xref: /freebsd/sys/vm/vm_radix.c (revision 2e654ff9dfeab072161ca370e2b3f621ed67e393)
1 /*
2  * Copyright (c) 2013 EMC Corp.
3  * Copyright (c) 2011 Jeffrey Roberson <jeff@freebsd.org>
4  * Copyright (c) 2008 Mayur Shardul <mayur.shardul@gmail.com>
5  * All rights reserved.
6  *
7  * Redistribution and use in source and binary forms, with or without
8  * modification, are permitted provided that the following conditions
9  * are met:
10  * 1. Redistributions of source code must retain the above copyright
11  *    notice, this list of conditions and the following disclaimer.
12  * 2. Redistributions in binary form must reproduce the above copyright
13  *    notice, this list of conditions and the following disclaimer in the
14  *    documentation and/or other materials provided with the distribution.
15  *
16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26  * SUCH DAMAGE.
27  *
28  */
29 
30 /*
31  * Path-compressed radix trie implementation.
32  * The following code is not generalized into a general purpose library
33  * because there are way too many parameters embedded that should really
34  * be decided by the library consumers.  At the same time, consumers
35  * of this code must achieve highest possible performance.
36  *
37  * The implementation takes into account the following rationale:
38  * - Size of the nodes should be as small as possible but still big enough
39  *   to avoid a large maximum depth for the trie.  This is a balance
40  *   between the necessity to not wire too much physical memory for the nodes
41  *   and the necessity to avoid too much cache pollution during the trie
42  *   operations.
43  * - There is not a huge bias toward the number of lookup operations over
44  *   the number of insert and remove operations.  This basically implies
45  *   that optimizations supposedly helping one operation but hurting the
46  *   other might be carefully evaluated.
47  * - On average not many nodes are expected to be fully populated, hence
48  *   level compression may just complicate things.
49  */
50 
51 #include <sys/cdefs.h>
52 __FBSDID("$FreeBSD$");
53 
54 #include "opt_ddb.h"
55 
56 #include <sys/param.h>
57 #include <sys/systm.h>
58 #include <sys/kernel.h>
59 #include <sys/vmmeter.h>
60 
61 #include <vm/uma.h>
62 #include <vm/vm.h>
63 #include <vm/vm_param.h>
64 #include <vm/vm_page.h>
65 #include <vm/vm_radix.h>
66 
67 #ifdef DDB
68 #include <ddb/ddb.h>
69 #endif
70 
71 /*
72  * These widths should allow the pointers to a node's children to fit within
73  * a single cache line.  The extra levels from a narrow width should not be
74  * a problem thanks to path compression.
75  */
76 #ifdef __LP64__
77 #define	VM_RADIX_WIDTH	4
78 #else
79 #define	VM_RADIX_WIDTH	3
80 #endif
81 
82 #define	VM_RADIX_COUNT	(1 << VM_RADIX_WIDTH)
83 #define	VM_RADIX_MASK	(VM_RADIX_COUNT - 1)
84 #define	VM_RADIX_LIMIT							\
85 	(howmany((sizeof(vm_pindex_t) * NBBY), VM_RADIX_WIDTH) - 1)
86 
87 /* Flag bits stored in node pointers. */
88 #define	VM_RADIX_ISLEAF	0x1
89 #define	VM_RADIX_FLAGS	0x1
90 #define	VM_RADIX_PAD	VM_RADIX_FLAGS
91 
92 /* Returns one unit associated with specified level. */
93 #define	VM_RADIX_UNITLEVEL(lev)						\
94 	((vm_pindex_t)1 << ((VM_RADIX_LIMIT - (lev)) * VM_RADIX_WIDTH))
95 
96 struct vm_radix_node {
97 	vm_pindex_t	 rn_owner;			/* Owner of record. */
98 	uint16_t	 rn_count;			/* Valid children. */
99 	uint16_t	 rn_clev;			/* Current level. */
100 	void		*rn_child[VM_RADIX_COUNT];	/* Child nodes. */
101 };
102 
103 static uma_zone_t vm_radix_node_zone;
104 
105 /*
106  * Allocate a radix node.  Pre-allocation should ensure that the request
107  * will always be satisfied.
108  */
109 static __inline struct vm_radix_node *
110 vm_radix_node_get(vm_pindex_t owner, uint16_t count, uint16_t clevel)
111 {
112 	struct vm_radix_node *rnode;
113 
114 	rnode = uma_zalloc(vm_radix_node_zone, M_NOWAIT);
115 
116 	/*
117 	 * The required number of nodes should already be pre-allocated
118 	 * by vm_radix_prealloc().  However, UMA can hold a few nodes
119 	 * in per-CPU buckets, which will not be accessible by the
120 	 * current CPU.  Thus, the allocation could return NULL when
121 	 * the pre-allocated pool is close to exhaustion.  Anyway,
122 	 * in practice this should never occur because a new node
123 	 * is not always required for insert.  Thus, the pre-allocated
124 	 * pool should have some extra pages that prevent this from
125 	 * becoming a problem.
126 	 */
127 	if (rnode == NULL)
128 		panic("%s: uma_zalloc() returned NULL for a new node",
129 		    __func__);
130 	rnode->rn_owner = owner;
131 	rnode->rn_count = count;
132 	rnode->rn_clev = clevel;
133 	return (rnode);
134 }
135 
136 /*
137  * Free radix node.
138  */
139 static __inline void
140 vm_radix_node_put(struct vm_radix_node *rnode)
141 {
142 
143 	uma_zfree(vm_radix_node_zone, rnode);
144 }
145 
146 /*
147  * Return the position in the array for a given level.
148  */
149 static __inline int
150 vm_radix_slot(vm_pindex_t index, uint16_t level)
151 {
152 
153 	return ((index >> ((VM_RADIX_LIMIT - level) * VM_RADIX_WIDTH)) &
154 	    VM_RADIX_MASK);
155 }
156 
157 /* Trims the key after the specified level. */
158 static __inline vm_pindex_t
159 vm_radix_trimkey(vm_pindex_t index, uint16_t level)
160 {
161 	vm_pindex_t ret;
162 
163 	ret = index;
164 	if (level < VM_RADIX_LIMIT) {
165 		ret >>= (VM_RADIX_LIMIT - level) * VM_RADIX_WIDTH;
166 		ret <<= (VM_RADIX_LIMIT - level) * VM_RADIX_WIDTH;
167 	}
168 	return (ret);
169 }
170 
171 /*
172  * Get the root node for a radix tree.
173  */
174 static __inline struct vm_radix_node *
175 vm_radix_getroot(struct vm_radix *rtree)
176 {
177 
178 	return ((struct vm_radix_node *)rtree->rt_root);
179 }
180 
181 /*
182  * Set the root node for a radix tree.
183  */
184 static __inline void
185 vm_radix_setroot(struct vm_radix *rtree, struct vm_radix_node *rnode)
186 {
187 
188 	rtree->rt_root = (uintptr_t)rnode;
189 }
190 
191 /*
192  * Returns TRUE if the specified radix node is a leaf and FALSE otherwise.
193  */
194 static __inline boolean_t
195 vm_radix_isleaf(struct vm_radix_node *rnode)
196 {
197 
198 	return (((uintptr_t)rnode & VM_RADIX_ISLEAF) != 0);
199 }
200 
201 /*
202  * Returns the associated page extracted from rnode.
203  */
204 static __inline vm_page_t
205 vm_radix_topage(struct vm_radix_node *rnode)
206 {
207 
208 	return ((vm_page_t)((uintptr_t)rnode & ~VM_RADIX_FLAGS));
209 }
210 
211 /*
212  * Adds the page as a child of the provided node.
213  */
214 static __inline void
215 vm_radix_addpage(struct vm_radix_node *rnode, vm_pindex_t index, uint16_t clev,
216     vm_page_t page)
217 {
218 	int slot;
219 
220 	slot = vm_radix_slot(index, clev);
221 	rnode->rn_child[slot] = (void *)((uintptr_t)page | VM_RADIX_ISLEAF);
222 }
223 
224 /*
225  * Returns the slot where two keys differ.
226  * It cannot accept 2 equal keys.
227  */
228 static __inline uint16_t
229 vm_radix_keydiff(vm_pindex_t index1, vm_pindex_t index2)
230 {
231 	uint16_t clev;
232 
233 	KASSERT(index1 != index2, ("%s: passing the same key value %jx",
234 	    __func__, (uintmax_t)index1));
235 
236 	index1 ^= index2;
237 	for (clev = 0; clev <= VM_RADIX_LIMIT ; clev++)
238 		if (vm_radix_slot(index1, clev))
239 			return (clev);
240 	panic("%s: cannot reach this point", __func__);
241 	return (0);
242 }
243 
244 /*
245  * Returns TRUE if it can be determined that key does not belong to the
246  * specified rnode.  Otherwise, returns FALSE.
247  */
248 static __inline boolean_t
249 vm_radix_keybarr(struct vm_radix_node *rnode, vm_pindex_t idx)
250 {
251 
252 	if (rnode->rn_clev > 0) {
253 		idx = vm_radix_trimkey(idx, rnode->rn_clev - 1);
254 		return (idx != rnode->rn_owner);
255 	}
256 	return (FALSE);
257 }
258 
259 /*
260  * Adjusts the idx key to the first upper level available, based on a valid
261  * initial level and map of available levels.
262  * Returns a value bigger than 0 to signal that there are not valid levels
263  * available.
264  */
265 static __inline int
266 vm_radix_addlev(vm_pindex_t *idx, boolean_t *levels, uint16_t ilev)
267 {
268 	vm_pindex_t wrapidx;
269 
270 	for (; levels[ilev] == FALSE ||
271 	    vm_radix_slot(*idx, ilev) == (VM_RADIX_COUNT - 1); ilev--)
272 		if (ilev == 0)
273 			return (1);
274 	wrapidx = *idx;
275 	*idx = vm_radix_trimkey(*idx, ilev);
276 	*idx += VM_RADIX_UNITLEVEL(ilev);
277 	return (*idx < wrapidx);
278 }
279 
280 /*
281  * Adjusts the idx key to the first lower level available, based on a valid
282  * initial level and map of available levels.
283  * Returns a value bigger than 0 to signal that there are not valid levels
284  * available.
285  */
286 static __inline int
287 vm_radix_declev(vm_pindex_t *idx, boolean_t *levels, uint16_t ilev)
288 {
289 	vm_pindex_t wrapidx;
290 
291 	for (; levels[ilev] == FALSE ||
292 	    vm_radix_slot(*idx, ilev) == 0; ilev--)
293 		if (ilev == 0)
294 			return (1);
295 	wrapidx = *idx;
296 	*idx = vm_radix_trimkey(*idx, ilev);
297 	*idx |= VM_RADIX_UNITLEVEL(ilev) - 1;
298 	*idx -= VM_RADIX_UNITLEVEL(ilev);
299 	return (*idx > wrapidx);
300 }
301 
302 /*
303  * Internal helper for vm_radix_reclaim_allnodes().
304  * This function is recursive.
305  */
306 static void
307 vm_radix_reclaim_allnodes_int(struct vm_radix_node *rnode)
308 {
309 	int slot;
310 
311 	KASSERT(rnode->rn_count <= VM_RADIX_COUNT,
312 	    ("vm_radix_reclaim_allnodes_int: bad count in rnode %p", rnode));
313 	for (slot = 0; rnode->rn_count != 0; slot++) {
314 		if (rnode->rn_child[slot] == NULL)
315 			continue;
316 		if (!vm_radix_isleaf(rnode->rn_child[slot]))
317 			vm_radix_reclaim_allnodes_int(rnode->rn_child[slot]);
318 		rnode->rn_child[slot] = NULL;
319 		rnode->rn_count--;
320 	}
321 	vm_radix_node_put(rnode);
322 }
323 
324 #ifdef INVARIANTS
325 /*
326  * Radix node zone destructor.
327  */
328 static void
329 vm_radix_node_zone_dtor(void *mem, int size __unused, void *arg __unused)
330 {
331 	struct vm_radix_node *rnode;
332 	int slot;
333 
334 	rnode = mem;
335 	KASSERT(rnode->rn_count == 0,
336 	    ("vm_radix_node_put: rnode %p has %d children", rnode,
337 	    rnode->rn_count));
338 	for (slot = 0; slot < VM_RADIX_COUNT; slot++)
339 		KASSERT(rnode->rn_child[slot] == NULL,
340 		    ("vm_radix_node_put: rnode %p has a child", rnode));
341 }
342 #endif
343 
344 /*
345  * Radix node zone initializer.
346  */
347 static int
348 vm_radix_node_zone_init(void *mem, int size __unused, int flags __unused)
349 {
350 	struct vm_radix_node *rnode;
351 
352 	rnode = mem;
353 	memset(rnode->rn_child, 0, sizeof(rnode->rn_child));
354 	return (0);
355 }
356 
357 /*
358  * Pre-allocate intermediate nodes from the UMA slab zone.
359  */
360 static void
361 vm_radix_prealloc(void *arg __unused)
362 {
363 
364 	if (!uma_zone_reserve_kva(vm_radix_node_zone, cnt.v_page_count))
365 		panic("%s: unable to create new zone", __func__);
366 	uma_prealloc(vm_radix_node_zone, cnt.v_page_count);
367 }
368 SYSINIT(vm_radix_prealloc, SI_SUB_KMEM, SI_ORDER_SECOND, vm_radix_prealloc,
369     NULL);
370 
371 /*
372  * Initialize the UMA slab zone.
373  * Until vm_radix_prealloc() is called, the zone will be served by the
374  * UMA boot-time pre-allocated pool of pages.
375  */
376 void
377 vm_radix_init(void)
378 {
379 
380 	vm_radix_node_zone = uma_zcreate("RADIX NODE",
381 	    sizeof(struct vm_radix_node), NULL,
382 #ifdef INVARIANTS
383 	    vm_radix_node_zone_dtor,
384 #else
385 	    NULL,
386 #endif
387 	    vm_radix_node_zone_init, NULL, VM_RADIX_PAD, UMA_ZONE_VM |
388 	    UMA_ZONE_NOFREE);
389 }
390 
391 /*
392  * Inserts the key-value pair into the trie.
393  * Panics if the key already exists.
394  */
395 void
396 vm_radix_insert(struct vm_radix *rtree, vm_page_t page)
397 {
398 	vm_pindex_t index, newind;
399 	void **parentp;
400 	struct vm_radix_node *rnode, *tmp;
401 	vm_page_t m;
402 	int slot;
403 	uint16_t clev;
404 
405 	index = page->pindex;
406 
407 	/*
408 	 * The owner of record for root is not really important because it
409 	 * will never be used.
410 	 */
411 	rnode = vm_radix_getroot(rtree);
412 	if (rnode == NULL) {
413 		rtree->rt_root = (uintptr_t)page | VM_RADIX_ISLEAF;
414 		return;
415 	}
416 	parentp = (void **)&rtree->rt_root;
417 	for (;;) {
418 		if (vm_radix_isleaf(rnode)) {
419 			m = vm_radix_topage(rnode);
420 			if (m->pindex == index)
421 				panic("%s: key %jx is already present",
422 				    __func__, (uintmax_t)index);
423 			clev = vm_radix_keydiff(m->pindex, index);
424 			tmp = vm_radix_node_get(vm_radix_trimkey(index,
425 			    clev - 1), 2, clev);
426 			*parentp = tmp;
427 			vm_radix_addpage(tmp, index, clev, page);
428 			vm_radix_addpage(tmp, m->pindex, clev, m);
429 			return;
430 		} else if (vm_radix_keybarr(rnode, index))
431 			break;
432 		slot = vm_radix_slot(index, rnode->rn_clev);
433 		if (rnode->rn_child[slot] == NULL) {
434 			rnode->rn_count++;
435 			vm_radix_addpage(rnode, index, rnode->rn_clev, page);
436 			return;
437 		}
438 		parentp = &rnode->rn_child[slot];
439 		rnode = rnode->rn_child[slot];
440 	}
441 
442 	/*
443 	 * A new node is needed because the right insertion level is reached.
444 	 * Setup the new intermediate node and add the 2 children: the
445 	 * new object and the older edge.
446 	 */
447 	newind = rnode->rn_owner;
448 	clev = vm_radix_keydiff(newind, index);
449 	tmp = vm_radix_node_get(vm_radix_trimkey(index, clev - 1), 2,
450 	    clev);
451 	*parentp = tmp;
452 	vm_radix_addpage(tmp, index, clev, page);
453 	slot = vm_radix_slot(newind, clev);
454 	tmp->rn_child[slot] = rnode;
455 }
456 
457 /*
458  * Returns the value stored at the index.  If the index is not present,
459  * NULL is returned.
460  */
461 vm_page_t
462 vm_radix_lookup(struct vm_radix *rtree, vm_pindex_t index)
463 {
464 	struct vm_radix_node *rnode;
465 	vm_page_t m;
466 	int slot;
467 
468 	rnode = vm_radix_getroot(rtree);
469 	while (rnode != NULL) {
470 		if (vm_radix_isleaf(rnode)) {
471 			m = vm_radix_topage(rnode);
472 			if (m->pindex == index)
473 				return (m);
474 			else
475 				break;
476 		} else if (vm_radix_keybarr(rnode, index))
477 			break;
478 		slot = vm_radix_slot(index, rnode->rn_clev);
479 		rnode = rnode->rn_child[slot];
480 	}
481 	return (NULL);
482 }
483 
484 /*
485  * Look up the nearest entry at a position bigger than or equal to index.
486  */
487 vm_page_t
488 vm_radix_lookup_ge(struct vm_radix *rtree, vm_pindex_t index)
489 {
490 	vm_pindex_t inc;
491 	vm_page_t m;
492 	struct vm_radix_node *child, *rnode;
493 	int slot;
494 	uint16_t difflev;
495 	boolean_t maplevels[VM_RADIX_LIMIT + 1];
496 #ifdef INVARIANTS
497 	int loops = 0;
498 #endif
499 
500 	rnode = vm_radix_getroot(rtree);
501 	if (rnode == NULL)
502 		return (NULL);
503 	else if (vm_radix_isleaf(rnode)) {
504 		m = vm_radix_topage(rnode);
505 		if (m->pindex >= index)
506 			return (m);
507 		else
508 			return (NULL);
509 	}
510 restart:
511 	KASSERT(++loops < 1000, ("%s: too many loops", __func__));
512 	for (difflev = 0; difflev < (VM_RADIX_LIMIT + 1); difflev++)
513 		maplevels[difflev] = FALSE;
514 	for (;;) {
515 		maplevels[rnode->rn_clev] = TRUE;
516 
517 		/*
518 		 * If the keys differ before the current bisection node
519 		 * the search key might rollback to the earliest
520 		 * available bisection node, or to the smaller value
521 		 * in the current domain (if the owner is bigger than the
522 		 * search key).
523 		 * The maplevels array records any node has been seen
524 		 * at a given level.  This aids the search for a valid
525 		 * bisection node.
526 		 */
527 		if (vm_radix_keybarr(rnode, index)) {
528 			difflev = vm_radix_keydiff(index, rnode->rn_owner);
529 			if (index > rnode->rn_owner) {
530 				if (vm_radix_addlev(&index, maplevels,
531 				    difflev) > 0)
532 					break;
533 			} else
534 				index = vm_radix_trimkey(rnode->rn_owner,
535 				    difflev);
536 			rnode = vm_radix_getroot(rtree);
537 			goto restart;
538 		}
539 		slot = vm_radix_slot(index, rnode->rn_clev);
540 		child = rnode->rn_child[slot];
541 		if (vm_radix_isleaf(child)) {
542 			m = vm_radix_topage(child);
543 			if (m->pindex >= index)
544 				return (m);
545 		} else if (child != NULL)
546 			goto descend;
547 
548 		/*
549 		 * Look for an available edge or page within the current
550 		 * bisection node.
551 		 */
552                 if (slot < (VM_RADIX_COUNT - 1)) {
553 			inc = VM_RADIX_UNITLEVEL(rnode->rn_clev);
554 			index = vm_radix_trimkey(index, rnode->rn_clev);
555 			do {
556 				index += inc;
557 				slot++;
558 				child = rnode->rn_child[slot];
559 				if (vm_radix_isleaf(child)) {
560 					m = vm_radix_topage(child);
561 					if (m->pindex >= index)
562 						return (m);
563 				} else if (child != NULL)
564 					goto descend;
565 			} while (slot < (VM_RADIX_COUNT - 1));
566 		}
567 		KASSERT(child == NULL || vm_radix_isleaf(child),
568 		    ("vm_radix_lookup_ge: child is radix node"));
569 
570 		/*
571 		 * If a valid page or edge bigger than the search slot is
572 		 * found in the traversal, skip to the next higher-level key.
573 		 */
574 		if (rnode->rn_clev == 0 || vm_radix_addlev(&index, maplevels,
575 		    rnode->rn_clev - 1) > 0)
576 			break;
577 		rnode = vm_radix_getroot(rtree);
578 		goto restart;
579 descend:
580 		rnode = child;
581 	}
582 	return (NULL);
583 }
584 
585 /*
586  * Look up the nearest entry at a position less than or equal to index.
587  */
588 vm_page_t
589 vm_radix_lookup_le(struct vm_radix *rtree, vm_pindex_t index)
590 {
591 	vm_pindex_t inc;
592 	vm_page_t m;
593 	struct vm_radix_node *child, *rnode;
594 	int slot;
595 	uint16_t difflev;
596 	boolean_t maplevels[VM_RADIX_LIMIT + 1];
597 #ifdef INVARIANTS
598 	int loops = 0;
599 #endif
600 
601 	rnode = vm_radix_getroot(rtree);
602 	if (rnode == NULL)
603 		return (NULL);
604 	else if (vm_radix_isleaf(rnode)) {
605 		m = vm_radix_topage(rnode);
606 		if (m->pindex <= index)
607 			return (m);
608 		else
609 			return (NULL);
610 	}
611 restart:
612 	KASSERT(++loops < 1000, ("%s: too many loops", __func__));
613 	for (difflev = 0; difflev < (VM_RADIX_LIMIT + 1); difflev++)
614 		maplevels[difflev] = FALSE;
615 	for (;;) {
616 		maplevels[rnode->rn_clev] = TRUE;
617 
618 		/*
619 		 * If the keys differ before the current bisection node
620 		 * the search key might rollback to the earliest
621 		 * available bisection node, or to the higher value
622 		 * in the current domain (if the owner is smaller than the
623 		 * search key).
624 		 * The maplevels array records any node has been seen
625 		 * at a given level.  This aids the search for a valid
626 		 * bisection node.
627 		 */
628 		if (vm_radix_keybarr(rnode, index)) {
629 			difflev = vm_radix_keydiff(index, rnode->rn_owner);
630 			if (index > rnode->rn_owner) {
631 				index = vm_radix_trimkey(rnode->rn_owner,
632 				    difflev);
633 				index |= VM_RADIX_UNITLEVEL(difflev) - 1;
634 			} else if (vm_radix_declev(&index, maplevels,
635 			    difflev) > 0)
636 				break;
637 			rnode = vm_radix_getroot(rtree);
638 			goto restart;
639 		}
640 		slot = vm_radix_slot(index, rnode->rn_clev);
641 		child = rnode->rn_child[slot];
642 		if (vm_radix_isleaf(child)) {
643 			m = vm_radix_topage(child);
644 			if (m->pindex <= index)
645 				return (m);
646 		} else if (child != NULL)
647 			goto descend;
648 
649 		/*
650 		 * Look for an available edge or page within the current
651 		 * bisection node.
652 		 */
653 		if (slot > 0) {
654 			inc = VM_RADIX_UNITLEVEL(rnode->rn_clev);
655 			index = vm_radix_trimkey(index, rnode->rn_clev);
656 			index |= inc - 1;
657 			do {
658 				index -= inc;
659 				slot--;
660 				child = rnode->rn_child[slot];
661 				if (vm_radix_isleaf(child)) {
662 					m = vm_radix_topage(child);
663 					if (m->pindex <= index)
664 						return (m);
665 				} else if (child != NULL)
666 					goto descend;
667 			} while (slot > 0);
668 		}
669 		KASSERT(child == NULL || vm_radix_isleaf(child),
670 		    ("vm_radix_lookup_le: child is radix node"));
671 
672 		/*
673 		 * If a valid page or edge smaller than the search slot is
674 		 * found in the traversal, skip to the next higher-level key.
675 		 */
676 		if (rnode->rn_clev == 0 || vm_radix_declev(&index, maplevels,
677 		    rnode->rn_clev - 1) > 0)
678 			break;
679 		rnode = vm_radix_getroot(rtree);
680 		goto restart;
681 descend:
682 		rnode = child;
683 	}
684 	return (NULL);
685 }
686 
687 /*
688  * Remove the specified index from the tree.
689  * Panics if the key is not present.
690  */
691 void
692 vm_radix_remove(struct vm_radix *rtree, vm_pindex_t index)
693 {
694 	struct vm_radix_node *rnode, *parent;
695 	vm_page_t m;
696 	int i, slot;
697 
698 	rnode = vm_radix_getroot(rtree);
699 	if (vm_radix_isleaf(rnode)) {
700 		m = vm_radix_topage(rnode);
701 		if (m->pindex != index)
702 			panic("%s: invalid key found", __func__);
703 		vm_radix_setroot(rtree, NULL);
704 		return;
705 	}
706 	parent = NULL;
707 	for (;;) {
708 		if (rnode == NULL)
709 			panic("vm_radix_remove: impossible to locate the key");
710 		slot = vm_radix_slot(index, rnode->rn_clev);
711 		if (vm_radix_isleaf(rnode->rn_child[slot])) {
712 			m = vm_radix_topage(rnode->rn_child[slot]);
713 			if (m->pindex != index)
714 				panic("%s: invalid key found", __func__);
715 			rnode->rn_child[slot] = NULL;
716 			rnode->rn_count--;
717 			if (rnode->rn_count > 1)
718 				break;
719 			for (i = 0; i < VM_RADIX_COUNT; i++)
720 				if (rnode->rn_child[i] != NULL)
721 					break;
722 			KASSERT(i != VM_RADIX_COUNT,
723 			    ("%s: invalid node configuration", __func__));
724 			if (parent == NULL)
725 				vm_radix_setroot(rtree, rnode->rn_child[i]);
726 			else {
727 				slot = vm_radix_slot(index, parent->rn_clev);
728 				KASSERT(parent->rn_child[slot] == rnode,
729 				    ("%s: invalid child value", __func__));
730 				parent->rn_child[slot] = rnode->rn_child[i];
731 			}
732 			rnode->rn_count--;
733 			rnode->rn_child[i] = NULL;
734 			vm_radix_node_put(rnode);
735 			break;
736 		}
737 		parent = rnode;
738 		rnode = rnode->rn_child[slot];
739 	}
740 }
741 
742 /*
743  * Remove and free all the nodes from the radix tree.
744  * This function is recursive but there is a tight control on it as the
745  * maximum depth of the tree is fixed.
746  */
747 void
748 vm_radix_reclaim_allnodes(struct vm_radix *rtree)
749 {
750 	struct vm_radix_node *root;
751 
752 	root = vm_radix_getroot(rtree);
753 	if (root == NULL)
754 		return;
755 	vm_radix_setroot(rtree, NULL);
756 	if (!vm_radix_isleaf(root))
757 		vm_radix_reclaim_allnodes_int(root);
758 }
759 
760 #ifdef DDB
761 /*
762  * Show details about the given radix node.
763  */
764 DB_SHOW_COMMAND(radixnode, db_show_radixnode)
765 {
766 	struct vm_radix_node *rnode;
767 	int i;
768 
769         if (!have_addr)
770                 return;
771 	rnode = (struct vm_radix_node *)addr;
772 	db_printf("radixnode %p, owner %jx, children count %u, level %u:\n",
773 	    (void *)rnode, (uintmax_t)rnode->rn_owner, rnode->rn_count,
774 	    rnode->rn_clev);
775 	for (i = 0; i < VM_RADIX_COUNT; i++)
776 		if (rnode->rn_child[i] != NULL)
777 			db_printf("slot: %d, val: %p, page: %p, clev: %d\n",
778 			    i, (void *)rnode->rn_child[i],
779 			    vm_radix_isleaf(rnode->rn_child[i]) ?
780 			    vm_radix_topage(rnode->rn_child[i]) : NULL,
781 			    rnode->rn_clev);
782 }
783 #endif /* DDB */
784