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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 | ||
835cc0c8 DM |
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 | */ | |
043b3f7b | 15 | __attribute__((nonnull(2,3,4))) |
4f0f586b | 16 | static struct list_head *merge(void *priv, list_cmp_func_t cmp, |
835cc0c8 DM |
17 | struct list_head *a, struct list_head *b) |
18 | { | |
043b3f7b | 19 | struct list_head *head, **tail = &head; |
835cc0c8 | 20 | |
043b3f7b | 21 | for (;;) { |
835cc0c8 | 22 | /* if equal, take 'a' -- important for sort stability */ |
043b3f7b GS |
23 | if (cmp(priv, a, b) <= 0) { |
24 | *tail = a; | |
25 | tail = &a->next; | |
835cc0c8 | 26 | a = a->next; |
043b3f7b GS |
27 | if (!a) { |
28 | *tail = b; | |
29 | break; | |
30 | } | |
835cc0c8 | 31 | } else { |
043b3f7b GS |
32 | *tail = b; |
33 | tail = &b->next; | |
835cc0c8 | 34 | b = b->next; |
043b3f7b GS |
35 | if (!b) { |
36 | *tail = a; | |
37 | break; | |
38 | } | |
835cc0c8 | 39 | } |
835cc0c8 | 40 | } |
043b3f7b | 41 | return head; |
835cc0c8 DM |
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 | */ | |
043b3f7b | 51 | __attribute__((nonnull(2,3,4,5))) |
4f0f586b | 52 | static void merge_final(void *priv, list_cmp_func_t cmp, struct list_head *head, |
043b3f7b | 53 | struct list_head *a, struct list_head *b) |
835cc0c8 DM |
54 | { |
55 | struct list_head *tail = head; | |
61b3d6c4 | 56 | u8 count = 0; |
835cc0c8 | 57 | |
043b3f7b | 58 | for (;;) { |
835cc0c8 | 59 | /* if equal, take 'a' -- important for sort stability */ |
043b3f7b | 60 | if (cmp(priv, a, b) <= 0) { |
835cc0c8 DM |
61 | tail->next = a; |
62 | a->prev = tail; | |
043b3f7b | 63 | tail = a; |
835cc0c8 | 64 | a = a->next; |
043b3f7b GS |
65 | if (!a) |
66 | break; | |
835cc0c8 DM |
67 | } else { |
68 | tail->next = b; | |
69 | b->prev = tail; | |
043b3f7b | 70 | tail = b; |
835cc0c8 | 71 | b = b->next; |
043b3f7b GS |
72 | if (!b) { |
73 | b = a; | |
74 | break; | |
75 | } | |
835cc0c8 | 76 | } |
835cc0c8 | 77 | } |
835cc0c8 | 78 | |
043b3f7b GS |
79 | /* Finish linking remainder of list b on to tail */ |
80 | tail->next = b; | |
835cc0c8 DM |
81 | do { |
82 | /* | |
043b3f7b GS |
83 | * If the merge is highly unbalanced (e.g. the input is |
84 | * already sorted), this loop may run many iterations. | |
835cc0c8 DM |
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 | */ | |
043b3f7b GS |
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 */ | |
835cc0c8 DM |
97 | tail->next = head; |
98 | head->prev = tail; | |
99 | } | |
100 | ||
2c761270 | 101 | /** |
02b12b7a DM |
102 | * list_sort - sort a list |
103 | * @priv: private data, opaque to list_sort(), passed to @cmp | |
2c761270 DC |
104 | * @head: the list to sort |
105 | * @cmp: the elements comparison function | |
106 | * | |
9dbbc3b9 | 107 | * The comparison function @cmp must return > 0 if @a should sort after |
043b3f7b GS |
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. | |
2c761270 | 113 | * |
043b3f7b GS |
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 | * | |
f35a1abd JC |
120 | * A good way to write a multi-word comparison is:: |
121 | * | |
043b3f7b GS |
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; | |
b5c56e0c GS |
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 | |
e89b6358 | 140 | * pending lists. This is beautifully simple code, but rather subtle. |
b5c56e0c GS |
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: | |
4ae5b8f2 | 157 | * |
b5c56e0c GS |
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)). | |
4ae5b8f2 | 161 | * |
b5c56e0c GS |
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). | |
2c761270 | 183 | */ |
043b3f7b | 184 | __attribute__((nonnull(2,3))) |
4f0f586b | 185 | void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp) |
2c761270 | 186 | { |
043b3f7b GS |
187 | struct list_head *list = head->next, *pending = NULL; |
188 | size_t count = 0; /* Count of pending */ | |
2c761270 | 189 | |
043b3f7b | 190 | if (list == head->prev) /* Zero or one elements */ |
2c761270 DC |
191 | return; |
192 | ||
043b3f7b | 193 | /* Convert to a null-terminated singly-linked list. */ |
835cc0c8 | 194 | head->prev->next = NULL; |
2c761270 | 195 | |
043b3f7b GS |
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. | |
b5c56e0c | 202 | * - Each of the sorted sublists is power-of-two in size. |
043b3f7b | 203 | * - Sublists are sorted by size and age, smallest & newest at front. |
b5c56e0c GS |
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. | |
043b3f7b GS |
213 | */ |
214 | do { | |
215 | size_t bits; | |
b5c56e0c | 216 | struct list_head **tail = &pending; |
043b3f7b | 217 | |
b5c56e0c GS |
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; | |
835cc0c8 | 224 | |
4f0f586b | 225 | a = merge(priv, cmp, b, a); |
b5c56e0c GS |
226 | /* Install the merged result in place of the inputs */ |
227 | a->prev = b->prev; | |
228 | *tail = a; | |
835cc0c8 | 229 | } |
b5c56e0c GS |
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; | |
043b3f7b | 236 | count++; |
b5c56e0c GS |
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; | |
043b3f7b | 244 | |
b5c56e0c GS |
245 | if (!next) |
246 | break; | |
4f0f586b | 247 | list = merge(priv, cmp, pending, list); |
b5c56e0c | 248 | pending = next; |
835cc0c8 | 249 | } |
043b3f7b | 250 | /* The final merge, rebuilding prev links */ |
4f0f586b | 251 | merge_final(priv, cmp, head, pending, list); |
835cc0c8 DM |
252 | } |
253 | EXPORT_SYMBOL(list_sort); |