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 : /*
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 0 : struct list_head *head, **tail = &head;
20 :
21 : for (;;) {
22 : /* if equal, take 'a' -- important for sort stability */
23 0 : if (cmp(priv, a, b) <= 0) {
24 0 : *tail = a;
25 0 : tail = &a->next;
26 0 : a = a->next;
27 0 : if (!a) {
28 0 : *tail = b;
29 : break;
30 : }
31 : } else {
32 0 : *tail = b;
33 0 : tail = &b->next;
34 0 : b = b->next;
35 0 : if (!b) {
36 0 : *tail = a;
37 : break;
38 : }
39 : }
40 : }
41 0 : 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 0 : 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 0 : struct list_head *tail = head;
56 0 : u8 count = 0;
57 :
58 : for (;;) {
59 : /* if equal, take 'a' -- important for sort stability */
60 0 : if (cmp(priv, a, b) <= 0) {
61 0 : tail->next = a;
62 0 : a->prev = tail;
63 0 : tail = a;
64 0 : a = a->next;
65 0 : if (!a)
66 : break;
67 : } else {
68 0 : tail->next = b;
69 0 : b->prev = tail;
70 0 : tail = b;
71 0 : b = b->next;
72 0 : if (!b) {
73 : b = a;
74 : break;
75 : }
76 : }
77 : }
78 :
79 : /* Finish linking remainder of list b on to tail */
80 0 : 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 0 : if (unlikely(!++count))
90 0 : cmp(priv, b, b);
91 0 : b->prev = tail;
92 0 : tail = b;
93 0 : b = b->next;
94 0 : } while (b);
95 :
96 : /* And the final links to make a circular doubly-linked list */
97 0 : tail->next = head;
98 0 : head->prev = tail;
99 0 : }
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 0 : void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
186 : {
187 0 : struct list_head *list = head->next, *pending = NULL;
188 0 : size_t count = 0; /* Count of pending */
189 :
190 0 : if (list == head->prev) /* Zero or one elements */
191 0 : return;
192 :
193 : /* Convert to a null-terminated singly-linked list. */
194 0 : 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 0 : struct list_head **tail = &pending;
217 :
218 : /* Find the least-significant clear bit in count */
219 0 : for (bits = count; bits & 1; bits >>= 1)
220 0 : tail = &(*tail)->prev;
221 : /* Do the indicated merge */
222 0 : if (likely(bits)) {
223 0 : struct list_head *a = *tail, *b = a->prev;
224 :
225 0 : a = merge(priv, cmp, b, a);
226 : /* Install the merged result in place of the inputs */
227 0 : a->prev = b->prev;
228 0 : *tail = a;
229 : }
230 :
231 : /* Move one element from input list to pending */
232 0 : list->prev = pending;
233 0 : pending = list;
234 0 : list = list->next;
235 0 : pending->next = NULL;
236 0 : count++;
237 0 : } while (list);
238 :
239 : /* End of input; merge together all the pending lists. */
240 0 : list = pending;
241 0 : pending = pending->prev;
242 0 : for (;;) {
243 0 : struct list_head *next = pending->prev;
244 :
245 0 : if (!next)
246 : break;
247 0 : list = merge(priv, cmp, pending, list);
248 0 : pending = next;
249 : }
250 : /* The final merge, rebuilding prev links */
251 0 : merge_final(priv, cmp, head, pending, list);
252 : }
253 : EXPORT_SYMBOL(list_sort);
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