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
56 for (;;) {
57 /* if equal, take 'a' -- important for sort stability */
58 if (cmp(priv, a, b) <= 0) {
59 tail->next = a;
60 a->prev = tail;
61 tail = a;
62 a = a->next;
63 if (!a)
64 break;
65 } else {
66 tail->next = b;
67 b->prev = tail;
68 tail = b;
69 b = b->next;
70 if (!b) {
71 b = a;
72 break;
73 }
74 }
75 }
76
77 /* Finish linking remainder of list b on to tail */
78 tail->next = b;
79 do {
80 b->prev = tail;
81 tail = b;
82 b = b->next;
83 } while (b);
84
85 /* And the final links to make a circular doubly-linked list */
86 tail->next = head;
87 head->prev = tail;
88 }
89
90 /**
91 * list_sort - sort a list
92 * @priv: private data, opaque to list_sort(), passed to @cmp
93 * @head: the list to sort
94 * @cmp: the elements comparison function
95 *
96 * The comparison function @cmp must return > 0 if @a should sort after
97 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
98 * sort before @b *or* their original order should be preserved. It is
99 * always called with the element that came first in the input in @a,
100 * and list_sort is a stable sort, so it is not necessary to distinguish
101 * the @a < @b and @a == @b cases.
102 *
103 * This is compatible with two styles of @cmp function:
104 * - The traditional style which returns <0 / =0 / >0, or
105 * - Returning a boolean 0/1.
106 * The latter offers a chance to save a few cycles in the comparison
107 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
108 *
109 * A good way to write a multi-word comparison is::
110 *
111 * if (a->high != b->high)
112 * return a->high > b->high;
113 * if (a->middle != b->middle)
114 * return a->middle > b->middle;
115 * return a->low > b->low;
116 *
117 *
118 * This mergesort is as eager as possible while always performing at least
119 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are
120 * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
121 *
122 * Thus, it will avoid cache thrashing as long as 3*2^k elements can
123 * fit into the cache. Not quite as good as a fully-eager bottom-up
124 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
125 * the common case that everything fits into L1.
126 *
127 *
128 * The merging is controlled by "count", the number of elements in the
129 * pending lists. This is beautifully simple code, but rather subtle.
130 *
131 * Each time we increment "count", we set one bit (bit k) and clear
132 * bits k-1 .. 0. Each time this happens (except the very first time
133 * for each bit, when count increments to 2^k), we merge two lists of
134 * size 2^k into one list of size 2^(k+1).
135 *
136 * This merge happens exactly when the count reaches an odd multiple of
137 * 2^k, which is when we have 2^k elements pending in smaller lists,
138 * so it's safe to merge away two lists of size 2^k.
139 *
140 * After this happens twice, we have created two lists of size 2^(k+1),
141 * which will be merged into a list of size 2^(k+2) before we create
142 * a third list of size 2^(k+1), so there are never more than two pending.
143 *
144 * The number of pending lists of size 2^k is determined by the
145 * state of bit k of "count" plus two extra pieces of information:
146 *
147 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
148 * - Whether the higher-order bits are zero or non-zero (i.e.
149 * is count >= 2^(k+1)).
150 *
151 * There are six states we distinguish. "x" represents some arbitrary
152 * bits, and "y" represents some arbitrary non-zero bits:
153 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k
154 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
155 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k
156 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
157 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k
158 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
159 * (merge and loop back to state 2)
160 *
161 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
162 * bit k-1 is set while the more significant bits are non-zero) and
163 * merge them away in the 5->2 transition. Note in particular that just
164 * before the 5->2 transition, all lower-order bits are 11 (state 3),
165 * so there is one list of each smaller size.
166 *
167 * When we reach the end of the input, we merge all the pending
168 * lists, from smallest to largest. If you work through cases 2 to
169 * 5 above, you can see that the number of elements we merge with a list
170 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
171 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
172 */
173 __attribute__((nonnull(2,3)))
174 void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
175 {
176 struct list_head *list = head->next, *pending = NULL;
177 size_t count = 0; /* Count of pending */
178
179 if (list == head->prev) /* Zero or one elements */
180 return;
181
182 /* Convert to a null-terminated singly-linked list. */
183 head->prev->next = NULL;
184
185 /*
186 * Data structure invariants:
187 * - All lists are singly linked and null-terminated; prev
188 * pointers are not maintained.
189 * - pending is a prev-linked "list of lists" of sorted
190 * sublists awaiting further merging.
191 * - Each of the sorted sublists is power-of-two in size.
192 * - Sublists are sorted by size and age, smallest & newest at front.
193 * - There are zero to two sublists of each size.
194 * - A pair of pending sublists are merged as soon as the number
195 * of following pending elements equals their size (i.e.
196 * each time count reaches an odd multiple of that size).
197 * That ensures each later final merge will be at worst 2:1.
198 * - Each round consists of:
199 * - Merging the two sublists selected by the highest bit
200 * which flips when count is incremented, and
201 * - Adding an element from the input as a size-1 sublist.
202 */
203 do {
204 size_t bits;
205 struct list_head **tail = &pending;
206
207 /* Find the least-significant clear bit in count */
208 for (bits = count; bits & 1; bits >>= 1)
209 tail = &(*tail)->prev;
210 /* Do the indicated merge */
211 if (likely(bits)) {
212 struct list_head *a = *tail, *b = a->prev;
213
214 a = merge(priv, cmp, b, a);
215 /* Install the merged result in place of the inputs */
216 a->prev = b->prev;
217 *tail = a;
218 }
219
220 /* Move one element from input list to pending */
221 list->prev = pending;
222 pending = list;
223 list = list->next;
224 pending->next = NULL;
225 count++;
226 } while (list);
227
228 /* End of input; merge together all the pending lists. */
229 list = pending;
230 pending = pending->prev;
231 for (;;) {
232 struct list_head *next = pending->prev;
233
234 if (!next)
235 break;
236 list = merge(priv, cmp, pending, list);
237 pending = next;
238 }
239 /* The final merge, rebuilding prev links */
240 merge_final(priv, cmp, head, pending, list);
241 }
242 EXPORT_SYMBOL(list_sort);
243
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