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))) 13 static 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))) 49 static 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))) 172 void 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 } 240 EXPORT_SYMBOL(list_sort); 241