The Design and Implementation of the FreeBSD Operating System, Second Edition
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FreeBSD/Linux Kernel Cross Reference
sys/vm/vm_radix.c

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    1 /*-
    2  * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
    3  *
    4  * Copyright (c) 2013 EMC Corp.
    5  * Copyright (c) 2011 Jeffrey Roberson <jeff@freebsd.org>
    6  * Copyright (c) 2008 Mayur Shardul <mayur.shardul@gmail.com>
    7  * All rights reserved.
    8  *
    9  * Redistribution and use in source and binary forms, with or without
   10  * modification, are permitted provided that the following conditions
   11  * are met:
   12  * 1. Redistributions of source code must retain the above copyright
   13  *    notice, this list of conditions and the following disclaimer.
   14  * 2. Redistributions in binary form must reproduce the above copyright
   15  *    notice, this list of conditions and the following disclaimer in the
   16  *    documentation and/or other materials provided with the distribution.
   17  *
   18  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
   19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
   21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
   22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
   23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
   24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
   27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   28  * SUCH DAMAGE.
   29  *
   30  */
   31 
   32 /*
   33  * Path-compressed radix trie implementation.
   34  * The following code is not generalized into a general purpose library
   35  * because there are way too many parameters embedded that should really
   36  * be decided by the library consumers.  At the same time, consumers
   37  * of this code must achieve highest possible performance.
   38  *
   39  * The implementation takes into account the following rationale:
   40  * - Size of the nodes should be as small as possible but still big enough
   41  *   to avoid a large maximum depth for the trie.  This is a balance
   42  *   between the necessity to not wire too much physical memory for the nodes
   43  *   and the necessity to avoid too much cache pollution during the trie
   44  *   operations.
   45  * - There is not a huge bias toward the number of lookup operations over
   46  *   the number of insert and remove operations.  This basically implies
   47  *   that optimizations supposedly helping one operation but hurting the
   48  *   other might be carefully evaluated.
   49  * - On average not many nodes are expected to be fully populated, hence
   50  *   level compression may just complicate things.
   51  */
   52 
   53 #include <sys/cdefs.h>
   54 __FBSDID("$FreeBSD: releng/12.0/sys/vm/vm_radix.c 335600 2018-06-24 13:08:05Z mjg $");
   55 
   56 #include "opt_ddb.h"
   57 
   58 #include <sys/param.h>
   59 #include <sys/systm.h>
   60 #include <sys/kernel.h>
   61 #include <sys/vmmeter.h>
   62 
   63 #include <vm/uma.h>
   64 #include <vm/vm.h>
   65 #include <vm/vm_param.h>
   66 #include <vm/vm_page.h>
   67 #include <vm/vm_radix.h>
   68 
   69 #ifdef DDB
   70 #include <ddb/ddb.h>
   71 #endif
   72 
   73 /*
   74  * These widths should allow the pointers to a node's children to fit within
   75  * a single cache line.  The extra levels from a narrow width should not be
   76  * a problem thanks to path compression.
   77  */
   78 #ifdef __LP64__
   79 #define VM_RADIX_WIDTH  4
   80 #else
   81 #define VM_RADIX_WIDTH  3
   82 #endif
   83 
   84 #define VM_RADIX_COUNT  (1 << VM_RADIX_WIDTH)
   85 #define VM_RADIX_MASK   (VM_RADIX_COUNT - 1)
   86 #define VM_RADIX_LIMIT                                                  \
   87         (howmany(sizeof(vm_pindex_t) * NBBY, VM_RADIX_WIDTH) - 1)
   88 
   89 /* Flag bits stored in node pointers. */
   90 #define VM_RADIX_ISLEAF 0x1
   91 #define VM_RADIX_FLAGS  0x1
   92 #define VM_RADIX_PAD    VM_RADIX_FLAGS
   93 
   94 /* Returns one unit associated with specified level. */
   95 #define VM_RADIX_UNITLEVEL(lev)                                         \
   96         ((vm_pindex_t)1 << ((lev) * VM_RADIX_WIDTH))
   97 
   98 struct vm_radix_node {
   99         vm_pindex_t      rn_owner;                      /* Owner of record. */
  100         uint16_t         rn_count;                      /* Valid children. */
  101         uint16_t         rn_clev;                       /* Current level. */
  102         void            *rn_child[VM_RADIX_COUNT];      /* Child nodes. */
  103 };
  104 
  105 static uma_zone_t vm_radix_node_zone;
  106 
  107 /*
  108  * Allocate a radix node.
  109  */
  110 static __inline struct vm_radix_node *
  111 vm_radix_node_get(vm_pindex_t owner, uint16_t count, uint16_t clevel)
  112 {
  113         struct vm_radix_node *rnode;
  114 
  115         rnode = uma_zalloc(vm_radix_node_zone, M_NOWAIT);
  116         if (rnode == NULL)
  117                 return (NULL);
  118         rnode->rn_owner = owner;
  119         rnode->rn_count = count;
  120         rnode->rn_clev = clevel;
  121         return (rnode);
  122 }
  123 
  124 /*
  125  * Free radix node.
  126  */
  127 static __inline void
  128 vm_radix_node_put(struct vm_radix_node *rnode)
  129 {
  130 
  131         uma_zfree(vm_radix_node_zone, rnode);
  132 }
  133 
  134 /*
  135  * Return the position in the array for a given level.
  136  */
  137 static __inline int
  138 vm_radix_slot(vm_pindex_t index, uint16_t level)
  139 {
  140 
  141         return ((index >> (level * VM_RADIX_WIDTH)) & VM_RADIX_MASK);
  142 }
  143 
  144 /* Trims the key after the specified level. */
  145 static __inline vm_pindex_t
  146 vm_radix_trimkey(vm_pindex_t index, uint16_t level)
  147 {
  148         vm_pindex_t ret;
  149 
  150         ret = index;
  151         if (level > 0) {
  152                 ret >>= level * VM_RADIX_WIDTH;
  153                 ret <<= level * VM_RADIX_WIDTH;
  154         }
  155         return (ret);
  156 }
  157 
  158 /*
  159  * Get the root node for a radix tree.
  160  */
  161 static __inline struct vm_radix_node *
  162 vm_radix_getroot(struct vm_radix *rtree)
  163 {
  164 
  165         return ((struct vm_radix_node *)rtree->rt_root);
  166 }
  167 
  168 /*
  169  * Set the root node for a radix tree.
  170  */
  171 static __inline void
  172 vm_radix_setroot(struct vm_radix *rtree, struct vm_radix_node *rnode)
  173 {
  174 
  175         rtree->rt_root = (uintptr_t)rnode;
  176 }
  177 
  178 /*
  179  * Returns TRUE if the specified radix node is a leaf and FALSE otherwise.
  180  */
  181 static __inline boolean_t
  182 vm_radix_isleaf(struct vm_radix_node *rnode)
  183 {
  184 
  185         return (((uintptr_t)rnode & VM_RADIX_ISLEAF) != 0);
  186 }
  187 
  188 /*
  189  * Returns the associated page extracted from rnode.
  190  */
  191 static __inline vm_page_t
  192 vm_radix_topage(struct vm_radix_node *rnode)
  193 {
  194 
  195         return ((vm_page_t)((uintptr_t)rnode & ~VM_RADIX_FLAGS));
  196 }
  197 
  198 /*
  199  * Adds the page as a child of the provided node.
  200  */
  201 static __inline void
  202 vm_radix_addpage(struct vm_radix_node *rnode, vm_pindex_t index, uint16_t clev,
  203     vm_page_t page)
  204 {
  205         int slot;
  206 
  207         slot = vm_radix_slot(index, clev);
  208         rnode->rn_child[slot] = (void *)((uintptr_t)page | VM_RADIX_ISLEAF);
  209 }
  210 
  211 /*
  212  * Returns the slot where two keys differ.
  213  * It cannot accept 2 equal keys.
  214  */
  215 static __inline uint16_t
  216 vm_radix_keydiff(vm_pindex_t index1, vm_pindex_t index2)
  217 {
  218         uint16_t clev;
  219 
  220         KASSERT(index1 != index2, ("%s: passing the same key value %jx",
  221             __func__, (uintmax_t)index1));
  222 
  223         index1 ^= index2;
  224         for (clev = VM_RADIX_LIMIT;; clev--)
  225                 if (vm_radix_slot(index1, clev) != 0)
  226                         return (clev);
  227 }
  228 
  229 /*
  230  * Returns TRUE if it can be determined that key does not belong to the
  231  * specified rnode.  Otherwise, returns FALSE.
  232  */
  233 static __inline boolean_t
  234 vm_radix_keybarr(struct vm_radix_node *rnode, vm_pindex_t idx)
  235 {
  236 
  237         if (rnode->rn_clev < VM_RADIX_LIMIT) {
  238                 idx = vm_radix_trimkey(idx, rnode->rn_clev + 1);
  239                 return (idx != rnode->rn_owner);
  240         }
  241         return (FALSE);
  242 }
  243 
  244 /*
  245  * Internal helper for vm_radix_reclaim_allnodes().
  246  * This function is recursive.
  247  */
  248 static void
  249 vm_radix_reclaim_allnodes_int(struct vm_radix_node *rnode)
  250 {
  251         int slot;
  252 
  253         KASSERT(rnode->rn_count <= VM_RADIX_COUNT,
  254             ("vm_radix_reclaim_allnodes_int: bad count in rnode %p", rnode));
  255         for (slot = 0; rnode->rn_count != 0; slot++) {
  256                 if (rnode->rn_child[slot] == NULL)
  257                         continue;
  258                 if (!vm_radix_isleaf(rnode->rn_child[slot]))
  259                         vm_radix_reclaim_allnodes_int(rnode->rn_child[slot]);
  260                 rnode->rn_child[slot] = NULL;
  261                 rnode->rn_count--;
  262         }
  263         vm_radix_node_put(rnode);
  264 }
  265 
  266 #ifdef INVARIANTS
  267 /*
  268  * Radix node zone destructor.
  269  */
  270 static void
  271 vm_radix_node_zone_dtor(void *mem, int size __unused, void *arg __unused)
  272 {
  273         struct vm_radix_node *rnode;
  274         int slot;
  275 
  276         rnode = mem;
  277         KASSERT(rnode->rn_count == 0,
  278             ("vm_radix_node_put: rnode %p has %d children", rnode,
  279             rnode->rn_count));
  280         for (slot = 0; slot < VM_RADIX_COUNT; slot++)
  281                 KASSERT(rnode->rn_child[slot] == NULL,
  282                     ("vm_radix_node_put: rnode %p has a child", rnode));
  283 }
  284 #endif
  285 
  286 static int
  287 vm_radix_node_zone_init(void *mem, int size __unused, int flags __unused)
  288 {
  289         struct vm_radix_node *rnode;
  290 
  291         rnode = mem;
  292         bzero(rnode, sizeof(*rnode));
  293         return (0);
  294 }
  295 
  296 #ifndef UMA_MD_SMALL_ALLOC
  297 void vm_radix_reserve_kva(void);
  298 /*
  299  * Reserve the KVA necessary to satisfy the node allocation.
  300  * This is mandatory in architectures not supporting direct
  301  * mapping as they will need otherwise to carve into the kernel maps for
  302  * every node allocation, resulting into deadlocks for consumers already
  303  * working with kernel maps.
  304  */
  305 void
  306 vm_radix_reserve_kva(void)
  307 {
  308 
  309         /*
  310          * Calculate the number of reserved nodes, discounting the pages that
  311          * are needed to store them.
  312          */
  313         if (!uma_zone_reserve_kva(vm_radix_node_zone,
  314             ((vm_paddr_t)vm_cnt.v_page_count * PAGE_SIZE) / (PAGE_SIZE +
  315             sizeof(struct vm_radix_node))))
  316                 panic("%s: unable to reserve KVA", __func__);
  317 }
  318 #endif
  319 
  320 /*
  321  * Initialize the UMA slab zone.
  322  */
  323 void
  324 vm_radix_zinit(void)
  325 {
  326 
  327         vm_radix_node_zone = uma_zcreate("RADIX NODE",
  328             sizeof(struct vm_radix_node), NULL,
  329 #ifdef INVARIANTS
  330             vm_radix_node_zone_dtor,
  331 #else
  332             NULL,
  333 #endif
  334             vm_radix_node_zone_init, NULL, VM_RADIX_PAD, UMA_ZONE_VM);
  335 }
  336 
  337 /*
  338  * Inserts the key-value pair into the trie.
  339  * Panics if the key already exists.
  340  */
  341 int
  342 vm_radix_insert(struct vm_radix *rtree, vm_page_t page)
  343 {
  344         vm_pindex_t index, newind;
  345         void **parentp;
  346         struct vm_radix_node *rnode, *tmp;
  347         vm_page_t m;
  348         int slot;
  349         uint16_t clev;
  350 
  351         index = page->pindex;
  352 
  353         /*
  354          * The owner of record for root is not really important because it
  355          * will never be used.
  356          */
  357         rnode = vm_radix_getroot(rtree);
  358         if (rnode == NULL) {
  359                 rtree->rt_root = (uintptr_t)page | VM_RADIX_ISLEAF;
  360                 return (0);
  361         }
  362         parentp = (void **)&rtree->rt_root;
  363         for (;;) {
  364                 if (vm_radix_isleaf(rnode)) {
  365                         m = vm_radix_topage(rnode);
  366                         if (m->pindex == index)
  367                                 panic("%s: key %jx is already present",
  368                                     __func__, (uintmax_t)index);
  369                         clev = vm_radix_keydiff(m->pindex, index);
  370                         tmp = vm_radix_node_get(vm_radix_trimkey(index,
  371                             clev + 1), 2, clev);
  372                         if (tmp == NULL)
  373                                 return (ENOMEM);
  374                         *parentp = tmp;
  375                         vm_radix_addpage(tmp, index, clev, page);
  376                         vm_radix_addpage(tmp, m->pindex, clev, m);
  377                         return (0);
  378                 } else if (vm_radix_keybarr(rnode, index))
  379                         break;
  380                 slot = vm_radix_slot(index, rnode->rn_clev);
  381                 if (rnode->rn_child[slot] == NULL) {
  382                         rnode->rn_count++;
  383                         vm_radix_addpage(rnode, index, rnode->rn_clev, page);
  384                         return (0);
  385                 }
  386                 parentp = &rnode->rn_child[slot];
  387                 rnode = rnode->rn_child[slot];
  388         }
  389 
  390         /*
  391          * A new node is needed because the right insertion level is reached.
  392          * Setup the new intermediate node and add the 2 children: the
  393          * new object and the older edge.
  394          */
  395         newind = rnode->rn_owner;
  396         clev = vm_radix_keydiff(newind, index);
  397         tmp = vm_radix_node_get(vm_radix_trimkey(index, clev + 1), 2, clev);
  398         if (tmp == NULL)
  399                 return (ENOMEM);
  400         *parentp = tmp;
  401         vm_radix_addpage(tmp, index, clev, page);
  402         slot = vm_radix_slot(newind, clev);
  403         tmp->rn_child[slot] = rnode;
  404         return (0);
  405 }
  406 
  407 /*
  408  * Returns TRUE if the specified radix tree contains a single leaf and FALSE
  409  * otherwise.
  410  */
  411 boolean_t
  412 vm_radix_is_singleton(struct vm_radix *rtree)
  413 {
  414         struct vm_radix_node *rnode;
  415 
  416         rnode = vm_radix_getroot(rtree);
  417         if (rnode == NULL)
  418                 return (FALSE);
  419         return (vm_radix_isleaf(rnode));
  420 }
  421 
  422 /*
  423  * Returns the value stored at the index.  If the index is not present,
  424  * NULL is returned.
  425  */
  426 vm_page_t
  427 vm_radix_lookup(struct vm_radix *rtree, vm_pindex_t index)
  428 {
  429         struct vm_radix_node *rnode;
  430         vm_page_t m;
  431         int slot;
  432 
  433         rnode = vm_radix_getroot(rtree);
  434         while (rnode != NULL) {
  435                 if (vm_radix_isleaf(rnode)) {
  436                         m = vm_radix_topage(rnode);
  437                         if (m->pindex == index)
  438                                 return (m);
  439                         else
  440                                 break;
  441                 } else if (vm_radix_keybarr(rnode, index))
  442                         break;
  443                 slot = vm_radix_slot(index, rnode->rn_clev);
  444                 rnode = rnode->rn_child[slot];
  445         }
  446         return (NULL);
  447 }
  448 
  449 /*
  450  * Look up the nearest entry at a position bigger than or equal to index.
  451  */
  452 vm_page_t
  453 vm_radix_lookup_ge(struct vm_radix *rtree, vm_pindex_t index)
  454 {
  455         struct vm_radix_node *stack[VM_RADIX_LIMIT];
  456         vm_pindex_t inc;
  457         vm_page_t m;
  458         struct vm_radix_node *child, *rnode;
  459 #ifdef INVARIANTS
  460         int loops = 0;
  461 #endif
  462         int slot, tos;
  463 
  464         rnode = vm_radix_getroot(rtree);
  465         if (rnode == NULL)
  466                 return (NULL);
  467         else if (vm_radix_isleaf(rnode)) {
  468                 m = vm_radix_topage(rnode);
  469                 if (m->pindex >= index)
  470                         return (m);
  471                 else
  472                         return (NULL);
  473         }
  474         tos = 0;
  475         for (;;) {
  476                 /*
  477                  * If the keys differ before the current bisection node,
  478                  * then the search key might rollback to the earliest
  479                  * available bisection node or to the smallest key
  480                  * in the current node (if the owner is bigger than the
  481                  * search key).
  482                  */
  483                 if (vm_radix_keybarr(rnode, index)) {
  484                         if (index > rnode->rn_owner) {
  485 ascend:
  486                                 KASSERT(++loops < 1000,
  487                                     ("vm_radix_lookup_ge: too many loops"));
  488 
  489                                 /*
  490                                  * Pop nodes from the stack until either the
  491                                  * stack is empty or a node that could have a
  492                                  * matching descendant is found.
  493                                  */
  494                                 do {
  495                                         if (tos == 0)
  496                                                 return (NULL);
  497                                         rnode = stack[--tos];
  498                                 } while (vm_radix_slot(index,
  499                                     rnode->rn_clev) == (VM_RADIX_COUNT - 1));
  500 
  501                                 /*
  502                                  * The following computation cannot overflow
  503                                  * because index's slot at the current level
  504                                  * is less than VM_RADIX_COUNT - 1.
  505                                  */
  506                                 index = vm_radix_trimkey(index,
  507                                     rnode->rn_clev);
  508                                 index += VM_RADIX_UNITLEVEL(rnode->rn_clev);
  509                         } else
  510                                 index = rnode->rn_owner;
  511                         KASSERT(!vm_radix_keybarr(rnode, index),
  512                             ("vm_radix_lookup_ge: keybarr failed"));
  513                 }
  514                 slot = vm_radix_slot(index, rnode->rn_clev);
  515                 child = rnode->rn_child[slot];
  516                 if (vm_radix_isleaf(child)) {
  517                         m = vm_radix_topage(child);
  518                         if (m->pindex >= index)
  519                                 return (m);
  520                 } else if (child != NULL)
  521                         goto descend;
  522 
  523                 /*
  524                  * Look for an available edge or page within the current
  525                  * bisection node.
  526                  */
  527                 if (slot < (VM_RADIX_COUNT - 1)) {
  528                         inc = VM_RADIX_UNITLEVEL(rnode->rn_clev);
  529                         index = vm_radix_trimkey(index, rnode->rn_clev);
  530                         do {
  531                                 index += inc;
  532                                 slot++;
  533                                 child = rnode->rn_child[slot];
  534                                 if (vm_radix_isleaf(child)) {
  535                                         m = vm_radix_topage(child);
  536                                         if (m->pindex >= index)
  537                                                 return (m);
  538                                 } else if (child != NULL)
  539                                         goto descend;
  540                         } while (slot < (VM_RADIX_COUNT - 1));
  541                 }
  542                 KASSERT(child == NULL || vm_radix_isleaf(child),
  543                     ("vm_radix_lookup_ge: child is radix node"));
  544 
  545                 /*
  546                  * If a page or edge bigger than the search slot is not found
  547                  * in the current node, ascend to the next higher-level node.
  548                  */
  549                 goto ascend;
  550 descend:
  551                 KASSERT(rnode->rn_clev > 0,
  552                     ("vm_radix_lookup_ge: pushing leaf's parent"));
  553                 KASSERT(tos < VM_RADIX_LIMIT,
  554                     ("vm_radix_lookup_ge: stack overflow"));
  555                 stack[tos++] = rnode;
  556                 rnode = child;
  557         }
  558 }
  559 
  560 /*
  561  * Look up the nearest entry at a position less than or equal to index.
  562  */
  563 vm_page_t
  564 vm_radix_lookup_le(struct vm_radix *rtree, vm_pindex_t index)
  565 {
  566         struct vm_radix_node *stack[VM_RADIX_LIMIT];
  567         vm_pindex_t inc;
  568         vm_page_t m;
  569         struct vm_radix_node *child, *rnode;
  570 #ifdef INVARIANTS
  571         int loops = 0;
  572 #endif
  573         int slot, tos;
  574 
  575         rnode = vm_radix_getroot(rtree);
  576         if (rnode == NULL)
  577                 return (NULL);
  578         else if (vm_radix_isleaf(rnode)) {
  579                 m = vm_radix_topage(rnode);
  580                 if (m->pindex <= index)
  581                         return (m);
  582                 else
  583                         return (NULL);
  584         }
  585         tos = 0;
  586         for (;;) {
  587                 /*
  588                  * If the keys differ before the current bisection node,
  589                  * then the search key might rollback to the earliest
  590                  * available bisection node or to the largest key
  591                  * in the current node (if the owner is smaller than the
  592                  * search key).
  593                  */
  594                 if (vm_radix_keybarr(rnode, index)) {
  595                         if (index > rnode->rn_owner) {
  596                                 index = rnode->rn_owner + VM_RADIX_COUNT *
  597                                     VM_RADIX_UNITLEVEL(rnode->rn_clev);
  598                         } else {
  599 ascend:
  600                                 KASSERT(++loops < 1000,
  601                                     ("vm_radix_lookup_le: too many loops"));
  602 
  603                                 /*
  604                                  * Pop nodes from the stack until either the
  605                                  * stack is empty or a node that could have a
  606                                  * matching descendant is found.
  607                                  */
  608                                 do {
  609                                         if (tos == 0)
  610                                                 return (NULL);
  611                                         rnode = stack[--tos];
  612                                 } while (vm_radix_slot(index,
  613                                     rnode->rn_clev) == 0);
  614 
  615                                 /*
  616                                  * The following computation cannot overflow
  617                                  * because index's slot at the current level
  618                                  * is greater than 0.
  619                                  */
  620                                 index = vm_radix_trimkey(index,
  621                                     rnode->rn_clev);
  622                         }
  623                         index--;
  624                         KASSERT(!vm_radix_keybarr(rnode, index),
  625                             ("vm_radix_lookup_le: keybarr failed"));
  626                 }
  627                 slot = vm_radix_slot(index, rnode->rn_clev);
  628                 child = rnode->rn_child[slot];
  629                 if (vm_radix_isleaf(child)) {
  630                         m = vm_radix_topage(child);
  631                         if (m->pindex <= index)
  632                                 return (m);
  633                 } else if (child != NULL)
  634                         goto descend;
  635 
  636                 /*
  637                  * Look for an available edge or page within the current
  638                  * bisection node.
  639                  */
  640                 if (slot > 0) {
  641                         inc = VM_RADIX_UNITLEVEL(rnode->rn_clev);
  642                         index |= inc - 1;
  643                         do {
  644                                 index -= inc;
  645                                 slot--;
  646                                 child = rnode->rn_child[slot];
  647                                 if (vm_radix_isleaf(child)) {
  648                                         m = vm_radix_topage(child);
  649                                         if (m->pindex <= index)
  650                                                 return (m);
  651                                 } else if (child != NULL)
  652                                         goto descend;
  653                         } while (slot > 0);
  654                 }
  655                 KASSERT(child == NULL || vm_radix_isleaf(child),
  656                     ("vm_radix_lookup_le: child is radix node"));
  657 
  658                 /*
  659                  * If a page or edge smaller than the search slot is not found
  660                  * in the current node, ascend to the next higher-level node.
  661                  */
  662                 goto ascend;
  663 descend:
  664                 KASSERT(rnode->rn_clev > 0,
  665                     ("vm_radix_lookup_le: pushing leaf's parent"));
  666                 KASSERT(tos < VM_RADIX_LIMIT,
  667                     ("vm_radix_lookup_le: stack overflow"));
  668                 stack[tos++] = rnode;
  669                 rnode = child;
  670         }
  671 }
  672 
  673 /*
  674  * Remove the specified index from the trie, and return the value stored at
  675  * that index.  If the index is not present, return NULL.
  676  */
  677 vm_page_t
  678 vm_radix_remove(struct vm_radix *rtree, vm_pindex_t index)
  679 {
  680         struct vm_radix_node *rnode, *parent;
  681         vm_page_t m;
  682         int i, slot;
  683 
  684         rnode = vm_radix_getroot(rtree);
  685         if (vm_radix_isleaf(rnode)) {
  686                 m = vm_radix_topage(rnode);
  687                 if (m->pindex != index)
  688                         return (NULL);
  689                 vm_radix_setroot(rtree, NULL);
  690                 return (m);
  691         }
  692         parent = NULL;
  693         for (;;) {
  694                 if (rnode == NULL)
  695                         return (NULL);
  696                 slot = vm_radix_slot(index, rnode->rn_clev);
  697                 if (vm_radix_isleaf(rnode->rn_child[slot])) {
  698                         m = vm_radix_topage(rnode->rn_child[slot]);
  699                         if (m->pindex != index)
  700                                 return (NULL);
  701                         rnode->rn_child[slot] = NULL;
  702                         rnode->rn_count--;
  703                         if (rnode->rn_count > 1)
  704                                 return (m);
  705                         for (i = 0; i < VM_RADIX_COUNT; i++)
  706                                 if (rnode->rn_child[i] != NULL)
  707                                         break;
  708                         KASSERT(i != VM_RADIX_COUNT,
  709                             ("%s: invalid node configuration", __func__));
  710                         if (parent == NULL)
  711                                 vm_radix_setroot(rtree, rnode->rn_child[i]);
  712                         else {
  713                                 slot = vm_radix_slot(index, parent->rn_clev);
  714                                 KASSERT(parent->rn_child[slot] == rnode,
  715                                     ("%s: invalid child value", __func__));
  716                                 parent->rn_child[slot] = rnode->rn_child[i];
  717                         }
  718                         rnode->rn_count--;
  719                         rnode->rn_child[i] = NULL;
  720                         vm_radix_node_put(rnode);
  721                         return (m);
  722                 }
  723                 parent = rnode;
  724                 rnode = rnode->rn_child[slot];
  725         }
  726 }
  727 
  728 /*
  729  * Remove and free all the nodes from the radix tree.
  730  * This function is recursive but there is a tight control on it as the
  731  * maximum depth of the tree is fixed.
  732  */
  733 void
  734 vm_radix_reclaim_allnodes(struct vm_radix *rtree)
  735 {
  736         struct vm_radix_node *root;
  737 
  738         root = vm_radix_getroot(rtree);
  739         if (root == NULL)
  740                 return;
  741         vm_radix_setroot(rtree, NULL);
  742         if (!vm_radix_isleaf(root))
  743                 vm_radix_reclaim_allnodes_int(root);
  744 }
  745 
  746 /*
  747  * Replace an existing page in the trie with another one.
  748  * Panics if there is not an old page in the trie at the new page's index.
  749  */
  750 vm_page_t
  751 vm_radix_replace(struct vm_radix *rtree, vm_page_t newpage)
  752 {
  753         struct vm_radix_node *rnode;
  754         vm_page_t m;
  755         vm_pindex_t index;
  756         int slot;
  757 
  758         index = newpage->pindex;
  759         rnode = vm_radix_getroot(rtree);
  760         if (rnode == NULL)
  761                 panic("%s: replacing page on an empty trie", __func__);
  762         if (vm_radix_isleaf(rnode)) {
  763                 m = vm_radix_topage(rnode);
  764                 if (m->pindex != index)
  765                         panic("%s: original replacing root key not found",
  766                             __func__);
  767                 rtree->rt_root = (uintptr_t)newpage | VM_RADIX_ISLEAF;
  768                 return (m);
  769         }
  770         for (;;) {
  771                 slot = vm_radix_slot(index, rnode->rn_clev);
  772                 if (vm_radix_isleaf(rnode->rn_child[slot])) {
  773                         m = vm_radix_topage(rnode->rn_child[slot]);
  774                         if (m->pindex == index) {
  775                                 rnode->rn_child[slot] =
  776                                     (void *)((uintptr_t)newpage |
  777                                     VM_RADIX_ISLEAF);
  778                                 return (m);
  779                         } else
  780                                 break;
  781                 } else if (rnode->rn_child[slot] == NULL ||
  782                     vm_radix_keybarr(rnode->rn_child[slot], index))
  783                         break;
  784                 rnode = rnode->rn_child[slot];
  785         }
  786         panic("%s: original replacing page not found", __func__);
  787 }
  788 
  789 void
  790 vm_radix_wait(void)
  791 {
  792         uma_zwait(vm_radix_node_zone);
  793 }
  794 
  795 #ifdef DDB
  796 /*
  797  * Show details about the given radix node.
  798  */
  799 DB_SHOW_COMMAND(radixnode, db_show_radixnode)
  800 {
  801         struct vm_radix_node *rnode;
  802         int i;
  803 
  804         if (!have_addr)
  805                 return;
  806         rnode = (struct vm_radix_node *)addr;
  807         db_printf("radixnode %p, owner %jx, children count %u, level %u:\n",
  808             (void *)rnode, (uintmax_t)rnode->rn_owner, rnode->rn_count,
  809             rnode->rn_clev);
  810         for (i = 0; i < VM_RADIX_COUNT; i++)
  811                 if (rnode->rn_child[i] != NULL)
  812                         db_printf("slot: %d, val: %p, page: %p, clev: %d\n",
  813                             i, (void *)rnode->rn_child[i],
  814                             vm_radix_isleaf(rnode->rn_child[i]) ?
  815                             vm_radix_topage(rnode->rn_child[i]) : NULL,
  816                             rnode->rn_clev);
  817 }
  818 #endif /* DDB */

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