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1// SPDX-License-Identifier: GPL-2.02#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 suited11 * to chaining of merge() calls: null-terminated, no reserved or12 * 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-linked45 * list structure. This approach duplicates code from merge(), but46 * runs faster than the tidier alternatives of either a separate final47 * prev-link restoration pass, or maintaining the prev links48 * 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 56 for (;;) {57 /* if equal, take 'a' -- important for sort stability */58 if (cmp(priv, a, b) <= 0) {59 tail->next = a;60 a->prev = tail;61 tail = a;62 a = a->next;63 if (!a)64 break;65 } else {66 tail->next = b;67 b->prev = tail;68 tail = b;69 b = b->next;70 if (!b) {71 b = a;72 break;73 }74 }75 }76 77 /* Finish linking remainder of list b on to tail */78 tail->next = b;79 do {80 b->prev = tail;81 tail = b;82 b = b->next;83 } while (b);84 85 /* And the final links to make a circular doubly-linked list */86 tail->next = head;87 head->prev = tail;88}89 90/**91 * list_sort - sort a list92 * @priv: private data, opaque to list_sort(), passed to @cmp93 * @head: the list to sort94 * @cmp: the elements comparison function95 *96 * The comparison function @cmp must return > 0 if @a should sort after97 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should98 * sort before @b *or* their original order should be preserved. It is99 * always called with the element that came first in the input in @a,100 * and list_sort is a stable sort, so it is not necessary to distinguish101 * the @a < @b and @a == @b cases.102 *103 * This is compatible with two styles of @cmp function:104 * - The traditional style which returns <0 / =0 / >0, or105 * - Returning a boolean 0/1.106 * The latter offers a chance to save a few cycles in the comparison107 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).108 *109 * A good way to write a multi-word comparison is::110 *111 * if (a->high != b->high)112 * return a->high > b->high;113 * if (a->middle != b->middle)114 * return a->middle > b->middle;115 * return a->low > b->low;116 *117 *118 * This mergesort is as eager as possible while always performing at least119 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are120 * merged to a size-2^(k+1) list as soon as we have 2^k following elements.121 *122 * Thus, it will avoid cache thrashing as long as 3*2^k elements can123 * fit into the cache. Not quite as good as a fully-eager bottom-up124 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in125 * the common case that everything fits into L1.126 *127 *128 * The merging is controlled by "count", the number of elements in the129 * pending lists. This is beautifully simple code, but rather subtle.130 *131 * Each time we increment "count", we set one bit (bit k) and clear132 * bits k-1 .. 0. Each time this happens (except the very first time133 * for each bit, when count increments to 2^k), we merge two lists of134 * size 2^k into one list of size 2^(k+1).135 *136 * This merge happens exactly when the count reaches an odd multiple of137 * 2^k, which is when we have 2^k elements pending in smaller lists,138 * so it's safe to merge away two lists of size 2^k.139 *140 * After this happens twice, we have created two lists of size 2^(k+1),141 * which will be merged into a list of size 2^(k+2) before we create142 * a third list of size 2^(k+1), so there are never more than two pending.143 *144 * The number of pending lists of size 2^k is determined by the145 * state of bit k of "count" plus two extra pieces of information:146 *147 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and148 * - Whether the higher-order bits are zero or non-zero (i.e.149 * is count >= 2^(k+1)).150 *151 * There are six states we distinguish. "x" represents some arbitrary152 * bits, and "y" represents some arbitrary non-zero bits:153 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k154 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k155 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k156 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k157 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k158 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k159 * (merge and loop back to state 2)160 *161 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because162 * bit k-1 is set while the more significant bits are non-zero) and163 * merge them away in the 5->2 transition. Note in particular that just164 * before the 5->2 transition, all lower-order bits are 11 (state 3),165 * so there is one list of each smaller size.166 *167 * When we reach the end of the input, we merge all the pending168 * lists, from smallest to largest. If you work through cases 2 to169 * 5 above, you can see that the number of elements we merge with a list170 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to171 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).172 */173__attribute__((nonnull(2,3)))174void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)175{176 struct list_head *list = head->next, *pending = NULL;177 size_t count = 0; /* Count of pending */178 179 if (list == head->prev) /* Zero or one elements */180 return;181 182 /* Convert to a null-terminated singly-linked list. */183 head->prev->next = NULL;184 185 /*186 * Data structure invariants:187 * - All lists are singly linked and null-terminated; prev188 * pointers are not maintained.189 * - pending is a prev-linked "list of lists" of sorted190 * sublists awaiting further merging.191 * - Each of the sorted sublists is power-of-two in size.192 * - Sublists are sorted by size and age, smallest & newest at front.193 * - There are zero to two sublists of each size.194 * - A pair of pending sublists are merged as soon as the number195 * of following pending elements equals their size (i.e.196 * each time count reaches an odd multiple of that size).197 * That ensures each later final merge will be at worst 2:1.198 * - Each round consists of:199 * - Merging the two sublists selected by the highest bit200 * which flips when count is incremented, and201 * - Adding an element from the input as a size-1 sublist.202 */203 do {204 size_t bits;205 struct list_head **tail = &pending;206 207 /* Find the least-significant clear bit in count */208 for (bits = count; bits & 1; bits >>= 1)209 tail = &(*tail)->prev;210 /* Do the indicated merge */211 if (likely(bits)) {212 struct list_head *a = *tail, *b = a->prev;213 214 a = merge(priv, cmp, b, a);215 /* Install the merged result in place of the inputs */216 a->prev = b->prev;217 *tail = a;218 }219 220 /* Move one element from input list to pending */221 list->prev = pending;222 pending = list;223 list = list->next;224 pending->next = NULL;225 count++;226 } while (list);227 228 /* End of input; merge together all the pending lists. */229 list = pending;230 pending = pending->prev;231 for (;;) {232 struct list_head *next = pending->prev;233 234 if (!next)235 break;236 list = merge(priv, cmp, pending, list);237 pending = next;238 }239 /* The final merge, rebuilding prev links */240 merge_final(priv, cmp, head, pending, list);241}242EXPORT_SYMBOL(list_sort);243