Line data Source code
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 : typedef int __attribute__((nonnull(2,3))) (*cmp_func)(void *,
11 : struct list_head const *, struct list_head const *);
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 : */
18 : __attribute__((nonnull(2,3,4)))
19 0 : static struct list_head *merge(void *priv, cmp_func cmp,
20 : struct list_head *a, struct list_head *b)
21 : {
22 0 : struct list_head *head, **tail = &head;
23 :
24 0 : for (;;) {
25 : /* if equal, take 'a' -- important for sort stability */
26 0 : if (cmp(priv, a, b) <= 0) {
27 0 : *tail = a;
28 0 : tail = &a->next;
29 0 : a = a->next;
30 0 : if (!a) {
31 0 : *tail = b;
32 0 : break;
33 : }
34 : } else {
35 0 : *tail = b;
36 0 : tail = &b->next;
37 0 : b = b->next;
38 0 : if (!b) {
39 0 : *tail = a;
40 0 : break;
41 : }
42 : }
43 : }
44 0 : return head;
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 : */
54 : __attribute__((nonnull(2,3,4,5)))
55 0 : static void merge_final(void *priv, cmp_func cmp, struct list_head *head,
56 : struct list_head *a, struct list_head *b)
57 : {
58 0 : struct list_head *tail = head;
59 0 : u8 count = 0;
60 :
61 0 : for (;;) {
62 : /* if equal, take 'a' -- important for sort stability */
63 0 : if (cmp(priv, a, b) <= 0) {
64 0 : tail->next = a;
65 0 : a->prev = tail;
66 0 : tail = a;
67 0 : a = a->next;
68 0 : if (!a)
69 : break;
70 : } else {
71 0 : tail->next = b;
72 0 : b->prev = tail;
73 0 : tail = b;
74 0 : b = b->next;
75 0 : if (!b) {
76 : b = a;
77 : break;
78 : }
79 : }
80 : }
81 :
82 : /* Finish linking remainder of list b on to tail */
83 0 : tail->next = b;
84 0 : do {
85 : /*
86 : * If the merge is highly unbalanced (e.g. the input is
87 : * already sorted), this loop may run many iterations.
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 : */
92 0 : if (unlikely(!++count))
93 0 : cmp(priv, b, b);
94 0 : b->prev = tail;
95 0 : tail = b;
96 0 : b = b->next;
97 0 : } while (b);
98 :
99 : /* And the final links to make a circular doubly-linked list */
100 0 : tail->next = head;
101 0 : head->prev = tail;
102 0 : }
103 :
104 : /**
105 : * list_sort - sort a list
106 : * @priv: private data, opaque to list_sort(), passed to @cmp
107 : * @head: the list to sort
108 : * @cmp: the elements comparison function
109 : *
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.
116 : *
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 : *
123 : * A good way to write a multi-word comparison is::
124 : *
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;
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:
160 : *
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)).
164 : *
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).
186 : */
187 : __attribute__((nonnull(2,3)))
188 0 : void list_sort(void *priv, struct list_head *head,
189 : int (*cmp)(void *priv, struct list_head *a,
190 : struct list_head *b))
191 : {
192 0 : struct list_head *list = head->next, *pending = NULL;
193 0 : size_t count = 0; /* Count of pending */
194 :
195 0 : if (list == head->prev) /* Zero or one elements */
196 0 : return;
197 :
198 : /* Convert to a null-terminated singly-linked list. */
199 0 : head->prev->next = NULL;
200 :
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.
207 : * - Each of the sorted sublists is power-of-two in size.
208 : * - Sublists are sorted by size and age, smallest & newest at front.
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.
218 : */
219 0 : do {
220 0 : size_t bits;
221 0 : struct list_head **tail = &pending;
222 :
223 : /* Find the least-significant clear bit in count */
224 0 : for (bits = count; bits & 1; bits >>= 1)
225 0 : tail = &(*tail)->prev;
226 : /* Do the indicated merge */
227 0 : if (likely(bits)) {
228 0 : struct list_head *a = *tail, *b = a->prev;
229 :
230 0 : a = merge(priv, (cmp_func)cmp, b, a);
231 : /* Install the merged result in place of the inputs */
232 0 : a->prev = b->prev;
233 0 : *tail = a;
234 : }
235 :
236 : /* Move one element from input list to pending */
237 0 : list->prev = pending;
238 0 : pending = list;
239 0 : list = list->next;
240 0 : pending->next = NULL;
241 0 : count++;
242 0 : } while (list);
243 :
244 : /* End of input; merge together all the pending lists. */
245 0 : list = pending;
246 0 : pending = pending->prev;
247 0 : for (;;) {
248 0 : struct list_head *next = pending->prev;
249 :
250 0 : if (!next)
251 : break;
252 0 : list = merge(priv, (cmp_func)cmp, pending, list);
253 0 : pending = next;
254 : }
255 : /* The final merge, rebuilding prev links */
256 0 : merge_final(priv, (cmp_func)cmp, head, pending, list);
257 : }
258 : EXPORT_SYMBOL(list_sort);
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