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)))
merge(void * priv,list_cmp_func_t cmp,struct list_head * a,struct list_head * b)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)))
merge_final(void * priv,list_cmp_func_t cmp,struct list_head * head,struct list_head * a,struct list_head * b)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 	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)))
list_sort(void * priv,struct list_head * head,list_cmp_func_t cmp)184 void 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 }
252 EXPORT_SYMBOL(list_sort);
253