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tree.h
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1 /* $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $ */
2 /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */
3 /* $FreeBSD: src/sys/sys/tree.h,v 1.9.2.1.4.1 2010/06/14 02:09:06 kensmith Exp $ */
4 
5 /*-
6  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
7  * All rights reserved.
8  *
9  * Redistribution and use in source and binary forms, with or without
10  * modification, are permitted provided that the following conditions
11  * are met:
12  * 1. Redistributions of source code must retain the above copyright
13  * notice, this list of conditions and the following disclaimer.
14  * 2. Redistributions in binary form must reproduce the above copyright
15  * notice, this list of conditions and the following disclaimer in the
16  * documentation and/or other materials provided with the distribution.
17  *
18  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
19  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
20  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
21  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
22  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
23  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
24  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
25  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
26  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
27  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28  */
29 
30 #ifndef _SYS_TREE_H_
31 #define _SYS_TREE_H_
32 
33 //#include <sys/cdefs.h>
34 
35 /*
36  * This file defines data structures for different types of trees:
37  * splay trees and red-black trees.
38  *
39  * A splay tree is a self-organizing data structure. Every operation
40  * on the tree causes a splay to happen. The splay moves the requested
41  * node to the root of the tree and partly rebalances it.
42  *
43  * This has the benefit that request locality causes faster lookups as
44  * the requested nodes move to the top of the tree. On the other hand,
45  * every lookup causes memory writes.
46  *
47  * The Balance Theorem bounds the total access time for m operations
48  * and n inserts on an initially empty tree as O((m + n)lg n). The
49  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
50  *
51  * A red-black tree is a binary search tree with the node color as an
52  * extra attribute. It fulfills a set of conditions:
53  * - every search path from the root to a leaf consists of the
54  * same number of black nodes,
55  * - each red node (except for the root) has a black parent,
56  * - each leaf node is black.
57  *
58  * Every operation on a red-black tree is bounded as O(lg n).
59  * The maximum height of a red-black tree is 2lg (n+1).
60  */
61 
62 #define SPLAY_HEAD(name, type) \
63 struct name { \
64  struct type *sph_root; /* root of the tree */ \
65 }
66 
67 #define SPLAY_INITIALIZER(root) \
68  { NULL }
69 
70 #define SPLAY_INIT(root) do { \
71  (root)->sph_root = NULL; \
72 } while (/*CONSTCOND*/ 0)
73 
74 #define SPLAY_ENTRY(type) \
75 struct { \
76  struct type *spe_left; /* left element */ \
77  struct type *spe_right; /* right element */ \
78 }
79 
80 #define SPLAY_LEFT(elm, field) (elm)->field.spe_left
81 #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
82 #define SPLAY_ROOT(head) (head)->sph_root
83 #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)
84 
85 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
86 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \
87  SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
88  SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
89  (head)->sph_root = tmp; \
90 } while (/*CONSTCOND*/ 0)
91 
92 #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \
93  SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
94  SPLAY_LEFT(tmp, field) = (head)->sph_root; \
95  (head)->sph_root = tmp; \
96 } while (/*CONSTCOND*/ 0)
97 
98 #define SPLAY_LINKLEFT(head, tmp, field) do { \
99  SPLAY_LEFT(tmp, field) = (head)->sph_root; \
100  tmp = (head)->sph_root; \
101  (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
102 } while (/*CONSTCOND*/ 0)
103 
104 #define SPLAY_LINKRIGHT(head, tmp, field) do { \
105  SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
106  tmp = (head)->sph_root; \
107  (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
108 } while (/*CONSTCOND*/ 0)
109 
110 #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \
111  SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
112  SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
113  SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
114  SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
115 } while (/*CONSTCOND*/ 0)
116 
117 /* Generates prototypes and inline functions */
118 
119 #define SPLAY_PROTOTYPE(name, type, field, cmp) \
120 void name##_SPLAY(struct name *, struct type *); \
121 void name##_SPLAY_MINMAX(struct name *, int); \
122 struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
123 struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
124  \
125 /* Finds the node with the same key as elm */ \
126 static __inline struct type * \
127 name##_SPLAY_FIND(struct name *head, struct type *elm) \
128 { \
129  if (SPLAY_EMPTY(head)) \
130  return(NULL); \
131  name##_SPLAY(head, elm); \
132  if ((cmp)(elm, (head)->sph_root) == 0) \
133  return (head->sph_root); \
134  return (NULL); \
135 } \
136  \
137 static __inline struct type * \
138 name##_SPLAY_NEXT(struct name *head, struct type *elm) \
139 { \
140  name##_SPLAY(head, elm); \
141  if (SPLAY_RIGHT(elm, field) != NULL) { \
142  elm = SPLAY_RIGHT(elm, field); \
143  while (SPLAY_LEFT(elm, field) != NULL) { \
144  elm = SPLAY_LEFT(elm, field); \
145  } \
146  } else \
147  elm = NULL; \
148  return (elm); \
149 } \
150  \
151 static __inline struct type * \
152 name##_SPLAY_MIN_MAX(struct name *head, int val) \
153 { \
154  name##_SPLAY_MINMAX(head, val); \
155  return (SPLAY_ROOT(head)); \
156 }
157 
158 /* Main splay operation.
159  * Moves node close to the key of elm to top
160  */
161 #define SPLAY_GENERATE(name, type, field, cmp) \
162 struct type * \
163 name##_SPLAY_INSERT(struct name *head, struct type *elm) \
164 { \
165  if (SPLAY_EMPTY(head)) { \
166  SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
167  } else { \
168  int __comp; \
169  name##_SPLAY(head, elm); \
170  __comp = (cmp)(elm, (head)->sph_root); \
171  if(__comp < 0) { \
172  SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
173  SPLAY_RIGHT(elm, field) = (head)->sph_root; \
174  SPLAY_LEFT((head)->sph_root, field) = NULL; \
175  } else if (__comp > 0) { \
176  SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
177  SPLAY_LEFT(elm, field) = (head)->sph_root; \
178  SPLAY_RIGHT((head)->sph_root, field) = NULL; \
179  } else \
180  return ((head)->sph_root); \
181  } \
182  (head)->sph_root = (elm); \
183  return (NULL); \
184 } \
185  \
186 struct type * \
187 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
188 { \
189  struct type *__tmp; \
190  if (SPLAY_EMPTY(head)) \
191  return (NULL); \
192  name##_SPLAY(head, elm); \
193  if ((cmp)(elm, (head)->sph_root) == 0) { \
194  if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
195  (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
196  } else { \
197  __tmp = SPLAY_RIGHT((head)->sph_root, field); \
198  (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
199  name##_SPLAY(head, elm); \
200  SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
201  } \
202  return (elm); \
203  } \
204  return (NULL); \
205 } \
206  \
207 void \
208 name##_SPLAY(struct name *head, struct type *elm) \
209 { \
210  struct type __node, *__left, *__right, *__tmp; \
211  int __comp; \
212 \
213  SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
214  __left = __right = &__node; \
215 \
216  while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \
217  if (__comp < 0) { \
218  __tmp = SPLAY_LEFT((head)->sph_root, field); \
219  if (__tmp == NULL) \
220  break; \
221  if ((cmp)(elm, __tmp) < 0){ \
222  SPLAY_ROTATE_RIGHT(head, __tmp, field); \
223  if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
224  break; \
225  } \
226  SPLAY_LINKLEFT(head, __right, field); \
227  } else if (__comp > 0) { \
228  __tmp = SPLAY_RIGHT((head)->sph_root, field); \
229  if (__tmp == NULL) \
230  break; \
231  if ((cmp)(elm, __tmp) > 0){ \
232  SPLAY_ROTATE_LEFT(head, __tmp, field); \
233  if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
234  break; \
235  } \
236  SPLAY_LINKRIGHT(head, __left, field); \
237  } \
238  } \
239  SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
240 } \
241  \
242 /* Splay with either the minimum or the maximum element \
243  * Used to find minimum or maximum element in tree. \
244  */ \
245 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
246 { \
247  struct type __node, *__left, *__right, *__tmp; \
248 \
249  SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
250  __left = __right = &__node; \
251 \
252  while (1) { \
253  if (__comp < 0) { \
254  __tmp = SPLAY_LEFT((head)->sph_root, field); \
255  if (__tmp == NULL) \
256  break; \
257  if (__comp < 0){ \
258  SPLAY_ROTATE_RIGHT(head, __tmp, field); \
259  if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
260  break; \
261  } \
262  SPLAY_LINKLEFT(head, __right, field); \
263  } else if (__comp > 0) { \
264  __tmp = SPLAY_RIGHT((head)->sph_root, field); \
265  if (__tmp == NULL) \
266  break; \
267  if (__comp > 0) { \
268  SPLAY_ROTATE_LEFT(head, __tmp, field); \
269  if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
270  break; \
271  } \
272  SPLAY_LINKRIGHT(head, __left, field); \
273  } \
274  } \
275  SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
276 }
277 
278 #define SPLAY_NEGINF -1
279 #define SPLAY_INF 1
280 
281 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
282 #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
283 #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
284 #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
285 #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
286  : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
287 #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
288  : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
289 
290 #define SPLAY_FOREACH(x, name, head) \
291  for ((x) = SPLAY_MIN(name, head); \
292  (x) != NULL; \
293  (x) = SPLAY_NEXT(name, head, x))
294 
295 /* Macros that define a red-black tree */
296 #define RB_HEAD(name, type) \
297 struct name { \
298  struct type *rbh_root; /* root of the tree */ \
299 }
300 
301 #define RB_INITIALIZER(root) \
302  { NULL }
303 
304 #define RB_INIT(root) do { \
305  (root)->rbh_root = NULL; \
306 } while (/*CONSTCOND*/ 0)
307 
308 #define RB_BLACK 0
309 #define RB_RED 1
310 #define RB_ENTRY(type) \
311 struct { \
312  struct type *rbe_left; /* left element */ \
313  struct type *rbe_right; /* right element */ \
314  struct type *rbe_parent; /* parent element */ \
315  int rbe_color; /* node color */ \
316 }
317 
318 #define RB_LEFT(elm, field) (elm)->field.rbe_left
319 #define RB_RIGHT(elm, field) (elm)->field.rbe_right
320 #define RB_PARENT(elm, field) (elm)->field.rbe_parent
321 #define RB_COLOR(elm, field) (elm)->field.rbe_color
322 #define RB_ROOT(head) (head)->rbh_root
323 #define RB_EMPTY(head) (RB_ROOT(head) == NULL)
324 
325 #define RB_SET(elm, parent, field) do { \
326  RB_PARENT(elm, field) = parent; \
327  RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
328  RB_COLOR(elm, field) = RB_RED; \
329 } while (/*CONSTCOND*/ 0)
330 
331 #define RB_SET_BLACKRED(black, red, field) do { \
332  RB_COLOR(black, field) = RB_BLACK; \
333  RB_COLOR(red, field) = RB_RED; \
334 } while (/*CONSTCOND*/ 0)
335 
336 #ifndef RB_AUGMENT
337 #define RB_AUGMENT(x) do {} while (0)
338 #endif
339 
340 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
341  (tmp) = RB_RIGHT(elm, field); \
342  if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \
343  RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
344  } \
345  RB_AUGMENT(elm); \
346  if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
347  if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
348  RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
349  else \
350  RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
351  } else \
352  (head)->rbh_root = (tmp); \
353  RB_LEFT(tmp, field) = (elm); \
354  RB_PARENT(elm, field) = (tmp); \
355  RB_AUGMENT(tmp); \
356  if ((RB_PARENT(tmp, field))) \
357  RB_AUGMENT(RB_PARENT(tmp, field)); \
358 } while (/*CONSTCOND*/ 0)
359 
360 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
361  (tmp) = RB_LEFT(elm, field); \
362  if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \
363  RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
364  } \
365  RB_AUGMENT(elm); \
366  if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
367  if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
368  RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
369  else \
370  RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
371  } else \
372  (head)->rbh_root = (tmp); \
373  RB_RIGHT(tmp, field) = (elm); \
374  RB_PARENT(elm, field) = (tmp); \
375  RB_AUGMENT(tmp); \
376  if ((RB_PARENT(tmp, field))) \
377  RB_AUGMENT(RB_PARENT(tmp, field)); \
378 } while (/*CONSTCOND*/ 0)
379 
380 /* Generates prototypes and inline functions */
381 #define RB_PROTOTYPE(name, type, field, cmp) \
382  RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
383 #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \
384  RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
385 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \
386 attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \
387 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
388 attr struct type *name##_RB_REMOVE(struct name *, struct type *); \
389 attr struct type *name##_RB_INSERT(struct name *, struct type *); \
390 attr struct type *name##_RB_FIND(struct name *, struct type *); \
391 attr struct type *name##_RB_NFIND(struct name *, struct type *); \
392 attr struct type *name##_RB_NEXT(struct type *); \
393 attr struct type *name##_RB_PREV(struct type *); \
394 attr struct type *name##_RB_MINMAX(struct name *, int); \
395  \
396 
397 /* Main rb operation.
398  * Moves node close to the key of elm to top
399  */
400 #define RB_GENERATE(name, type, field, cmp) \
401  RB_GENERATE_INTERNAL(name, type, field, cmp,)
402 #define RB_GENERATE_STATIC(name, type, field, cmp) \
403  RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
404 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
405 attr void \
406 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
407 { \
408  struct type *parent, *gparent, *tmp; \
409  while ((parent = RB_PARENT(elm, field)) != NULL && \
410  RB_COLOR(parent, field) == RB_RED) { \
411  gparent = RB_PARENT(parent, field); \
412  if (parent == RB_LEFT(gparent, field)) { \
413  tmp = RB_RIGHT(gparent, field); \
414  if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
415  RB_COLOR(tmp, field) = RB_BLACK; \
416  RB_SET_BLACKRED(parent, gparent, field);\
417  elm = gparent; \
418  continue; \
419  } \
420  if (RB_RIGHT(parent, field) == elm) { \
421  RB_ROTATE_LEFT(head, parent, tmp, field);\
422  tmp = parent; \
423  parent = elm; \
424  elm = tmp; \
425  } \
426  RB_SET_BLACKRED(parent, gparent, field); \
427  RB_ROTATE_RIGHT(head, gparent, tmp, field); \
428  } else { \
429  tmp = RB_LEFT(gparent, field); \
430  if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
431  RB_COLOR(tmp, field) = RB_BLACK; \
432  RB_SET_BLACKRED(parent, gparent, field);\
433  elm = gparent; \
434  continue; \
435  } \
436  if (RB_LEFT(parent, field) == elm) { \
437  RB_ROTATE_RIGHT(head, parent, tmp, field);\
438  tmp = parent; \
439  parent = elm; \
440  elm = tmp; \
441  } \
442  RB_SET_BLACKRED(parent, gparent, field); \
443  RB_ROTATE_LEFT(head, gparent, tmp, field); \
444  } \
445  } \
446  RB_COLOR(head->rbh_root, field) = RB_BLACK; \
447 } \
448  \
449 attr void \
450 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
451 { \
452  struct type *tmp; \
453  while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
454  elm != RB_ROOT(head)) { \
455  if (RB_LEFT(parent, field) == elm) { \
456  tmp = RB_RIGHT(parent, field); \
457  if (RB_COLOR(tmp, field) == RB_RED) { \
458  RB_SET_BLACKRED(tmp, parent, field); \
459  RB_ROTATE_LEFT(head, parent, tmp, field);\
460  tmp = RB_RIGHT(parent, field); \
461  } \
462  if ((RB_LEFT(tmp, field) == NULL || \
463  RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
464  (RB_RIGHT(tmp, field) == NULL || \
465  RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
466  RB_COLOR(tmp, field) = RB_RED; \
467  elm = parent; \
468  parent = RB_PARENT(elm, field); \
469  } else { \
470  if (RB_RIGHT(tmp, field) == NULL || \
471  RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
472  struct type *oleft; \
473  if ((oleft = RB_LEFT(tmp, field)) \
474  != NULL) \
475  RB_COLOR(oleft, field) = RB_BLACK;\
476  RB_COLOR(tmp, field) = RB_RED; \
477  RB_ROTATE_RIGHT(head, tmp, oleft, field);\
478  tmp = RB_RIGHT(parent, field); \
479  } \
480  RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
481  RB_COLOR(parent, field) = RB_BLACK; \
482  if (RB_RIGHT(tmp, field)) \
483  RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
484  RB_ROTATE_LEFT(head, parent, tmp, field);\
485  elm = RB_ROOT(head); \
486  break; \
487  } \
488  } else { \
489  tmp = RB_LEFT(parent, field); \
490  if (RB_COLOR(tmp, field) == RB_RED) { \
491  RB_SET_BLACKRED(tmp, parent, field); \
492  RB_ROTATE_RIGHT(head, parent, tmp, field);\
493  tmp = RB_LEFT(parent, field); \
494  } \
495  if ((RB_LEFT(tmp, field) == NULL || \
496  RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
497  (RB_RIGHT(tmp, field) == NULL || \
498  RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
499  RB_COLOR(tmp, field) = RB_RED; \
500  elm = parent; \
501  parent = RB_PARENT(elm, field); \
502  } else { \
503  if (RB_LEFT(tmp, field) == NULL || \
504  RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
505  struct type *oright; \
506  if ((oright = RB_RIGHT(tmp, field)) \
507  != NULL) \
508  RB_COLOR(oright, field) = RB_BLACK;\
509  RB_COLOR(tmp, field) = RB_RED; \
510  RB_ROTATE_LEFT(head, tmp, oright, field);\
511  tmp = RB_LEFT(parent, field); \
512  } \
513  RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
514  RB_COLOR(parent, field) = RB_BLACK; \
515  if (RB_LEFT(tmp, field)) \
516  RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
517  RB_ROTATE_RIGHT(head, parent, tmp, field);\
518  elm = RB_ROOT(head); \
519  break; \
520  } \
521  } \
522  } \
523  if (elm) \
524  RB_COLOR(elm, field) = RB_BLACK; \
525 } \
526  \
527 attr struct type * \
528 name##_RB_REMOVE(struct name *head, struct type *elm) \
529 { \
530  struct type *child, *parent, *old = elm; \
531  int color; \
532  if (RB_LEFT(elm, field) == NULL) \
533  child = RB_RIGHT(elm, field); \
534  else if (RB_RIGHT(elm, field) == NULL) \
535  child = RB_LEFT(elm, field); \
536  else { \
537  struct type *left; \
538  elm = RB_RIGHT(elm, field); \
539  while ((left = RB_LEFT(elm, field)) != NULL) \
540  elm = left; \
541  child = RB_RIGHT(elm, field); \
542  parent = RB_PARENT(elm, field); \
543  color = RB_COLOR(elm, field); \
544  if (child) \
545  RB_PARENT(child, field) = parent; \
546  if (parent) { \
547  if (RB_LEFT(parent, field) == elm) \
548  RB_LEFT(parent, field) = child; \
549  else \
550  RB_RIGHT(parent, field) = child; \
551  RB_AUGMENT(parent); \
552  } else \
553  RB_ROOT(head) = child; \
554  if (RB_PARENT(elm, field) == old) \
555  parent = elm; \
556  (elm)->field = (old)->field; \
557  if (RB_PARENT(old, field)) { \
558  if (RB_LEFT(RB_PARENT(old, field), field) == old)\
559  RB_LEFT(RB_PARENT(old, field), field) = elm;\
560  else \
561  RB_RIGHT(RB_PARENT(old, field), field) = elm;\
562  RB_AUGMENT(RB_PARENT(old, field)); \
563  } else \
564  RB_ROOT(head) = elm; \
565  RB_PARENT(RB_LEFT(old, field), field) = elm; \
566  if (RB_RIGHT(old, field)) \
567  RB_PARENT(RB_RIGHT(old, field), field) = elm; \
568  if (parent) { \
569  left = parent; \
570  do { \
571  RB_AUGMENT(left); \
572  } while ((left = RB_PARENT(left, field)) != NULL); \
573  } \
574  goto color; \
575  } \
576  parent = RB_PARENT(elm, field); \
577  color = RB_COLOR(elm, field); \
578  if (child) \
579  RB_PARENT(child, field) = parent; \
580  if (parent) { \
581  if (RB_LEFT(parent, field) == elm) \
582  RB_LEFT(parent, field) = child; \
583  else \
584  RB_RIGHT(parent, field) = child; \
585  RB_AUGMENT(parent); \
586  } else \
587  RB_ROOT(head) = child; \
588 color: \
589  if (color == RB_BLACK) \
590  name##_RB_REMOVE_COLOR(head, parent, child); \
591  return (old); \
592 } \
593  \
594 /* Inserts a node into the RB tree */ \
595 attr struct type * \
596 name##_RB_INSERT(struct name *head, struct type *elm) \
597 { \
598  struct type *tmp; \
599  struct type *parent = NULL; \
600  int comp = 0; \
601  tmp = RB_ROOT(head); \
602  while (tmp) { \
603  parent = tmp; \
604  comp = (cmp)(elm, parent); \
605  if (comp < 0) \
606  tmp = RB_LEFT(tmp, field); \
607  else if (comp > 0) \
608  tmp = RB_RIGHT(tmp, field); \
609  else \
610  return (tmp); \
611  } \
612  RB_SET(elm, parent, field); \
613  if (parent != NULL) { \
614  if (comp < 0) \
615  RB_LEFT(parent, field) = elm; \
616  else \
617  RB_RIGHT(parent, field) = elm; \
618  RB_AUGMENT(parent); \
619  } else \
620  RB_ROOT(head) = elm; \
621  name##_RB_INSERT_COLOR(head, elm); \
622  return (NULL); \
623 } \
624  \
625 /* Finds the node with the same key as elm */ \
626 attr struct type * \
627 name##_RB_FIND(struct name *head, struct type *elm) \
628 { \
629  struct type *tmp = RB_ROOT(head); \
630  int comp; \
631  while (tmp) { \
632  comp = cmp(elm, tmp); \
633  if (comp < 0) \
634  tmp = RB_LEFT(tmp, field); \
635  else if (comp > 0) \
636  tmp = RB_RIGHT(tmp, field); \
637  else \
638  return (tmp); \
639  } \
640  return (NULL); \
641 } \
642  \
643 /* Finds the first node greater than or equal to the search key */ \
644 attr struct type * \
645 name##_RB_NFIND(struct name *head, struct type *elm) \
646 { \
647  struct type *tmp = RB_ROOT(head); \
648  struct type *res = NULL; \
649  int comp; \
650  while (tmp) { \
651  comp = cmp(elm, tmp); \
652  if (comp < 0) { \
653  res = tmp; \
654  tmp = RB_LEFT(tmp, field); \
655  } \
656  else if (comp > 0) \
657  tmp = RB_RIGHT(tmp, field); \
658  else \
659  return (tmp); \
660  } \
661  return (res); \
662 } \
663  \
664 /* ARGSUSED */ \
665 attr struct type * \
666 name##_RB_NEXT(struct type *elm) \
667 { \
668  if (RB_RIGHT(elm, field)) { \
669  elm = RB_RIGHT(elm, field); \
670  while (RB_LEFT(elm, field)) \
671  elm = RB_LEFT(elm, field); \
672  } else { \
673  if (RB_PARENT(elm, field) && \
674  (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
675  elm = RB_PARENT(elm, field); \
676  else { \
677  while (RB_PARENT(elm, field) && \
678  (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
679  elm = RB_PARENT(elm, field); \
680  elm = RB_PARENT(elm, field); \
681  } \
682  } \
683  return (elm); \
684 } \
685  \
686 /* ARGSUSED */ \
687 attr struct type * \
688 name##_RB_PREV(struct type *elm) \
689 { \
690  if (RB_LEFT(elm, field)) { \
691  elm = RB_LEFT(elm, field); \
692  while (RB_RIGHT(elm, field)) \
693  elm = RB_RIGHT(elm, field); \
694  } else { \
695  if (RB_PARENT(elm, field) && \
696  (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
697  elm = RB_PARENT(elm, field); \
698  else { \
699  while (RB_PARENT(elm, field) && \
700  (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
701  elm = RB_PARENT(elm, field); \
702  elm = RB_PARENT(elm, field); \
703  } \
704  } \
705  return (elm); \
706 } \
707  \
708 attr struct type * \
709 name##_RB_MINMAX(struct name *head, int val) \
710 { \
711  struct type *tmp = RB_ROOT(head); \
712  struct type *parent = NULL; \
713  while (tmp) { \
714  parent = tmp; \
715  if (val < 0) \
716  tmp = RB_LEFT(tmp, field); \
717  else \
718  tmp = RB_RIGHT(tmp, field); \
719  } \
720  return (parent); \
721 }
722 
723 #define RB_NEGINF -1
724 #define RB_INF 1
725 
726 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
727 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
728 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
729 #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
730 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
731 #define RB_PREV(name, x, y) name##_RB_PREV(y)
732 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
733 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
734 
735 #define RB_FOREACH(x, name, head) \
736  for ((x) = RB_MIN(name, head); \
737  (x) != NULL; \
738  (x) = name##_RB_NEXT(x))
739 
740 #define RB_FOREACH_FROM(x, name, y) \
741  for ((x) = (y); \
742  ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
743  (x) = (y))
744 
745 #define RB_FOREACH_SAFE(x, name, head, y) \
746  for ((x) = RB_MIN(name, head); \
747  ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
748  (x) = (y))
749 
750 #define RB_FOREACH_REVERSE(x, name, head) \
751  for ((x) = RB_MAX(name, head); \
752  (x) != NULL; \
753  (x) = name##_RB_PREV(x))
754 
755 #define RB_FOREACH_REVERSE_FROM(x, name, y) \
756  for ((x) = (y); \
757  ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
758  (x) = (y))
759 
760 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
761  for ((x) = RB_MAX(name, head); \
762  ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
763  (x) = (y))
764 
765 #endif /* _SYS_TREE_H_ */