xref: /freebsd/sys/kern/subr_pctrie.c (revision d0b225d16418e224b5d30d13f45515aa70ad47a3)

/*-
 * SPDX-License-Identifier: BSD-2-Clause
 *
 * 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 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>
#include "opt_ddb.h"

#include <sys/param.h>
#include <sys/systm.h>
#include <sys/kernel.h>
#include <sys/libkern.h>
#include <sys/pctrie.h>
#include <sys/proc.h>	/* smr.h depends on struct thread. */
#include <sys/smr.h>
#include <sys/smr_types.h>

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

#if PCTRIE_WIDTH == 3
typedef uint8_t pn_popmap_t;
#elif PCTRIE_WIDTH == 4
typedef uint16_t pn_popmap_t;
#elif PCTRIE_WIDTH == 5
typedef uint32_t pn_popmap_t;
#else
#error Unsupported width
#endif
_Static_assert(sizeof(pn_popmap_t) <= sizeof(int),
    "pn_popmap_t too wide");

struct pctrie_node;
typedef SMR_POINTER(struct pctrie_node *) smr_pctnode_t;

struct pctrie_node {
	uint64_t	pn_owner;			/* Owner of record. */
	pn_popmap_t	pn_popmap;			/* Valid children. */
	uint8_t		pn_clev;			/* Level * WIDTH. */
	smr_pctnode_t	pn_child[PCTRIE_COUNT];		/* Child nodes. */
};

/*
 * Map index to an array position for the children of node,
 */
static __inline int
pctrie_slot(struct pctrie_node *node, uint64_t index)
{
	return ((index >> node->pn_clev) & (PCTRIE_COUNT - 1));
}

/*
 * Returns true if index does not belong to the specified node.  Otherwise,
 * sets slot value, and returns false.
 */
static __inline bool
pctrie_keybarr(struct pctrie_node *node, uint64_t index, int *slot)
{
	index = (index - node->pn_owner) >> node->pn_clev;
	if (index >= PCTRIE_COUNT)
		return (true);
	*slot = index;
	return (false);
}

/*
 * Check radix node.
 */
static __inline void
pctrie_node_put(struct pctrie_node *node)
{
#ifdef INVARIANTS
	int slot;

	KASSERT(powerof2(node->pn_popmap),
	    ("pctrie_node_put: node %p has too many children %04x", node,
	    node->pn_popmap));
	for (slot = 0; slot < PCTRIE_COUNT; slot++) {
		if ((node->pn_popmap & (1 << slot)) != 0)
			continue;
		KASSERT(smr_unserialized_load(&node->pn_child[slot], true) ==
		    PCTRIE_NULL,
		    ("pctrie_node_put: node %p has a child", node));
	}
#endif
}

enum pctrie_access { PCTRIE_SMR, PCTRIE_LOCKED, PCTRIE_UNSERIALIZED };

/*
 * Fetch a node pointer from a slot.
 */
static __inline struct pctrie_node *
pctrie_node_load(smr_pctnode_t *p, smr_t smr, enum pctrie_access access)
{
	switch (access) {
	case PCTRIE_UNSERIALIZED:
		return (smr_unserialized_load(p, true));
	case PCTRIE_LOCKED:
		return (smr_serialized_load(p, true));
	case PCTRIE_SMR:
		return (smr_entered_load(p, smr));
	}
	__assert_unreachable();
}

static __inline void
pctrie_node_store(smr_pctnode_t *p, void *v, enum pctrie_access access)
{
	switch (access) {
	case PCTRIE_UNSERIALIZED:
		smr_unserialized_store(p, v, true);
		break;
	case PCTRIE_LOCKED:
		smr_serialized_store(p, v, true);
		break;
	case PCTRIE_SMR:
		panic("%s: Not supported in SMR section.", __func__);
		break;
	default:
		__assert_unreachable();
		break;
	}
}

/*
 * Get the root node for a tree.
 */
static __inline struct pctrie_node *
pctrie_root_load(struct pctrie *ptree, smr_t smr, enum pctrie_access access)
{
	return (pctrie_node_load((smr_pctnode_t *)&ptree->pt_root, smr, access));
}

/*
 * Set the root node for a tree.
 */
static __inline void
pctrie_root_store(struct pctrie *ptree, struct pctrie_node *node,
    enum pctrie_access access)
{
	pctrie_node_store((smr_pctnode_t *)&ptree->pt_root, node, access);
}

/*
 * Returns TRUE if the specified node is a leaf and FALSE otherwise.
 */
static __inline bool
pctrie_isleaf(struct pctrie_node *node)
{
	return (((uintptr_t)node & PCTRIE_ISLEAF) != 0);
}

/*
 * Returns val with leaf bit set.
 */
static __inline void *
pctrie_toleaf(uint64_t *val)
{
	return ((void *)((uintptr_t)val | PCTRIE_ISLEAF));
}

/*
 * Returns the associated val extracted from node.
 */
static __inline uint64_t *
pctrie_toval(struct pctrie_node *node)
{
	return ((uint64_t *)((uintptr_t)node & ~PCTRIE_FLAGS));
}

/*
 * Returns the associated pointer extracted from node and field offset.
 */
static __inline void *
pctrie_toptr(struct pctrie_node *node, int keyoff)
{
	return ((void *)(((uintptr_t)node & ~PCTRIE_FLAGS) - keyoff));
}

/*
 * Make 'child' a child of 'node'.
 */
static __inline void
pctrie_addnode(struct pctrie_node *node, uint64_t index,
    struct pctrie_node *child, enum pctrie_access access)
{
	int slot;

	slot = pctrie_slot(node, index);
	pctrie_node_store(&node->pn_child[slot], child, access);
	node->pn_popmap ^= 1 << slot;
	KASSERT((node->pn_popmap & (1 << slot)) != 0,
	    ("%s: bad popmap slot %d in node %p", __func__, slot, node));
}

/*
 * pctrie node zone initializer.
 */
int
pctrie_zone_init(void *mem, int size __unused, int flags __unused)
{
	struct pctrie_node *node;

	node = mem;
	node->pn_popmap = 0;
	for (int i = 0; i < nitems(node->pn_child); i++)
		pctrie_node_store(&node->pn_child[i], PCTRIE_NULL,
		    PCTRIE_UNSERIALIZED);
	return (0);
}

size_t
pctrie_node_size(void)
{

	return (sizeof(struct pctrie_node));
}

enum pctrie_insert_neighbor_mode {
	PCTRIE_INSERT_NEIGHBOR_NONE,
	PCTRIE_INSERT_NEIGHBOR_LT,
	PCTRIE_INSERT_NEIGHBOR_GT,
};

/*
 * Look for where to insert the key-value pair into the trie.  Complete the
 * insertion if it replaces a null leaf.  Return the insertion location if the
 * insertion needs to be completed by the caller; otherwise return NULL.
 *
 * If the key is already present in the trie, populate *found_out as if by
 * pctrie_lookup().
 *
 * With mode PCTRIE_INSERT_NEIGHBOR_GT or PCTRIE_INSERT_NEIGHBOR_LT, set
 * *neighbor_out to the lowest level node we encounter during the insert lookup
 * that is a parent of the next greater or lesser entry.  The value is not
 * defined if the key was already present in the trie.
 *
 * Note that mode is expected to be a compile-time constant, and this procedure
 * is expected to be inlined into callers with extraneous code optimized out.
 */
static __always_inline void *
pctrie_insert_lookup_compound(struct pctrie *ptree, uint64_t *val,
    uint64_t **found_out, struct pctrie_node **neighbor_out,
    enum pctrie_insert_neighbor_mode mode)
{
	uint64_t index;
	struct pctrie_node *node, *parent;
	int slot;

	index = *val;

	/*
	 * The owner of record for root is not really important because it
	 * will never be used.
	 */
	node = pctrie_root_load(ptree, NULL, PCTRIE_LOCKED);
	parent = NULL;
	for (;;) {
		if (pctrie_isleaf(node)) {
			if (node == PCTRIE_NULL) {
				if (parent == NULL)
					pctrie_root_store(ptree,
					    pctrie_toleaf(val), PCTRIE_LOCKED);
				else
					pctrie_addnode(parent, index,
					    pctrie_toleaf(val), PCTRIE_LOCKED);
				return (NULL);
			}
			if (*pctrie_toval(node) == index) {
				*found_out = pctrie_toval(node);
				return (NULL);
			}
			break;
		}
		if (pctrie_keybarr(node, index, &slot))
			break;
		/*
		 * Descend.  If we're tracking the next neighbor and this node
		 * contains a neighboring entry in the right direction, record
		 * it.
		 */
		if (mode == PCTRIE_INSERT_NEIGHBOR_LT) {
			if ((node->pn_popmap & ((1 << slot) - 1)) != 0)
				*neighbor_out = node;
		} else if (mode == PCTRIE_INSERT_NEIGHBOR_GT) {
			if ((node->pn_popmap >> slot) > 1)
				*neighbor_out = node;
		}
		parent = node;
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}

	/*
	 * The caller will split this node.  If we're tracking the next
	 * neighbor, record the old node if the old entry is in the right
	 * direction.
	 */
	if (mode == PCTRIE_INSERT_NEIGHBOR_LT) {
		if (*pctrie_toval(node) < index)
			*neighbor_out = node;
	} else if (mode == PCTRIE_INSERT_NEIGHBOR_GT) {
		if (*pctrie_toval(node) > index)
			*neighbor_out = node;
	}

	/*
	 * 'node' must be replaced in the tree with a new branch node, with
	 * children 'node' and 'val'. Return the place that points to 'node'
	 * now, and will point to to the new branching node later.
	 */
	return ((parent != NULL) ? &parent->pn_child[slot]:
	    (smr_pctnode_t *)&ptree->pt_root);
}

/*
 * Wrap pctrie_insert_lookup_compound to implement a strict insertion.  Panic
 * if the key already exists, and do not look for neighboring entries.
 */
void *
pctrie_insert_lookup_strict(struct pctrie *ptree, uint64_t *val)
{
	void *parentp;
	uint64_t *found;

	found = NULL;
	parentp = pctrie_insert_lookup_compound(ptree, val, &found, NULL,
	    PCTRIE_INSERT_NEIGHBOR_NONE);
	if (__predict_false(found != NULL))
		panic("%s: key %jx is already present", __func__,
		    (uintmax_t)*val);
	return (parentp);
}

/*
 * Wrap pctrie_insert_lookup_compound to implement find-or-insert.  Do not look
 * for neighboring entries.
 */
void *
pctrie_insert_lookup(struct pctrie *ptree, uint64_t *val,
    uint64_t **found_out)
{
	*found_out = NULL;
	return (pctrie_insert_lookup_compound(ptree, val, found_out, NULL,
	    PCTRIE_INSERT_NEIGHBOR_NONE));
}

/*
 * Wrap pctrie_insert_lookup_compound to implement find or insert and find next
 * greater entry.  Find a subtree that contains the next entry greater than the
 * newly-inserted or to-be-inserted entry.
 */
void *
pctrie_insert_lookup_gt(struct pctrie *ptree, uint64_t *val,
    uint64_t **found_out, struct pctrie_node **neighbor_out)
{
	*found_out = NULL;
	*neighbor_out = NULL;
	return (pctrie_insert_lookup_compound(ptree, val, found_out,
	    neighbor_out, PCTRIE_INSERT_NEIGHBOR_GT));
}

/*
 * Wrap pctrie_insert_lookup_compound to implement find or insert and find next
 * lesser entry.  Find a subtree that contains the next entry less than the
 * newly-inserted or to-be-inserted entry.
 */
void *
pctrie_insert_lookup_lt(struct pctrie *ptree, uint64_t *val,
    uint64_t **found_out, struct pctrie_node **neighbor_out)
{
	*found_out = NULL;
	*neighbor_out = NULL;
	return (pctrie_insert_lookup_compound(ptree, val, found_out,
	    neighbor_out, PCTRIE_INSERT_NEIGHBOR_LT));
}

/*
 * Uses new node to insert key-value pair into the trie at given location.
 */
void
pctrie_insert_node(void *parentp, struct pctrie_node *parent, uint64_t *val)
{
	struct pctrie_node *node;
	uint64_t index, newind;

	/*
	 * Clear the last child pointer of the newly allocated parent.  We want
	 * to clear it 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 (parent->pn_popmap != 0) {
		pctrie_node_store(&parent->pn_child[ffs(parent->pn_popmap) - 1],
		    PCTRIE_NULL, PCTRIE_UNSERIALIZED);
		parent->pn_popmap = 0;
	}

	/*
	 * Recover the values of the two children of the new parent node.  If
	 * 'node' is not a leaf, this stores into 'newind' the 'owner' field,
	 * which must be first in the node.
	 */
	index = *val;
	node = pctrie_node_load(parentp, NULL, PCTRIE_UNSERIALIZED);
	newind = *pctrie_toval(node);

	/*
	 * From the highest-order bit where the indexes differ,
	 * compute the highest level in the trie where they differ.  Then,
	 * compute the least index of this subtrie.
	 */
	_Static_assert(sizeof(long long) >= sizeof(uint64_t),
	    "uint64 too wide");
	_Static_assert(sizeof(uint64_t) * NBBY <=
	    (1 << (sizeof(parent->pn_clev) * NBBY)), "pn_clev too narrow");
	parent->pn_clev = rounddown(ilog2(index ^ newind), PCTRIE_WIDTH);
	parent->pn_owner = PCTRIE_COUNT;
	parent->pn_owner = index & -(parent->pn_owner << parent->pn_clev);


	/* These writes are not yet visible due to ordering. */
	pctrie_addnode(parent, index, pctrie_toleaf(val), PCTRIE_UNSERIALIZED);
	pctrie_addnode(parent, newind, node, PCTRIE_UNSERIALIZED);
	/* Synchronize to make the above visible. */
	pctrie_node_store(parentp, parent, PCTRIE_LOCKED);
}

/*
 * Return the value associated with the node, if the node is a leaf that matches
 * the index; otherwise NULL.
 */
static __always_inline uint64_t *
pctrie_match_value(struct pctrie_node *node, uint64_t index)
{
	uint64_t *m;

	if (!pctrie_isleaf(node) || (m = pctrie_toval(node)) == NULL ||
	    *m != index)
		m = NULL;
	return (m);
}

/*
 * Returns the value stored at the index.  If the index is not present,
 * NULL is returned.
 */
static __always_inline uint64_t *
_pctrie_lookup(struct pctrie *ptree, uint64_t index, smr_t smr,
    enum pctrie_access access)
{
	struct pctrie_node *node;
	int slot;

	node = pctrie_root_load(ptree, smr, access);
	/* Seek a node that matches index. */
	while (!pctrie_isleaf(node) && !pctrie_keybarr(node, index, &slot))
		node = pctrie_node_load(&node->pn_child[slot], smr, access);
	return (pctrie_match_value(node, index));
}

/*
 * Returns the value stored at the index, assuming access is externally
 * synchronized by a lock.
 *
 * If the index is not present, NULL is returned.
 */
uint64_t *
pctrie_lookup(struct pctrie *ptree, uint64_t index)
{
	return (_pctrie_lookup(ptree, index, NULL, PCTRIE_LOCKED));
}

/*
 * Returns the value stored at the index without requiring an external lock.
 *
 * If the index is not present, NULL is returned.
 */
uint64_t *
pctrie_lookup_unlocked(struct pctrie *ptree, uint64_t index, smr_t smr)
{
	uint64_t *res;

	smr_enter(smr);
	res = _pctrie_lookup(ptree, index, smr, PCTRIE_SMR);
	smr_exit(smr);
	return (res);
}

/*
 * Returns the last node examined in the search for the index, and updates the
 * search path to that node.
 */
static __always_inline struct pctrie_node *
_pctrie_iter_lookup_node(struct pctrie_iter *it, uint64_t index, smr_t smr,
    enum pctrie_access access)
{
	struct pctrie_node *node;
	int slot;

	/*
	 * Climb the search path to find the lowest node from which to start the
	 * search for a value matching 'index'.
	 */
	while (it->top != 0) {
		node = it->path[it->top - 1];
		KASSERT(!powerof2(node->pn_popmap),
		    ("%s: freed node in iter path", __func__));
		if (!pctrie_keybarr(node, index, &slot)) {
			node = pctrie_node_load(
			    &node->pn_child[slot], smr, access);
			break;
		}
		--it->top;
	}
	if (it->top == 0)
		node = pctrie_root_load(it->ptree, smr, access);

	/* Seek a node that matches index. */
	while (!pctrie_isleaf(node) && !pctrie_keybarr(node, index, &slot)) {
		KASSERT(it->top < nitems(it->path),
		    ("%s: path overflow in trie %p", __func__, it->ptree));
		it->path[it->top++] = node;
		node = pctrie_node_load(&node->pn_child[slot], smr, access);
	}
	return (node);
}

/*
 * Returns the value stored at a given index value, possibly NULL.
 */
static __always_inline uint64_t *
_pctrie_iter_lookup(struct pctrie_iter *it, uint64_t index, smr_t smr,
    enum pctrie_access access)
{
	struct pctrie_node *node;

	it->index = index;
	node = _pctrie_iter_lookup_node(it, index, smr, access);
	return (pctrie_match_value(node, index));
}

/*
 * Returns the value stored at a given index value, possibly NULL.
 */
uint64_t *
pctrie_iter_lookup(struct pctrie_iter *it, uint64_t index)
{
	return (_pctrie_iter_lookup(it, index, NULL, PCTRIE_LOCKED));
}

/*
 * Insert the val in the trie, starting search with iterator.  Return a pointer
 * to indicate where a new node must be allocated to complete insertion.
 * Assumes access is externally synchronized by a lock.
 */
void *
pctrie_iter_insert_lookup(struct pctrie_iter *it, uint64_t *val)
{
	struct pctrie_node *node;

	it->index = *val;
	node = _pctrie_iter_lookup_node(it, *val, NULL, PCTRIE_LOCKED);
	if (node == PCTRIE_NULL) {
		if (it->top == 0)
			pctrie_root_store(it->ptree,
			    pctrie_toleaf(val), PCTRIE_LOCKED);
		else
			pctrie_addnode(it->path[it->top - 1], it->index,
			    pctrie_toleaf(val), PCTRIE_LOCKED);
		return (NULL);
	}
	if (__predict_false(pctrie_match_value(node, it->index) != NULL))
		panic("%s: key %jx is already present", __func__,
		    (uintmax_t)it->index);

	/*
	 * 'node' must be replaced in the tree with a new branch node, with
	 * children 'node' and 'val'. Return the place that points to 'node'
	 * now, and will point to to the new branching node later.
	 */
	if (it->top == 0)
		return ((smr_pctnode_t *)&it->ptree->pt_root);
	node = it->path[it->top - 1];
	return (&node->pn_child[pctrie_slot(node, it->index)]);
}

/*
 * Returns the value stored at a fixed offset from the current index value,
 * possibly NULL.
 */
static __always_inline uint64_t *
_pctrie_iter_stride(struct pctrie_iter *it, int stride, smr_t smr,
    enum pctrie_access access)
{
	uint64_t index = it->index + stride;

	/* Detect stride overflow. */
	if ((stride > 0) != (index > it->index))
		return (NULL);
	/* Detect crossing limit */
	if ((index < it->limit) != (it->index < it->limit))
		return (NULL);

	return (_pctrie_iter_lookup(it, index, smr, access));
}

/*
 * Returns the value stored at a fixed offset from the current index value,
 * possibly NULL.
 */
uint64_t *
pctrie_iter_stride(struct pctrie_iter *it, int stride)
{
	return (_pctrie_iter_stride(it, stride, NULL, PCTRIE_LOCKED));
}

/*
 * Returns the value stored at one more than the current index value, possibly
 * NULL, assuming access is externally synchronized by a lock.
 */
uint64_t *
pctrie_iter_next(struct pctrie_iter *it)
{
	return (_pctrie_iter_stride(it, 1, NULL, PCTRIE_LOCKED));
}

/*
 * Returns the value stored at one less than the current index value, possibly
 * NULL, assuming access is externally synchronized by a lock.
 */
uint64_t *
pctrie_iter_prev(struct pctrie_iter *it)
{
	return (_pctrie_iter_stride(it, -1, NULL, PCTRIE_LOCKED));
}

/*
 * Returns the value with the least index that is greater than or equal to the
 * specified index, or NULL if there are no such values.
 *
 * Requires that access be externally synchronized by a lock.
 */
static __inline uint64_t *
pctrie_lookup_ge_node(struct pctrie_node *node, uint64_t index)
{
	struct pctrie_node *succ;
	uint64_t *m;
	int slot;

	/*
	 * Descend the trie as if performing an ordinary lookup for the
	 * specified value.  However, unlike an ordinary lookup, as we descend
	 * the trie, we use "succ" to remember the last branching-off point,
	 * that is, the interior node under which the least value that is both
	 * outside our current path down the trie and greater than the specified
	 * index resides.  (The node's popmap makes it fast and easy to
	 * recognize a branching-off point.)  If our ordinary lookup fails to
	 * yield a value that is greater than or equal to the specified index,
	 * then we will exit this loop and perform a lookup starting from
	 * "succ".  If "succ" is not NULL, then that lookup is guaranteed to
	 * succeed.
	 */
	succ = NULL;
	for (;;) {
		if (pctrie_isleaf(node)) {
			if ((m = pctrie_toval(node)) != NULL && *m >= index)
				return (m);
			break;
		}
		if (pctrie_keybarr(node, index, &slot)) {
			/*
			 * If all values in this subtree are > index, then the
			 * least value in this subtree is the answer.
			 */
			if (node->pn_owner > index)
				succ = node;
			break;
		}

		/*
		 * Just in case the next search step leads to a subtree of all
		 * values < index, check popmap to see if a next bigger step, to
		 * a subtree of all pages with values > index, is available.  If
		 * so, remember to restart the search here.
		 */
		if ((node->pn_popmap >> slot) > 1)
			succ = node;
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}

	/*
	 * Restart the search from the last place visited in the subtree that
	 * included some values > index, if there was such a place.
	 */
	if (succ == NULL)
		return (NULL);
	if (succ != node) {
		/*
		 * Take a step to the next bigger sibling of the node chosen
		 * last time.  In that subtree, all values > index.
		 */
		slot = pctrie_slot(succ, index) + 1;
		KASSERT((succ->pn_popmap >> slot) != 0,
		    ("%s: no popmap siblings past slot %d in node %p",
		    __func__, slot, succ));
		slot += ffs(succ->pn_popmap >> slot) - 1;
		succ = pctrie_node_load(&succ->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}

	/*
	 * Find the value in the subtree rooted at "succ" with the least index.
	 */
	while (!pctrie_isleaf(succ)) {
		KASSERT(succ->pn_popmap != 0,
		    ("%s: no popmap children in node %p",  __func__, succ));
		slot = ffs(succ->pn_popmap) - 1;
		succ = pctrie_node_load(&succ->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	return (pctrie_toval(succ));
}

uint64_t *
pctrie_lookup_ge(struct pctrie *ptree, uint64_t index)
{
	return (pctrie_lookup_ge_node(
	    pctrie_root_load(ptree, NULL, PCTRIE_LOCKED), index));
}

uint64_t *
pctrie_subtree_lookup_gt(struct pctrie_node *node, uint64_t index)
{
	if (node == NULL || index + 1 == 0)
		return (NULL);
	return (pctrie_lookup_ge_node(node, index + 1));
}

/*
 * Find first leaf >= index, and fill iter with the path to the parent of that
 * leaf.  Return NULL if there is no such leaf less than limit.
 */
uint64_t *
pctrie_iter_lookup_ge(struct pctrie_iter *it, uint64_t index)
{
	struct pctrie_node *node;
	uint64_t *m;
	int slot;

	/* Seek a node that matches index. */
	node = _pctrie_iter_lookup_node(it, index, NULL, PCTRIE_LOCKED);

	/*
	 * If no such node was found, and instead this path leads only to nodes
	 * < index, back up to find a subtrie with the least value > index.
	 */
	if (pctrie_isleaf(node) ?
	    (m = pctrie_toval(node)) == NULL || *m < index :
	    node->pn_owner < index) {
		/* Climb the path to find a node with a descendant > index. */
		while (it->top != 0) {
			node = it->path[it->top - 1];
			slot = pctrie_slot(node, index) + 1;
			if ((node->pn_popmap >> slot) != 0)
				break;
			--it->top;
		}
		if (it->top == 0)
			return (NULL);

		/* Step to the least child with a descendant > index. */
		slot += ffs(node->pn_popmap >> slot) - 1;
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	/* Descend to the least leaf of the subtrie. */
	while (!pctrie_isleaf(node)) {
		if (it->limit != 0 && node->pn_owner >= it->limit)
			return (NULL);
		slot = ffs(node->pn_popmap) - 1;
		KASSERT(it->top < nitems(it->path),
		    ("%s: path overflow in trie %p", __func__, it->ptree));
		it->path[it->top++] = node;
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	m = pctrie_toval(node);
	if (it->limit != 0 && *m >= it->limit)
		return (NULL);
	it->index = *m;
	return (m);
}

/*
 * Find the first leaf with value at least 'jump' greater than the previous
 * leaf.  Return NULL if that value is >= limit.
 */
uint64_t *
pctrie_iter_jump_ge(struct pctrie_iter *it, int64_t jump)
{
	uint64_t index = it->index + jump;

	/* Detect jump overflow. */
	if ((jump > 0) != (index > it->index))
		return (NULL);
	if (it->limit != 0 && index >= it->limit)
		return (NULL);
	return (pctrie_iter_lookup_ge(it, index));
}

#ifdef INVARIANTS
void
pctrie_subtree_lookup_gt_assert(struct pctrie_node *node, uint64_t index,
    struct pctrie *ptree, uint64_t *res)
{
	uint64_t *expected;

	if (index + 1 == 0)
		expected = NULL;
	else
		expected = pctrie_lookup_ge(ptree, index + 1);
	KASSERT(res == expected,
	    ("pctrie subtree lookup gt result different from root lookup: "
	    "ptree %p, index %ju, subtree %p, found %p, expected %p", ptree,
	    (uintmax_t)index, node, res, expected));
}
#endif

/*
 * Returns the value with the greatest index that is less than or equal to the
 * specified index, or NULL if there are no such values.
 *
 * Requires that access be externally synchronized by a lock.
 */
static __inline uint64_t *
pctrie_lookup_le_node(struct pctrie_node *node, uint64_t index)
{
	struct pctrie_node *pred;
	uint64_t *m;
	int slot;

	/*
	 * Mirror the implementation of pctrie_lookup_ge_node, described above.
	 */
	pred = NULL;
	for (;;) {
		if (pctrie_isleaf(node)) {
			if ((m = pctrie_toval(node)) != NULL && *m <= index)
				return (m);
			break;
		}
		if (pctrie_keybarr(node, index, &slot)) {
			if (node->pn_owner < index)
				pred = node;
			break;
		}
		if ((node->pn_popmap & ((1 << slot) - 1)) != 0)
			pred = node;
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	if (pred == NULL)
		return (NULL);
	if (pred != node) {
		slot = pctrie_slot(pred, index);
		KASSERT((pred->pn_popmap & ((1 << slot) - 1)) != 0,
		    ("%s: no popmap siblings before slot %d in node %p",
		    __func__, slot, pred));
		slot = ilog2(pred->pn_popmap & ((1 << slot) - 1));
		pred = pctrie_node_load(&pred->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	while (!pctrie_isleaf(pred)) {
		KASSERT(pred->pn_popmap != 0,
		    ("%s: no popmap children in node %p",  __func__, pred));
		slot = ilog2(pred->pn_popmap);
		pred = pctrie_node_load(&pred->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	return (pctrie_toval(pred));
}

uint64_t *
pctrie_lookup_le(struct pctrie *ptree, uint64_t index)
{
	return (pctrie_lookup_le_node(
	    pctrie_root_load(ptree, NULL, PCTRIE_LOCKED), index));
}

uint64_t *
pctrie_subtree_lookup_lt(struct pctrie_node *node, uint64_t index)
{
	if (node == NULL || index == 0)
		return (NULL);
	return (pctrie_lookup_le_node(node, index - 1));
}

/*
 * Find first leaf <= index, and fill iter with the path to the parent of that
 * leaf.  Return NULL if there is no such leaf greater than limit.
 */
uint64_t *
pctrie_iter_lookup_le(struct pctrie_iter *it, uint64_t index)
{
	struct pctrie_node *node;
	uint64_t *m;
	int slot;

	/* Seek a node that matches index. */
	node = _pctrie_iter_lookup_node(it, index, NULL, PCTRIE_LOCKED);

	/*
	 * If no such node was found, and instead this path leads only to nodes
	 * > index, back up to find a subtrie with the least value > index.
	 */
	if (pctrie_isleaf(node) ?
	    (m = pctrie_toval(node)) == NULL || *m > index :
	    node->pn_owner > index) {
		/* Climb the path to find a node with a descendant < index. */
		while (it->top != 0) {
			node = it->path[it->top - 1];
			slot = pctrie_slot(node, index);
			if ((node->pn_popmap & ((1 << slot) - 1)) != 0)
				break;
			--it->top;
		}
		if (it->top == 0)
			return (NULL);

		/* Step to the greatest child with a descendant < index. */
		slot = ilog2(node->pn_popmap & ((1 << slot) - 1));
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	/* Descend to the greatest leaf of the subtrie. */
	while (!pctrie_isleaf(node)) {
		if (it->limit != 0 && it->limit >=
		    node->pn_owner + (PCTRIE_COUNT << node->pn_clev) - 1)
			return (NULL);
		slot = ilog2(node->pn_popmap);
		KASSERT(it->top < nitems(it->path),
		    ("%s: path overflow in trie %p", __func__, it->ptree));
		it->path[it->top++] = node;
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	m = pctrie_toval(node);
	if (it->limit != 0 && *m <= it->limit)
		return (NULL);
	it->index = *m;
	return (m);
}

/*
 * Find the first leaf with value at most 'jump' less than the previous
 * leaf.  Return NULL if that value is <= limit.
 */
uint64_t *
pctrie_iter_jump_le(struct pctrie_iter *it, int64_t jump)
{
	uint64_t index = it->index - jump;

	/* Detect jump overflow. */
	if ((jump > 0) != (index < it->index))
		return (NULL);
	if (it->limit != 0 && index <= it->limit)
		return (NULL);
	return (pctrie_iter_lookup_le(it, index));
}

#ifdef INVARIANTS
void
pctrie_subtree_lookup_lt_assert(struct pctrie_node *node, uint64_t index,
    struct pctrie *ptree, uint64_t *res)
{
	uint64_t *expected;

	if (index == 0)
		expected = NULL;
	else
		expected = pctrie_lookup_le(ptree, index - 1);
	KASSERT(res == expected,
	    ("pctrie subtree lookup lt result different from root lookup: "
	    "ptree %p, index %ju, subtree %p, found %p, expected %p", ptree,
	    (uintmax_t)index, node, res, expected));
}
#endif

static void
pctrie_remove(struct pctrie *ptree, uint64_t index, struct pctrie_node *parent,
    struct pctrie_node *node, struct pctrie_node **freenode)
{
	struct pctrie_node *child;
	int slot;

	if (node == NULL) {
		pctrie_root_store(ptree, PCTRIE_NULL, PCTRIE_LOCKED);
		return;
	}
	slot = pctrie_slot(node, index);
	KASSERT((node->pn_popmap & (1 << slot)) != 0,
	    ("%s: bad popmap slot %d in node %p",
	    __func__, slot, node));
	node->pn_popmap ^= 1 << slot;
	pctrie_node_store(&node->pn_child[slot], PCTRIE_NULL, PCTRIE_LOCKED);
	if (!powerof2(node->pn_popmap))
		return;
	KASSERT(node->pn_popmap != 0, ("%s: bad popmap all zeroes", __func__));
	slot = ffs(node->pn_popmap) - 1;
	child = pctrie_node_load(&node->pn_child[slot], NULL, PCTRIE_LOCKED);
	KASSERT(child != PCTRIE_NULL,
	    ("%s: bad popmap slot %d in node %p", __func__, slot, node));
	if (parent == NULL)
		pctrie_root_store(ptree, child, PCTRIE_LOCKED);
	else {
		slot = pctrie_slot(parent, index);
		KASSERT(node ==
		    pctrie_node_load(&parent->pn_child[slot], NULL,
		    PCTRIE_LOCKED), ("%s: invalid child value", __func__));
		pctrie_node_store(&parent->pn_child[slot], child,
		    PCTRIE_LOCKED);
	}
	/*
	 * The child is still valid and we can not zero the
	 * pointer until all SMR references are gone.
	 */
	pctrie_node_put(node);
	*freenode = node;
}

/*
 * Remove the specified index from the tree, and return the value stored at
 * that index.  If the index is not present, return NULL.
 */
uint64_t *
pctrie_remove_lookup(struct pctrie *ptree, uint64_t index,
    struct pctrie_node **freenode)
{
	struct pctrie_node *child, *node, *parent;
	uint64_t *m;
	int slot;

	DEBUG_POISON_POINTER(parent);
	*freenode = node = NULL;
	child = pctrie_root_load(ptree, NULL, PCTRIE_LOCKED);
	while (!pctrie_isleaf(child)) {
		parent = node;
		node = child;
		slot = pctrie_slot(node, index);
		child = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	m = pctrie_match_value(child, index);
	if (m != NULL)
		pctrie_remove(ptree, index, parent, node, freenode);
	return (m);
}

/*
 * Remove from the trie the leaf last chosen by the iterator, and
 * adjust the path if it's last member is to be freed.
 */
uint64_t *
pctrie_iter_remove(struct pctrie_iter *it, struct pctrie_node **freenode)
{
	struct pctrie_node *child, *node, *parent;
	uint64_t *m;
	int slot;

	DEBUG_POISON_POINTER(parent);
	*freenode = NULL;
	if (it->top >= 1) {
		parent = (it->top >= 2) ? it->path[it->top - 2] : NULL;
		node = it->path[it->top - 1];
		slot = pctrie_slot(node, it->index);
		child = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	} else {
		node = NULL;
		child = pctrie_root_load(it->ptree, NULL, PCTRIE_LOCKED);
	}
	m = pctrie_match_value(child, it->index);
	if (m != NULL)
		pctrie_remove(it->ptree, it->index, parent, node, freenode);
	if (*freenode != NULL)
		--it->top;
	return (m);
}

/*
 * Return the current leaf, assuming access is externally synchronized by a
 * lock.
 */
uint64_t *
pctrie_iter_value(struct pctrie_iter *it)
{
	struct pctrie_node *node;
	int slot;

	if (it->top == 0)
		node = pctrie_root_load(it->ptree, NULL,
		    PCTRIE_LOCKED);
	else {
		node = it->path[it->top - 1];
		slot = pctrie_slot(node, it->index);
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	return (pctrie_toval(node));
}

/*
 * Walk the subtrie rooted at *pnode in order, invoking callback on leaves and
 * using the leftmost child pointer for path reversal, until an interior node
 * is stripped of all children, and returned for deallocation, with *pnode left
 * pointing to the parent of that node.
 */
static __always_inline struct pctrie_node *
pctrie_reclaim_prune(struct pctrie_node **pnode, struct pctrie_node *parent,
    pctrie_cb_t callback, int keyoff, void *arg)
{
	struct pctrie_node *child, *node;
	int slot;

	node = *pnode;
	while (node->pn_popmap != 0) {
		slot = ffs(node->pn_popmap) - 1;
		node->pn_popmap ^= 1 << slot;
		child = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_UNSERIALIZED);
		pctrie_node_store(&node->pn_child[slot], PCTRIE_NULL,
		    PCTRIE_UNSERIALIZED);
		if (pctrie_isleaf(child)) {
			if (callback != NULL)
				callback(pctrie_toptr(child, keyoff), arg);
			continue;
		}
		/* Climb one level down the trie. */
		pctrie_node_store(&node->pn_child[0], parent,
		    PCTRIE_UNSERIALIZED);
		parent = node;
		node = child;
	}
	*pnode = parent;
	return (node);
}

/*
 * Recover the node parent from its first child and continue pruning.
 */
static __always_inline struct pctrie_node *
pctrie_reclaim_resume_compound(struct pctrie_node **pnode,
    pctrie_cb_t callback, int keyoff, void *arg)
{
	struct pctrie_node *parent, *node;

	node = *pnode;
	if (node == NULL)
		return (NULL);
	/* Climb one level up the trie. */
	parent = pctrie_node_load(&node->pn_child[0], NULL,
	    PCTRIE_UNSERIALIZED);
	pctrie_node_store(&node->pn_child[0], PCTRIE_NULL, PCTRIE_UNSERIALIZED);
	return (pctrie_reclaim_prune(pnode, parent, callback, keyoff, arg));
}

/*
 * Find the trie root, and start pruning with a NULL parent.
 */
static __always_inline struct pctrie_node *
pctrie_reclaim_begin_compound(struct pctrie_node **pnode,
    struct pctrie *ptree,
    pctrie_cb_t callback, int keyoff, void *arg)
{
	struct pctrie_node *node;

	node = pctrie_root_load(ptree, NULL, PCTRIE_UNSERIALIZED);
	pctrie_root_store(ptree, PCTRIE_NULL, PCTRIE_UNSERIALIZED);
	if (pctrie_isleaf(node)) {
		if (callback != NULL && node != PCTRIE_NULL)
			callback(pctrie_toptr(node, keyoff), arg);
		return (NULL);
	}
	*pnode = node;
	return (pctrie_reclaim_prune(pnode, NULL, callback, keyoff, arg));
}

struct pctrie_node *
pctrie_reclaim_resume(struct pctrie_node **pnode)
{
	return (pctrie_reclaim_resume_compound(pnode, NULL, 0, NULL));
}

struct pctrie_node *
pctrie_reclaim_begin(struct pctrie_node **pnode, struct pctrie *ptree)
{
	return (pctrie_reclaim_begin_compound(pnode, ptree, NULL, 0, NULL));
}

struct pctrie_node *
pctrie_reclaim_resume_cb(struct pctrie_node **pnode,
    pctrie_cb_t callback, int keyoff, void *arg)
{
	return (pctrie_reclaim_resume_compound(pnode, callback, keyoff, arg));
}

struct pctrie_node *
pctrie_reclaim_begin_cb(struct pctrie_node **pnode, struct pctrie *ptree,
    pctrie_cb_t callback, int keyoff, void *arg)
{
	return (pctrie_reclaim_begin_compound(pnode, ptree,
	    callback, keyoff, arg));
}

/*
 * Replace an existing value in the trie with another one.
 * Panics if there is not an old value in the trie at the new value's index.
 */
uint64_t *
pctrie_replace(struct pctrie *ptree, uint64_t *newval)
{
	struct pctrie_node *leaf, *parent, *node;
	uint64_t *m;
	uint64_t index;
	int slot;

	leaf = pctrie_toleaf(newval);
	index = *newval;
	node = pctrie_root_load(ptree, NULL, PCTRIE_LOCKED);
	parent = NULL;
	for (;;) {
		if (pctrie_isleaf(node)) {
			if ((m = pctrie_toval(node)) != NULL && *m == index) {
				if (parent == NULL)
					pctrie_root_store(ptree,
					    leaf, PCTRIE_LOCKED);
				else
					pctrie_node_store(
					    &parent->pn_child[slot], leaf,
					    PCTRIE_LOCKED);
				return (m);
			}
			break;
		}
		if (pctrie_keybarr(node, index, &slot))
			break;
		parent = node;
		node = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_LOCKED);
	}
	panic("%s: original replacing value not found", __func__);
}

#ifdef DDB
/*
 * Show details about the given node.
 */
DB_SHOW_COMMAND(pctrienode, db_show_pctrienode)
{
	struct pctrie_node *node, *tmp;
	int slot;
	pn_popmap_t popmap;

        if (!have_addr)
                return;
	node = (struct pctrie_node *)addr;
	db_printf("node %p, owner %jx, children popmap %04x, level %u:\n",
	    (void *)node, (uintmax_t)node->pn_owner, node->pn_popmap,
	    node->pn_clev / PCTRIE_WIDTH);
	for (popmap = node->pn_popmap; popmap != 0; popmap ^= 1 << slot) {
		slot = ffs(popmap) - 1;
		tmp = pctrie_node_load(&node->pn_child[slot], NULL,
		    PCTRIE_UNSERIALIZED);
		db_printf("slot: %d, val: %p, value: %p, clev: %d\n",
		    slot, (void *)tmp,
		    pctrie_isleaf(tmp) ? pctrie_toval(tmp) : NULL,
		    node->pn_clev / PCTRIE_WIDTH);
	}
}
#endif /* DDB */