1 // SPDX-License-Identifier: GPL-2.0 2 #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 suited 11 * to chaining of merge() calls: null-terminated, no reserved or 12 * sentinel head node, "prev" links not maintained. 13 */ 14 __attribute__((nonnull(2,3,4))) 15 static 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-linked 45 * list structure. This approach duplicates code from merge(), but 46 * runs faster than the tidier alternatives of either a separate final 47 * prev-link restoration pass, or maintaining the prev links 48 * throughout. 49 */ 50 __attribute__((nonnull(2,3,4,5))) 51 static 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 u8 count = 0; 56 57 for (;;) { 58 /* if equal, take 'a' -- important for sort stability */ 59 if (cmp(priv, a, b) <= 0) { 60 tail->next = a; 61 a->prev = tail; 62 tail = a; 63 a = a->next; 64 if (!a) 65 break; 66 } else { 67 tail->next = b; 68 b->prev = tail; 69 tail = b; 70 b = b->next; 71 if (!b) { 72 b = a; 73 break; 74 } 75 } 76 } 77 78 /* Finish linking remainder of list b on to tail */ 79 tail->next = b; 80 do { 81 /* 82 * If the merge is highly unbalanced (e.g. the input is 83 * already sorted), this loop may run many iterations. 84 * Continue callbacks to the client even though no 85 * element comparison is needed, so the client's cmp() 86 * routine can invoke cond_resched() periodically. 87 */ 88 if (unlikely(!++count)) 89 cmp(priv, b, b); 90 b->prev = tail; 91 tail = b; 92 b = b->next; 93 } while (b); 94 95 /* And the final links to make a circular doubly-linked list */ 96 tail->next = head; 97 head->prev = tail; 98 } 99 100 /** 101 * list_sort - sort a list 102 * @priv: private data, opaque to list_sort(), passed to @cmp 103 * @head: the list to sort 104 * @cmp: the elements comparison function 105 * 106 * The comparison function @cmp must return > 0 if @a should sort after 107 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should 108 * sort before @b *or* their original order should be preserved. It is 109 * always called with the element that came first in the input in @a, 110 * and list_sort is a stable sort, so it is not necessary to distinguish 111 * the @a < @b and @a == @b cases. 112 * 113 * This is compatible with two styles of @cmp function: 114 * - The traditional style which returns <0 / =0 / >0, or 115 * - Returning a boolean 0/1. 116 * The latter offers a chance to save a few cycles in the comparison 117 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c). 118 * 119 * A good way to write a multi-word comparison is:: 120 * 121 * if (a->high != b->high) 122 * return a->high > b->high; 123 * if (a->middle != b->middle) 124 * return a->middle > b->middle; 125 * return a->low > b->low; 126 * 127 * 128 * This mergesort is as eager as possible while always performing at least 129 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are 130 * merged to a size-2^(k+1) list as soon as we have 2^k following elements. 131 * 132 * Thus, it will avoid cache thrashing as long as 3*2^k elements can 133 * fit into the cache. Not quite as good as a fully-eager bottom-up 134 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in 135 * the common case that everything fits into L1. 136 * 137 * 138 * The merging is controlled by "count", the number of elements in the 139 * pending lists. This is beautifully simple code, but rather subtle. 140 * 141 * Each time we increment "count", we set one bit (bit k) and clear 142 * bits k-1 .. 0. Each time this happens (except the very first time 143 * for each bit, when count increments to 2^k), we merge two lists of 144 * size 2^k into one list of size 2^(k+1). 145 * 146 * This merge happens exactly when the count reaches an odd multiple of 147 * 2^k, which is when we have 2^k elements pending in smaller lists, 148 * so it's safe to merge away two lists of size 2^k. 149 * 150 * After this happens twice, we have created two lists of size 2^(k+1), 151 * which will be merged into a list of size 2^(k+2) before we create 152 * a third list of size 2^(k+1), so there are never more than two pending. 153 * 154 * The number of pending lists of size 2^k is determined by the 155 * state of bit k of "count" plus two extra pieces of information: 156 * 157 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and 158 * - Whether the higher-order bits are zero or non-zero (i.e. 159 * is count >= 2^(k+1)). 160 * 161 * There are six states we distinguish. "x" represents some arbitrary 162 * bits, and "y" represents some arbitrary non-zero bits: 163 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k 164 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 165 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k 166 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 167 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k 168 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 169 * (merge and loop back to state 2) 170 * 171 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because 172 * bit k-1 is set while the more significant bits are non-zero) and 173 * merge them away in the 5->2 transition. Note in particular that just 174 * before the 5->2 transition, all lower-order bits are 11 (state 3), 175 * so there is one list of each smaller size. 176 * 177 * When we reach the end of the input, we merge all the pending 178 * lists, from smallest to largest. If you work through cases 2 to 179 * 5 above, you can see that the number of elements we merge with a list 180 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to 181 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1). 182 */ 183 __attribute__((nonnull(2,3))) 184 void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp) 185 { 186 struct list_head *list = head->next, *pending = NULL; 187 size_t count = 0; /* Count of pending */ 188 189 if (list == head->prev) /* Zero or one elements */ 190 return; 191 192 /* Convert to a null-terminated singly-linked list. */ 193 head->prev->next = NULL; 194 195 /* 196 * Data structure invariants: 197 * - All lists are singly linked and null-terminated; prev 198 * pointers are not maintained. 199 * - pending is a prev-linked "list of lists" of sorted 200 * sublists awaiting further merging. 201 * - Each of the sorted sublists is power-of-two in size. 202 * - Sublists are sorted by size and age, smallest & newest at front. 203 * - There are zero to two sublists of each size. 204 * - A pair of pending sublists are merged as soon as the number 205 * of following pending elements equals their size (i.e. 206 * each time count reaches an odd multiple of that size). 207 * That ensures each later final merge will be at worst 2:1. 208 * - Each round consists of: 209 * - Merging the two sublists selected by the highest bit 210 * which flips when count is incremented, and 211 * - Adding an element from the input as a size-1 sublist. 212 */ 213 do { 214 size_t bits; 215 struct list_head **tail = &pending; 216 217 /* Find the least-significant clear bit in count */ 218 for (bits = count; bits & 1; bits >>= 1) 219 tail = &(*tail)->prev; 220 /* Do the indicated merge */ 221 if (likely(bits)) { 222 struct list_head *a = *tail, *b = a->prev; 223 224 a = merge(priv, cmp, b, a); 225 /* Install the merged result in place of the inputs */ 226 a->prev = b->prev; 227 *tail = a; 228 } 229 230 /* Move one element from input list to pending */ 231 list->prev = pending; 232 pending = list; 233 list = list->next; 234 pending->next = NULL; 235 count++; 236 } while (list); 237 238 /* End of input; merge together all the pending lists. */ 239 list = pending; 240 pending = pending->prev; 241 for (;;) { 242 struct list_head *next = pending->prev; 243 244 if (!next) 245 break; 246 list = merge(priv, cmp, pending, list); 247 pending = next; 248 } 249 /* The final merge, rebuilding prev links */ 250 merge_final(priv, cmp, head, pending, list); 251 } 252 EXPORT_SYMBOL(list_sort); 253