1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
|
/*
File: list_sort.c
Copyright (C) 2011 Christophe GRENIER <grenier@cgsecurity.org>
This software is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write the Free Software Foundation, Inc., 51
Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#ifdef HAVE_STRING_H
#include <string.h>
#endif
#include "types.h"
#include "list.h"
#include "list_sort.h"
#define MAX_LIST_LENGTH_BITS 20
/*
* Returns a list organized in an intermediate format suited
* to chaining of merge() calls: null-terminated, no reserved or
* sentinel head node, "prev" links not maintained.
*/
/*@
@ decreases 0;
@*/
static struct td_list_head *merge(
int (*cmp)(const struct td_list_head *a, const struct td_list_head *b),
struct td_list_head *a, struct td_list_head *b)
{
struct td_list_head head, *tail = &head;
/*@
@ loop invariant \valid_function(cmp);
@ loop invariant \valid(tail);
@ loop invariant \valid(a);
@ loop invariant \valid(b);
@*/
while (a && b) {
/* if equal, take 'a' -- important for sort stability */
if ((*cmp)(a, b) <= 0) {
tail->next = a;
a = a->next;
} else {
tail->next = b;
b = b->next;
}
tail = tail->next;
}
tail->next = a?a:b;
return head.next;
}
/*
* Combine final list merge with restoration of standard doubly-linked
* list structure. This approach duplicates code from merge(), but
* runs faster than the tidier alternatives of either a separate final
* prev-link restoration pass, or maintaining the prev links
* throughout.
*/
/*@
@ decreases 0;
@*/
static void merge_and_restore_back_links(
int (*cmp)(const struct td_list_head *a, const struct td_list_head *b),
struct td_list_head *head,
struct td_list_head *a, struct td_list_head *b)
{
struct td_list_head *tail = head;
while (a && b) {
/* if equal, take 'a' -- important for sort stability */
if ((*cmp)(a, b) <= 0) {
tail->next = a;
a->prev = tail;
a = a->next;
} else {
tail->next = b;
b->prev = tail;
b = b->next;
}
tail = tail->next;
}
tail->next = a ? a : b;
do {
/*
* In worst cases this loop may run many iterations.
* Continue callbacks to the client even though no
* element comparison is needed, so the client's cmp()
* routine can invoke cond_resched() periodically.
*/
(*cmp)(tail->next, tail->next);
tail->next->prev = tail;
tail = tail->next;
} while (tail->next);
tail->next = head;
head->prev = tail;
}
/**
* td_list_sort - sort a list
* @head: the list to sort
* @cmp: the elements comparison function
*
* This function implements "merge sort", which has O(nlog(n))
* complexity.
*
* The comparison function @cmp must return a negative value if @a
* should sort before @b, and a positive value if @a should sort after
* @b. If @a and @b are equivalent, and their original relative
* ordering is to be preserved, @cmp must return 0.
*/
void td_list_sort(struct td_list_head *head,
int (*cmp)(const struct td_list_head *a, const struct td_list_head *b))
{
struct td_list_head *part[MAX_LIST_LENGTH_BITS+1]; /* sorted partial lists
-- last slot is a sentinel */
unsigned int lev; /* index into part[] */
unsigned int max_lev = 0;
struct td_list_head *list;
if (td_list_empty(head))
return;
memset(part, 0, sizeof(part));
head->prev->next = NULL;
list = head->next;
/*@
@ loop invariant \valid_function(cmp);
@*/
while (list) {
struct td_list_head *cur = list;
list = list->next;
cur->next = NULL;
/*@
@ loop invariant \valid_function(cmp);
@*/
for (lev = 0; part[lev]; lev++) {
cur = merge(cmp, part[lev], cur);
part[lev] = NULL;
}
if (lev > max_lev) {
if (lev >= MAX_LIST_LENGTH_BITS)
{
// list passed to td_list_sort() too long for efficiency
lev--;
}
max_lev = lev;
}
part[lev] = cur;
}
/*@
@ loop invariant \valid_function(cmp);
@*/
for (lev = 0; lev < max_lev; lev++)
if (part[lev])
list = merge(cmp, part[lev], list);
merge_and_restore_back_links(cmp, head, part[max_lev], list);
}
|
