Linux kernel mirror (for testing)
git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git
kernel
os
linux
1// SPDX-License-Identifier: GPL-2.0
2#include <linux/compiler.h>
3#include <linux/export.h>
4#include <linux/list_sort.h>
5#include <linux/list.h>
6
7/*
8 * Returns a list organized in an intermediate format suited
9 * to chaining of merge() calls: null-terminated, no reserved or
10 * sentinel head node, "prev" links not maintained.
11 */
12__attribute__((nonnull(2,3,4)))
13static struct list_head *merge(void *priv, list_cmp_func_t cmp,
14 struct list_head *a, struct list_head *b)
15{
16 struct list_head *head, **tail = &head;
17
18 for (;;) {
19 /* if equal, take 'a' -- important for sort stability */
20 if (cmp(priv, a, b) <= 0) {
21 *tail = a;
22 tail = &a->next;
23 a = a->next;
24 if (!a) {
25 *tail = b;
26 break;
27 }
28 } else {
29 *tail = b;
30 tail = &b->next;
31 b = b->next;
32 if (!b) {
33 *tail = a;
34 break;
35 }
36 }
37 }
38 return head;
39}
40
41/*
42 * Combine final list merge with restoration of standard doubly-linked
43 * list structure. This approach duplicates code from merge(), but
44 * runs faster than the tidier alternatives of either a separate final
45 * prev-link restoration pass, or maintaining the prev links
46 * throughout.
47 */
48__attribute__((nonnull(2,3,4,5)))
49static void merge_final(void *priv, list_cmp_func_t cmp, struct list_head *head,
50 struct list_head *a, struct list_head *b)
51{
52 struct list_head *tail = head;
53
54 for (;;) {
55 /* if equal, take 'a' -- important for sort stability */
56 if (cmp(priv, a, b) <= 0) {
57 tail->next = a;
58 a->prev = tail;
59 tail = a;
60 a = a->next;
61 if (!a)
62 break;
63 } else {
64 tail->next = b;
65 b->prev = tail;
66 tail = b;
67 b = b->next;
68 if (!b) {
69 b = a;
70 break;
71 }
72 }
73 }
74
75 /* Finish linking remainder of list b on to tail */
76 tail->next = b;
77 do {
78 b->prev = tail;
79 tail = b;
80 b = b->next;
81 } while (b);
82
83 /* And the final links to make a circular doubly-linked list */
84 tail->next = head;
85 head->prev = tail;
86}
87
88/**
89 * list_sort - sort a list
90 * @priv: private data, opaque to list_sort(), passed to @cmp
91 * @head: the list to sort
92 * @cmp: the elements comparison function
93 *
94 * The comparison function @cmp must return > 0 if @a should sort after
95 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
96 * sort before @b *or* their original order should be preserved. It is
97 * always called with the element that came first in the input in @a,
98 * and list_sort is a stable sort, so it is not necessary to distinguish
99 * the @a < @b and @a == @b cases.
100 *
101 * The comparison function must adhere to specific mathematical properties
102 * to ensure correct and stable sorting:
103 * - Antisymmetry: cmp(@a, @b) must return the opposite sign of
104 * cmp(@b, @a).
105 * - Transitivity: if cmp(@a, @b) <= 0 and cmp(@b, @c) <= 0, then
106 * cmp(@a, @c) <= 0.
107 *
108 * This is compatible with two styles of @cmp function:
109 * - The traditional style which returns <0 / =0 / >0, or
110 * - Returning a boolean 0/1.
111 * The latter offers a chance to save a few cycles in the comparison
112 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
113 *
114 * A good way to write a multi-word comparison is::
115 *
116 * if (a->high != b->high)
117 * return a->high > b->high;
118 * if (a->middle != b->middle)
119 * return a->middle > b->middle;
120 * return a->low > b->low;
121 *
122 *
123 * This mergesort is as eager as possible while always performing at least
124 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are
125 * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
126 *
127 * Thus, it will avoid cache thrashing as long as 3*2^k elements can
128 * fit into the cache. Not quite as good as a fully-eager bottom-up
129 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
130 * the common case that everything fits into L1.
131 *
132 *
133 * The merging is controlled by "count", the number of elements in the
134 * pending lists. This is beautifully simple code, but rather subtle.
135 *
136 * Each time we increment "count", we set one bit (bit k) and clear
137 * bits k-1 .. 0. Each time this happens (except the very first time
138 * for each bit, when count increments to 2^k), we merge two lists of
139 * size 2^k into one list of size 2^(k+1).
140 *
141 * This merge happens exactly when the count reaches an odd multiple of
142 * 2^k, which is when we have 2^k elements pending in smaller lists,
143 * so it's safe to merge away two lists of size 2^k.
144 *
145 * After this happens twice, we have created two lists of size 2^(k+1),
146 * which will be merged into a list of size 2^(k+2) before we create
147 * a third list of size 2^(k+1), so there are never more than two pending.
148 *
149 * The number of pending lists of size 2^k is determined by the
150 * state of bit k of "count" plus two extra pieces of information:
151 *
152 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
153 * - Whether the higher-order bits are zero or non-zero (i.e.
154 * is count >= 2^(k+1)).
155 *
156 * There are six states we distinguish. "x" represents some arbitrary
157 * bits, and "y" represents some arbitrary non-zero bits:
158 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k
159 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
160 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k
161 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
162 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k
163 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
164 * (merge and loop back to state 2)
165 *
166 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
167 * bit k-1 is set while the more significant bits are non-zero) and
168 * merge them away in the 5->2 transition. Note in particular that just
169 * before the 5->2 transition, all lower-order bits are 11 (state 3),
170 * so there is one list of each smaller size.
171 *
172 * When we reach the end of the input, we merge all the pending
173 * lists, from smallest to largest. If you work through cases 2 to
174 * 5 above, you can see that the number of elements we merge with a list
175 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
176 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
177 */
178__attribute__((nonnull(2,3)))
179void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
180{
181 struct list_head *list = head->next, *pending = NULL;
182 size_t count = 0; /* Count of pending */
183
184 if (list == head->prev) /* Zero or one elements */
185 return;
186
187 /* Convert to a null-terminated singly-linked list. */
188 head->prev->next = NULL;
189
190 /*
191 * Data structure invariants:
192 * - All lists are singly linked and null-terminated; prev
193 * pointers are not maintained.
194 * - pending is a prev-linked "list of lists" of sorted
195 * sublists awaiting further merging.
196 * - Each of the sorted sublists is power-of-two in size.
197 * - Sublists are sorted by size and age, smallest & newest at front.
198 * - There are zero to two sublists of each size.
199 * - A pair of pending sublists are merged as soon as the number
200 * of following pending elements equals their size (i.e.
201 * each time count reaches an odd multiple of that size).
202 * That ensures each later final merge will be at worst 2:1.
203 * - Each round consists of:
204 * - Merging the two sublists selected by the highest bit
205 * which flips when count is incremented, and
206 * - Adding an element from the input as a size-1 sublist.
207 */
208 do {
209 size_t bits;
210 struct list_head **tail = &pending;
211
212 /* Find the least-significant clear bit in count */
213 for (bits = count; bits & 1; bits >>= 1)
214 tail = &(*tail)->prev;
215 /* Do the indicated merge */
216 if (likely(bits)) {
217 struct list_head *a = *tail, *b = a->prev;
218
219 a = merge(priv, cmp, b, a);
220 /* Install the merged result in place of the inputs */
221 a->prev = b->prev;
222 *tail = a;
223 }
224
225 /* Move one element from input list to pending */
226 list->prev = pending;
227 pending = list;
228 list = list->next;
229 pending->next = NULL;
230 count++;
231 } while (list);
232
233 /* End of input; merge together all the pending lists. */
234 list = pending;
235 pending = pending->prev;
236 for (;;) {
237 struct list_head *next = pending->prev;
238
239 if (!next)
240 break;
241 list = merge(priv, cmp, pending, list);
242 pending = next;
243 }
244 /* The final merge, rebuilding prev links */
245 merge_final(priv, cmp, head, pending, list);
246}
247EXPORT_SYMBOL(list_sort);