1 // SPDX-License-Identifier: GPL-2.0 2 #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 typedef int __attribute__((nonnull(2,3))) (*cmp_func)(void *, 11 struct list_head const *, struct list_head const *); 12 13 /* 14 * Returns a list organized in an intermediate format suited 15 * to chaining of merge() calls: null-terminated, no reserved or 16 * sentinel head node, "prev" links not maintained. 17 */ 18 __attribute__((nonnull(2,3,4))) 19 static struct list_head *merge(void *priv, cmp_func cmp, 20 struct list_head *a, struct list_head *b) 21 { 22 struct list_head *head, **tail = &head; 23 24 for (;;) { 25 /* if equal, take 'a' -- important for sort stability */ 26 if (cmp(priv, a, b) <= 0) { 27 *tail = a; 28 tail = &a->next; 29 a = a->next; 30 if (!a) { 31 *tail = b; 32 break; 33 } 34 } else { 35 *tail = b; 36 tail = &b->next; 37 b = b->next; 38 if (!b) { 39 *tail = a; 40 break; 41 } 42 } 43 } 44 return head; 45 } 46 47 /* 48 * Combine final list merge with restoration of standard doubly-linked 49 * list structure. This approach duplicates code from merge(), but 50 * runs faster than the tidier alternatives of either a separate final 51 * prev-link restoration pass, or maintaining the prev links 52 * throughout. 53 */ 54 __attribute__((nonnull(2,3,4,5))) 55 static void merge_final(void *priv, cmp_func cmp, struct list_head *head, 56 struct list_head *a, struct list_head *b) 57 { 58 struct list_head *tail = head; 59 u8 count = 0; 60 61 for (;;) { 62 /* if equal, take 'a' -- important for sort stability */ 63 if (cmp(priv, a, b) <= 0) { 64 tail->next = a; 65 a->prev = tail; 66 tail = a; 67 a = a->next; 68 if (!a) 69 break; 70 } else { 71 tail->next = b; 72 b->prev = tail; 73 tail = b; 74 b = b->next; 75 if (!b) { 76 b = a; 77 break; 78 } 79 } 80 } 81 82 /* Finish linking remainder of list b on to tail */ 83 tail->next = b; 84 do { 85 /* 86 * If the merge is highly unbalanced (e.g. the input is 87 * already sorted), this loop may run many iterations. 88 * Continue callbacks to the client even though no 89 * element comparison is needed, so the client's cmp() 90 * routine can invoke cond_resched() periodically. 91 */ 92 if (unlikely(!++count)) 93 cmp(priv, b, b); 94 b->prev = tail; 95 tail = b; 96 b = b->next; 97 } while (b); 98 99 /* And the final links to make a circular doubly-linked list */ 100 tail->next = head; 101 head->prev = tail; 102 } 103 104 /** 105 * list_sort - sort a list 106 * @priv: private data, opaque to list_sort(), passed to @cmp 107 * @head: the list to sort 108 * @cmp: the elements comparison function 109 * 110 * The comparison funtion @cmp must return > 0 if @a should sort after 111 * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should 112 * sort before @b *or* their original order should be preserved. It is 113 * always called with the element that came first in the input in @a, 114 * and list_sort is a stable sort, so it is not necessary to distinguish 115 * the @a < @b and @a == @b cases. 116 * 117 * This is compatible with two styles of @cmp function: 118 * - The traditional style which returns <0 / =0 / >0, or 119 * - Returning a boolean 0/1. 120 * The latter offers a chance to save a few cycles in the comparison 121 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c). 122 * 123 * A good way to write a multi-word comparison is:: 124 * 125 * if (a->high != b->high) 126 * return a->high > b->high; 127 * if (a->middle != b->middle) 128 * return a->middle > b->middle; 129 * return a->low > b->low; 130 * 131 * 132 * This mergesort is as eager as possible while always performing at least 133 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are 134 * merged to a size-2^(k+1) list as soon as we have 2^k following elements. 135 * 136 * Thus, it will avoid cache thrashing as long as 3*2^k elements can 137 * fit into the cache. Not quite as good as a fully-eager bottom-up 138 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in 139 * the common case that everything fits into L1. 140 * 141 * 142 * The merging is controlled by "count", the number of elements in the 143 * pending lists. This is beautiully simple code, but rather subtle. 144 * 145 * Each time we increment "count", we set one bit (bit k) and clear 146 * bits k-1 .. 0. Each time this happens (except the very first time 147 * for each bit, when count increments to 2^k), we merge two lists of 148 * size 2^k into one list of size 2^(k+1). 149 * 150 * This merge happens exactly when the count reaches an odd multiple of 151 * 2^k, which is when we have 2^k elements pending in smaller lists, 152 * so it's safe to merge away two lists of size 2^k. 153 * 154 * After this happens twice, we have created two lists of size 2^(k+1), 155 * which will be merged into a list of size 2^(k+2) before we create 156 * a third list of size 2^(k+1), so there are never more than two pending. 157 * 158 * The number of pending lists of size 2^k is determined by the 159 * state of bit k of "count" plus two extra pieces of information: 160 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and 161 * - Whether the higher-order bits are zero or non-zero (i.e. 162 * is count >= 2^(k+1)). 163 * There are six states we distinguish. "x" represents some arbitrary 164 * bits, and "y" represents some arbitrary non-zero bits: 165 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k 166 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 167 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k 168 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 169 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k 170 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 171 * (merge and loop back to state 2) 172 * 173 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because 174 * bit k-1 is set while the more significant bits are non-zero) and 175 * merge them away in the 5->2 transition. Note in particular that just 176 * before the 5->2 transition, all lower-order bits are 11 (state 3), 177 * so there is one list of each smaller size. 178 * 179 * When we reach the end of the input, we merge all the pending 180 * lists, from smallest to largest. If you work through cases 2 to 181 * 5 above, you can see that the number of elements we merge with a list 182 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to 183 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1). 184 */ 185 __attribute__((nonnull(2,3))) 186 void list_sort(void *priv, struct list_head *head, 187 int (*cmp)(void *priv, struct list_head *a, 188 struct list_head *b)) 189 { 190 struct list_head *list = head->next, *pending = NULL; 191 size_t count = 0; /* Count of pending */ 192 193 if (list == head->prev) /* Zero or one elements */ 194 return; 195 196 /* Convert to a null-terminated singly-linked list. */ 197 head->prev->next = NULL; 198 199 /* 200 * Data structure invariants: 201 * - All lists are singly linked and null-terminated; prev 202 * pointers are not maintained. 203 * - pending is a prev-linked "list of lists" of sorted 204 * sublists awaiting further merging. 205 * - Each of the sorted sublists is power-of-two in size. 206 * - Sublists are sorted by size and age, smallest & newest at front. 207 * - There are zero to two sublists of each size. 208 * - A pair of pending sublists are merged as soon as the number 209 * of following pending elements equals their size (i.e. 210 * each time count reaches an odd multiple of that size). 211 * That ensures each later final merge will be at worst 2:1. 212 * - Each round consists of: 213 * - Merging the two sublists selected by the highest bit 214 * which flips when count is incremented, and 215 * - Adding an element from the input as a size-1 sublist. 216 */ 217 do { 218 size_t bits; 219 struct list_head **tail = &pending; 220 221 /* Find the least-significant clear bit in count */ 222 for (bits = count; bits & 1; bits >>= 1) 223 tail = &(*tail)->prev; 224 /* Do the indicated merge */ 225 if (likely(bits)) { 226 struct list_head *a = *tail, *b = a->prev; 227 228 a = merge(priv, (cmp_func)cmp, b, a); 229 /* Install the merged result in place of the inputs */ 230 a->prev = b->prev; 231 *tail = a; 232 } 233 234 /* Move one element from input list to pending */ 235 list->prev = pending; 236 pending = list; 237 list = list->next; 238 pending->next = NULL; 239 count++; 240 } while (list); 241 242 /* End of input; merge together all the pending lists. */ 243 list = pending; 244 pending = pending->prev; 245 for (;;) { 246 struct list_head *next = pending->prev; 247 248 if (!next) 249 break; 250 list = merge(priv, (cmp_func)cmp, pending, list); 251 pending = next; 252 } 253 /* The final merge, rebuilding prev links */ 254 merge_final(priv, (cmp_func)cmp, head, pending, list); 255 } 256 EXPORT_SYMBOL(list_sort); 257