Document the O(log n) algorithm for finding free space.
Submitted by: Mark W. Krentel
This commit is contained in:
Alan Cox
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@ -252,6 +252,7 @@ MAN= accept_filter.9 \
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vm_map_clean.9 \
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vm_map_create.9 \
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vm_map_delete.9 \
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vm_map_entry_resize_free.9 \
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vm_map_find.9 \
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vm_map_findspace.9 \
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vm_map_inherit.9 \
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233
share/man/man9/vm_map_entry_resize_free.9
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233
share/man/man9/vm_map_entry_resize_free.9
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.\"
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.\" Copyright (c) 2004 Mark W. Krentel <krentel@dreamscape.com>
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" $FreeBSD$
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.\"
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.Dd August 17, 2004
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.Os
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.Dt VM_MAP_ENTRY_RESIZE_FREE 9
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.Sh NAME
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.Nm vm_map_entry_resize_free
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.Nd vm map free space algorithm
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.Sh SYNOPSIS
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.In sys/param.h
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.In vm/vm.h
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.In vm/vm_map.h
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.Ft void
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.Fo vm_map_entry_resize_free
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.Fa "vm_map_t map" "vm_map_entry_t entry"
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.Fc
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.Sh DESCRIPTION
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This manual page describes the
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.Vt vm_map_entry
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fields used in the VM map free space algorithm, how to maintain
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consistency of these variables, and the
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.Fn vm_map_entry_resize_free
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function.
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.Pp
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VM map entries are organized as both a doubly-linked list
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.Va ( prev
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and
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.Va next
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pointers) and as a binary search tree
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.Va ( left
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and
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.Va right
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pointers).
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The search tree is organized as a Sleator and Tarjan splay tree,
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also known as a
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.Dq self-adjusting tree.
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.Bd -literal -offset indent
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struct vm_map_entry {
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struct vm_map_entry *prev;
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struct vm_map_entry *next;
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struct vm_map_entry *left;
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struct vm_map_entry *right;
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vm_offset_t start;
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vm_offset_t end;
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vm_offset_t avail_ssize;
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vm_size_t adj_free;
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vm_size_t max_free;
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...
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};
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.Ed
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.Pp
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The free space algorithm adds two fields to
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.Vt struct vm_map_entry :
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.Va adj_free
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and
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.Va max_free .
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.Va adj_free
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is the amount of free address space adjacent to and immediately
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following (higher address) the map entry.
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This field is unused in the map header.
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Note that
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.Va adj_free
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depends on the linked list, not the splay tree and that
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.Va adj_free
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can be computed as:
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.Bd -literal -offset indent
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entry->adj_free = (entry->next == &map->header ?
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map->max_offset : entry->next->start) - entry->end;
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.Ed
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.Pp
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.Va max_free
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is the maximum amount of contiguous free space in the entry's subtree.
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Note that
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.Va max_free
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depends on the splay tree, not the linked list and that
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.Va max_free
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is computed by taking the maximum of its own
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.Va adj_free
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and the
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.Va max_free
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of its left and right subtrees.
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Again,
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.Va max_free
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is unused in the map header.
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.Pp
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These fields allow for an O(log\~n) implementation of
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.Fn vm_map_findspace .
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Using
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.Va max_free ,
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we can immediately test for a sufficiently large free region
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in an entire subtree.
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This makes it possible to find a first-fit free region of a given size
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in one pass down the tree, so O(log\~n) amortized using splay trees.
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.Pp
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When a free region changes size, we must update
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.Va adj_free
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and
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.Va max_free
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in the preceding map entry and propagate
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.Va max_free
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up the tree.
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This is handled in
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.Fn vm_map_entry_link
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and
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.Fn vm_map_entry_unlink
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for the cases of inserting and deleting an entry.
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Note that
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.Fn vm_map_entry_link
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updates both the new entry and the previous entry, and that
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.Fn vm_map_entry_unlink
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updates the previous entry.
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Also note that
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.Va max_free
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is not actually propagated up the tree.
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Instead, that entry is first splayed to the root and
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then the change is made there.
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This is a common technique in splay trees and is also
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how map entries are linked and unlinked into the tree.
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.Pp
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The
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.Fn vm_map_entry_resize_free
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function updates the free space variables in the given
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.Fa entry
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and propagates those values up the tree.
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This function should be called whenever a map entry is resized
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in-place, that is, by modifying its
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.Va start
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or
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.Va end
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values.
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Note that if you change
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.Va end ,
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then you should resize that entry, but if you change
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.Va start ,
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then you should resize the previous entry.
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The map must be locked before calling this function,
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and again, propagating
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.Va max_free
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is performed by splaying that entry to the root.
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.Sh EXAMPLES
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Consider adding a map entry with
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.Fn vm_map_insert .
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.Bd -literal -offset indent
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ret = vm_map_insert(map, object, offset, start, end, prot,
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max_prot, cow);
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.Ed
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.Pp
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In this case, no further action is required to maintain
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consistency of the free space variables.
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.Fn vm_map_insert
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calls
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.Fn vm_map_entry_link
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which updates both the new entry and the previous entry.
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The same would be true for
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.Fn vm_map_delete
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and for calling
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.Fn vm_map_entry_link
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or
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.Fn vm_map_entry_unlink
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directly.
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.Pp
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Now consider resizing an entry in-place without a call to
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.Fn vm_map_entry_link
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or
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.Fn vm_map_entry_unlink .
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.Bd -literal -offset indent
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entry->start = new_start;
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if (entry->prev != &map->header)
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vm_map_entry_resize_free(map, entry->prev);
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.Ed
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.Pp
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In this case, resetting
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.Va start
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changes the amount of free space following the previous entry,
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so we use
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.Fn vm_map_entry_resize_free
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to update the previous entry.
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.Pp
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Finally, suppose we change an entry's
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.Va end
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address.
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.Bd -literal -offset indent
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entry->end = new_end;
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vm_map_entry_resize_free(map, entry);
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.Ed
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.Pp
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Here, we call
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.Fn vm_map_entry_resize_free
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on the entry itself.
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.Sh SEE ALSO
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.Xr vm_map 9 ,
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.Xr vm_map_findspace 9
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.Rs
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.%A Daniel D. Sleator
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.%A Robert E. Tarjan
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.%T Self-Adjusting Binary Search Trees
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.%J JACM
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.%V vol. 32(3)
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.%P pp. 652-686
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.%D July 1985
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.Re
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.Sh HISTORY
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Splay trees were added to the VM map in FreeBSD 5.0, and the
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O(log\~n) tree-based free space algorithm was added in FreeBSD 5.3.
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.Sh AUTHORS
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The tree-based free space algorithm and this manual page were written by
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.An Mark W. Krentel
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.Aq krentel@dreamscape.com .
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