vm_radix.c

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/*-
 * 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 */