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1// SPDX-License-Identifier: GPL-2.02#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 suited12 * to chaining of merge() calls: null-terminated, no reserved or13 * 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-linked46 * list structure. This approach duplicates code from merge(), but47 * runs faster than the tidier alternatives of either a separate final48 * prev-link restoration pass, or maintaining the prev links49 * 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 is84 * already sorted), this loop may run many iterations.85 * Continue callbacks to the client even though no86 * 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 list103 * @priv: private data, opaque to list_sort(), passed to @cmp104 * @head: the list to sort105 * @cmp: the elements comparison function106 *107 * The comparison function @cmp must return > 0 if @a should sort after108 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should109 * sort before @b *or* their original order should be preserved. It is110 * 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 distinguish112 * 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, or116 * - Returning a boolean 0/1.117 * The latter offers a chance to save a few cycles in the comparison118 * (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 least130 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are131 * 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 can134 * fit into the cache. Not quite as good as a fully-eager bottom-up135 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in136 * the common case that everything fits into L1.137 *138 *139 * The merging is controlled by "count", the number of elements in the140 * pending lists. This is beautifully simple code, but rather subtle.141 *142 * Each time we increment "count", we set one bit (bit k) and clear143 * bits k-1 .. 0. Each time this happens (except the very first time144 * for each bit, when count increments to 2^k), we merge two lists of145 * size 2^k into one list of size 2^(k+1).146 *147 * This merge happens exactly when the count reaches an odd multiple of148 * 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 create153 * 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 the156 * 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), and159 * - 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 arbitrary163 * bits, and "y" represents some arbitrary non-zero bits:164 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k165 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k166 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k167 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k168 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k169 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k170 * (merge and loop back to state 2)171 *172 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because173 * bit k-1 is set while the more significant bits are non-zero) and174 * merge them away in the 5->2 transition. Note in particular that just175 * 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 pending179 * lists, from smallest to largest. If you work through cases 2 to180 * 5 above, you can see that the number of elements we merge with a list181 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to182 * 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; prev199 * pointers are not maintained.200 * - pending is a prev-linked "list of lists" of sorted201 * 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 number206 * 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 bit211 * which flips when count is incremented, and212 * - 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