1 | // SPDX-License-Identifier: GPL-2.0 |
2 | #include <linux/kernel.h> |
3 | #include <linux/compiler.h> |
4 | #include <linux/export.h> |
5 | #include <linux/string.h> |
6 | #include <linux/list_sort.h> |
7 | #include <linux/list.h> |
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 | */ |
14 | __attribute__((nonnull(2,3,4))) |
15 | static struct list_head *merge(void *priv, list_cmp_func_t cmp, |
16 | struct list_head *a, struct list_head *b) |
17 | { |
18 | struct list_head *head, **tail = &head; |
19 | |
20 | for (;;) { |
21 | /* if equal, take 'a' -- important for sort stability */ |
22 | if (cmp(priv, a, b) <= 0) { |
23 | *tail = a; |
24 | tail = &a->next; |
25 | a = a->next; |
26 | if (!a) { |
27 | *tail = b; |
28 | break; |
29 | } |
30 | } else { |
31 | *tail = b; |
32 | tail = &b->next; |
33 | b = b->next; |
34 | if (!b) { |
35 | *tail = a; |
36 | break; |
37 | } |
38 | } |
39 | } |
40 | return head; |
41 | } |
42 | |
43 | /* |
44 | * Combine final list merge with restoration of standard doubly-linked |
45 | * list structure. This approach duplicates code from merge(), but |
46 | * runs faster than the tidier alternatives of either a separate final |
47 | * prev-link restoration pass, or maintaining the prev links |
48 | * throughout. |
49 | */ |
50 | __attribute__((nonnull(2,3,4,5))) |
51 | static void merge_final(void *priv, list_cmp_func_t cmp, struct list_head *head, |
52 | struct list_head *a, struct list_head *b) |
53 | { |
54 | struct list_head *tail = head; |
55 | u8 count = 0; |
56 | |
57 | for (;;) { |
58 | /* if equal, take 'a' -- important for sort stability */ |
59 | if (cmp(priv, a, b) <= 0) { |
60 | tail->next = a; |
61 | a->prev = tail; |
62 | tail = a; |
63 | a = a->next; |
64 | if (!a) |
65 | break; |
66 | } else { |
67 | tail->next = b; |
68 | b->prev = tail; |
69 | tail = b; |
70 | b = b->next; |
71 | if (!b) { |
72 | b = a; |
73 | break; |
74 | } |
75 | } |
76 | } |
77 | |
78 | /* Finish linking remainder of list b on to tail */ |
79 | tail->next = b; |
80 | do { |
81 | /* |
82 | * If the merge is highly unbalanced (e.g. the input is |
83 | * already sorted), this loop may run many iterations. |
84 | * Continue callbacks to the client even though no |
85 | * element comparison is needed, so the client's cmp() |
86 | * routine can invoke cond_resched() periodically. |
87 | */ |
88 | if (unlikely(!++count)) |
89 | cmp(priv, b, b); |
90 | b->prev = tail; |
91 | tail = b; |
92 | b = b->next; |
93 | } while (b); |
94 | |
95 | /* And the final links to make a circular doubly-linked list */ |
96 | tail->next = head; |
97 | head->prev = tail; |
98 | } |
99 | |
100 | /** |
101 | * list_sort - sort a list |
102 | * @priv: private data, opaque to list_sort(), passed to @cmp |
103 | * @head: the list to sort |
104 | * @cmp: the elements comparison function |
105 | * |
106 | * The comparison function @cmp must return > 0 if @a should sort after |
107 | * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should |
108 | * sort before @b *or* their original order should be preserved. It is |
109 | * always called with the element that came first in the input in @a, |
110 | * and list_sort is a stable sort, so it is not necessary to distinguish |
111 | * the @a < @b and @a == @b cases. |
112 | * |
113 | * This is compatible with two styles of @cmp function: |
114 | * - The traditional style which returns <0 / =0 / >0, or |
115 | * - Returning a boolean 0/1. |
116 | * The latter offers a chance to save a few cycles in the comparison |
117 | * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c). |
118 | * |
119 | * A good way to write a multi-word comparison is:: |
120 | * |
121 | * if (a->high != b->high) |
122 | * return a->high > b->high; |
123 | * if (a->middle != b->middle) |
124 | * return a->middle > b->middle; |
125 | * return a->low > b->low; |
126 | * |
127 | * |
128 | * This mergesort is as eager as possible while always performing at least |
129 | * 2:1 balanced merges. Given two pending sublists of size 2^k, they are |
130 | * merged to a size-2^(k+1) list as soon as we have 2^k following elements. |
131 | * |
132 | * Thus, it will avoid cache thrashing as long as 3*2^k elements can |
133 | * fit into the cache. Not quite as good as a fully-eager bottom-up |
134 | * mergesort, but it does use 0.2*n fewer comparisons, so is faster in |
135 | * the common case that everything fits into L1. |
136 | * |
137 | * |
138 | * The merging is controlled by "count", the number of elements in the |
139 | * pending lists. This is beautifully simple code, but rather subtle. |
140 | * |
141 | * Each time we increment "count", we set one bit (bit k) and clear |
142 | * bits k-1 .. 0. Each time this happens (except the very first time |
143 | * for each bit, when count increments to 2^k), we merge two lists of |
144 | * size 2^k into one list of size 2^(k+1). |
145 | * |
146 | * This merge happens exactly when the count reaches an odd multiple of |
147 | * 2^k, which is when we have 2^k elements pending in smaller lists, |
148 | * so it's safe to merge away two lists of size 2^k. |
149 | * |
150 | * After this happens twice, we have created two lists of size 2^(k+1), |
151 | * which will be merged into a list of size 2^(k+2) before we create |
152 | * a third list of size 2^(k+1), so there are never more than two pending. |
153 | * |
154 | * The number of pending lists of size 2^k is determined by the |
155 | * state of bit k of "count" plus two extra pieces of information: |
156 | * |
157 | * - The state of bit k-1 (when k == 0, consider bit -1 always set), and |
158 | * - Whether the higher-order bits are zero or non-zero (i.e. |
159 | * is count >= 2^(k+1)). |
160 | * |
161 | * There are six states we distinguish. "x" represents some arbitrary |
162 | * bits, and "y" represents some arbitrary non-zero bits: |
163 | * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k |
164 | * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k |
165 | * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k |
166 | * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k |
167 | * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k |
168 | * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k |
169 | * (merge and loop back to state 2) |
170 | * |
171 | * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because |
172 | * bit k-1 is set while the more significant bits are non-zero) and |
173 | * merge them away in the 5->2 transition. Note in particular that just |
174 | * before the 5->2 transition, all lower-order bits are 11 (state 3), |
175 | * so there is one list of each smaller size. |
176 | * |
177 | * When we reach the end of the input, we merge all the pending |
178 | * lists, from smallest to largest. If you work through cases 2 to |
179 | * 5 above, you can see that the number of elements we merge with a list |
180 | * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to |
181 | * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1). |
182 | */ |
183 | __attribute__((nonnull(2,3))) |
184 | void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp) |
185 | { |
186 | struct list_head *list = head->next, *pending = NULL; |
187 | size_t count = 0; /* Count of pending */ |
188 | |
189 | if (list == head->prev) /* Zero or one elements */ |
190 | return; |
191 | |
192 | /* Convert to a null-terminated singly-linked list. */ |
193 | head->prev->next = NULL; |
194 | |
195 | /* |
196 | * Data structure invariants: |
197 | * - All lists are singly linked and null-terminated; prev |
198 | * pointers are not maintained. |
199 | * - pending is a prev-linked "list of lists" of sorted |
200 | * sublists awaiting further merging. |
201 | * - Each of the sorted sublists is power-of-two in size. |
202 | * - Sublists are sorted by size and age, smallest & newest at front. |
203 | * - There are zero to two sublists of each size. |
204 | * - A pair of pending sublists are merged as soon as the number |
205 | * of following pending elements equals their size (i.e. |
206 | * each time count reaches an odd multiple of that size). |
207 | * That ensures each later final merge will be at worst 2:1. |
208 | * - Each round consists of: |
209 | * - Merging the two sublists selected by the highest bit |
210 | * which flips when count is incremented, and |
211 | * - Adding an element from the input as a size-1 sublist. |
212 | */ |
213 | do { |
214 | size_t bits; |
215 | struct list_head **tail = &pending; |
216 | |
217 | /* Find the least-significant clear bit in count */ |
218 | for (bits = count; bits & 1; bits >>= 1) |
219 | tail = &(*tail)->prev; |
220 | /* Do the indicated merge */ |
221 | if (likely(bits)) { |
222 | struct list_head *a = *tail, *b = a->prev; |
223 | |
224 | a = merge(priv, cmp, a: b, b: a); |
225 | /* Install the merged result in place of the inputs */ |
226 | a->prev = b->prev; |
227 | *tail = a; |
228 | } |
229 | |
230 | /* Move one element from input list to pending */ |
231 | list->prev = pending; |
232 | pending = list; |
233 | list = list->next; |
234 | pending->next = NULL; |
235 | count++; |
236 | } while (list); |
237 | |
238 | /* End of input; merge together all the pending lists. */ |
239 | list = pending; |
240 | pending = pending->prev; |
241 | for (;;) { |
242 | struct list_head *next = pending->prev; |
243 | |
244 | if (!next) |
245 | break; |
246 | list = merge(priv, cmp, a: pending, b: list); |
247 | pending = next; |
248 | } |
249 | /* The final merge, rebuilding prev links */ |
250 | merge_final(priv, cmp, head, a: pending, b: list); |
251 | } |
252 | EXPORT_SYMBOL(list_sort); |
253 | |