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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
10/*
11 * Returns a list organized in an intermediate format suited
12 * to chaining of merge() calls: null-terminated, no reserved or
13 * sentinel head node, "prev" links not maintained.
14 */
15__attribute__((nonnull(2,3,4)))
16static struct list_head *merge(void *priv, list_cmp_func_t cmp,
17 struct list_head *a, struct list_head *b)
18{
19 struct list_head *head, **tail = &head;
20
21 for (;;) {
22 /* if equal, take 'a' -- important for sort stability */
23 if (cmp(priv, a, b) <= 0) {
24 *tail = a;
25 tail = &a->next;
26 a = a->next;
27 if (!a) {
28 *tail = b;
29 break;
30 }
31 } else {
32 *tail = b;
33 tail = &b->next;
34 b = b->next;
35 if (!b) {
36 *tail = a;
37 break;
38 }
39 }
40 }
41 return head;
42}
43
44/*
45 * Combine final list merge with restoration of standard doubly-linked
46 * list structure. This approach duplicates code from merge(), but
47 * runs faster than the tidier alternatives of either a separate final
48 * prev-link restoration pass, or maintaining the prev links
49 * throughout.
50 */
51__attribute__((nonnull(2,3,4,5)))
52static void merge_final(void *priv, list_cmp_func_t cmp, struct list_head *head,
53 struct list_head *a, struct list_head *b)
54{
55 struct list_head *tail = head;
56 u8 count = 0;
57
58 for (;;) {
59 /* if equal, take 'a' -- important for sort stability */
60 if (cmp(priv, a, b) <= 0) {
61 tail->next = a;
62 a->prev = tail;
63 tail = a;
64 a = a->next;
65 if (!a)
66 break;
67 } else {
68 tail->next = b;
69 b->prev = tail;
70 tail = b;
71 b = b->next;
72 if (!b) {
73 b = a;
74 break;
75 }
76 }
77 }
78
79 /* Finish linking remainder of list b on to tail */
80 tail->next = b;
81 do {
82 /*
83 * If the merge is highly unbalanced (e.g. the input is
84 * already sorted), this loop may run many iterations.
85 * Continue callbacks to the client even though no
86 * element comparison is needed, so the client's cmp()
87 * routine can invoke cond_resched() periodically.
88 */
89 if (unlikely(!++count))
90 cmp(priv, b, b);
91 b->prev = tail;
92 tail = b;
93 b = b->next;
94 } while (b);
95
96 /* And the final links to make a circular doubly-linked list */
97 tail->next = head;
98 head->prev = tail;
99}
100
101/**
102 * list_sort - sort a list
103 * @priv: private data, opaque to list_sort(), passed to @cmp
104 * @head: the list to sort
105 * @cmp: the elements comparison function
106 *
107 * The comparison function @cmp must return > 0 if @a should sort after
108 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
109 * sort before @b *or* their original order should be preserved. It is
110 * always called with the element that came first in the input in @a,
111 * and list_sort is a stable sort, so it is not necessary to distinguish
112 * the @a < @b and @a == @b cases.
113 *
114 * This is compatible with two styles of @cmp function:
115 * - The traditional style which returns <0 / =0 / >0, or
116 * - Returning a boolean 0/1.
117 * The latter offers a chance to save a few cycles in the comparison
118 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
119 *
120 * A good way to write a multi-word comparison is::
121 *
122 * if (a->high != b->high)
123 * return a->high > b->high;
124 * if (a->middle != b->middle)
125 * return a->middle > b->middle;
126 * return a->low > b->low;
127 *
128 *
129 * This mergesort is as eager as possible while always performing at least
130 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are
131 * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
132 *
133 * Thus, it will avoid cache thrashing as long as 3*2^k elements can
134 * fit into the cache. Not quite as good as a fully-eager bottom-up
135 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
136 * the common case that everything fits into L1.
137 *
138 *
139 * The merging is controlled by "count", the number of elements in the
140 * pending lists. This is beautifully simple code, but rather subtle.
141 *
142 * Each time we increment "count", we set one bit (bit k) and clear
143 * bits k-1 .. 0. Each time this happens (except the very first time
144 * for each bit, when count increments to 2^k), we merge two lists of
145 * size 2^k into one list of size 2^(k+1).
146 *
147 * This merge happens exactly when the count reaches an odd multiple of
148 * 2^k, which is when we have 2^k elements pending in smaller lists,
149 * so it's safe to merge away two lists of size 2^k.
150 *
151 * After this happens twice, we have created two lists of size 2^(k+1),
152 * which will be merged into a list of size 2^(k+2) before we create
153 * a third list of size 2^(k+1), so there are never more than two pending.
154 *
155 * The number of pending lists of size 2^k is determined by the
156 * state of bit k of "count" plus two extra pieces of information:
157 *
158 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
159 * - Whether the higher-order bits are zero or non-zero (i.e.
160 * is count >= 2^(k+1)).
161 *
162 * There are six states we distinguish. "x" represents some arbitrary
163 * bits, and "y" represents some arbitrary non-zero bits:
164 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k
165 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
166 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k
167 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
168 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k
169 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
170 * (merge and loop back to state 2)
171 *
172 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
173 * bit k-1 is set while the more significant bits are non-zero) and
174 * merge them away in the 5->2 transition. Note in particular that just
175 * before the 5->2 transition, all lower-order bits are 11 (state 3),
176 * so there is one list of each smaller size.
177 *
178 * When we reach the end of the input, we merge all the pending
179 * lists, from smallest to largest. If you work through cases 2 to
180 * 5 above, you can see that the number of elements we merge with a list
181 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
182 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
183 */
184__attribute__((nonnull(2,3)))
185void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
186{
187 struct list_head *list = head->next, *pending = NULL;
188 size_t count = 0; /* Count of pending */
189
190 if (list == head->prev) /* Zero or one elements */
191 return;
192
193 /* Convert to a null-terminated singly-linked list. */
194 head->prev->next = NULL;
195
196 /*
197 * Data structure invariants:
198 * - All lists are singly linked and null-terminated; prev
199 * pointers are not maintained.
200 * - pending is a prev-linked "list of lists" of sorted
201 * sublists awaiting further merging.
202 * - Each of the sorted sublists is power-of-two in size.
203 * - Sublists are sorted by size and age, smallest & newest at front.
204 * - There are zero to two sublists of each size.
205 * - A pair of pending sublists are merged as soon as the number
206 * of following pending elements equals their size (i.e.
207 * each time count reaches an odd multiple of that size).
208 * That ensures each later final merge will be at worst 2:1.
209 * - Each round consists of:
210 * - Merging the two sublists selected by the highest bit
211 * which flips when count is incremented, and
212 * - Adding an element from the input as a size-1 sublist.
213 */
214 do {
215 size_t bits;
216 struct list_head **tail = &pending;
217
218 /* Find the least-significant clear bit in count */
219 for (bits = count; bits & 1; bits >>= 1)
220 tail = &(*tail)->prev;
221 /* Do the indicated merge */
222 if (likely(bits)) {
223 struct list_head *a = *tail, *b = a->prev;
224
225 a = merge(priv, cmp, b, a);
226 /* Install the merged result in place of the inputs */
227 a->prev = b->prev;
228 *tail = a;
229 }
230
231 /* Move one element from input list to pending */
232 list->prev = pending;
233 pending = list;
234 list = list->next;
235 pending->next = NULL;
236 count++;
237 } while (list);
238
239 /* End of input; merge together all the pending lists. */
240 list = pending;
241 pending = pending->prev;
242 for (;;) {
243 struct list_head *next = pending->prev;
244
245 if (!next)
246 break;
247 list = merge(priv, cmp, pending, list);
248 pending = next;
249 }
250 /* The final merge, rebuilding prev links */
251 merge_final(priv, cmp, head, pending, list);
252}
253EXPORT_SYMBOL(list_sort);
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 = random32() % (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 */