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 * This is compatible with two styles of @cmp function:
102 * - The traditional style which returns <0 / =0 / >0, or
103 * - Returning a boolean 0/1.
104 * The latter offers a chance to save a few cycles in the comparison
105 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
106 *
107 * A good way to write a multi-word comparison is::
108 *
109 *	if (a->high != b->high)
110 *		return a->high > b->high;
111 *	if (a->middle != b->middle)
112 *		return a->middle > b->middle;
113 *	return a->low > b->low;
114 *
115 *
116 * This mergesort is as eager as possible while always performing at least
117 * 2:1 balanced merges.  Given two pending sublists of size 2^k, they are
118 * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
119 *
120 * Thus, it will avoid cache thrashing as long as 3*2^k elements can
121 * fit into the cache.  Not quite as good as a fully-eager bottom-up
122 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
123 * the common case that everything fits into L1.
124 *
125 *
126 * The merging is controlled by "count", the number of elements in the
127 * pending lists.  This is beautifully simple code, but rather subtle.
128 *
129 * Each time we increment "count", we set one bit (bit k) and clear
130 * bits k-1 .. 0.  Each time this happens (except the very first time
131 * for each bit, when count increments to 2^k), we merge two lists of
132 * size 2^k into one list of size 2^(k+1).
133 *
134 * This merge happens exactly when the count reaches an odd multiple of
135 * 2^k, which is when we have 2^k elements pending in smaller lists,
136 * so it's safe to merge away two lists of size 2^k.
137 *
138 * After this happens twice, we have created two lists of size 2^(k+1),
139 * which will be merged into a list of size 2^(k+2) before we create
140 * a third list of size 2^(k+1), so there are never more than two pending.
141 *
142 * The number of pending lists of size 2^k is determined by the
143 * state of bit k of "count" plus two extra pieces of information:
144 *
145 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
146 * - Whether the higher-order bits are zero or non-zero (i.e.
147 *   is count >= 2^(k+1)).
148 *
149 * There are six states we distinguish.  "x" represents some arbitrary
150 * bits, and "y" represents some arbitrary non-zero bits:
151 * 0:  00x: 0 pending of size 2^k;           x pending of sizes < 2^k
152 * 1:  01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
153 * 2: x10x: 0 pending of size 2^k; 2^k     + x pending of sizes < 2^k
154 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
155 * 4: y00x: 1 pending of size 2^k; 2^k     + x pending of sizes < 2^k
156 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
157 * (merge and loop back to state 2)
158 *
159 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
160 * bit k-1 is set while the more significant bits are non-zero) and
161 * merge them away in the 5->2 transition.  Note in particular that just
162 * before the 5->2 transition, all lower-order bits are 11 (state 3),
163 * so there is one list of each smaller size.
164 *
165 * When we reach the end of the input, we merge all the pending
166 * lists, from smallest to largest.  If you work through cases 2 to
167 * 5 above, you can see that the number of elements we merge with a list
168 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
169 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
170 */
171__attribute__((nonnull(2,3)))
172void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
173{
174	struct list_head *list = head->next, *pending = NULL;
175	size_t count = 0;	/* Count of pending */
176
177	if (list == head->prev)	/* Zero or one elements */
178		return;
179
180	/* Convert to a null-terminated singly-linked list. */
181	head->prev->next = NULL;
182
183	/*
184	 * Data structure invariants:
185	 * - All lists are singly linked and null-terminated; prev
186	 *   pointers are not maintained.
187	 * - pending is a prev-linked "list of lists" of sorted
188	 *   sublists awaiting further merging.
189	 * - Each of the sorted sublists is power-of-two in size.
190	 * - Sublists are sorted by size and age, smallest & newest at front.
191	 * - There are zero to two sublists of each size.
192	 * - A pair of pending sublists are merged as soon as the number
193	 *   of following pending elements equals their size (i.e.
194	 *   each time count reaches an odd multiple of that size).
195	 *   That ensures each later final merge will be at worst 2:1.
196	 * - Each round consists of:
197	 *   - Merging the two sublists selected by the highest bit
198	 *     which flips when count is incremented, and
199	 *   - Adding an element from the input as a size-1 sublist.
200	 */
201	do {
202		size_t bits;
203		struct list_head **tail = &pending;
204
205		/* Find the least-significant clear bit in count */
206		for (bits = count; bits & 1; bits >>= 1)
207			tail = &(*tail)->prev;
208		/* Do the indicated merge */
209		if (likely(bits)) {
210			struct list_head *a = *tail, *b = a->prev;
211
212			a = merge(priv, cmp, b, a);
213			/* Install the merged result in place of the inputs */
214			a->prev = b->prev;
215			*tail = a;
216		}
217
218		/* Move one element from input list to pending */
219		list->prev = pending;
220		pending = list;
221		list = list->next;
222		pending->next = NULL;
223		count++;
224	} while (list);
225
226	/* End of input; merge together all the pending lists. */
227	list = pending;
228	pending = pending->prev;
229	for (;;) {
230		struct list_head *next = pending->prev;
231
232		if (!next)
233			break;
234		list = merge(priv, cmp, pending, list);
235		pending = next;
236	}
237	/* The final merge, rebuilding prev links */
238	merge_final(priv, cmp, head, pending, list);
239}
240EXPORT_SYMBOL(list_sort);