about summary refs log tree commit diff
path: root/misc/tsearch.c
blob: aef9c7c1eebe4ccd9689050f762cc58ae231b949 (plain) (blame)
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
/* Copyright (C) 1995-2017 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Bernd Schmidt <crux@Pool.Informatik.RWTH-Aachen.DE>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library 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
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */

/* Tree search for red/black trees.
   The algorithm for adding nodes is taken from one of the many "Algorithms"
   books by Robert Sedgewick, although the implementation differs.
   The algorithm for deleting nodes can probably be found in a book named
   "Introduction to Algorithms" by Cormen/Leiserson/Rivest.  At least that's
   the book that my professor took most algorithms from during the "Data
   Structures" course...

   Totally public domain.  */

/* Red/black trees are binary trees in which the edges are colored either red
   or black.  They have the following properties:
   1. The number of black edges on every path from the root to a leaf is
      constant.
   2. No two red edges are adjacent.
   Therefore there is an upper bound on the length of every path, it's
   O(log n) where n is the number of nodes in the tree.  No path can be longer
   than 1+2*P where P is the length of the shortest path in the tree.
   Useful for the implementation:
   3. If one of the children of a node is NULL, then the other one is red
      (if it exists).

   In the implementation, not the edges are colored, but the nodes.  The color
   interpreted as the color of the edge leading to this node.  The color is
   meaningless for the root node, but we color the root node black for
   convenience.  All added nodes are red initially.

   Adding to a red/black tree is rather easy.  The right place is searched
   with a usual binary tree search.  Additionally, whenever a node N is
   reached that has two red successors, the successors are colored black and
   the node itself colored red.  This moves red edges up the tree where they
   pose less of a problem once we get to really insert the new node.  Changing
   N's color to red may violate rule 2, however, so rotations may become
   necessary to restore the invariants.  Adding a new red leaf may violate
   the same rule, so afterwards an additional check is run and the tree
   possibly rotated.

   Deleting is hairy.  There are mainly two nodes involved: the node to be
   deleted (n1), and another node that is to be unchained from the tree (n2).
   If n1 has a successor (the node with a smallest key that is larger than
   n1), then the successor becomes n2 and its contents are copied into n1,
   otherwise n1 becomes n2.
   Unchaining a node may violate rule 1: if n2 is black, one subtree is
   missing one black edge afterwards.  The algorithm must try to move this
   error upwards towards the root, so that the subtree that does not have
   enough black edges becomes the whole tree.  Once that happens, the error
   has disappeared.  It may not be necessary to go all the way up, since it
   is possible that rotations and recoloring can fix the error before that.

   Although the deletion algorithm must walk upwards through the tree, we
   do not store parent pointers in the nodes.  Instead, delete allocates a
   small array of parent pointers and fills it while descending the tree.
   Since we know that the length of a path is O(log n), where n is the number
   of nodes, this is likely to use less memory.  */

/* Tree rotations look like this:
      A                C
     / \              / \
    B   C            A   G
   / \ / \  -->     / \
   D E F G         B   F
                  / \
                 D   E

   In this case, A has been rotated left.  This preserves the ordering of the
   binary tree.  */

#include <assert.h>
#include <stdalign.h>
#include <stddef.h>
#include <stdlib.h>
#include <string.h>
#include <search.h>

/* Assume malloc returns naturally aligned (alignof (max_align_t))
   pointers so we can use the low bits to store some extra info.  This
   works for the left/right node pointers since they are not user
   visible and always allocated by malloc.  The user provides the key
   pointer and so that can point anywhere and doesn't have to be
   aligned.  */
#define USE_MALLOC_LOW_BIT 1

#ifndef USE_MALLOC_LOW_BIT
typedef struct node_t
{
  /* Callers expect this to be the first element in the structure - do not
     move!  */
  const void *key;
  struct node_t *left_node;
  struct node_t *right_node;
  unsigned int is_red:1;
} *node;

#define RED(N) (N)->is_red
#define SETRED(N) (N)->is_red = 1
#define SETBLACK(N) (N)->is_red = 0
#define SETNODEPTR(NP,P) (*NP) = (P)
#define LEFT(N) (N)->left_node
#define LEFTPTR(N) (&(N)->left_node)
#define SETLEFT(N,L) (N)->left_node = (L)
#define RIGHT(N) (N)->right_node
#define RIGHTPTR(N) (&(N)->right_node)
#define SETRIGHT(N,R) (N)->right_node = (R)
#define DEREFNODEPTR(NP) (*(NP))

#else /* USE_MALLOC_LOW_BIT */

typedef struct node_t
{
  /* Callers expect this to be the first element in the structure - do not
     move!  */
  const void *key;
  uintptr_t left_node; /* Includes whether the node is red in low-bit. */
  uintptr_t right_node;
} *node;

#define RED(N) (node)((N)->left_node & ((uintptr_t) 0x1))
#define SETRED(N) (N)->left_node |= ((uintptr_t) 0x1)
#define SETBLACK(N) (N)->left_node &= ~((uintptr_t) 0x1)
#define SETNODEPTR(NP,P) (*NP) = (node)((((uintptr_t)(*NP)) \
					 & (uintptr_t) 0x1) | (uintptr_t)(P))
#define LEFT(N) (node)((N)->left_node & ~((uintptr_t) 0x1))
#define LEFTPTR(N) (node *)(&(N)->left_node)
#define SETLEFT(N,L) (N)->left_node = (((N)->left_node & (uintptr_t) 0x1) \
				       | (uintptr_t)(L))
#define RIGHT(N) (node)((N)->right_node)
#define RIGHTPTR(N) (node *)(&(N)->right_node)
#define SETRIGHT(N,R) (N)->right_node = (uintptr_t)(R)
#define DEREFNODEPTR(NP) (node)((uintptr_t)(*(NP)) & ~((uintptr_t) 0x1))

#endif /* USE_MALLOC_LOW_BIT */
typedef const struct node_t *const_node;

#undef DEBUGGING

#ifdef DEBUGGING

/* Routines to check tree invariants.  */

#define CHECK_TREE(a) check_tree(a)

static void
check_tree_recurse (node p, int d_sofar, int d_total)
{
  if (p == NULL)
    {
      assert (d_sofar == d_total);
      return;
    }

  check_tree_recurse (LEFT(p), d_sofar + (LEFT(p) && !RED(LEFT(p))),
		      d_total);
  check_tree_recurse (RIGHT(p), d_sofar + (RIGHT(p) && !RED(RIGHT(p))),
		      d_total);
  if (LEFT(p))
    assert (!(RED(LEFT(p)) && RED(p)));
  if (RIGHT(p))
    assert (!(RED(RIGHT(p)) && RED(p)));
}

static void
check_tree (node root)
{
  int cnt = 0;
  node p;
  if (root == NULL)
    return;
  SETBLACK(root);
  for(p = LEFT(root); p; p = LEFT(p))
    cnt += !RED(p);
  check_tree_recurse (root, 0, cnt);
}

#else

#define CHECK_TREE(a)

#endif

/* Possibly "split" a node with two red successors, and/or fix up two red
   edges in a row.  ROOTP is a pointer to the lowest node we visited, PARENTP
   and GPARENTP pointers to its parent/grandparent.  P_R and GP_R contain the
   comparison values that determined which way was taken in the tree to reach
   ROOTP.  MODE is 1 if we need not do the split, but must check for two red
   edges between GPARENTP and ROOTP.  */
static void
maybe_split_for_insert (node *rootp, node *parentp, node *gparentp,
			int p_r, int gp_r, int mode)
{
  node root = DEREFNODEPTR(rootp);
  node *rp, *lp;
  node rpn, lpn;
  rp = RIGHTPTR(root);
  rpn = RIGHT(root);
  lp = LEFTPTR(root);
  lpn = LEFT(root);

  /* See if we have to split this node (both successors red).  */
  if (mode == 1
      || ((rpn) != NULL && (lpn) != NULL && RED(rpn) && RED(lpn)))
    {
      /* This node becomes red, its successors black.  */
      SETRED(root);
      if (rpn)
	SETBLACK(rpn);
      if (lpn)
	SETBLACK(lpn);

      /* If the parent of this node is also red, we have to do
	 rotations.  */
      if (parentp != NULL && RED(DEREFNODEPTR(parentp)))
	{
	  node gp = DEREFNODEPTR(gparentp);
	  node p = DEREFNODEPTR(parentp);
	  /* There are two main cases:
	     1. The edge types (left or right) of the two red edges differ.
	     2. Both red edges are of the same type.
	     There exist two symmetries of each case, so there is a total of
	     4 cases.  */
	  if ((p_r > 0) != (gp_r > 0))
	    {
	      /* Put the child at the top of the tree, with its parent
		 and grandparent as successors.  */
	      SETRED(p);
	      SETRED(gp);
	      SETBLACK(root);
	      if (p_r < 0)
		{
		  /* Child is left of parent.  */
		  SETLEFT(p,rpn);
		  SETNODEPTR(rp,p);
		  SETRIGHT(gp,lpn);
		  SETNODEPTR(lp,gp);
		}
	      else
		{
		  /* Child is right of parent.  */
		  SETRIGHT(p,lpn);
		  SETNODEPTR(lp,p);
		  SETLEFT(gp,rpn);
		  SETNODEPTR(rp,gp);
		}
	      SETNODEPTR(gparentp,root);
	    }
	  else
	    {
	      SETNODEPTR(gparentp,p);
	      /* Parent becomes the top of the tree, grandparent and
		 child are its successors.  */
	      SETBLACK(p);
	      SETRED(gp);
	      if (p_r < 0)
		{
		  /* Left edges.  */
		  SETLEFT(gp,RIGHT(p));
		  SETRIGHT(p,gp);
		}
	      else
		{
		  /* Right edges.  */
		  SETRIGHT(gp,LEFT(p));
		  SETLEFT(p,gp);
		}
	    }
	}
    }
}

/* Find or insert datum into search tree.
   KEY is the key to be located, ROOTP is the address of tree root,
   COMPAR the ordering function.  */
void *
__tsearch (const void *key, void **vrootp, __compar_fn_t compar)
{
  node q, root;
  node *parentp = NULL, *gparentp = NULL;
  node *rootp = (node *) vrootp;
  node *nextp;
  int r = 0, p_r = 0, gp_r = 0; /* No they might not, Mr Compiler.  */

#ifdef USE_MALLOC_LOW_BIT
  static_assert (alignof (max_align_t) > 1, "malloc must return aligned ptrs");
#endif

  if (rootp == NULL)
    return NULL;

  /* This saves some additional tests below.  */
  root = DEREFNODEPTR(rootp);
  if (root != NULL)
    SETBLACK(root);

  CHECK_TREE (root);

  nextp = rootp;
  while (DEREFNODEPTR(nextp) != NULL)
    {
      root = DEREFNODEPTR(rootp);
      r = (*compar) (key, root->key);
      if (r == 0)
	return root;

      maybe_split_for_insert (rootp, parentp, gparentp, p_r, gp_r, 0);
      /* If that did any rotations, parentp and gparentp are now garbage.
	 That doesn't matter, because the values they contain are never
	 used again in that case.  */

      nextp = r < 0 ? LEFTPTR(root) : RIGHTPTR(root);
      if (DEREFNODEPTR(nextp) == NULL)
	break;

      gparentp = parentp;
      parentp = rootp;
      rootp = nextp;

      gp_r = p_r;
      p_r = r;
    }

  q = (struct node_t *) malloc (sizeof (struct node_t));
  if (q != NULL)
    {
      /* Make sure the malloc implementation returns naturally aligned
	 memory blocks when expected.  Or at least even pointers, so we
	 can use the low bit as red/black flag.  Even though we have a
	 static_assert to make sure alignof (max_align_t) > 1 there could
	 be an interposed malloc implementation that might cause havoc by
	 not obeying the malloc contract.  */
#ifdef USE_MALLOC_LOW_BIT
      assert (((uintptr_t) q & (uintptr_t) 0x1) == 0);
#endif
      SETNODEPTR(nextp,q);		/* link new node to old */
      q->key = key;			/* initialize new node */
      SETRED(q);
      SETLEFT(q,NULL);
      SETRIGHT(q,NULL);

      if (nextp != rootp)
	/* There may be two red edges in a row now, which we must avoid by
	   rotating the tree.  */
	maybe_split_for_insert (nextp, rootp, parentp, r, p_r, 1);
    }

  return q;
}
libc_hidden_def (__tsearch)
weak_alias (__tsearch, tsearch)


/* Find datum in search tree.
   KEY is the key to be located, ROOTP is the address of tree root,
   COMPAR the ordering function.  */
void *
__tfind (const void *key, void *const *vrootp, __compar_fn_t compar)
{
  node root;
  node *rootp = (node *) vrootp;

  if (rootp == NULL)
    return NULL;

  root = DEREFNODEPTR(rootp);
  CHECK_TREE (root);

  while (DEREFNODEPTR(rootp) != NULL)
    {
      root = DEREFNODEPTR(rootp);
      int r;

      r = (*compar) (key, root->key);
      if (r == 0)
	return root;

      rootp = r < 0 ? LEFTPTR(root) : RIGHTPTR(root);
    }
  return NULL;
}
libc_hidden_def (__tfind)
weak_alias (__tfind, tfind)


/* Delete node with given key.
   KEY is the key to be deleted, ROOTP is the address of the root of tree,
   COMPAR the comparison function.  */
void *
__tdelete (const void *key, void **vrootp, __compar_fn_t compar)
{
  node p, q, r, retval;
  int cmp;
  node *rootp = (node *) vrootp;
  node root, unchained;
  /* Stack of nodes so we remember the parents without recursion.  It's
     _very_ unlikely that there are paths longer than 40 nodes.  The tree
     would need to have around 250.000 nodes.  */
  int stacksize = 40;
  int sp = 0;
  node **nodestack = alloca (sizeof (node *) * stacksize);

  if (rootp == NULL)
    return NULL;
  p = DEREFNODEPTR(rootp);
  if (p == NULL)
    return NULL;

  CHECK_TREE (p);

  root = DEREFNODEPTR(rootp);
  while ((cmp = (*compar) (key, root->key)) != 0)
    {
      if (sp == stacksize)
	{
	  node **newstack;
	  stacksize += 20;
	  newstack = alloca (sizeof (node *) * stacksize);
	  nodestack = memcpy (newstack, nodestack, sp * sizeof (node *));
	}

      nodestack[sp++] = rootp;
      p = DEREFNODEPTR(rootp);
      if (cmp < 0)
	{
	  rootp = LEFTPTR(p);
	  root = LEFT(p);
	}
      else
	{
	  rootp = RIGHTPTR(p);
	  root = RIGHT(p);
	}
      if (root == NULL)
	return NULL;
    }

  /* This is bogus if the node to be deleted is the root... this routine
     really should return an integer with 0 for success, -1 for failure
     and errno = ESRCH or something.  */
  retval = p;

  /* We don't unchain the node we want to delete. Instead, we overwrite
     it with its successor and unchain the successor.  If there is no
     successor, we really unchain the node to be deleted.  */

  root = DEREFNODEPTR(rootp);

  r = RIGHT(root);
  q = LEFT(root);

  if (q == NULL || r == NULL)
    unchained = root;
  else
    {
      node *parentp = rootp, *up = RIGHTPTR(root);
      node upn;
      for (;;)
	{
	  if (sp == stacksize)
	    {
	      node **newstack;
	      stacksize += 20;
	      newstack = alloca (sizeof (node *) * stacksize);
	      nodestack = memcpy (newstack, nodestack, sp * sizeof (node *));
	    }
	  nodestack[sp++] = parentp;
	  parentp = up;
	  upn = DEREFNODEPTR(up);
	  if (LEFT(upn) == NULL)
	    break;
	  up = LEFTPTR(upn);
	}
      unchained = DEREFNODEPTR(up);
    }

  /* We know that either the left or right successor of UNCHAINED is NULL.
     R becomes the other one, it is chained into the parent of UNCHAINED.  */
  r = LEFT(unchained);
  if (r == NULL)
    r = RIGHT(unchained);
  if (sp == 0)
    SETNODEPTR(rootp,r);
  else
    {
      q = DEREFNODEPTR(nodestack[sp-1]);
      if (unchained == RIGHT(q))
	SETRIGHT(q,r);
      else
	SETLEFT(q,r);
    }

  if (unchained != root)
    root->key = unchained->key;
  if (!RED(unchained))
    {
      /* Now we lost a black edge, which means that the number of black
	 edges on every path is no longer constant.  We must balance the
	 tree.  */
      /* NODESTACK now contains all parents of R.  R is likely to be NULL
	 in the first iteration.  */
      /* NULL nodes are considered black throughout - this is necessary for
	 correctness.  */
      while (sp > 0 && (r == NULL || !RED(r)))
	{
	  node *pp = nodestack[sp - 1];
	  p = DEREFNODEPTR(pp);
	  /* Two symmetric cases.  */
	  if (r == LEFT(p))
	    {
	      /* Q is R's brother, P is R's parent.  The subtree with root
		 R has one black edge less than the subtree with root Q.  */
	      q = RIGHT(p);
	      if (RED(q))
		{
		  /* If Q is red, we know that P is black. We rotate P left
		     so that Q becomes the top node in the tree, with P below
		     it.  P is colored red, Q is colored black.
		     This action does not change the black edge count for any
		     leaf in the tree, but we will be able to recognize one
		     of the following situations, which all require that Q
		     is black.  */
		  SETBLACK(q);
		  SETRED(p);
		  /* Left rotate p.  */
		  SETRIGHT(p,LEFT(q));
		  SETLEFT(q,p);
		  SETNODEPTR(pp,q);
		  /* Make sure pp is right if the case below tries to use
		     it.  */
		  nodestack[sp++] = pp = LEFTPTR(q);
		  q = RIGHT(p);
		}
	      /* We know that Q can't be NULL here.  We also know that Q is
		 black.  */
	      if ((LEFT(q) == NULL || !RED(LEFT(q)))
		  && (RIGHT(q) == NULL || !RED(RIGHT(q))))
		{
		  /* Q has two black successors.  We can simply color Q red.
		     The whole subtree with root P is now missing one black
		     edge.  Note that this action can temporarily make the
		     tree invalid (if P is red).  But we will exit the loop
		     in that case and set P black, which both makes the tree
		     valid and also makes the black edge count come out
		     right.  If P is black, we are at least one step closer
		     to the root and we'll try again the next iteration.  */
		  SETRED(q);
		  r = p;
		}
	      else
		{
		  /* Q is black, one of Q's successors is red.  We can
		     repair the tree with one operation and will exit the
		     loop afterwards.  */
		  if (RIGHT(q) == NULL || !RED(RIGHT(q)))
		    {
		      /* The left one is red.  We perform the same action as
			 in maybe_split_for_insert where two red edges are
			 adjacent but point in different directions:
			 Q's left successor (let's call it Q2) becomes the
			 top of the subtree we are looking at, its parent (Q)
			 and grandparent (P) become its successors. The former
			 successors of Q2 are placed below P and Q.
			 P becomes black, and Q2 gets the color that P had.
			 This changes the black edge count only for node R and
			 its successors.  */
		      node q2 = LEFT(q);
		      if (RED(p))
			SETRED(q2);
		      else
			SETBLACK(q2);
		      SETRIGHT(p,LEFT(q2));
		      SETLEFT(q,RIGHT(q2));
		      SETRIGHT(q2,q);
		      SETLEFT(q2,p);
		      SETNODEPTR(pp,q2);
		      SETBLACK(p);
		    }
		  else
		    {
		      /* It's the right one.  Rotate P left. P becomes black,
			 and Q gets the color that P had.  Q's right successor
			 also becomes black.  This changes the black edge
			 count only for node R and its successors.  */
		      if (RED(p))
			SETRED(q);
		      else
			SETBLACK(q);
		      SETBLACK(p);

		      SETBLACK(RIGHT(q));

		      /* left rotate p */
		      SETRIGHT(p,LEFT(q));
		      SETLEFT(q,p);
		      SETNODEPTR(pp,q);
		    }

		  /* We're done.  */
		  sp = 1;
		  r = NULL;
		}
	    }
	  else
	    {
	      /* Comments: see above.  */
	      q = LEFT(p);
	      if (RED(q))
		{
		  SETBLACK(q);
		  SETRED(p);
		  SETLEFT(p,RIGHT(q));
		  SETRIGHT(q,p);
		  SETNODEPTR(pp,q);
		  nodestack[sp++] = pp = RIGHTPTR(q);
		  q = LEFT(p);
		}
	      if ((RIGHT(q) == NULL || !RED(RIGHT(q)))
		  && (LEFT(q) == NULL || !RED(LEFT(q))))
		{
		  SETRED(q);
		  r = p;
		}
	      else
		{
		  if (LEFT(q) == NULL || !RED(LEFT(q)))
		    {
		      node q2 = RIGHT(q);
		      if (RED(p))
			SETRED(q2);
		      else
			SETBLACK(q2);
		      SETLEFT(p,RIGHT(q2));
		      SETRIGHT(q,LEFT(q2));
		      SETLEFT(q2,q);
		      SETRIGHT(q2,p);
		      SETNODEPTR(pp,q2);
		      SETBLACK(p);
		    }
		  else
		    {
		      if (RED(p))
			SETRED(q);
		      else
			SETBLACK(q);
		      SETBLACK(p);
		      SETBLACK(LEFT(q));
		      SETLEFT(p,RIGHT(q));
		      SETRIGHT(q,p);
		      SETNODEPTR(pp,q);
		    }
		  sp = 1;
		  r = NULL;
		}
	    }
	  --sp;
	}
      if (r != NULL)
	SETBLACK(r);
    }

  free (unchained);
  return retval;
}
libc_hidden_def (__tdelete)
weak_alias (__tdelete, tdelete)


/* Walk the nodes of a tree.
   ROOT is the root of the tree to be walked, ACTION the function to be
   called at each node.  LEVEL is the level of ROOT in the whole tree.  */
static void
trecurse (const void *vroot, __action_fn_t action, int level)
{
  const_node root = (const_node) vroot;

  if (LEFT(root) == NULL && RIGHT(root) == NULL)
    (*action) (root, leaf, level);
  else
    {
      (*action) (root, preorder, level);
      if (LEFT(root) != NULL)
	trecurse (LEFT(root), action, level + 1);
      (*action) (root, postorder, level);
      if (RIGHT(root) != NULL)
	trecurse (RIGHT(root), action, level + 1);
      (*action) (root, endorder, level);
    }
}


/* Walk the nodes of a tree.
   ROOT is the root of the tree to be walked, ACTION the function to be
   called at each node.  */
void
__twalk (const void *vroot, __action_fn_t action)
{
  const_node root = (const_node) vroot;

  CHECK_TREE ((node) root);

  if (root != NULL && action != NULL)
    trecurse (root, action, 0);
}
libc_hidden_def (__twalk)
weak_alias (__twalk, twalk)



/* The standardized functions miss an important functionality: the
   tree cannot be removed easily.  We provide a function to do this.  */
static void
tdestroy_recurse (node root, __free_fn_t freefct)
{
  if (LEFT(root) != NULL)
    tdestroy_recurse (LEFT(root), freefct);
  if (RIGHT(root) != NULL)
    tdestroy_recurse (RIGHT(root), freefct);
  (*freefct) ((void *) root->key);
  /* Free the node itself.  */
  free (root);
}

void
__tdestroy (void *vroot, __free_fn_t freefct)
{
  node root = (node) vroot;

  CHECK_TREE (root);

  if (root != NULL)
    tdestroy_recurse (root, freefct);
}
weak_alias (__tdestroy, tdestroy)