summaryrefslogtreecommitdiff
path: root/lib/gl_anyrbtree_list2.h
blob: a90d16e948aba3feb1ce20aa7c18a65d08bdadf4 (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
/* Sequential list data type implemented by a binary tree.
   Copyright (C) 2006-2007, 2009-2017 Free Software Foundation, Inc.
   Written by Bruno Haible <bruno@clisp.org>, 2006.

   This program is free software: you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 3 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program.  If not, see <http://www.gnu.org/licenses/>.  */

/* Common code of gl_rbtree_list.c and gl_rbtreehash_list.c.  */

/* -------------------------- gl_list_t Data Type -------------------------- */

/* Create a subtree for count >= 1 elements.
   Its black-height bh is passed as argument, with
   2^bh - 1 <= count <= 2^(bh+1) - 1.  bh == 0 implies count == 1.
   Its height is h where 2^(h-1) <= count <= 2^h - 1.
   Return NULL upon out-of-memory.  */
static gl_list_node_t
create_subtree_with_contents (unsigned int bh,
                              size_t count, const void **contents)
{
  size_t half1 = (count - 1) / 2;
  size_t half2 = count / 2;
  /* Note: half1 + half2 = count - 1.  */
  gl_list_node_t node =
    (struct gl_list_node_impl *) malloc (sizeof (struct gl_list_node_impl));
  if (node == NULL)
    return NULL;

  if (half1 > 0)
    {
      /* half1 > 0 implies count > 1, implies bh >= 1, implies
           2^(bh-1) - 1 <= half1 <= 2^bh - 1.  */
      node->left =
        create_subtree_with_contents (bh - 1, half1, contents);
      if (node->left == NULL)
        goto fail1;
      node->left->parent = node;
    }
  else
    node->left = NULL;

  node->value = contents[half1];

  if (half2 > 0)
    {
      /* half2 > 0 implies count > 1, implies bh >= 1, implies
           2^(bh-1) - 1 <= half2 <= 2^bh - 1.  */
      node->right =
       create_subtree_with_contents (bh - 1, half2, contents + half1 + 1);
      if (node->right == NULL)
        goto fail2;
      node->right->parent = node;
    }
  else
    node->right = NULL;

  node->color = (bh == 0 ? RED : BLACK);

  node->branch_size = count;

  return node;

 fail2:
  if (node->left != NULL)
    free_subtree (node->left);
 fail1:
  free (node);
  return NULL;
}

static gl_list_t
gl_tree_nx_create (gl_list_implementation_t implementation,
                   gl_listelement_equals_fn equals_fn,
                   gl_listelement_hashcode_fn hashcode_fn,
                   gl_listelement_dispose_fn dispose_fn,
                   bool allow_duplicates,
                   size_t count, const void **contents)
{
  struct gl_list_impl *list =
    (struct gl_list_impl *) malloc (sizeof (struct gl_list_impl));

  if (list == NULL)
    return NULL;

  list->base.vtable = implementation;
  list->base.equals_fn = equals_fn;
  list->base.hashcode_fn = hashcode_fn;
  list->base.dispose_fn = dispose_fn;
  list->base.allow_duplicates = allow_duplicates;
#if WITH_HASHTABLE
  {
    size_t estimate = xsum (count, count / 2); /* 1.5 * count */
    if (estimate < 10)
      estimate = 10;
    list->table_size = next_prime (estimate);
    if (size_overflow_p (xtimes (list->table_size, sizeof (gl_hash_entry_t))))
      goto fail1;
    list->table =
      (gl_hash_entry_t *) calloc (list->table_size, sizeof (gl_hash_entry_t));
    if (list->table == NULL)
      goto fail1;
  }
#endif
  if (count > 0)
    {
      /* Assuming 2^bh - 1 <= count <= 2^(bh+1) - 2, we create a tree whose
         upper bh levels are black, and only the partially present lowest
         level is red.  */
      unsigned int bh;
      {
        size_t n;
        for (n = count + 1, bh = 0; n > 1; n = n >> 1)
          bh++;
      }

      list->root = create_subtree_with_contents (bh, count, contents);
      if (list->root == NULL)
        goto fail2;
      list->root->parent = NULL;

#if WITH_HASHTABLE
      /* Now that the tree is built, node_position() works.  Now we can
         add the nodes to the hash table.  */
      if (add_nodes_to_buckets (list) < 0)
        goto fail3;
#endif
    }
  else
    list->root = NULL;

  return list;

#if WITH_HASHTABLE
 fail3:
  free_subtree (list->root);
#endif
 fail2:
#if WITH_HASHTABLE
  free (list->table);
 fail1:
#endif
  free (list);
  return NULL;
}

/* Rotate left a subtree.

                         B                         D
                       /   \                     /   \
                     A       D       -->       B       E
                            / \               / \
                           C   E             A   C

   Change the tree structure, update the branch sizes.
   The caller must update the colors and register D as child of its parent.  */
static gl_list_node_t
rotate_left (gl_list_node_t b_node, gl_list_node_t d_node)
{
  gl_list_node_t a_node = b_node->left;
  gl_list_node_t c_node = d_node->left;
  gl_list_node_t e_node = d_node->right;

  b_node->right = c_node;
  d_node->left = b_node;

  d_node->parent = b_node->parent;
  b_node->parent = d_node;
  if (c_node != NULL)
    c_node->parent = b_node;

  b_node->branch_size =
    (a_node != NULL ? a_node->branch_size : 0)
    + 1 + (c_node != NULL ? c_node->branch_size : 0);
  d_node->branch_size =
    b_node->branch_size + 1 + (e_node != NULL ? e_node->branch_size : 0);

  return d_node;
}

/* Rotate right a subtree.

                           D                     B
                         /   \                 /   \
                       B       E     -->     A       D
                      / \                           / \
                     A   C                         C   E

   Change the tree structure, update the branch sizes.
   The caller must update the colors and register B as child of its parent.  */
static gl_list_node_t
rotate_right (gl_list_node_t b_node, gl_list_node_t d_node)
{
  gl_list_node_t a_node = b_node->left;
  gl_list_node_t c_node = b_node->right;
  gl_list_node_t e_node = d_node->right;

  d_node->left = c_node;
  b_node->right = d_node;

  b_node->parent = d_node->parent;
  d_node->parent = b_node;
  if (c_node != NULL)
    c_node->parent = d_node;

  d_node->branch_size =
    (c_node != NULL ? c_node->branch_size : 0)
    + 1 + (e_node != NULL ? e_node->branch_size : 0);
  b_node->branch_size =
    (a_node != NULL ? a_node->branch_size : 0) + 1 + d_node->branch_size;

  return b_node;
}

/* Ensure the tree is balanced, after an insertion operation.
   Also assigns node->color.
   parent is the given node's parent, known to be non-NULL.  */
static void
rebalance_after_add (gl_list_t list, gl_list_node_t node, gl_list_node_t parent)
{
  for (;;)
    {
      /* At this point, parent = node->parent != NULL.
         Think of node->color being RED (although node->color is not yet
         assigned.)  */
      gl_list_node_t grandparent;
      gl_list_node_t uncle;

      if (parent->color == BLACK)
        {
          /* A RED color for node is acceptable.  */
          node->color = RED;
          return;
        }

      grandparent = parent->parent;
      /* Since parent is RED, we know that
         grandparent is != NULL and colored BLACK.  */

      if (grandparent->left == parent)
        uncle = grandparent->right;
      else if (grandparent->right == parent)
        uncle = grandparent->left;
      else
        abort ();

      if (uncle != NULL && uncle->color == RED)
        {
          /* Change grandparent from BLACK to RED, and
             change parent and uncle from RED to BLACK.
             This makes it acceptable for node to be RED.  */
          node->color = RED;
          parent->color = uncle->color = BLACK;
          node = grandparent;
        }
      else
        {
          /* grandparent and uncle are BLACK.  parent is RED.  node wants
             to be RED too.
             In this case, recoloring is not sufficient.  Need to perform
             one or two rotations.  */
          gl_list_node_t *grandparentp;

          if (grandparent->parent == NULL)
            grandparentp = &list->root;
          else if (grandparent->parent->left == grandparent)
            grandparentp = &grandparent->parent->left;
          else if (grandparent->parent->right == grandparent)
            grandparentp = &grandparent->parent->right;
          else
            abort ();

          if (grandparent->left == parent)
            {
              if (parent->right == node)
                {
                  /* Rotation between node and parent.  */
                  grandparent->left = rotate_left (parent, node);
                  node = parent;
                  parent = grandparent->left;
                }
              /* grandparent and uncle are BLACK.  parent and node want to be
                 RED.  parent = grandparent->left.  node = parent->left.

                      grandparent              parent
                         bh+1                   bh+1
                         /   \                 /   \
                     parent  uncle    -->   node  grandparent
                      bh      bh             bh      bh
                      / \                           / \
                   node  C                         C  uncle
                    bh   bh                       bh    bh
               */
              *grandparentp = rotate_right (parent, grandparent);
              parent->color = BLACK;
              node->color = grandparent->color = RED;
            }
          else /* grandparent->right == parent */
            {
              if (parent->left == node)
                {
                  /* Rotation between node and parent.  */
                  grandparent->right = rotate_right (node, parent);
                  node = parent;
                  parent = grandparent->right;
                }
              /* grandparent and uncle are BLACK.  parent and node want to be
                 RED.  parent = grandparent->right.  node = parent->right.

                    grandparent                    parent
                       bh+1                         bh+1
                       /   \                       /   \
                   uncle  parent     -->   grandparent  node
                     bh     bh                  bh       bh
                            / \                 / \
                           C  node          uncle  C
                          bh   bh            bh    bh
               */
              *grandparentp = rotate_left (grandparent, parent);
              parent->color = BLACK;
              node->color = grandparent->color = RED;
            }
          return;
        }

      /* Start again with a new (node, parent) pair.  */
      parent = node->parent;

      if (parent == NULL)
        {
          /* Change node's color from RED to BLACK.  This increases the
             tree's black-height.  */
          node->color = BLACK;
          return;
        }
    }
}

/* Ensure the tree is balanced, after a deletion operation.
   CHILD was a grandchild of PARENT and is now its child.  Between them,
   a black node was removed.  CHILD is also black, or NULL.
   (CHILD can also be NULL.  But PARENT is non-NULL.)  */
static void
rebalance_after_remove (gl_list_t list, gl_list_node_t child, gl_list_node_t parent)
{
  for (;;)
    {
      /* At this point, we reduced the black-height of the CHILD subtree by 1.
         To make up, either look for a possibility to turn a RED to a BLACK
         node, or try to reduce the black-height tree of CHILD's sibling
         subtree as well.  */
      gl_list_node_t *parentp;

      if (parent->parent == NULL)
        parentp = &list->root;
      else if (parent->parent->left == parent)
        parentp = &parent->parent->left;
      else if (parent->parent->right == parent)
        parentp = &parent->parent->right;
      else
        abort ();

      if (parent->left == child)
        {
          gl_list_node_t sibling = parent->right;
          /* sibling's black-height is >= 1.  In particular,
             sibling != NULL.

                      parent
                       /   \
                   child  sibling
                     bh    bh+1
           */

          if (sibling->color == RED)
            {
              /* sibling is RED, hence parent is BLACK and sibling's children
                 are non-NULL and BLACK.

                      parent                       sibling
                       bh+2                         bh+2
                       /   \                        /   \
                   child  sibling     -->       parent    SR
                     bh    bh+1                  bh+1    bh+1
                            / \                  / \
                          SL   SR            child  SL
                         bh+1 bh+1             bh  bh+1
               */
              *parentp = rotate_left (parent, sibling);
              parent->color = RED;
              sibling->color = BLACK;

              /* Concentrate on the subtree of parent.  The new sibling is
                 one of the old sibling's children, and known to be BLACK.  */
              parentp = &sibling->left;
              sibling = parent->right;
            }
          /* Now we know that sibling is BLACK.

                      parent
                       /   \
                   child  sibling
                     bh    bh+1
           */
          if (sibling->right != NULL && sibling->right->color == RED)
            {
              /*
                      parent                     sibling
                     bh+1|bh+2                  bh+1|bh+2
                       /   \                      /   \
                   child  sibling    -->      parent    SR
                     bh    bh+1                bh+1    bh+1
                            / \                / \
                          SL   SR           child  SL
                          bh   bh             bh   bh
               */
              *parentp = rotate_left (parent, sibling);
              sibling->color = parent->color;
              parent->color = BLACK;
              sibling->right->color = BLACK;
              return;
            }
          else if (sibling->left != NULL && sibling->left->color == RED)
            {
              /*
                      parent                   parent
                     bh+1|bh+2                bh+1|bh+2
                       /   \                    /   \
                   child  sibling    -->    child    SL
                     bh    bh+1               bh    bh+1
                            / \                     /  \
                          SL   SR                 SLL  sibling
                          bh   bh                 bh     bh
                         /  \                           /   \
                       SLL  SLR                       SLR    SR
                       bh    bh                       bh     bh

                 where SLL, SLR, SR are all black.
               */
              parent->right = rotate_right (sibling->left, sibling);
              /* Change sibling from BLACK to RED and SL from RED to BLACK.  */
              sibling->color = RED;
              sibling = parent->right;
              sibling->color = BLACK;

              /* Now do as in the previous case.  */
              *parentp = rotate_left (parent, sibling);
              sibling->color = parent->color;
              parent->color = BLACK;
              sibling->right->color = BLACK;
              return;
            }
          else
            {
              if (parent->color == BLACK)
                {
                  /* Change sibling from BLACK to RED.  Then the entire
                     subtree at parent has decreased its black-height.
                              parent                   parent
                               bh+2                     bh+1
                               /   \                    /   \
                           child  sibling    -->    child  sibling
                             bh    bh+1               bh     bh
                   */
                  sibling->color = RED;

                  child = parent;
                }
              else
                {
                  /* Change parent from RED to BLACK, but compensate by
                     changing sibling from BLACK to RED.
                              parent                   parent
                               bh+1                     bh+1
                               /   \                    /   \
                           child  sibling    -->    child  sibling
                             bh    bh+1               bh     bh
                   */
                  parent->color = BLACK;
                  sibling->color = RED;
                  return;
                }
            }
        }
      else if (parent->right == child)
        {
          gl_list_node_t sibling = parent->left;
          /* sibling's black-height is >= 1.  In particular,
             sibling != NULL.

                      parent
                       /   \
                  sibling  child
                    bh+1     bh
           */

          if (sibling->color == RED)
            {
              /* sibling is RED, hence parent is BLACK and sibling's children
                 are non-NULL and BLACK.

                      parent                 sibling
                       bh+2                    bh+2
                       /   \                  /   \
                  sibling  child    -->     SR    parent
                    bh+1     ch            bh+1    bh+1
                    / \                            / \
                  SL   SR                        SL  child
                 bh+1 bh+1                      bh+1   bh
               */
              *parentp = rotate_right (sibling, parent);
              parent->color = RED;
              sibling->color = BLACK;

              /* Concentrate on the subtree of parent.  The new sibling is
                 one of the old sibling's children, and known to be BLACK.  */
              parentp = &sibling->right;
              sibling = parent->left;
            }
          /* Now we know that sibling is BLACK.

                      parent
                       /   \
                  sibling  child
                    bh+1     bh
           */
          if (sibling->left != NULL && sibling->left->color == RED)
            {
              /*
                       parent                 sibling
                      bh+1|bh+2              bh+1|bh+2
                        /   \                  /   \
                   sibling  child    -->     SL   parent
                     bh+1     bh            bh+1   bh+1
                     / \                           / \
                   SL   SR                       SR  child
                   bh   bh                       bh    bh
               */
              *parentp = rotate_right (sibling, parent);
              sibling->color = parent->color;
              parent->color = BLACK;
              sibling->left->color = BLACK;
              return;
            }
          else if (sibling->right != NULL && sibling->right->color == RED)
            {
              /*
                      parent                       parent
                     bh+1|bh+2                    bh+1|bh+2
                       /   \                        /   \
                   sibling  child    -->          SR    child
                    bh+1      bh                 bh+1     bh
                     / \                         /  \
                   SL   SR                  sibling  SRR
                   bh   bh                    bh      bh
                       /  \                  /   \
                     SRL  SRR               SL   SRL
                     bh    bh               bh    bh

                 where SL, SRL, SRR are all black.
               */
              parent->left = rotate_left (sibling, sibling->right);
              /* Change sibling from BLACK to RED and SL from RED to BLACK.  */
              sibling->color = RED;
              sibling = parent->left;
              sibling->color = BLACK;

              /* Now do as in the previous case.  */
              *parentp = rotate_right (sibling, parent);
              sibling->color = parent->color;
              parent->color = BLACK;
              sibling->left->color = BLACK;
              return;
            }
          else
            {
              if (parent->color == BLACK)
                {
                  /* Change sibling from BLACK to RED.  Then the entire
                     subtree at parent has decreased its black-height.
                              parent                   parent
                               bh+2                     bh+1
                               /   \                    /   \
                           sibling  child    -->    sibling  child
                            bh+1      bh              bh       bh
                   */
                  sibling->color = RED;

                  child = parent;
                }
              else
                {
                  /* Change parent from RED to BLACK, but compensate by
                     changing sibling from BLACK to RED.
                              parent                   parent
                               bh+1                     bh+1
                               /   \                    /   \
                           sibling  child    -->    sibling  child
                            bh+1      bh              bh       bh
                   */
                  parent->color = BLACK;
                  sibling->color = RED;
                  return;
                }
            }
        }
      else
        abort ();

      /* Start again with a new (child, parent) pair.  */
      parent = child->parent;

#if 0 /* Already handled.  */
      if (child != NULL && child->color == RED)
        {
          child->color = BLACK;
          return;
        }
#endif

      if (parent == NULL)
        return;
    }
}

static void
gl_tree_remove_node_from_tree (gl_list_t list, gl_list_node_t node)
{
  gl_list_node_t parent = node->parent;

  if (node->left == NULL)
    {
      /* Replace node with node->right.  */
      gl_list_node_t child = node->right;

      if (child != NULL)
        {
          child->parent = parent;
          /* Since node->left == NULL, child must be RED and of height 1,
             hence node must have been BLACK.  Recolor the child.  */
          child->color = BLACK;
        }
      if (parent == NULL)
        list->root = child;
      else
        {
          if (parent->left == node)
            parent->left = child;
          else /* parent->right == node */
            parent->right = child;

          /* Update branch_size fields of the parent nodes.  */
          {
            gl_list_node_t p;

            for (p = parent; p != NULL; p = p->parent)
              p->branch_size--;
          }

          if (child == NULL && node->color == BLACK)
            rebalance_after_remove (list, child, parent);
        }
    }
  else if (node->right == NULL)
    {
      /* It is not absolutely necessary to treat this case.  But the more
         general case below is more complicated, hence slower.  */
      /* Replace node with node->left.  */
      gl_list_node_t child = node->left;

      child->parent = parent;
      /* Since node->right == NULL, child must be RED and of height 1,
         hence node must have been BLACK.  Recolor the child.  */
      child->color = BLACK;
      if (parent == NULL)
        list->root = child;
      else
        {
          if (parent->left == node)
            parent->left = child;
          else /* parent->right == node */
            parent->right = child;

          /* Update branch_size fields of the parent nodes.  */
          {
            gl_list_node_t p;

            for (p = parent; p != NULL; p = p->parent)
              p->branch_size--;
          }
        }
    }
  else
    {
      /* Replace node with the rightmost element of the node->left subtree.  */
      gl_list_node_t subst;
      gl_list_node_t subst_parent;
      gl_list_node_t child;
      color_t removed_color;

      for (subst = node->left; subst->right != NULL; )
        subst = subst->right;

      subst_parent = subst->parent;

      child = subst->left;

      removed_color = subst->color;

      /* The case subst_parent == node is special:  If we do nothing special,
         we get confusion about node->left, subst->left and child->parent.
           subst_parent == node
           <==> The 'for' loop above terminated immediately.
           <==> subst == subst_parent->left
                [otherwise subst == subst_parent->right]
         In this case, we would need to first set
           child->parent = node; node->left = child;
         and later - when we copy subst into node's position - again
           child->parent = subst; subst->left = child;
         Altogether a no-op.  */
      if (subst_parent != node)
        {
          if (child != NULL)
            child->parent = subst_parent;
          subst_parent->right = child;
        }

      /* Update branch_size fields of the parent nodes.  */
      {
        gl_list_node_t p;

        for (p = subst_parent; p != NULL; p = p->parent)
          p->branch_size--;
      }

      /* Copy subst into node's position.
         (This is safer than to copy subst's value into node, keep node in
         place, and free subst.)  */
      if (subst_parent != node)
        {
          subst->left = node->left;
          subst->left->parent = subst;
        }
      subst->right = node->right;
      subst->right->parent = subst;
      subst->color = node->color;
      subst->branch_size = node->branch_size;
      subst->parent = parent;
      if (parent == NULL)
        list->root = subst;
      else if (parent->left == node)
        parent->left = subst;
      else /* parent->right == node */
        parent->right = subst;

      if (removed_color == BLACK)
        {
          if (child != NULL && child->color == RED)
            /* Recolor the child.  */
            child->color = BLACK;
          else
            /* Rebalancing starts at child's parent, that is subst_parent -
               except when subst_parent == node.  In this case, we need to use
               its replacement, subst.  */
            rebalance_after_remove (list, child,
                                    subst_parent != node ? subst_parent : subst);
        }
    }
}

static gl_list_node_t
gl_tree_nx_add_first (gl_list_t list, const void *elt)
{
  /* Create new node.  */
  gl_list_node_t new_node =
    (struct gl_list_node_impl *) malloc (sizeof (struct gl_list_node_impl));

  if (new_node == NULL)
    return NULL;

  new_node->left = NULL;
  new_node->right = NULL;
  new_node->branch_size = 1;
  new_node->value = elt;
#if WITH_HASHTABLE
  new_node->h.hashcode =
    (list->base.hashcode_fn != NULL
     ? list->base.hashcode_fn (new_node->value)
     : (size_t)(uintptr_t) new_node->value);
#endif

  /* Add it to the tree.  */
  if (list->root == NULL)
    {
      new_node->color = BLACK;
      list->root = new_node;
      new_node->parent = NULL;
    }
  else
    {
      gl_list_node_t node;

      for (node = list->root; node->left != NULL; )
        node = node->left;

      node->left = new_node;
      new_node->parent = node;

      /* Update branch_size fields of the parent nodes.  */
      {
        gl_list_node_t p;

        for (p = node; p != NULL; p = p->parent)
          p->branch_size++;
      }

      /* Color and rebalance.  */
      rebalance_after_add (list, new_node, node);
    }

#if WITH_HASHTABLE
  /* Add node to the hash table.
     Note that this is only possible _after_ the node has been added to the
     tree structure, because add_to_bucket() uses node_position().  */
  if (add_to_bucket (list, new_node) < 0)
    {
      gl_tree_remove_node_from_tree (list, new_node);
      free (new_node);
      return NULL;
    }
  hash_resize_after_add (list);
#endif

  return new_node;
}

static gl_list_node_t
gl_tree_nx_add_last (gl_list_t list, const void *elt)
{
  /* Create new node.  */
  gl_list_node_t new_node =
    (struct gl_list_node_impl *) malloc (sizeof (struct gl_list_node_impl));

  if (new_node == NULL)
    return NULL;

  new_node->left = NULL;
  new_node->right = NULL;
  new_node->branch_size = 1;
  new_node->value = elt;
#if WITH_HASHTABLE
  new_node->h.hashcode =
    (list->base.hashcode_fn != NULL
     ? list->base.hashcode_fn (new_node->value)
     : (size_t)(uintptr_t) new_node->value);
#endif

  /* Add it to the tree.  */
  if (list->root == NULL)
    {
      new_node->color = BLACK;
      list->root = new_node;
      new_node->parent = NULL;
    }
  else
    {
      gl_list_node_t node;

      for (node = list->root; node->right != NULL; )
        node = node->right;

      node->right = new_node;
      new_node->parent = node;

      /* Update branch_size fields of the parent nodes.  */
      {
        gl_list_node_t p;

        for (p = node; p != NULL; p = p->parent)
          p->branch_size++;
      }

      /* Color and rebalance.  */
      rebalance_after_add (list, new_node, node);
    }

#if WITH_HASHTABLE
  /* Add node to the hash table.
     Note that this is only possible _after_ the node has been added to the
     tree structure, because add_to_bucket() uses node_position().  */
  if (add_to_bucket (list, new_node) < 0)
    {
      gl_tree_remove_node_from_tree (list, new_node);
      free (new_node);
      return NULL;
    }
  hash_resize_after_add (list);
#endif

  return new_node;
}

static gl_list_node_t
gl_tree_nx_add_before (gl_list_t list, gl_list_node_t node, const void *elt)
{
  /* Create new node.  */
  gl_list_node_t new_node =
    (struct gl_list_node_impl *) malloc (sizeof (struct gl_list_node_impl));

  if (new_node == NULL)
    return NULL;

  new_node->left = NULL;
  new_node->right = NULL;
  new_node->branch_size = 1;
  new_node->value = elt;
#if WITH_HASHTABLE
  new_node->h.hashcode =
    (list->base.hashcode_fn != NULL
     ? list->base.hashcode_fn (new_node->value)
     : (size_t)(uintptr_t) new_node->value);
#endif

  /* Add it to the tree.  */
  if (node->left == NULL)
    node->left = new_node;
  else
    {
      for (node = node->left; node->right != NULL; )
        node = node->right;
      node->right = new_node;
    }
  new_node->parent = node;

  /* Update branch_size fields of the parent nodes.  */
  {
    gl_list_node_t p;

    for (p = node; p != NULL; p = p->parent)
      p->branch_size++;
  }

  /* Color and rebalance.  */
  rebalance_after_add (list, new_node, node);

#if WITH_HASHTABLE
  /* Add node to the hash table.
     Note that this is only possible _after_ the node has been added to the
     tree structure, because add_to_bucket() uses node_position().  */
  if (add_to_bucket (list, new_node) < 0)
    {
      gl_tree_remove_node_from_tree (list, new_node);
      free (new_node);
      return NULL;
    }
  hash_resize_after_add (list);
#endif

  return new_node;
}

static gl_list_node_t
gl_tree_nx_add_after (gl_list_t list, gl_list_node_t node, const void *elt)
{
  /* Create new node.  */
  gl_list_node_t new_node =
    (struct gl_list_node_impl *) malloc (sizeof (struct gl_list_node_impl));

  if (new_node == NULL)
    return NULL;

  new_node->left = NULL;
  new_node->right = NULL;
  new_node->branch_size = 1;
  new_node->value = elt;
#if WITH_HASHTABLE
  new_node->h.hashcode =
    (list->base.hashcode_fn != NULL
     ? list->base.hashcode_fn (new_node->value)
     : (size_t)(uintptr_t) new_node->value);
#endif

  /* Add it to the tree.  */
  if (node->right == NULL)
    node->right = new_node;
  else
    {
      for (node = node->right; node->left != NULL; )
        node = node->left;
      node->left = new_node;
    }
  new_node->parent = node;

  /* Update branch_size fields of the parent nodes.  */
  {
    gl_list_node_t p;

    for (p = node; p != NULL; p = p->parent)
      p->branch_size++;
  }

  /* Color and rebalance.  */
  rebalance_after_add (list, new_node, node);

#if WITH_HASHTABLE
  /* Add node to the hash table.
     Note that this is only possible _after_ the node has been added to the
     tree structure, because add_to_bucket() uses node_position().  */
  if (add_to_bucket (list, new_node) < 0)
    {
      gl_tree_remove_node_from_tree (list, new_node);
      free (new_node);
      return NULL;
    }
  hash_resize_after_add (list);
#endif

  return new_node;
}