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>
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.
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)
18 struct list_head *head, **tail = &head;
21 /* if equal, take 'a' -- important for sort stability */
22 if (cmp(priv, a, b) <= 0) {
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
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)
54 struct list_head *tail = head;
58 /* if equal, take 'a' -- important for sort stability */
59 if (cmp(priv, a, b) <= 0) {
78 /* Finish linking remainder of list b on to tail */
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.
88 if (unlikely(!++count))
95 /* And the final links to make a circular doubly-linked list */
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
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.
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).
119 * A good way to write a multi-word comparison is::
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;
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.
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.
138 * The merging is controlled by "count", the number of elements in the
139 * pending lists. This is beautifully simple code, but rather subtle.
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).
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.
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.
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:
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)).
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)
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.
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).
183 __attribute__((nonnull(2,3)))
184 void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
186 struct list_head *list = head->next, *pending = NULL;
187 size_t count = 0; /* Count of pending */
189 if (list == head->prev) /* Zero or one elements */
192 /* Convert to a null-terminated singly-linked list. */
193 head->prev->next = NULL;
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.
215 struct list_head **tail = &pending;
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 */
222 struct list_head *a = *tail, *b = a->prev;
224 a = merge(priv, cmp, b, a);
225 /* Install the merged result in place of the inputs */
230 /* Move one element from input list to pending */
231 list->prev = pending;
234 pending->next = NULL;
238 /* End of input; merge together all the pending lists. */
240 pending = pending->prev;
242 struct list_head *next = pending->prev;
246 list = merge(priv, cmp, pending, list);
249 /* The final merge, rebuilding prev links */
250 merge_final(priv, cmp, head, pending, list);
252 EXPORT_SYMBOL(list_sort);