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)))
15static 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)))
51static 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	u8 count = 0;
56
57	for (;;) {
58		/* if equal, take 'a' -- important for sort stability */
59		if (cmp(priv, a, b) <= 0) {
60			tail->next = a;
61			a->prev = tail;
62			tail = a;
63			a = a->next;
64			if (!a)
65				break;
66		} else {
67			tail->next = b;
68			b->prev = tail;
69			tail = b;
70			b = b->next;
71			if (!b) {
72				b = a;
73				break;
74			}
75		}
76	}
77
78	/* Finish linking remainder of list b on to tail */
79	tail->next = b;
80	do {
81		/*
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.
87		 */
88		if (unlikely(!++count))
89			cmp(priv, b, b);
90		b->prev = tail;
91		tail = b;
92		b = b->next;
93	} while (b);
94
95	/* And the final links to make a circular doubly-linked list */
96	tail->next = head;
97	head->prev = tail;
98}
99
100/**
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
105 *
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.
112 *
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).
118 *
119 * A good way to write a multi-word comparison is::
120 *
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;
126 *
127 *
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.
131 *
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.
136 *
137 *
138 * The merging is controlled by "count", the number of elements in the
139 * pending lists.  This is beautifully simple code, but rather subtle.
140 *
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).
145 *
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.
149 *
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.
153 *
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:
156 *
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)).
160 *
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)
170 *
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.
176 *
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).
182 */
183__attribute__((nonnull(2,3)))
184void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
185{
186	struct list_head *list = head->next, *pending = NULL;
187	size_t count = 0;	/* Count of pending */
188
189	if (list == head->prev)	/* Zero or one elements */
190		return;
191
192	/* Convert to a null-terminated singly-linked list. */
193	head->prev->next = NULL;
194
195	/*
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.
212	 */
213	do {
214		size_t bits;
215		struct list_head **tail = &pending;
216
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 */
221		if (likely(bits)) {
222			struct list_head *a = *tail, *b = a->prev;
223
224			a = merge(priv, cmp, b, a);
225			/* Install the merged result in place of the inputs */
226			a->prev = b->prev;
227			*tail = a;
228		}
229
230		/* Move one element from input list to pending */
231		list->prev = pending;
232		pending = list;
233		list = list->next;
234		pending->next = NULL;
235		count++;
236	} while (list);
237
238	/* End of input; merge together all the pending lists. */
239	list = pending;
240	pending = pending->prev;
241	for (;;) {
242		struct list_head *next = pending->prev;
243
244		if (!next)
245			break;
246		list = merge(priv, cmp, pending, list);
247		pending = next;
248	}
249	/* The final merge, rebuilding prev links */
250	merge_final(priv, cmp, head, pending, list);
251}
252EXPORT_SYMBOL(list_sort);
253