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1#include <linux/kernel.h>
2#include <linux/module.h>
3#include <linux/list_sort.h>
4#include <linux/slab.h>
5#include <linux/list.h>
6
7#define MAX_LIST_LENGTH_BITS 20
8
9/*
10 * Returns a list organized in an intermediate format suited
11 * to chaining of merge() calls: null-terminated, no reserved or
12 * sentinel head node, "prev" links not maintained.
13 */
14static struct list_head *merge(void *priv,
15 int (*cmp)(void *priv, struct list_head *a,
16 struct list_head *b),
17 struct list_head *a, struct list_head *b)
18{
19 struct list_head head, *tail = &head;
20
21 while (a && b) {
22 /* if equal, take 'a' -- important for sort stability */
23 if ((*cmp)(priv, a, b) <= 0) {
24 tail->next = a;
25 a = a->next;
26 } else {
27 tail->next = b;
28 b = b->next;
29 }
30 tail = tail->next;
31 }
32 tail->next = a?:b;
33 return head.next;
34}
35
36/*
37 * Combine final list merge with restoration of standard doubly-linked
38 * list structure. This approach duplicates code from merge(), but
39 * runs faster than the tidier alternatives of either a separate final
40 * prev-link restoration pass, or maintaining the prev links
41 * throughout.
42 */
43static void merge_and_restore_back_links(void *priv,
44 int (*cmp)(void *priv, struct list_head *a,
45 struct list_head *b),
46 struct list_head *head,
47 struct list_head *a, struct list_head *b)
48{
49 struct list_head *tail = head;
50
51 while (a && b) {
52 /* if equal, take 'a' -- important for sort stability */
53 if ((*cmp)(priv, a, b) <= 0) {
54 tail->next = a;
55 a->prev = tail;
56 a = a->next;
57 } else {
58 tail->next = b;
59 b->prev = tail;
60 b = b->next;
61 }
62 tail = tail->next;
63 }
64 tail->next = a ? : b;
65
66 do {
67 /*
68 * In worst cases this loop may run many iterations.
69 * Continue callbacks to the client even though no
70 * element comparison is needed, so the client's cmp()
71 * routine can invoke cond_resched() periodically.
72 */
73 (*cmp)(priv, tail->next, tail->next);
74
75 tail->next->prev = tail;
76 tail = tail->next;
77 } while (tail->next);
78
79 tail->next = head;
80 head->prev = tail;
81}
82
83/**
84 * list_sort - sort a list
85 * @priv: private data, opaque to list_sort(), passed to @cmp
86 * @head: the list to sort
87 * @cmp: the elements comparison function
88 *
89 * This function implements "merge sort", which has O(nlog(n))
90 * complexity.
91 *
92 * The comparison function @cmp must return a negative value if @a
93 * should sort before @b, and a positive value if @a should sort after
94 * @b. If @a and @b are equivalent, and their original relative
95 * ordering is to be preserved, @cmp must return 0.
96 */
97void list_sort(void *priv, struct list_head *head,
98 int (*cmp)(void *priv, struct list_head *a,
99 struct list_head *b))
100{
101 struct list_head *part[MAX_LIST_LENGTH_BITS+1]; /* sorted partial lists
102 -- last slot is a sentinel */
103 int lev; /* index into part[] */
104 int max_lev = 0;
105 struct list_head *list;
106
107 if (list_empty(head))
108 return;
109
110 memset(part, 0, sizeof(part));
111
112 head->prev->next = NULL;
113 list = head->next;
114
115 while (list) {
116 struct list_head *cur = list;
117 list = list->next;
118 cur->next = NULL;
119
120 for (lev = 0; part[lev]; lev++) {
121 cur = merge(priv, cmp, part[lev], cur);
122 part[lev] = NULL;
123 }
124 if (lev > max_lev) {
125 if (unlikely(lev >= ARRAY_SIZE(part)-1)) {
126 printk_once(KERN_DEBUG "list passed to"
127 " list_sort() too long for"
128 " efficiency\n");
129 lev--;
130 }
131 max_lev = lev;
132 }
133 part[lev] = cur;
134 }
135
136 for (lev = 0; lev < max_lev; lev++)
137 if (part[lev])
138 list = merge(priv, cmp, part[lev], list);
139
140 merge_and_restore_back_links(priv, cmp, head, part[max_lev], list);
141}
142EXPORT_SYMBOL(list_sort);
143
144#ifdef CONFIG_TEST_LIST_SORT
145
146#include <linux/random.h>
147
148/*
149 * The pattern of set bits in the list length determines which cases
150 * are hit in list_sort().
151 */
152#define TEST_LIST_LEN (512+128+2) /* not including head */
153
154#define TEST_POISON1 0xDEADBEEF
155#define TEST_POISON2 0xA324354C
156
157struct debug_el {
158 unsigned int poison1;
159 struct list_head list;
160 unsigned int poison2;
161 int value;
162 unsigned serial;
163};
164
165/* Array, containing pointers to all elements in the test list */
166static struct debug_el **elts __initdata;
167
168static int __init check(struct debug_el *ela, struct debug_el *elb)
169{
170 if (ela->serial >= TEST_LIST_LEN) {
171 printk(KERN_ERR "list_sort_test: error: incorrect serial %d\n",
172 ela->serial);
173 return -EINVAL;
174 }
175 if (elb->serial >= TEST_LIST_LEN) {
176 printk(KERN_ERR "list_sort_test: error: incorrect serial %d\n",
177 elb->serial);
178 return -EINVAL;
179 }
180 if (elts[ela->serial] != ela || elts[elb->serial] != elb) {
181 printk(KERN_ERR "list_sort_test: error: phantom element\n");
182 return -EINVAL;
183 }
184 if (ela->poison1 != TEST_POISON1 || ela->poison2 != TEST_POISON2) {
185 printk(KERN_ERR "list_sort_test: error: bad poison: %#x/%#x\n",
186 ela->poison1, ela->poison2);
187 return -EINVAL;
188 }
189 if (elb->poison1 != TEST_POISON1 || elb->poison2 != TEST_POISON2) {
190 printk(KERN_ERR "list_sort_test: error: bad poison: %#x/%#x\n",
191 elb->poison1, elb->poison2);
192 return -EINVAL;
193 }
194 return 0;
195}
196
197static int __init cmp(void *priv, struct list_head *a, struct list_head *b)
198{
199 struct debug_el *ela, *elb;
200
201 ela = container_of(a, struct debug_el, list);
202 elb = container_of(b, struct debug_el, list);
203
204 check(ela, elb);
205 return ela->value - elb->value;
206}
207
208static int __init list_sort_test(void)
209{
210 int i, count = 1, err = -EINVAL;
211 struct debug_el *el;
212 struct list_head *cur, *tmp;
213 LIST_HEAD(head);
214
215 printk(KERN_DEBUG "list_sort_test: start testing list_sort()\n");
216
217 elts = kmalloc(sizeof(void *) * TEST_LIST_LEN, GFP_KERNEL);
218 if (!elts) {
219 printk(KERN_ERR "list_sort_test: error: cannot allocate "
220 "memory\n");
221 goto exit;
222 }
223
224 for (i = 0; i < TEST_LIST_LEN; i++) {
225 el = kmalloc(sizeof(*el), GFP_KERNEL);
226 if (!el) {
227 printk(KERN_ERR "list_sort_test: error: cannot "
228 "allocate memory\n");
229 goto exit;
230 }
231 /* force some equivalencies */
232 el->value = prandom_u32() % (TEST_LIST_LEN / 3);
233 el->serial = i;
234 el->poison1 = TEST_POISON1;
235 el->poison2 = TEST_POISON2;
236 elts[i] = el;
237 list_add_tail(&el->list, &head);
238 }
239
240 list_sort(NULL, &head, cmp);
241
242 for (cur = head.next; cur->next != &head; cur = cur->next) {
243 struct debug_el *el1;
244 int cmp_result;
245
246 if (cur->next->prev != cur) {
247 printk(KERN_ERR "list_sort_test: error: list is "
248 "corrupted\n");
249 goto exit;
250 }
251
252 cmp_result = cmp(NULL, cur, cur->next);
253 if (cmp_result > 0) {
254 printk(KERN_ERR "list_sort_test: error: list is not "
255 "sorted\n");
256 goto exit;
257 }
258
259 el = container_of(cur, struct debug_el, list);
260 el1 = container_of(cur->next, struct debug_el, list);
261 if (cmp_result == 0 && el->serial >= el1->serial) {
262 printk(KERN_ERR "list_sort_test: error: order of "
263 "equivalent elements not preserved\n");
264 goto exit;
265 }
266
267 if (check(el, el1)) {
268 printk(KERN_ERR "list_sort_test: error: element check "
269 "failed\n");
270 goto exit;
271 }
272 count++;
273 }
274
275 if (count != TEST_LIST_LEN) {
276 printk(KERN_ERR "list_sort_test: error: bad list length %d",
277 count);
278 goto exit;
279 }
280
281 err = 0;
282exit:
283 kfree(elts);
284 list_for_each_safe(cur, tmp, &head) {
285 list_del(cur);
286 kfree(container_of(cur, struct debug_el, list));
287 }
288 return err;
289}
290module_init(list_sort_test);
291#endif /* CONFIG_TEST_LIST_SORT */
1// SPDX-License-Identifier: GPL-2.0
2#include <linux/kernel.h>
3#include <linux/bug.h>
4#include <linux/compiler.h>
5#include <linux/export.h>
6#include <linux/string.h>
7#include <linux/list_sort.h>
8#include <linux/list.h>
9
10typedef int __attribute__((nonnull(2,3))) (*cmp_func)(void *,
11 struct list_head const *, struct list_head const *);
12
13/*
14 * Returns a list organized in an intermediate format suited
15 * to chaining of merge() calls: null-terminated, no reserved or
16 * sentinel head node, "prev" links not maintained.
17 */
18__attribute__((nonnull(2,3,4)))
19static struct list_head *merge(void *priv, cmp_func cmp,
20 struct list_head *a, struct list_head *b)
21{
22 struct list_head *head, **tail = &head;
23
24 for (;;) {
25 /* if equal, take 'a' -- important for sort stability */
26 if (cmp(priv, a, b) <= 0) {
27 *tail = a;
28 tail = &a->next;
29 a = a->next;
30 if (!a) {
31 *tail = b;
32 break;
33 }
34 } else {
35 *tail = b;
36 tail = &b->next;
37 b = b->next;
38 if (!b) {
39 *tail = a;
40 break;
41 }
42 }
43 }
44 return head;
45}
46
47/*
48 * Combine final list merge with restoration of standard doubly-linked
49 * list structure. This approach duplicates code from merge(), but
50 * runs faster than the tidier alternatives of either a separate final
51 * prev-link restoration pass, or maintaining the prev links
52 * throughout.
53 */
54__attribute__((nonnull(2,3,4,5)))
55static void merge_final(void *priv, cmp_func cmp, struct list_head *head,
56 struct list_head *a, struct list_head *b)
57{
58 struct list_head *tail = head;
59 u8 count = 0;
60
61 for (;;) {
62 /* if equal, take 'a' -- important for sort stability */
63 if (cmp(priv, a, b) <= 0) {
64 tail->next = a;
65 a->prev = tail;
66 tail = a;
67 a = a->next;
68 if (!a)
69 break;
70 } else {
71 tail->next = b;
72 b->prev = tail;
73 tail = b;
74 b = b->next;
75 if (!b) {
76 b = a;
77 break;
78 }
79 }
80 }
81
82 /* Finish linking remainder of list b on to tail */
83 tail->next = b;
84 do {
85 /*
86 * If the merge is highly unbalanced (e.g. the input is
87 * already sorted), this loop may run many iterations.
88 * Continue callbacks to the client even though no
89 * element comparison is needed, so the client's cmp()
90 * routine can invoke cond_resched() periodically.
91 */
92 if (unlikely(!++count))
93 cmp(priv, b, b);
94 b->prev = tail;
95 tail = b;
96 b = b->next;
97 } while (b);
98
99 /* And the final links to make a circular doubly-linked list */
100 tail->next = head;
101 head->prev = tail;
102}
103
104/**
105 * list_sort - sort a list
106 * @priv: private data, opaque to list_sort(), passed to @cmp
107 * @head: the list to sort
108 * @cmp: the elements comparison function
109 *
110 * The comparison funtion @cmp must return > 0 if @a should sort after
111 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
112 * sort before @b *or* their original order should be preserved. It is
113 * always called with the element that came first in the input in @a,
114 * and list_sort is a stable sort, so it is not necessary to distinguish
115 * the @a < @b and @a == @b cases.
116 *
117 * This is compatible with two styles of @cmp function:
118 * - The traditional style which returns <0 / =0 / >0, or
119 * - Returning a boolean 0/1.
120 * The latter offers a chance to save a few cycles in the comparison
121 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
122 *
123 * A good way to write a multi-word comparison is::
124 *
125 * if (a->high != b->high)
126 * return a->high > b->high;
127 * if (a->middle != b->middle)
128 * return a->middle > b->middle;
129 * return a->low > b->low;
130 *
131 *
132 * This mergesort is as eager as possible while always performing at least
133 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are
134 * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
135 *
136 * Thus, it will avoid cache thrashing as long as 3*2^k elements can
137 * fit into the cache. Not quite as good as a fully-eager bottom-up
138 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
139 * the common case that everything fits into L1.
140 *
141 *
142 * The merging is controlled by "count", the number of elements in the
143 * pending lists. This is beautiully simple code, but rather subtle.
144 *
145 * Each time we increment "count", we set one bit (bit k) and clear
146 * bits k-1 .. 0. Each time this happens (except the very first time
147 * for each bit, when count increments to 2^k), we merge two lists of
148 * size 2^k into one list of size 2^(k+1).
149 *
150 * This merge happens exactly when the count reaches an odd multiple of
151 * 2^k, which is when we have 2^k elements pending in smaller lists,
152 * so it's safe to merge away two lists of size 2^k.
153 *
154 * After this happens twice, we have created two lists of size 2^(k+1),
155 * which will be merged into a list of size 2^(k+2) before we create
156 * a third list of size 2^(k+1), so there are never more than two pending.
157 *
158 * The number of pending lists of size 2^k is determined by the
159 * state of bit k of "count" plus two extra pieces of information:
160 *
161 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
162 * - Whether the higher-order bits are zero or non-zero (i.e.
163 * is count >= 2^(k+1)).
164 *
165 * There are six states we distinguish. "x" represents some arbitrary
166 * bits, and "y" represents some arbitrary non-zero bits:
167 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k
168 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
169 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k
170 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
171 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k
172 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
173 * (merge and loop back to state 2)
174 *
175 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
176 * bit k-1 is set while the more significant bits are non-zero) and
177 * merge them away in the 5->2 transition. Note in particular that just
178 * before the 5->2 transition, all lower-order bits are 11 (state 3),
179 * so there is one list of each smaller size.
180 *
181 * When we reach the end of the input, we merge all the pending
182 * lists, from smallest to largest. If you work through cases 2 to
183 * 5 above, you can see that the number of elements we merge with a list
184 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
185 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
186 */
187__attribute__((nonnull(2,3)))
188void list_sort(void *priv, struct list_head *head,
189 int (*cmp)(void *priv, struct list_head *a,
190 struct list_head *b))
191{
192 struct list_head *list = head->next, *pending = NULL;
193 size_t count = 0; /* Count of pending */
194
195 if (list == head->prev) /* Zero or one elements */
196 return;
197
198 /* Convert to a null-terminated singly-linked list. */
199 head->prev->next = NULL;
200
201 /*
202 * Data structure invariants:
203 * - All lists are singly linked and null-terminated; prev
204 * pointers are not maintained.
205 * - pending is a prev-linked "list of lists" of sorted
206 * sublists awaiting further merging.
207 * - Each of the sorted sublists is power-of-two in size.
208 * - Sublists are sorted by size and age, smallest & newest at front.
209 * - There are zero to two sublists of each size.
210 * - A pair of pending sublists are merged as soon as the number
211 * of following pending elements equals their size (i.e.
212 * each time count reaches an odd multiple of that size).
213 * That ensures each later final merge will be at worst 2:1.
214 * - Each round consists of:
215 * - Merging the two sublists selected by the highest bit
216 * which flips when count is incremented, and
217 * - Adding an element from the input as a size-1 sublist.
218 */
219 do {
220 size_t bits;
221 struct list_head **tail = &pending;
222
223 /* Find the least-significant clear bit in count */
224 for (bits = count; bits & 1; bits >>= 1)
225 tail = &(*tail)->prev;
226 /* Do the indicated merge */
227 if (likely(bits)) {
228 struct list_head *a = *tail, *b = a->prev;
229
230 a = merge(priv, (cmp_func)cmp, b, a);
231 /* Install the merged result in place of the inputs */
232 a->prev = b->prev;
233 *tail = a;
234 }
235
236 /* Move one element from input list to pending */
237 list->prev = pending;
238 pending = list;
239 list = list->next;
240 pending->next = NULL;
241 count++;
242 } while (list);
243
244 /* End of input; merge together all the pending lists. */
245 list = pending;
246 pending = pending->prev;
247 for (;;) {
248 struct list_head *next = pending->prev;
249
250 if (!next)
251 break;
252 list = merge(priv, (cmp_func)cmp, pending, list);
253 pending = next;
254 }
255 /* The final merge, rebuilding prev links */
256 merge_final(priv, (cmp_func)cmp, head, pending, list);
257}
258EXPORT_SYMBOL(list_sort);