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