aboutsummaryrefslogtreecommitdiff
path: root/sys/vm/vm_radix.c
blob: b53398ece77ccb4ac04a193306d61ed05383dd9b (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
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
/*-
 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
 *
 * Copyright (c) 2013 EMC Corp.
 * Copyright (c) 2011 Jeffrey Roberson <jeff@freebsd.org>
 * Copyright (c) 2008 Mayur Shardul <mayur.shardul@gmail.com>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 */

/*
 * Path-compressed radix trie implementation.
 * The following code is not generalized into a general purpose library
 * because there are way too many parameters embedded that should really
 * be decided by the library consumers.  At the same time, consumers
 * of this code must achieve highest possible performance.
 *
 * The implementation takes into account the following rationale:
 * - Size of the nodes should be as small as possible but still big enough
 *   to avoid a large maximum depth for the trie.  This is a balance
 *   between the necessity to not wire too much physical memory for the nodes
 *   and the necessity to avoid too much cache pollution during the trie
 *   operations.
 * - There is not a huge bias toward the number of lookup operations over
 *   the number of insert and remove operations.  This basically implies
 *   that optimizations supposedly helping one operation but hurting the
 *   other might be carefully evaluated.
 * - On average not many nodes are expected to be fully populated, hence
 *   level compression may just complicate things.
 */

#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");

#include "opt_ddb.h"

#include <sys/param.h>
#include <sys/systm.h>
#include <sys/kernel.h>
#include <sys/proc.h>
#include <sys/vmmeter.h>
#include <sys/smr.h>
#include <sys/smr_types.h>

#include <vm/uma.h>
#include <vm/vm.h>
#include <vm/vm_param.h>
#include <vm/vm_object.h>
#include <vm/vm_page.h>
#include <vm/vm_radix.h>

#ifdef DDB
#include <ddb/ddb.h>
#endif

/*
 * These widths should allow the pointers to a node's children to fit within
 * a single cache line.  The extra levels from a narrow width should not be
 * a problem thanks to path compression.
 */
#ifdef __LP64__
#define	VM_RADIX_WIDTH	4
#else
#define	VM_RADIX_WIDTH	3
#endif

#define	VM_RADIX_COUNT	(1 << VM_RADIX_WIDTH)
#define	VM_RADIX_MASK	(VM_RADIX_COUNT - 1)
#define	VM_RADIX_LIMIT							\
	(howmany(sizeof(vm_pindex_t) * NBBY, VM_RADIX_WIDTH) - 1)

/* Flag bits stored in node pointers. */
#define	VM_RADIX_ISLEAF	0x1
#define	VM_RADIX_FLAGS	0x1
#define	VM_RADIX_PAD	VM_RADIX_FLAGS

/* Returns one unit associated with specified level. */
#define	VM_RADIX_UNITLEVEL(lev)						\
	((vm_pindex_t)1 << ((lev) * VM_RADIX_WIDTH))

enum vm_radix_access { SMR, LOCKED, UNSERIALIZED };

struct vm_radix_node;
typedef SMR_POINTER(struct vm_radix_node *) smrnode_t;

struct vm_radix_node {
	vm_pindex_t	rn_owner;			/* Owner of record. */
	uint16_t	rn_count;			/* Valid children. */
	uint8_t		rn_clev;			/* Current level. */
	int8_t		rn_last;			/* zero last ptr. */
	smrnode_t	rn_child[VM_RADIX_COUNT];	/* Child nodes. */
};

static uma_zone_t vm_radix_node_zone;
static smr_t vm_radix_smr;

static void vm_radix_node_store(smrnode_t *p, struct vm_radix_node *v,
    enum vm_radix_access access);

/*
 * Allocate a radix node.
 */
static struct vm_radix_node *
vm_radix_node_get(vm_pindex_t owner, uint16_t count, uint16_t clevel)
{
	struct vm_radix_node *rnode;

	rnode = uma_zalloc_smr(vm_radix_node_zone, M_NOWAIT);
	if (rnode == NULL)
		return (NULL);

	/*
	 * We want to clear the last child pointer after the final section
	 * has exited so lookup can not return false negatives.  It is done
	 * here because it will be cache-cold in the dtor callback.
	 */
	if (rnode->rn_last != 0) {
		vm_radix_node_store(&rnode->rn_child[rnode->rn_last - 1],
		    NULL, UNSERIALIZED);
		rnode->rn_last = 0;
	}
	rnode->rn_owner = owner;
	rnode->rn_count = count;
	rnode->rn_clev = clevel;
	return (rnode);
}

/*
 * Free radix node.
 */
static __inline void
vm_radix_node_put(struct vm_radix_node *rnode, int8_t last)
{
#ifdef INVARIANTS
	int slot;

	KASSERT(rnode->rn_count == 0,
	    ("vm_radix_node_put: rnode %p has %d children", rnode,
	    rnode->rn_count));
	for (slot = 0; slot < VM_RADIX_COUNT; slot++) {
		if (slot == last)
			continue;
		KASSERT(smr_unserialized_load(&rnode->rn_child[slot], true) ==
		    NULL, ("vm_radix_node_put: rnode %p has a child", rnode));
	}
#endif
	/* Off by one so a freshly zero'd node is not assigned to. */
	rnode->rn_last = last + 1;
	uma_zfree_smr(vm_radix_node_zone, rnode);
}

/*
 * Return the position in the array for a given level.
 */
static __inline int
vm_radix_slot(vm_pindex_t index, uint16_t level)
{

	return ((index >> (level * VM_RADIX_WIDTH)) & VM_RADIX_MASK);
}

/* Trims the key after the specified level. */
static __inline vm_pindex_t
vm_radix_trimkey(vm_pindex_t index, uint16_t level)
{
	vm_pindex_t ret;

	ret = index;
	if (level > 0) {
		ret >>= level * VM_RADIX_WIDTH;
		ret <<= level * VM_RADIX_WIDTH;
	}
	return (ret);
}

/*
 * Fetch a node pointer from a slot in another node.
 */
static __inline struct vm_radix_node *
vm_radix_node_load(smrnode_t *p, enum vm_radix_access access)
{

	switch (access) {
	case UNSERIALIZED:
		return (smr_unserialized_load(p, true));
	case LOCKED:
		return (smr_serialized_load(p, true));
	case SMR:
		return (smr_entered_load(p, vm_radix_smr));
	}
	__assert_unreachable();
}

static __inline void
vm_radix_node_store(smrnode_t *p, struct vm_radix_node *v,
    enum vm_radix_access access)
{

	switch (access) {
	case UNSERIALIZED:
		smr_unserialized_store(p, v, true);
		break;
	case LOCKED:
		smr_serialized_store(p, v, true);
		break;
	case SMR:
		panic("vm_radix_node_store: Not supported in smr section.");
	}
}

/*
 * Get the root node for a radix tree.
 */
static __inline struct vm_radix_node *
vm_radix_root_load(struct vm_radix *rtree, enum vm_radix_access access)
{

	return (vm_radix_node_load((smrnode_t *)&rtree->rt_root, access));
}

/*
 * Set the root node for a radix tree.
 */
static __inline void
vm_radix_root_store(struct vm_radix *rtree, struct vm_radix_node *rnode,
    enum vm_radix_access access)
{

	vm_radix_node_store((smrnode_t *)&rtree->rt_root, rnode, access);
}

/*
 * Returns TRUE if the specified radix node is a leaf and FALSE otherwise.
 */
static __inline boolean_t
vm_radix_isleaf(struct vm_radix_node *rnode)
{

	return (((uintptr_t)rnode & VM_RADIX_ISLEAF) != 0);
}

/*
 * Returns the associated page extracted from rnode.
 */
static __inline vm_page_t
vm_radix_topage(struct vm_radix_node *rnode)
{

	return ((vm_page_t)((uintptr_t)rnode & ~VM_RADIX_FLAGS));
}

/*
 * Adds the page as a child of the provided node.
 */
static __inline void
vm_radix_addpage(struct vm_radix_node *rnode, vm_pindex_t index, uint16_t clev,
    vm_page_t page, enum vm_radix_access access)
{
	int slot;

	slot = vm_radix_slot(index, clev);
	vm_radix_node_store(&rnode->rn_child[slot],
	    (struct vm_radix_node *)((uintptr_t)page | VM_RADIX_ISLEAF), access);
}

/*
 * Returns the slot where two keys differ.
 * It cannot accept 2 equal keys.
 */
static __inline uint16_t
vm_radix_keydiff(vm_pindex_t index1, vm_pindex_t index2)
{
	uint16_t clev;

	KASSERT(index1 != index2, ("%s: passing the same key value %jx",
	    __func__, (uintmax_t)index1));

	index1 ^= index2;
	for (clev = VM_RADIX_LIMIT;; clev--)
		if (vm_radix_slot(index1, clev) != 0)
			return (clev);
}

/*
 * Returns TRUE if it can be determined that key does not belong to the
 * specified rnode.  Otherwise, returns FALSE.
 */
static __inline boolean_t
vm_radix_keybarr(struct vm_radix_node *rnode, vm_pindex_t idx)
{

	if (rnode->rn_clev < VM_RADIX_LIMIT) {
		idx = vm_radix_trimkey(idx, rnode->rn_clev + 1);
		return (idx != rnode->rn_owner);
	}
	return (FALSE);
}

/*
 * Internal helper for vm_radix_reclaim_allnodes().
 * This function is recursive.
 */
static void
vm_radix_reclaim_allnodes_int(struct vm_radix_node *rnode)
{
	struct vm_radix_node *child;
	int slot;

	KASSERT(rnode->rn_count <= VM_RADIX_COUNT,
	    ("vm_radix_reclaim_allnodes_int: bad count in rnode %p", rnode));
	for (slot = 0; rnode->rn_count != 0; slot++) {
		child = vm_radix_node_load(&rnode->rn_child[slot], UNSERIALIZED);
		if (child == NULL)
			continue;
		if (!vm_radix_isleaf(child))
			vm_radix_reclaim_allnodes_int(child);
		vm_radix_node_store(&rnode->rn_child[slot], NULL, UNSERIALIZED);
		rnode->rn_count--;
	}
	vm_radix_node_put(rnode, -1);
}

#ifndef UMA_MD_SMALL_ALLOC
void vm_radix_reserve_kva(void);
/*
 * Reserve the KVA necessary to satisfy the node allocation.
 * This is mandatory in architectures not supporting direct
 * mapping as they will need otherwise to carve into the kernel maps for
 * every node allocation, resulting into deadlocks for consumers already
 * working with kernel maps.
 */
void
vm_radix_reserve_kva(void)
{

	/*
	 * Calculate the number of reserved nodes, discounting the pages that
	 * are needed to store them.
	 */
	if (!uma_zone_reserve_kva(vm_radix_node_zone,
	    ((vm_paddr_t)vm_cnt.v_page_count * PAGE_SIZE) / (PAGE_SIZE +
	    sizeof(struct vm_radix_node))))
		panic("%s: unable to reserve KVA", __func__);
}
#endif

/*
 * Initialize the UMA slab zone.
 */
void
vm_radix_zinit(void)
{

	vm_radix_node_zone = uma_zcreate("RADIX NODE",
	    sizeof(struct vm_radix_node), NULL, NULL, NULL, NULL,
	    VM_RADIX_PAD, UMA_ZONE_VM | UMA_ZONE_SMR | UMA_ZONE_ZINIT);
	vm_radix_smr = uma_zone_get_smr(vm_radix_node_zone);
}

/*
 * Inserts the key-value pair into the trie.
 * Panics if the key already exists.
 */
int
vm_radix_insert(struct vm_radix *rtree, vm_page_t page)
{
	vm_pindex_t index, newind;
	struct vm_radix_node *rnode, *tmp;
	smrnode_t *parentp;
	vm_page_t m;
	int slot;
	uint16_t clev;

	index = page->pindex;

	/*
	 * The owner of record for root is not really important because it
	 * will never be used.
	 */
	rnode = vm_radix_root_load(rtree, LOCKED);
	if (rnode == NULL) {
		rtree->rt_root = (uintptr_t)page | VM_RADIX_ISLEAF;
		return (0);
	}
	parentp = (smrnode_t *)&rtree->rt_root;
	for (;;) {
		if (vm_radix_isleaf(rnode)) {
			m = vm_radix_topage(rnode);
			if (m->pindex == index)
				panic("%s: key %jx is already present",
				    __func__, (uintmax_t)index);
			clev = vm_radix_keydiff(m->pindex, index);
			tmp = vm_radix_node_get(vm_radix_trimkey(index,
			    clev + 1), 2, clev);
			if (tmp == NULL)
				return (ENOMEM);
			/* These writes are not yet visible due to ordering. */
			vm_radix_addpage(tmp, index, clev, page, UNSERIALIZED);
			vm_radix_addpage(tmp, m->pindex, clev, m, UNSERIALIZED);
			/* Synchronize to make leaf visible. */
			vm_radix_node_store(parentp, tmp, LOCKED);
			return (0);
		} else if (vm_radix_keybarr(rnode, index))
			break;
		slot = vm_radix_slot(index, rnode->rn_clev);
		parentp = &rnode->rn_child[slot];
		tmp = vm_radix_node_load(parentp, LOCKED);
		if (tmp == NULL) {
			rnode->rn_count++;
			vm_radix_addpage(rnode, index, rnode->rn_clev, page,
			    LOCKED);
			return (0);
		}
		rnode = tmp;
	}

	/*
	 * A new node is needed because the right insertion level is reached.
	 * Setup the new intermediate node and add the 2 children: the
	 * new object and the older edge.
	 */
	newind = rnode->rn_owner;
	clev = vm_radix_keydiff(newind, index);
	tmp = vm_radix_node_get(vm_radix_trimkey(index, clev + 1), 2, clev);
	if (tmp == NULL)
		return (ENOMEM);
	slot = vm_radix_slot(newind, clev);
	/* These writes are not yet visible due to ordering. */
	vm_radix_addpage(tmp, index, clev, page, UNSERIALIZED);
	vm_radix_node_store(&tmp->rn_child[slot], rnode, UNSERIALIZED);
	/* Serializing write to make the above visible. */
	vm_radix_node_store(parentp, tmp, LOCKED);

	return (0);
}

/*
 * Returns TRUE if the specified radix tree contains a single leaf and FALSE
 * otherwise.
 */
boolean_t
vm_radix_is_singleton(struct vm_radix *rtree)
{
	struct vm_radix_node *rnode;

	rnode = vm_radix_root_load(rtree, LOCKED);
	if (rnode == NULL)
		return (FALSE);
	return (vm_radix_isleaf(rnode));
}

/*
 * Returns the value stored at the index.  If the index is not present,
 * NULL is returned.
 */
static __always_inline vm_page_t
_vm_radix_lookup(struct vm_radix *rtree, vm_pindex_t index,
    enum vm_radix_access access)
{
	struct vm_radix_node *rnode;
	vm_page_t m;
	int slot;

	rnode = vm_radix_root_load(rtree, access);
	while (rnode != NULL) {
		if (vm_radix_isleaf(rnode)) {
			m = vm_radix_topage(rnode);
			if (m->pindex == index)
				return (m);
			break;
		}
		if (vm_radix_keybarr(rnode, index))
			break;
		slot = vm_radix_slot(index, rnode->rn_clev);
		rnode = vm_radix_node_load(&rnode->rn_child[slot], access);
	}
	return (NULL);
}

/*
 * Returns the value stored at the index assuming there is an external lock.
 *
 * If the index is not present, NULL is returned.
 */
vm_page_t
vm_radix_lookup(struct vm_radix *rtree, vm_pindex_t index)
{

	return _vm_radix_lookup(rtree, index, LOCKED);
}

/*
 * Returns the value stored at the index without requiring an external lock.
 *
 * If the index is not present, NULL is returned.
 */
vm_page_t
vm_radix_lookup_unlocked(struct vm_radix *rtree, vm_pindex_t index)
{
	vm_page_t m;

	smr_enter(vm_radix_smr);
	m = _vm_radix_lookup(rtree, index, SMR);
	smr_exit(vm_radix_smr);

	return (m);
}

/*
 * Look up the nearest entry at a position greater than or equal to index.
 */
vm_page_t
vm_radix_lookup_ge(struct vm_radix *rtree, vm_pindex_t index)
{
	struct vm_radix_node *stack[VM_RADIX_LIMIT];
	vm_pindex_t inc;
	vm_page_t m;
	struct vm_radix_node *child, *rnode;
#ifdef INVARIANTS
	int loops = 0;
#endif
	int slot, tos;

	rnode = vm_radix_root_load(rtree, LOCKED);
	if (rnode == NULL)
		return (NULL);
	else if (vm_radix_isleaf(rnode)) {
		m = vm_radix_topage(rnode);
		if (m->pindex >= index)
			return (m);
		else
			return (NULL);
	}
	tos = 0;
	for (;;) {
		/*
		 * If the keys differ before the current bisection node,
		 * then the search key might rollback to the earliest
		 * available bisection node or to the smallest key
		 * in the current node (if the owner is greater than the
		 * search key).
		 */
		if (vm_radix_keybarr(rnode, index)) {
			if (index > rnode->rn_owner) {
ascend:
				KASSERT(++loops < 1000,
				    ("vm_radix_lookup_ge: too many loops"));

				/*
				 * Pop nodes from the stack until either the
				 * stack is empty or a node that could have a
				 * matching descendant is found.
				 */
				do {
					if (tos == 0)
						return (NULL);
					rnode = stack[--tos];
				} while (vm_radix_slot(index,
				    rnode->rn_clev) == (VM_RADIX_COUNT - 1));

				/*
				 * The following computation cannot overflow
				 * because index's slot at the current level
				 * is less than VM_RADIX_COUNT - 1.
				 */
				index = vm_radix_trimkey(index,
				    rnode->rn_clev);
				index += VM_RADIX_UNITLEVEL(rnode->rn_clev);
			} else
				index = rnode->rn_owner;
			KASSERT(!vm_radix_keybarr(rnode, index),
			    ("vm_radix_lookup_ge: keybarr failed"));
		}
		slot = vm_radix_slot(index, rnode->rn_clev);
		child = vm_radix_node_load(&rnode->rn_child[slot], LOCKED);
		if (vm_radix_isleaf(child)) {
			m = vm_radix_topage(child);
			if (m->pindex >= index)
				return (m);
		} else if (child != NULL)
			goto descend;

		/*
		 * Look for an available edge or page within the current
		 * bisection node.
		 */
                if (slot < (VM_RADIX_COUNT - 1)) {
			inc = VM_RADIX_UNITLEVEL(rnode->rn_clev);
			index = vm_radix_trimkey(index, rnode->rn_clev);
			do {
				index += inc;
				slot++;
				child = vm_radix_node_load(&rnode->rn_child[slot],
				    LOCKED);
				if (vm_radix_isleaf(child)) {
					m = vm_radix_topage(child);
					if (m->pindex >= index)
						return (m);
				} else if (child != NULL)
					goto descend;
			} while (slot < (VM_RADIX_COUNT - 1));
		}
		KASSERT(child == NULL || vm_radix_isleaf(child),
		    ("vm_radix_lookup_ge: child is radix node"));

		/*
		 * If a page or edge greater than the search slot is not found
		 * in the current node, ascend to the next higher-level node.
		 */
		goto ascend;
descend:
		KASSERT(rnode->rn_clev > 0,
		    ("vm_radix_lookup_ge: pushing leaf's parent"));
		KASSERT(tos < VM_RADIX_LIMIT,
		    ("vm_radix_lookup_ge: stack overflow"));
		stack[tos++] = rnode;
		rnode = child;
	}
}

/*
 * Look up the nearest entry at a position less than or equal to index.
 */
vm_page_t
vm_radix_lookup_le(struct vm_radix *rtree, vm_pindex_t index)
{
	struct vm_radix_node *stack[VM_RADIX_LIMIT];
	vm_pindex_t inc;
	vm_page_t m;
	struct vm_radix_node *child, *rnode;
#ifdef INVARIANTS
	int loops = 0;
#endif
	int slot, tos;

	rnode = vm_radix_root_load(rtree, LOCKED);
	if (rnode == NULL)
		return (NULL);
	else if (vm_radix_isleaf(rnode)) {
		m = vm_radix_topage(rnode);
		if (m->pindex <= index)
			return (m);
		else
			return (NULL);
	}
	tos = 0;
	for (;;) {
		/*
		 * If the keys differ before the current bisection node,
		 * then the search key might rollback to the earliest
		 * available bisection node or to the largest key
		 * in the current node (if the owner is smaller than the
		 * search key).
		 */
		if (vm_radix_keybarr(rnode, index)) {
			if (index > rnode->rn_owner) {
				index = rnode->rn_owner + VM_RADIX_COUNT *
				    VM_RADIX_UNITLEVEL(rnode->rn_clev);
			} else {
ascend:
				KASSERT(++loops < 1000,
				    ("vm_radix_lookup_le: too many loops"));

				/*
				 * Pop nodes from the stack until either the
				 * stack is empty or a node that could have a
				 * matching descendant is found.
				 */
				do {
					if (tos == 0)
						return (NULL);
					rnode = stack[--tos];
				} while (vm_radix_slot(index,
				    rnode->rn_clev) == 0);

				/*
				 * The following computation cannot overflow
				 * because index's slot at the current level
				 * is greater than 0.
				 */
				index = vm_radix_trimkey(index,
				    rnode->rn_clev);
			}
			index--;
			KASSERT(!vm_radix_keybarr(rnode, index),
			    ("vm_radix_lookup_le: keybarr failed"));
		}
		slot = vm_radix_slot(index, rnode->rn_clev);
		child = vm_radix_node_load(&rnode->rn_child[slot], LOCKED);
		if (vm_radix_isleaf(child)) {
			m = vm_radix_topage(child);
			if (m->pindex <= index)
				return (m);
		} else if (child != NULL)
			goto descend;

		/*
		 * Look for an available edge or page within the current
		 * bisection node.
		 */
		if (slot > 0) {
			inc = VM_RADIX_UNITLEVEL(rnode->rn_clev);
			index |= inc - 1;
			do {
				index -= inc;
				slot--;
				child = vm_radix_node_load(&rnode->rn_child[slot],
				    LOCKED);
				if (vm_radix_isleaf(child)) {
					m = vm_radix_topage(child);
					if (m->pindex <= index)
						return (m);
				} else if (child != NULL)
					goto descend;
			} while (slot > 0);
		}
		KASSERT(child == NULL || vm_radix_isleaf(child),
		    ("vm_radix_lookup_le: child is radix node"));

		/*
		 * If a page or edge smaller than the search slot is not found
		 * in the current node, ascend to the next higher-level node.
		 */
		goto ascend;
descend:
		KASSERT(rnode->rn_clev > 0,
		    ("vm_radix_lookup_le: pushing leaf's parent"));
		KASSERT(tos < VM_RADIX_LIMIT,
		    ("vm_radix_lookup_le: stack overflow"));
		stack[tos++] = rnode;
		rnode = child;
	}
}

/*
 * Remove the specified index from the trie, and return the value stored at
 * that index.  If the index is not present, return NULL.
 */
vm_page_t
vm_radix_remove(struct vm_radix *rtree, vm_pindex_t index)
{
	struct vm_radix_node *rnode, *parent, *tmp;
	vm_page_t m;
	int i, slot;

	rnode = vm_radix_root_load(rtree, LOCKED);
	if (vm_radix_isleaf(rnode)) {
		m = vm_radix_topage(rnode);
		if (m->pindex != index)
			return (NULL);
		vm_radix_root_store(rtree, NULL, LOCKED);
		return (m);
	}
	parent = NULL;
	for (;;) {
		if (rnode == NULL)
			return (NULL);
		slot = vm_radix_slot(index, rnode->rn_clev);
		tmp = vm_radix_node_load(&rnode->rn_child[slot], LOCKED);
		if (vm_radix_isleaf(tmp)) {
			m = vm_radix_topage(tmp);
			if (m->pindex != index)
				return (NULL);
			vm_radix_node_store(&rnode->rn_child[slot], NULL, LOCKED);
			rnode->rn_count--;
			if (rnode->rn_count > 1)
				return (m);
			for (i = 0; i < VM_RADIX_COUNT; i++)
				if (vm_radix_node_load(&rnode->rn_child[i],
				    LOCKED) != NULL)
					break;
			KASSERT(i != VM_RADIX_COUNT,
			    ("%s: invalid node configuration", __func__));
			tmp = vm_radix_node_load(&rnode->rn_child[i], LOCKED);
			if (parent == NULL)
				vm_radix_root_store(rtree, tmp, LOCKED);
			else {
				slot = vm_radix_slot(index, parent->rn_clev);
				KASSERT(vm_radix_node_load(
				    &parent->rn_child[slot], LOCKED) == rnode,
				    ("%s: invalid child value", __func__));
				vm_radix_node_store(&parent->rn_child[slot],
				    tmp, LOCKED);
			}
			/*
			 * The child is still valid and we can not zero the
			 * pointer until all smr references are gone.
			 */
			rnode->rn_count--;
			vm_radix_node_put(rnode, i);
			return (m);
		}
		parent = rnode;
		rnode = tmp;
	}
}

/*
 * Remove and free all the nodes from the radix tree.
 * This function is recursive but there is a tight control on it as the
 * maximum depth of the tree is fixed.
 */
void
vm_radix_reclaim_allnodes(struct vm_radix *rtree)
{
	struct vm_radix_node *root;

	root = vm_radix_root_load(rtree, LOCKED);
	if (root == NULL)
		return;
	vm_radix_root_store(rtree, NULL, UNSERIALIZED);
	if (!vm_radix_isleaf(root))
		vm_radix_reclaim_allnodes_int(root);
}

/*
 * Replace an existing page in the trie with another one.
 * Panics if there is not an old page in the trie at the new page's index.
 */
vm_page_t
vm_radix_replace(struct vm_radix *rtree, vm_page_t newpage)
{
	struct vm_radix_node *rnode, *tmp;
	vm_page_t m;
	vm_pindex_t index;
	int slot;

	index = newpage->pindex;
	rnode = vm_radix_root_load(rtree, LOCKED);
	if (rnode == NULL)
		panic("%s: replacing page on an empty trie", __func__);
	if (vm_radix_isleaf(rnode)) {
		m = vm_radix_topage(rnode);
		if (m->pindex != index)
			panic("%s: original replacing root key not found",
			    __func__);
		rtree->rt_root = (uintptr_t)newpage | VM_RADIX_ISLEAF;
		return (m);
	}
	for (;;) {
		slot = vm_radix_slot(index, rnode->rn_clev);
		tmp = vm_radix_node_load(&rnode->rn_child[slot], LOCKED);
		if (vm_radix_isleaf(tmp)) {
			m = vm_radix_topage(tmp);
			if (m->pindex == index) {
				vm_radix_node_store(&rnode->rn_child[slot],
				    (struct vm_radix_node *)((uintptr_t)newpage |
				    VM_RADIX_ISLEAF), LOCKED);
				return (m);
			} else
				break;
		} else if (tmp == NULL || vm_radix_keybarr(tmp, index))
			break;
		rnode = tmp;
	}
	panic("%s: original replacing page not found", __func__);
}

void
vm_radix_wait(void)
{
	uma_zwait(vm_radix_node_zone);
}

#ifdef DDB
/*
 * Show details about the given radix node.
 */
DB_SHOW_COMMAND(radixnode, db_show_radixnode)
{
	struct vm_radix_node *rnode, *tmp;
	int i;

        if (!have_addr)
                return;
	rnode = (struct vm_radix_node *)addr;
	db_printf("radixnode %p, owner %jx, children count %u, level %u:\n",
	    (void *)rnode, (uintmax_t)rnode->rn_owner, rnode->rn_count,
	    rnode->rn_clev);
	for (i = 0; i < VM_RADIX_COUNT; i++) {
		tmp = vm_radix_node_load(&rnode->rn_child[i], UNSERIALIZED);
		if (tmp != NULL)
			db_printf("slot: %d, val: %p, page: %p, clev: %d\n",
			    i, (void *)tmp,
			    vm_radix_isleaf(tmp) ?  vm_radix_topage(tmp) : NULL,
			    rnode->rn_clev);
	}
}
#endif /* DDB */