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 u8 count = 0; 54 55 for (;;) { 56 /* if equal, take 'a' -- important for sort stability */ 57 if (cmp(priv, a, b) <= 0) { 58 tail->next = a; 59 a->prev = tail; 60 tail = a; 61 a = a->next; 62 if (!a) 63 break; 64 } else { 65 tail->next = b; 66 b->prev = tail; 67 tail = b; 68 b = b->next; 69 if (!b) { 70 b = a; 71 break; 72 } 73 } 74 } 75 76 /* Finish linking remainder of list b on to tail */ 77 tail->next = b; 78 do { 79 /* 80 * If the merge is highly unbalanced (e.g. the input is 81 * already sorted), this loop may run many iterations. 82 * Continue callbacks to the client even though no 83 * element comparison is needed, so the client's cmp() 84 * routine can invoke cond_resched() periodically. 85 */ 86 if (unlikely(!++count)) 87 cmp(priv, b, b); 88 b->prev = tail; 89 tail = b; 90 b = b->next; 91 } while (b); 92 93 /* And the final links to make a circular doubly-linked list */ 94 tail->next = head; 95 head->prev = tail; 96 } 97 98 /** 99 * list_sort - sort a list 100 * @priv: private data, opaque to list_sort(), passed to @cmp 101 * @head: the list to sort 102 * @cmp: the elements comparison function 103 * 104 * The comparison function @cmp must return > 0 if @a should sort after 105 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should 106 * sort before @b *or* their original order should be preserved. It is 107 * always called with the element that came first in the input in @a, 108 * and list_sort is a stable sort, so it is not necessary to distinguish 109 * the @a < @b and @a == @b cases. 110 * 111 * The comparison function must adhere to specific mathematical properties 112 * to ensure correct and stable sorting: 113 * - Antisymmetry: cmp(@a, @b) must return the opposite sign of 114 * cmp(@b, @a). 115 * - Transitivity: if cmp(@a, @b) <= 0 and cmp(@b, @c) <= 0, then 116 * cmp(@a, @c) <= 0. 117 * 118 * This is compatible with two styles of @cmp function: 119 * - The traditional style which returns <0 / =0 / >0, or 120 * - Returning a boolean 0/1. 121 * The latter offers a chance to save a few cycles in the comparison 122 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c). 123 * 124 * A good way to write a multi-word comparison is:: 125 * 126 * if (a->high != b->high) 127 * return a->high > b->high; 128 * if (a->middle != b->middle) 129 * return a->middle > b->middle; 130 * return a->low > b->low; 131 * 132 * 133 * This mergesort is as eager as possible while always performing at least 134 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are 135 * merged to a size-2^(k+1) list as soon as we have 2^k following elements. 136 * 137 * Thus, it will avoid cache thrashing as long as 3*2^k elements can 138 * fit into the cache. Not quite as good as a fully-eager bottom-up 139 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in 140 * the common case that everything fits into L1. 141 * 142 * 143 * The merging is controlled by "count", the number of elements in the 144 * pending lists. This is beautifully simple code, but rather subtle. 145 * 146 * Each time we increment "count", we set one bit (bit k) and clear 147 * bits k-1 .. 0. Each time this happens (except the very first time 148 * for each bit, when count increments to 2^k), we merge two lists of 149 * size 2^k into one list of size 2^(k+1). 150 * 151 * This merge happens exactly when the count reaches an odd multiple of 152 * 2^k, which is when we have 2^k elements pending in smaller lists, 153 * so it's safe to merge away two lists of size 2^k. 154 * 155 * After this happens twice, we have created two lists of size 2^(k+1), 156 * which will be merged into a list of size 2^(k+2) before we create 157 * a third list of size 2^(k+1), so there are never more than two pending. 158 * 159 * The number of pending lists of size 2^k is determined by the 160 * state of bit k of "count" plus two extra pieces of information: 161 * 162 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and 163 * - Whether the higher-order bits are zero or non-zero (i.e. 164 * is count >= 2^(k+1)). 165 * 166 * There are six states we distinguish. "x" represents some arbitrary 167 * bits, and "y" represents some arbitrary non-zero bits: 168 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k 169 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 170 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k 171 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 172 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k 173 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 174 * (merge and loop back to state 2) 175 * 176 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because 177 * bit k-1 is set while the more significant bits are non-zero) and 178 * merge them away in the 5->2 transition. Note in particular that just 179 * before the 5->2 transition, all lower-order bits are 11 (state 3), 180 * so there is one list of each smaller size. 181 * 182 * When we reach the end of the input, we merge all the pending 183 * lists, from smallest to largest. If you work through cases 2 to 184 * 5 above, you can see that the number of elements we merge with a list 185 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to 186 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1). 187 */ 188 __attribute__((nonnull(2,3))) 189 void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp) 190 { 191 struct list_head *list = head->next, *pending = NULL; 192 size_t count = 0; /* Count of pending */ 193 194 if (list == head->prev) /* Zero or one elements */ 195 return; 196 197 /* Convert to a null-terminated singly-linked list. */ 198 head->prev->next = NULL; 199 200 /* 201 * Data structure invariants: 202 * - All lists are singly linked and null-terminated; prev 203 * pointers are not maintained. 204 * - pending is a prev-linked "list of lists" of sorted 205 * sublists awaiting further merging. 206 * - Each of the sorted sublists is power-of-two in size. 207 * - Sublists are sorted by size and age, smallest & newest at front. 208 * - There are zero to two sublists of each size. 209 * - A pair of pending sublists are merged as soon as the number 210 * of following pending elements equals their size (i.e. 211 * each time count reaches an odd multiple of that size). 212 * That ensures each later final merge will be at worst 2:1. 213 * - Each round consists of: 214 * - Merging the two sublists selected by the highest bit 215 * which flips when count is incremented, and 216 * - Adding an element from the input as a size-1 sublist. 217 */ 218 do { 219 size_t bits; 220 struct list_head **tail = &pending; 221 222 /* Find the least-significant clear bit in count */ 223 for (bits = count; bits & 1; bits >>= 1) 224 tail = &(*tail)->prev; 225 /* Do the indicated merge */ 226 if (likely(bits)) { 227 struct list_head *a = *tail, *b = a->prev; 228 229 a = merge(priv, cmp, b, a); 230 /* Install the merged result in place of the inputs */ 231 a->prev = b->prev; 232 *tail = a; 233 } 234 235 /* Move one element from input list to pending */ 236 list->prev = pending; 237 pending = list; 238 list = list->next; 239 pending->next = NULL; 240 count++; 241 } while (list); 242 243 /* End of input; merge together all the pending lists. */ 244 list = pending; 245 pending = pending->prev; 246 for (;;) { 247 struct list_head *next = pending->prev; 248 249 if (!next) 250 break; 251 list = merge(priv, cmp, pending, list); 252 pending = next; 253 } 254 /* The final merge, rebuilding prev links */ 255 merge_final(priv, cmp, head, pending, list); 256 } 257 EXPORT_SYMBOL(list_sort); 258