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, a: b, 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, a: pending, b: list); |
248 | pending = next; |
249 | } |
250 | /* The final merge, rebuilding prev links */ |
251 | merge_final(priv, cmp, head, a: pending, b: list); |
252 | } |
253 | EXPORT_SYMBOL(list_sort); |
254 | |