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/*
11 * Returns a list organized in an intermediate format suited
12 * to chaining of merge() calls: null-terminated, no reserved or
13 * sentinel head node, "prev" links not maintained.
14 */
15__attribute__((nonnull(2,3,4)))
16static struct list_head *merge(void *priv, list_cmp_func_t cmp,
17				struct list_head *a, struct list_head *b)
18{
19	struct list_head *head, **tail = &head;
20
21	for (;;) {
22		/* if equal, take 'a' -- important for sort stability */
23		if (cmp(priv, a, b) <= 0) {
24			*tail = a;
25			tail = &a->next;
26			a = a->next;
27			if (!a) {
28				*tail = b;
29				break;
30			}
31		} else {
32			*tail = b;
33			tail = &b->next;
34			b = b->next;
35			if (!b) {
36				*tail = a;
37				break;
38			}
39		}
40	}
41	return head;
42}
43
44/*
45 * Combine final list merge with restoration of standard doubly-linked
46 * list structure.  This approach duplicates code from merge(), but
47 * runs faster than the tidier alternatives of either a separate final
48 * prev-link restoration pass, or maintaining the prev links
49 * throughout.
50 */
51__attribute__((nonnull(2,3,4,5)))
52static void merge_final(void *priv, list_cmp_func_t cmp, struct list_head *head,
53			struct list_head *a, struct list_head *b)
54{
55	struct list_head *tail = head;
56	u8 count = 0;
57
58	for (;;) {
59		/* if equal, take 'a' -- important for sort stability */
60		if (cmp(priv, a, b) <= 0) {
61			tail->next = a;
62			a->prev = tail;
63			tail = a;
64			a = a->next;
65			if (!a)
66				break;
67		} else {
68			tail->next = b;
69			b->prev = tail;
70			tail = b;
71			b = b->next;
72			if (!b) {
73				b = a;
74				break;
75			}
76		}
77	}
78
79	/* Finish linking remainder of list b on to tail */
80	tail->next = b;
81	do {
82		/*
83		 * If the merge is highly unbalanced (e.g. the input is
84		 * already sorted), this loop may run many iterations.
85		 * Continue callbacks to the client even though no
86		 * element comparison is needed, so the client's cmp()
87		 * routine can invoke cond_resched() periodically.
88		 */
89		if (unlikely(!++count))
90			cmp(priv, b, b);
91		b->prev = tail;
92		tail = b;
93		b = b->next;
94	} while (b);
95
96	/* And the final links to make a circular doubly-linked list */
97	tail->next = head;
98	head->prev = tail;
99}
100
101/**
102 * list_sort - sort a list
103 * @priv: private data, opaque to list_sort(), passed to @cmp
104 * @head: the list to sort
105 * @cmp: the elements comparison function
106 *
107 * The comparison function @cmp must return > 0 if @a should sort after
108 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
109 * sort before @b *or* their original order should be preserved.  It is
110 * always called with the element that came first in the input in @a,
111 * and list_sort is a stable sort, so it is not necessary to distinguish
112 * the @a < @b and @a == @b cases.
113 *
114 * This is compatible with two styles of @cmp function:
115 * - The traditional style which returns <0 / =0 / >0, or
116 * - Returning a boolean 0/1.
117 * The latter offers a chance to save a few cycles in the comparison
118 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
119 *
120 * A good way to write a multi-word comparison is::
121 *
122 *	if (a->high != b->high)
123 *		return a->high > b->high;
124 *	if (a->middle != b->middle)
125 *		return a->middle > b->middle;
126 *	return a->low > b->low;
127 *
128 *
129 * This mergesort is as eager as possible while always performing at least
130 * 2:1 balanced merges.  Given two pending sublists of size 2^k, they are
131 * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
132 *
133 * Thus, it will avoid cache thrashing as long as 3*2^k elements can
134 * fit into the cache.  Not quite as good as a fully-eager bottom-up
135 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
136 * the common case that everything fits into L1.
137 *
138 *
139 * The merging is controlled by "count", the number of elements in the
140 * pending lists.  This is beautifully simple code, but rather subtle.
141 *
142 * Each time we increment "count", we set one bit (bit k) and clear
143 * bits k-1 .. 0.  Each time this happens (except the very first time
144 * for each bit, when count increments to 2^k), we merge two lists of
145 * size 2^k into one list of size 2^(k+1).
146 *
147 * This merge happens exactly when the count reaches an odd multiple of
148 * 2^k, which is when we have 2^k elements pending in smaller lists,
149 * so it's safe to merge away two lists of size 2^k.
150 *
151 * After this happens twice, we have created two lists of size 2^(k+1),
152 * which will be merged into a list of size 2^(k+2) before we create
153 * a third list of size 2^(k+1), so there are never more than two pending.
154 *
155 * The number of pending lists of size 2^k is determined by the
156 * state of bit k of "count" plus two extra pieces of information:
157 *
158 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
159 * - Whether the higher-order bits are zero or non-zero (i.e.
160 *   is count >= 2^(k+1)).
161 *
162 * There are six states we distinguish.  "x" represents some arbitrary
163 * bits, and "y" represents some arbitrary non-zero bits:
164 * 0:  00x: 0 pending of size 2^k;           x pending of sizes < 2^k
165 * 1:  01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
166 * 2: x10x: 0 pending of size 2^k; 2^k     + x pending of sizes < 2^k
167 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
168 * 4: y00x: 1 pending of size 2^k; 2^k     + x pending of sizes < 2^k
169 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
170 * (merge and loop back to state 2)
171 *
172 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
173 * bit k-1 is set while the more significant bits are non-zero) and
174 * merge them away in the 5->2 transition.  Note in particular that just
175 * before the 5->2 transition, all lower-order bits are 11 (state 3),
176 * so there is one list of each smaller size.
177 *
178 * When we reach the end of the input, we merge all the pending
179 * lists, from smallest to largest.  If you work through cases 2 to
180 * 5 above, you can see that the number of elements we merge with a list
181 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
182 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
183 */
184__attribute__((nonnull(2,3)))
185void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
186{
187	struct list_head *list = head->next, *pending = NULL;
188	size_t count = 0;	/* Count of pending */
189
190	if (list == head->prev)	/* Zero or one elements */
191		return;
192
193	/* Convert to a null-terminated singly-linked list. */
194	head->prev->next = NULL;
195
196	/*
197	 * Data structure invariants:
198	 * - All lists are singly linked and null-terminated; prev
199	 *   pointers are not maintained.
200	 * - pending is a prev-linked "list of lists" of sorted
201	 *   sublists awaiting further merging.
202	 * - Each of the sorted sublists is power-of-two in size.
203	 * - Sublists are sorted by size and age, smallest & newest at front.
204	 * - There are zero to two sublists of each size.
205	 * - A pair of pending sublists are merged as soon as the number
206	 *   of following pending elements equals their size (i.e.
207	 *   each time count reaches an odd multiple of that size).
208	 *   That ensures each later final merge will be at worst 2:1.
209	 * - Each round consists of:
210	 *   - Merging the two sublists selected by the highest bit
211	 *     which flips when count is incremented, and
212	 *   - Adding an element from the input as a size-1 sublist.
213	 */
214	do {
215		size_t bits;
216		struct list_head **tail = &pending;
217
218		/* Find the least-significant clear bit in count */
219		for (bits = count; bits & 1; bits >>= 1)
220			tail = &(*tail)->prev;
221		/* Do the indicated merge */
222		if (likely(bits)) {
223			struct list_head *a = *tail, *b = a->prev;
224
225			a = merge(priv, cmp, b, a);
226			/* Install the merged result in place of the inputs */
227			a->prev = b->prev;
228			*tail = a;
229		}
230
231		/* Move one element from input list to pending */
232		list->prev = pending;
233		pending = list;
234		list = list->next;
235		pending->next = NULL;
236		count++;
237	} while (list);
238
239	/* End of input; merge together all the pending lists. */
240	list = pending;
241	pending = pending->prev;
242	for (;;) {
243		struct list_head *next = pending->prev;
244
245		if (!next)
246			break;
247		list = merge(priv, cmp, pending, list);
248		pending = next;
249	}
250	/* The final merge, rebuilding prev links */
251	merge_final(priv, cmp, head, pending, list);
252}
253EXPORT_SYMBOL(list_sort);
254