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b2441318 | 1 | // SPDX-License-Identifier: GPL-2.0 |
2c761270 | 2 | #include <linux/kernel.h> |
7259fa04 RV |
3 | #include <linux/bug.h> |
4 | #include <linux/compiler.h> | |
5 | #include <linux/export.h> | |
6 | #include <linux/string.h> | |
2c761270 | 7 | #include <linux/list_sort.h> |
2c761270 DC |
8 | #include <linux/list.h> |
9 | ||
043b3f7b GS |
10 | typedef int __attribute__((nonnull(2,3))) (*cmp_func)(void *, |
11 | struct list_head const *, struct list_head const *); | |
835cc0c8 DM |
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 | */ | |
043b3f7b GS |
18 | __attribute__((nonnull(2,3,4))) |
19 | static struct list_head *merge(void *priv, cmp_func cmp, | |
835cc0c8 DM |
20 | struct list_head *a, struct list_head *b) |
21 | { | |
043b3f7b | 22 | struct list_head *head, **tail = &head; |
835cc0c8 | 23 | |
043b3f7b | 24 | for (;;) { |
835cc0c8 | 25 | /* if equal, take 'a' -- important for sort stability */ |
043b3f7b GS |
26 | if (cmp(priv, a, b) <= 0) { |
27 | *tail = a; | |
28 | tail = &a->next; | |
835cc0c8 | 29 | a = a->next; |
043b3f7b GS |
30 | if (!a) { |
31 | *tail = b; | |
32 | break; | |
33 | } | |
835cc0c8 | 34 | } else { |
043b3f7b GS |
35 | *tail = b; |
36 | tail = &b->next; | |
835cc0c8 | 37 | b = b->next; |
043b3f7b GS |
38 | if (!b) { |
39 | *tail = a; | |
40 | break; | |
41 | } | |
835cc0c8 | 42 | } |
835cc0c8 | 43 | } |
043b3f7b | 44 | return head; |
835cc0c8 DM |
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 | */ | |
043b3f7b GS |
54 | __attribute__((nonnull(2,3,4,5))) |
55 | static void merge_final(void *priv, cmp_func cmp, struct list_head *head, | |
56 | struct list_head *a, struct list_head *b) | |
835cc0c8 DM |
57 | { |
58 | struct list_head *tail = head; | |
61b3d6c4 | 59 | u8 count = 0; |
835cc0c8 | 60 | |
043b3f7b | 61 | for (;;) { |
835cc0c8 | 62 | /* if equal, take 'a' -- important for sort stability */ |
043b3f7b | 63 | if (cmp(priv, a, b) <= 0) { |
835cc0c8 DM |
64 | tail->next = a; |
65 | a->prev = tail; | |
043b3f7b | 66 | tail = a; |
835cc0c8 | 67 | a = a->next; |
043b3f7b GS |
68 | if (!a) |
69 | break; | |
835cc0c8 DM |
70 | } else { |
71 | tail->next = b; | |
72 | b->prev = tail; | |
043b3f7b | 73 | tail = b; |
835cc0c8 | 74 | b = b->next; |
043b3f7b GS |
75 | if (!b) { |
76 | b = a; | |
77 | break; | |
78 | } | |
835cc0c8 | 79 | } |
835cc0c8 | 80 | } |
835cc0c8 | 81 | |
043b3f7b GS |
82 | /* Finish linking remainder of list b on to tail */ |
83 | tail->next = b; | |
835cc0c8 DM |
84 | do { |
85 | /* | |
043b3f7b GS |
86 | * If the merge is highly unbalanced (e.g. the input is |
87 | * already sorted), this loop may run many iterations. | |
835cc0c8 DM |
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 | */ | |
043b3f7b GS |
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 */ | |
835cc0c8 DM |
100 | tail->next = head; |
101 | head->prev = tail; | |
102 | } | |
103 | ||
2c761270 | 104 | /** |
02b12b7a DM |
105 | * list_sort - sort a list |
106 | * @priv: private data, opaque to list_sort(), passed to @cmp | |
2c761270 DC |
107 | * @head: the list to sort |
108 | * @cmp: the elements comparison function | |
109 | * | |
043b3f7b GS |
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. | |
2c761270 | 116 | * |
043b3f7b GS |
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 | * | |
f35a1abd JC |
123 | * A good way to write a multi-word comparison is:: |
124 | * | |
043b3f7b GS |
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; | |
b5c56e0c GS |
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: | |
4ae5b8f2 | 160 | * |
b5c56e0c GS |
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)). | |
4ae5b8f2 | 164 | * |
b5c56e0c GS |
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). | |
2c761270 | 186 | */ |
043b3f7b | 187 | __attribute__((nonnull(2,3))) |
2c761270 | 188 | void list_sort(void *priv, struct list_head *head, |
835cc0c8 DM |
189 | int (*cmp)(void *priv, struct list_head *a, |
190 | struct list_head *b)) | |
2c761270 | 191 | { |
043b3f7b GS |
192 | struct list_head *list = head->next, *pending = NULL; |
193 | size_t count = 0; /* Count of pending */ | |
2c761270 | 194 | |
043b3f7b | 195 | if (list == head->prev) /* Zero or one elements */ |
2c761270 DC |
196 | return; |
197 | ||
043b3f7b | 198 | /* Convert to a null-terminated singly-linked list. */ |
835cc0c8 | 199 | head->prev->next = NULL; |
2c761270 | 200 | |
043b3f7b GS |
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. | |
b5c56e0c | 207 | * - Each of the sorted sublists is power-of-two in size. |
043b3f7b | 208 | * - Sublists are sorted by size and age, smallest & newest at front. |
b5c56e0c GS |
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. | |
043b3f7b GS |
218 | */ |
219 | do { | |
220 | size_t bits; | |
b5c56e0c | 221 | struct list_head **tail = &pending; |
043b3f7b | 222 | |
b5c56e0c GS |
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; | |
835cc0c8 | 229 | |
b5c56e0c GS |
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; | |
835cc0c8 | 234 | } |
b5c56e0c GS |
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; | |
043b3f7b | 241 | count++; |
b5c56e0c GS |
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; | |
043b3f7b | 249 | |
b5c56e0c GS |
250 | if (!next) |
251 | break; | |
043b3f7b | 252 | list = merge(priv, (cmp_func)cmp, pending, list); |
b5c56e0c | 253 | pending = next; |
835cc0c8 | 254 | } |
043b3f7b GS |
255 | /* The final merge, rebuilding prev links */ |
256 | merge_final(priv, (cmp_func)cmp, head, pending, list); | |
835cc0c8 DM |
257 | } |
258 | EXPORT_SYMBOL(list_sort); |