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)))
16 static 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)))
52 static 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)))
185 void 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 }
253 EXPORT_SYMBOL(list_sort);
254
Linux® is a registered trademark of Linus Torvalds in the United States and other countries.
TOMOYO® is a registered trademark of NTT DATA CORPORATION.