Branch data 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 : : struct list_head *head, **tail = &head;
23 : :
24 : : 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 : : struct list_head *tail = head;
59 : : u8 count = 0;
60 : :
61 : : 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 : : 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 : : tail = b;
74 : 0 : b = b->next;
75 [ # # ]: 0 : if (!b) {
76 : 0 : b = a;
77 : 0 : break;
78 : : }
79 : : }
80 : : }
81 : :
82 : : /* Finish linking remainder of list b on to tail */
83 : 0 : tail->next = b;
84 : : 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 : : 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 : : 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 : : do {
220 : : size_t bits;
221 : : 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 : : 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 : 0 : }
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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