, a, b, y);
  }

  /// clear - Remove all entries.
  void clear();

  class const_iterator;
  class iterator;
  friend class const_iterator;
  friend class iterator;

  const_iterator begin() const {
    iterator I(*this);
    I.goToBegin();
    return I;
  }

  iterator begin() {
    iterator I(*this);
    I.goToBegin();
    return I;
  }

  const_iterator end() const {
    iterator I(*this);
    I.goToEnd();
    return I;
  }

  iterator end() {
    iterator I(*this);
    I.goToEnd();
    return I;
  }

  /// find - Return an iterator pointing to the first interval ending at or
  /// after x, or end().
  const_iterator find(KeyT x) const {
    iterator I(*this);
    I.find(x);
    return I;
  }

  iterator find(KeyT x) {
    iterator I(*this);
    I.find(x);
    return I;
  }

#ifndef NDEBUG
  raw_ostream *OS;
  void dump();
  void dumpNode(IntervalMapImpl::NodeRef Node, unsigned Height);
#endif
};

/// treeSafeLookup - Return the mapped value at x or NotFound, assuming a
/// branched root.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
ValT IntervalMap<KeyT, ValT, N, Traits>::
treeSafeLookup(KeyT x, ValT NotFound) const {
  assert(branched() && "treeLookup assumes a branched root");

  IntervalMapImpl::NodeRef NR = rootBranch().safeLookup(x);
  for (unsigned h = height-1; h; --h)
    NR = NR.get<Branch>().safeLookup(x);
  return NR.get<Leaf>().safeLookup(x, NotFound);
}


// branchRoot - Switch from a leaf root to a branched root.
// Return the new (root offset, node offset) corresponding to Position.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
IntervalMapImpl::IdxPair IntervalMap<KeyT, ValT, N, Traits>::
branchRoot(unsigned Position) {
  using namespace IntervalMapImpl;
  // How many external leaf nodes to hold RootLeaf+1?
  const unsigned Nodes = RootLeaf::Capacity / Leaf::Capacity + 1;

  // Compute element distribution among new nodes.
  unsigned size[Nodes];
  IdxPair NewOffset(0, Position);

  // Is is very common for the root node to be smaller than external nodes.
  if (Nodes == 1)
    size[0] = rootSize;
  else
    NewOffset = distribute(Nodes, rootSize, Leaf::Capacity,  NULL, size,
                           Position, true);

  // Allocate new nodes.
  unsigned pos = 0;
  NodeRef node[Nodes];
  for (unsigned n = 0; n != Nodes; ++n) {
    Leaf *L = newNode<Leaf>();
    L->copy(rootLeaf(), pos, 0, size[n]);
    node[n] = NodeRef(L, size[n]);
    pos += size[n];
  }

  // Destroy the old leaf node, construct branch node instead.
  switchRootToBranch();
  for (unsigned n = 0; n != Nodes; ++n) {
    rootBranch().stop(n) = node[n].template get<Leaf>().stop(size[n]-1);
    rootBranch().subtree(n) = node[n];
  }
  rootBranchStart() = node[0].template get<Leaf>().start(0);
  rootSize = Nodes;
  return NewOffset;
}

// splitRoot - Split the current BranchRoot into multiple Branch nodes.
// Return the new (root offset, node offset) corresponding to Position.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
IntervalMapImpl::IdxPair IntervalMap<KeyT, ValT, N, Traits>::
splitRoot(unsigned Position) {
  using namespace IntervalMapImpl;
  // How many external leaf nodes to hold RootBranch+1?
  const unsigned Nodes = RootBranch::Capacity / Branch::Capacity + 1;

  // Compute element distribution among new nodes.
  unsigned Size[Nodes];
  IdxPair NewOffset(0, Position);

  // Is is very common for the root node to be smaller than external nodes.
  if (Nodes == 1)
    Size[0] = rootSize;
  else
    NewOffset = distribute(Nodes, rootSize, Leaf::Capacity,  NULL, Size,
                           Position, true);

  // Allocate new nodes.
  unsigned Pos = 0;
  NodeRef Node[Nodes];
  for (unsigned n = 0; n != Nodes; ++n) {
    Branch *B = newNode<Branch>();
    B->copy(rootBranch(), Pos, 0, Size[n]);
    Node[n] = NodeRef(B, Size[n]);
    Pos += Size[n];
  }

  for (unsigned n = 0; n != Nodes; ++n) {
    rootBranch().stop(n) = Node[n].template get<Branch>().stop(Size[n]-1);
    rootBranch().subtree(n) = Node[n];
  }
  rootSize = Nodes;
  ++height;
  return NewOffset;
}

/// visitNodes - Visit each external node.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
visitNodes(void (IntervalMap::*f)(IntervalMapImpl::NodeRef, unsigned Height)) {
  if (!branched())
    return;
  SmallVector<IntervalMapImpl::NodeRef, 4> Refs, NextRefs;

  // Collect level 0 nodes from the root.
  for (unsigned i = 0; i != rootSize; ++i)
    Refs.push_back(rootBranch().subtree(i));

  // Visit all branch nodes.
  for (unsigned h = height - 1; h; --h) {
    for (unsigned i = 0, e = Refs.size(); i != e; ++i) {
      for (unsigned j = 0, s = Refs[i].size(); j != s; ++j)
        NextRefs.push_back(Refs[i].subtree(j));
      (this->*f)(Refs[i], h);
    }
    Refs.clear();
    Refs.swap(NextRefs);
  }

  // Visit all leaf nodes.
  for (unsigned i = 0, e = Refs.size(); i != e; ++i)
    (this->*f)(Refs[i], 0);
}

template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
deleteNode(IntervalMapImpl::NodeRef Node, unsigned Level) {
  if (Level)
    deleteNode(&Node.get<Branch>());
  else
    deleteNode(&Node.get<Leaf>());
}

template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
clear() {
  if (branched()) {
    visitNodes(&IntervalMap::deleteNode);
    switchRootToLeaf();
  }
  rootSize = 0;
}

#ifndef NDEBUG
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
dumpNode(IntervalMapImpl::NodeRef Node, unsigned Height) {
  if (Height)
    Node.get<Branch>().dump(*OS, Node.size());
  else
    Node.get<Leaf>().dump(*OS, Node.size());
}

template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
dump() {
  std::string errors;
  raw_fd_ostream ofs("tree.dot", errors);
  OS = &ofs;
  ofs << "digraph {\n";
  if (branched())
    rootBranch().dump(ofs, rootSize);
  else
    rootLeaf().dump(ofs, rootSize);
  visitNodes(&IntervalMap::dumpNode);
  ofs << "}\n";
}
#endif

//===----------------------------------------------------------------------===//
//---                   IntervalMap::const_iterator                       ----//
//===----------------------------------------------------------------------===//

template <typename KeyT, typename ValT, unsigned N, typename Traits>
class IntervalMap<KeyT, ValT, N, Traits>::const_iterator :
  public std::iterator<std::bidirectional_iterator_tag, ValT> {
protected:
  friend class IntervalMap;

  // The map referred to.
  IntervalMap *map;

  // We store a full path from the root to the current position.
  // The path may be partially filled, but never between iterator calls.
  IntervalMapImpl::Path path;

  explicit const_iterator(IntervalMap &map) : map(&map) {}

  bool branched() const {
    assert(map && "Invalid iterator");
    return map->branched();
  }

  void setRoot(unsigned Offset) {
    if (branched())
      path.setRoot(&map->rootBranch(), map->rootSize, Offset);
    else
      path.setRoot(&map->rootLeaf(), map->rootSize, Offset);
  }

  void pathFillFind(KeyT x);
  void treeFind(KeyT x);
  void treeAdvanceTo(KeyT x);

  /// unsafeStart - Writable access to start() for iterator.
  KeyT &unsafeStart() const {
    assert(valid() && "Cannot access invalid iterator");
    return branched() ? path.leaf<Leaf>().start(path.leafOffset()) :
                        path.leaf<RootLeaf>().start(path.leafOffset());
  }

  /// unsafeStop - Writable access to stop() for iterator.
  KeyT &unsafeStop() const {
    assert(valid() && "Cannot access invalid iterator");
    return branched() ? path.leaf<Leaf>().stop(path.leafOffset()) :
                        path.leaf<RootLeaf>().stop(path.leafOffset());
  }

  /// unsafeValue - Writable access to value() for iterator.
  ValT &unsafeValue() const {
    assert(valid() && "Cannot access invalid iterator");
    return branched() ? path.leaf<Leaf>().value(path.leafOffset()) :
                        path.leaf<RootLeaf>().value(path.leafOffset());
  }

public:
  /// const_iterator - Create an iterator that isn't pointing anywhere.
  const_iterator() : map(0) {}

  /// valid - Return true if the current position is valid, false for end().
  bool valid() const { return path.valid(); }

  /// start - Return the beginning of the current interval.
  const KeyT &start() const { return unsafeStart(); }

  /// stop - Return the end of the current interval.
  const KeyT &stop() const { return unsafeStop(); }

  /// value - Return the mapped value at the current interval.
  const ValT &value() const { return unsafeValue(); }

  const ValT &operator*() const { return value(); }

  bool operator==(const const_iterator &RHS) const {
    assert(map == RHS.map && "Cannot compare iterators from different maps");
    if (!valid())
      return !RHS.valid();
    if (path.leafOffset() != RHS.path.leafOffset())
      return false;
    return &path.template leaf<Leaf>() == &RHS.path.template leaf<Leaf>();
  }

  bool operator!=(const const_iterator &RHS) const {
    return !operator==(RHS);
  }

  /// goToBegin - Move to the first interval in map.
  void goToBegin() {
    setRoot(0);
    if (branched())
      path.fillLeft(map->height);
  }

  /// goToEnd - Move beyond the last interval in map.
  void goToEnd() {
    setRoot(map->rootSize);
  }

  /// preincrement - move to the next interval.
  const_iterator &operator++() {
    assert(valid() && "Cannot increment end()");
    if (++path.leafOffset() == path.leafSize() && branched())
      path.moveRight(map->height);
    return *this;
  }

  /// postincrement - Dont do that!
  const_iterator operator++(int) {
    const_iterator tmp = *this;
    operator++();
    return tmp;
  }

  /// predecrement - move to the previous interval.
  const_iterator &operator--() {
    if (path.leafOffset() && (valid() || !branched()))
      --path.leafOffset();
    else
      path.moveLeft(map->height);
    return *this;
  }

  /// postdecrement - Dont do that!
  const_iterator operator--(int) {
    const_iterator tmp = *this;
    operator--();
    return tmp;
  }

  /// find - Move to the first interval with stop >= x, or end().
  /// This is a full search from the root, the current position is ignored.
  void find(KeyT x) {
    if (branched())
      treeFind(x);
    else
      setRoot(map->rootLeaf().findFrom(0, map->rootSize, x));
  }

  /// advanceTo - Move to the first interval with stop >= x, or end().
  /// The search is started from the current position, and no earlier positions
  /// can be found. This is much faster than find() for small moves.
  void advanceTo(KeyT x) {
    if (branched())
      treeAdvanceTo(x);
    else
      path.leafOffset() =
        map->rootLeaf().findFrom(path.leafOffset(), map->rootSize, x);
  }

};

/// pathFillFind - Complete path by searching for x.
/// @param x Key to search for.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
const_iterator::pathFillFind(KeyT x) {
  IntervalMapImpl::NodeRef NR = path.subtree(path.height());
  for (unsigned i = map->height - path.height() - 1; i; --i) {
    unsigned p = NR.get<Branch>().safeFind(0, x);
    path.push(NR, p);
    NR = NR.subtree(p);
  }
  path.push(NR, NR.get<Leaf>().safeFind(0, x));
}

/// treeFind - Find in a branched tree.
/// @param x Key to search for.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
const_iterator::treeFind(KeyT x) {
  setRoot(map->rootBranch().findFrom(0, map->rootSize, x));
  if (valid())
    pathFillFind(x);
}

/// treeAdvanceTo - Find position after the current one.
/// @param x Key to search for.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
const_iterator::treeAdvanceTo(KeyT x) {
  // Can we stay on the same leaf node?
  if (!Traits::stopLess(path.leaf<Leaf>().stop(path.leafSize() - 1), x)) {
    path.leafOffset() = path.leaf<Leaf>().safeFind(path.leafOffset(), x);
    return;
  }

  // Drop the current leaf.
  path.pop();

  // Search towards the root for a usable subtree.
  if (path.height()) {
    for (unsigned l = path.height() - 1; l; --l) {
      if (!Traits::stopLess(path.node<Branch>(l).stop(path.offset(l)), x)) {
        // The branch node at l+1 is usable
        path.offset(l + 1) =
          path.node<Branch>(l + 1).safeFind(path.offset(l + 1), x);
        return pathFillFind(x);
      }
      path.pop();
    }
    // Is the level-1 Branch usable?
    if (!Traits::stopLess(map->rootBranch().stop(path.offset(0)), x)) {
      path.offset(1) = path.node<Branch>(1).safeFind(path.offset(1), x);
      return pathFillFind(x);
    }
  }

  // We reached the root.
  setRoot(map->rootBranch().findFrom(path.offset(0), map->rootSize, x));
  if (valid())
    pathFillFind(x);
}

//===----------------------------------------------------------------------===//
//---                       IntervalMap::iterator                         ----//
//===----------------------------------------------------------------------===//

template <typename KeyT, typename ValT, unsigned N, typename Traits>
class IntervalMap<KeyT, ValT, N, Traits>::iterator : public const_iterator {
  friend class IntervalMap;
  typedef IntervalMapImpl::IdxPair IdxPair;

  explicit iterator(IntervalMap &map) : const_iterator(map) {}

  void setNodeStop(unsigned Level, KeyT Stop);
  bool insertNode(unsigned Level, IntervalMapImpl::NodeRef Node, KeyT Stop);
  template <typename NodeT> bool overflow(unsigned Level);
  void treeInsert(KeyT a, KeyT b, ValT y);
  void eraseNode(unsigned Level);
  void treeErase(bool UpdateRoot = true);
  bool canCoalesceLeft(KeyT Start, ValT x);
  bool canCoalesceRight(KeyT Stop, ValT x);

public:
  /// iterator - Create null iterator.
  iterator() {}

  /// setStart - Move the start of the current interval.
  /// This may cause coalescing with the previous interval.
  /// @param a New start key, must not overlap the previous interval.
  void setStart(KeyT a);

  /// setStop - Move the end of the current interval.
  /// This may cause coalescing with the following interval.
  /// @param b New stop key, must not overlap the following interval.
  void setStop(KeyT b);

  /// setValue - Change the mapped value of the current interval.
  /// This may cause coalescing with the previous and following intervals.
  /// @param x New value.
  void setValue(ValT x);

  /// setStartUnchecked - Move the start of the current interval without
  /// checking for coalescing or overlaps.
  /// This should only be used when it is known that coalescing is not required.
  /// @param a New start key.
  void setStartUnchecked(KeyT a) { this->unsafeStart() = a; }

  /// setStopUnchecked - Move the end of the current interval without checking
  /// for coalescing or overlaps.
  /// This should only be used when it is known that coalescing is not required.
  /// @param b New stop key.
  void setStopUnchecked(KeyT b) {
    this->unsafeStop() = b;
    // Update keys in branch nodes as well.
    if (this->path.atLastEntry(this->path.height()))
      setNodeStop(this->path.height(), b);
  }

  /// setValueUnchecked - Change the mapped value of the current interval
  /// without checking for coalescing.
  /// @param x New value.
  void setValueUnchecked(ValT x) { this->unsafeValue() = x; }

  /// insert - Insert mapping [a;b] -> y before the current position.
  void insert(KeyT a, KeyT b, ValT y);

  /// erase - Erase the current interval.
  void erase();

  iterator &operator++() {
    const_iterator::operator++();
    return *this;
  }

  iterator operator++(int) {
    iterator tmp = *this;
    operator++();
    return tmp;
  }

  iterator &operator--() {
    const_iterator::operator--();
    return *this;
  }

  iterator operator--(int) {
    iterator tmp = *this;
    operator--();
    return tmp;
  }

};

/// canCoalesceLeft - Can the current interval coalesce to the left after
/// changing start or value?
/// @param Start New start of current interval.
/// @param Value New value for current interval.
/// @return True when updating the current interval would enable coalescing.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
bool IntervalMap<KeyT, ValT, N, Traits>::
iterator::canCoalesceLeft(KeyT Start, ValT Value) {
  using namespace IntervalMapImpl;
  Path &P = this->path;
  if (!this->branched()) {
    unsigned i = P.leafOffset();
    RootLeaf &Node = P.leaf<RootLeaf>();
    return i && Node.value(i-1) == Value &&
                Traits::adjacent(Node.stop(i-1), Start);
  }
  // Branched.
  if (unsigned i = P.leafOffset()) {
    Leaf &Node = P.leaf<Leaf>();
    return Node.value(i-1) == Value && Traits::adjacent(Node.stop(i-1), Start);
  } else if (NodeRef NR = P.getLeftSibling(P.height())) {
    unsigned i = NR.size() - 1;
    Leaf &Node = NR.get<Leaf>();
    return Node.value(i) == Value && Traits::adjacent(Node.stop(i), Start);
  }
  return false;
}

/// canCoalesceRight - Can the current interval coalesce to the right after
/// changing stop or value?
/// @param Stop New stop of current interval.
/// @param Value New value for current interval.
/// @return True when updating the current interval would enable coalescing.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
bool IntervalMap<KeyT, ValT, N, Traits>::
iterator::canCoalesceRight(KeyT Stop, ValT Value) {
  using namespace IntervalMapImpl;
  Path &P = this->path;
  unsigned i = P.leafOffset() + 1;
  if (!this->branched()) {
    if (i >= P.leafSize())
      return false;
    RootLeaf &Node = P.leaf<RootLeaf>();
    return Node.value(i) == Value && Traits::adjacent(Stop, Node.start(i));
  }
  // Branched.
  if (i < P.leafSize()) {
    Leaf &Node = P.leaf<Leaf>();
    return Node.value(i) == Value && Traits::adjacent(Stop, Node.start(i));
  } else if (NodeRef NR = P.getRightSibling(P.height())) {
    Leaf &Node = NR.get<Leaf>();
    return Node.value(0) == Value && Traits::adjacent(Stop, Node.start(0));
  }
  return false;
}

/// setNodeStop - Update the stop key of the current node at level and above.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::setNodeStop(unsigned Level, KeyT Stop) {
  // There are no references to the root node, so nothing to update.
  if (!Level)
    return;
  IntervalMapImpl::Path &P = this->path;
  // Update nodes pointing to the current node.
  while (--Level) {
    P.node<Branch>(Level).stop(P.offset(Level)) = Stop;
    if (!P.atLastEntry(Level))
      return;
  }
  // Update root separately since it has a different layout.
  P.node<RootBranch>(Level).stop(P.offset(Level)) = Stop;
}

template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::setStart(KeyT a) {
  assert(Traits::stopLess(a, this->stop()) && "Cannot move start beyond stop");
  KeyT &CurStart = this->unsafeStart();
  if (!Traits::startLess(a, CurStart) || !canCoalesceLeft(a, this->value())) {
    CurStart = a;
    return;
  }
  // Coalesce with the interval to the left.
  --*this;
  a = this->start();
  erase();
  setStartUnchecked(a);
}

template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::setStop(KeyT b) {
  assert(Traits::stopLess(this->start(), b) && "Cannot move stop beyond start");
  if (Traits::startLess(b, this->stop()) ||
      !canCoalesceRight(b, this->value())) {
    setStopUnchecked(b);
    return;
  }
  // Coalesce with interval to the right.
  KeyT a = this->start();
  erase();
  setStartUnchecked(a);
}

template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::setValue(ValT x) {
  setValueUnchecked(x);
  if (canCoalesceRight(this->stop(), x)) {
    KeyT a = this->start();
    erase();
    setStartUnchecked(a);
  }
  if (canCoalesceLeft(this->start(), x)) {
    --*this;
    KeyT a = this->start();
    erase();
    setStartUnchecked(a);
  }
}

/// insertNode - insert a node before the current path at level.
/// Leave the current path pointing at the new node.
/// @param Level path index of the node to be inserted.
/// @param Node The node to be inserted.
/// @param Stop The last index in the new node.
/// @return True if the tree height was increased.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
bool IntervalMap<KeyT, ValT, N, Traits>::
iterator::insertNode(unsigned Level, IntervalMapImpl::NodeRef Node, KeyT Stop) {
  assert(Level && "Cannot insert next to the root");
  bool SplitRoot = false;
  IntervalMap &IM = *this->map;
  IntervalMapImpl::Path &P = this->path;

  if (Level == 1) {
    // Insert into the root branch node.
    if (IM.rootSize < RootBranch::Capacity) {
      IM.rootBranch().insert(P.offset(0), IM.rootSize, Node, Stop);
      P.setSize(0, ++IM.rootSize);
      P.reset(Level);
      return SplitRoot;
    }

    // We need to split the root while keeping our position.
    SplitRoot = true;
    IdxPair Offset = IM.splitRoot(P.offset(0));
    P.replaceRoot(&IM.rootBranch(), IM.rootSize, Offset);

    // Fall through to insert at the new higher level.
    ++Level;
  }

  // When inserting before end(), make sure we have a valid path.
  P.legalizeForInsert(--Level);

  // Insert into the branch node at Level-1.
  if (P.size(Level) == Branch::Capacity) {
    // Branch node is full, handle handle the overflow.
    assert(!SplitRoot && "Cannot overflow after splitting the root");
    SplitRoot = overflow<Branch>(Level);
    Level += SplitRoot;
  }
  P.node<Branch>(Level).insert(P.offset(Level), P.size(Level), Node, Stop);
  P.setSize(Level, P.size(Level) + 1);
  if (P.atLastEntry(Level))
    setNodeStop(Level, Stop);
  P.reset(Level + 1);
  return SplitRoot;
}

// insert
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::insert(KeyT a, KeyT b, ValT y) {
  if (this->branched())
    return treeInsert(a, b, y);
  IntervalMap &IM = *this->map;
  IntervalMapImpl::Path &P = this->path;

  // Try simple root leaf insert.
  unsigned Size = IM.rootLeaf().insertFrom(P.leafOffset(), IM.rootSize, a, b, y);

  // Was the root node insert successful?
  if (Size <= RootLeaf::Capacity) {
    P.setSize(0, IM.rootSize = Size);
    return;
  }

  // Root leaf node is full, we must branch.
  IdxPair Offset = IM.branchRoot(P.leafOffset());
  P.replaceRoot(&IM.rootBranch(), IM.rootSize, Offset);

  // Now it fits in the new leaf.
  treeInsert(a, b, y);
}


template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::treeInsert(KeyT a, KeyT b, ValT y) {
  using namespace IntervalMapImpl;
  Path &P = this->path;

  if (!P.valid())
    P.legalizeForInsert(this->map->height);

  // Check if this insertion will extend the node to the left.
  if (P.leafOffset() == 0 && Traits::startLess(a, P.leaf<Leaf>().start(0))) {
    // Node is growing to the left, will it affect a left sibling node?
    if (NodeRef Sib = P.getLeftSibling(P.height())) {
      Leaf &SibLeaf = Sib.get<Leaf>();
      unsigned SibOfs = Sib.size() - 1;
      if (SibLeaf.value(SibOfs) == y &&
          Traits::adjacent(SibLeaf.stop(SibOfs), a)) {
        // This insertion will coalesce with the last entry in SibLeaf. We can
        // handle it in two ways:
        //  1. Extend SibLeaf.stop to b and be done, or
        //  2. Extend a to SibLeaf, erase the SibLeaf entry and continue.
        // We prefer 1., but need 2 when coalescing to the right as well.
        Leaf &CurLeaf = P.leaf<Leaf>();
        P.moveLeft(P.height());
        if (Traits::stopLess(b, CurLeaf.start(0)) &&
            (y != CurLeaf.value(0) || !Traits::adjacent(b, CurLeaf.start(0)))) {
          // Easy, just extend SibLeaf and we're done.
          setNodeStop(P.height(), SibLeaf.stop(SibOfs) = b);
          return;
        } else {
          // We have both left and right coalescing. Erase the old SibLeaf entry
          // and continue inserting the larger interval.
          a = SibLeaf.start(SibOfs);
          treeErase(/* UpdateRoot= */false);
        }
      }
    } else {
      // No left sibling means we are at begin(). Update cached bound.
      this->map->rootBranchStart() = a;
    }
  }

  // When we are inserting at the end of a leaf node, we must update stops.
  unsigned Size = P.leafSize();
  bool Grow = P.leafOffset() == Size;
  Size = P.leaf<Leaf>().insertFrom(P.leafOffset(), Size, a, b, y);

  // Leaf insertion unsuccessful? Overflow and try again.
  if (Size > Leaf::Capacity) {
    overflow<Leaf>(P.height());
    Grow = P.leafOffset() == P.leafSize();
    Size = P.leaf<Leaf>().insertFrom(P.leafOffset(), P.leafSize(), a, b, y);
    assert(Size <= Leaf::Capacity && "overflow() didn't make room");
  }

  // Inserted, update offset and leaf size.
  P.setSize(P.height(), Size);

  // Insert was the last node entry, update stops.
  if (Grow)
    setNodeStop(P.height(), b);
}

/// erase - erase the current interval and move to the next position.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::erase() {
  IntervalMap &IM = *this->map;
  IntervalMapImpl::Path &P = this->path;
  assert(P.valid() && "Cannot erase end()");
  if (this->branched())
    return treeErase();
  IM.rootLeaf().erase(P.leafOffset(), IM.rootSize);
  P.setSize(0, --IM.rootSize);
}

/// treeErase - erase() for a branched tree.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::treeErase(bool UpdateRoot) {
  IntervalMap &IM = *this->map;
  IntervalMapImpl::Path &P = this->path;
  Leaf &Node = P.leaf<Leaf>();

  // Nodes are not allowed to become empty.
  if (P.leafSize() == 1) {
    IM.deleteNode(&Node);
    eraseNode(IM.height);
    // Update rootBranchStart if we erased begin().
    if (UpdateRoot && IM.branched() && P.valid() && P.atBegin())
      IM.rootBranchStart() = P.leaf<Leaf>().start(0);
    return;
  }

  // Erase current entry.
  Node.erase(P.leafOffset(), P.leafSize());
  unsigned NewSize = P.leafSize() - 1;
  P.setSize(IM.height, NewSize);
  // When we erase the last entry, update stop and move to a legal position.
  if (P.leafOffset() == NewSize) {
    setNodeStop(IM.height, Node.stop(NewSize - 1));
    P.moveRight(IM.height);
  } else if (UpdateRoot && P.atBegin())
    IM.rootBranchStart() = P.leaf<Leaf>().start(0);
}

/// eraseNode - Erase the current node at Level from its parent and move path to
/// the first entry of the next sibling node.
/// The node must be deallocated by the caller.
/// @param Level 1..height, the root node cannot be erased.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
void IntervalMap<KeyT, ValT, N, Traits>::
iterator::eraseNode(unsigned Level) {
  assert(Level && "Cannot erase root node");
  IntervalMap &IM = *this->map;
  IntervalMapImpl::Path &P = this->path;

  if (--Level == 0) {
    IM.rootBranch().erase(P.offset(0), IM.rootSize);
    P.setSize(0, --IM.rootSize);
    // If this cleared the root, switch to height=0.
    if (IM.empty()) {
      IM.switchRootToLeaf();
      this->setRoot(0);
      return;
    }
  } else {
    // Remove node ref from branch node at Level.
    Branch &Parent = P.node<Branch>(Level);
    if (P.size(Level) == 1) {
      // Branch node became empty, remove it recursively.
      IM.deleteNode(&Parent);
      eraseNode(Level);
    } else {
      // Branch node won't become empty.
      Parent.erase(P.offset(Level), P.size(Level));
      unsigned NewSize = P.size(Level) - 1;
      P.setSize(Level, NewSize);
      // If we removed the last branch, update stop and move to a legal pos.
      if (P.offset(Level) == NewSize) {
        setNodeStop(Level, Parent.stop(NewSize - 1));
        P.moveRight(Level);
      }
    }
  }
  // Update path cache for the new right sibling position.
  if (P.valid()) {
    P.reset(Level + 1);
    P.offset(Level + 1) = 0;
  }
}

/// overflow - Distribute entries of the current node evenly among
/// its siblings and ensure that the current node is not full.
/// This may require allocating a new node.
/// @param NodeT The type of node at Level (Leaf or Branch).
/// @param Level path index of the overflowing node.
/// @return True when the tree height was changed.
template <typename KeyT, typename ValT, unsigned N, typename Traits>
template <typename NodeT>
bool IntervalMap<KeyT, ValT, N, Traits>::
iterator::overflow(unsigned Level) {
  using namespace IntervalMapImpl;
  Path &P = this->path;
  unsigned CurSize[4];
  NodeT *Node[4];
  unsigned Nodes = 0;
  unsigned Elements = 0;
  unsigned Offset = P.offset(Level);

  // Do we have a left sibling?
  NodeRef LeftSib = P.getLeftSibling(Level);
  if (LeftSib) {
    Offset += Elements = CurSize[Nodes] = LeftSib.size();
    Node[Nodes++] = &LeftSib.get<NodeT>();
  }

  // Current node.
  Elements += CurSize[Nodes] = P.size(Level);
  Node[Nodes++] = &P.node<NodeT>(Level);

  // Do we have a right sibling?
  NodeRef RightSib = P.getRightSibling(Level);
  if (RightSib) {
    Elements += CurSize[Nodes] = RightSib.size();
    Node[Nodes++] = &RightSib.get<NodeT>();
  }

  // Do we need to allocate a new node?
  unsigned NewNode = 0;
  if (Elements + 1 > Nodes * NodeT::Capacity) {
    // Insert NewNode at the penultimate position, or after a single node.
    NewNode = Nodes == 1 ? 1 : Nodes - 1;
    CurSize[Nodes] = CurSize[NewNode];
    Node[Nodes] = Node[NewNode];
    CurSize[NewNode] = 0;
    Node[NewNode] = this->map->newNode<NodeT>();
    ++Nodes;
  }

  // Compute the new element distribution.
  unsigned NewSize[4];
  IdxPair NewOffset = distribute(Nodes, Elements, NodeT::Capacity,
                                 CurSize, NewSize, Offset, true);
  adjustSiblingSizes(Node, Nodes, CurSize, NewSize);

  // Move current location to the leftmost node.
  if (LeftSib)
    P.moveLeft(Level);

  // Elements have been rearranged, now update node sizes and stops.
  bool SplitRoot = false;
  unsigned Pos = 0;
  for (;;) {
    KeyT Stop = Node[Pos]->stop(NewSize[Pos]-1);
    if (NewNode && Pos == NewNode) {
      SplitRoot = insertNode(Level, NodeRef(Node[Pos], NewSize[Pos]), Stop);
      Level += SplitRoot;
    } else {
      P.setSize(Level, NewSize[Pos]);
      setNodeStop(Level, Stop);
    }
    if (Pos + 1 == Nodes)
      break;
    P.moveRight(Level);
    ++Pos;
  }

  // Where was I? Find NewOffset.
  while(Pos != NewOffset.first) {
    P.moveLeft(Level);
    --Pos;
  }
  P.offset(Level) = NewOffset.second;
  return SplitRoot;
}

} // namespace llvm

#endif