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 * The comparison function must adhere to specific mathematical properties 102 * to ensure correct and stable sorting: 103 * - Antisymmetry: cmp(@a, @b) must return the opposite sign of 104 * cmp(@b, @a). 105 * - Transitivity: if cmp(@a, @b) <= 0 and cmp(@b, @c) <= 0, then 106 * cmp(@a, @c) <= 0. 107 * 108 * This is compatible with two styles of @cmp function: 109 * - The traditional style which returns <0 / =0 / >0, or 110 * - Returning a boolean 0/1. 111 * The latter offers a chance to save a few cycles in the comparison 112 * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c). 113 * 114 * A good way to write a multi-word comparison is:: 115 * 116 * if (a->high != b->high) 117 * return a->high > b->high; 118 * if (a->middle != b->middle) 119 * return a->middle > b->middle; 120 * return a->low > b->low; 121 * 122 * 123 * This mergesort is as eager as possible while always performing at least 124 * 2:1 balanced merges. Given two pending sublists of size 2^k, they are 125 * merged to a size-2^(k+1) list as soon as we have 2^k following elements. 126 * 127 * Thus, it will avoid cache thrashing as long as 3*2^k elements can 128 * fit into the cache. Not quite as good as a fully-eager bottom-up 129 * mergesort, but it does use 0.2*n fewer comparisons, so is faster in 130 * the common case that everything fits into L1. 131 * 132 * 133 * The merging is controlled by "count", the number of elements in the 134 * pending lists. This is beautifully simple code, but rather subtle. 135 * 136 * Each time we increment "count", we set one bit (bit k) and clear 137 * bits k-1 .. 0. Each time this happens (except the very first time 138 * for each bit, when count increments to 2^k), we merge two lists of 139 * size 2^k into one list of size 2^(k+1). 140 * 141 * This merge happens exactly when the count reaches an odd multiple of 142 * 2^k, which is when we have 2^k elements pending in smaller lists, 143 * so it's safe to merge away two lists of size 2^k. 144 * 145 * After this happens twice, we have created two lists of size 2^(k+1), 146 * which will be merged into a list of size 2^(k+2) before we create 147 * a third list of size 2^(k+1), so there are never more than two pending. 148 * 149 * The number of pending lists of size 2^k is determined by the 150 * state of bit k of "count" plus two extra pieces of information: 151 * 152 * - The state of bit k-1 (when k == 0, consider bit -1 always set), and 153 * - Whether the higher-order bits are zero or non-zero (i.e. 154 * is count >= 2^(k+1)). 155 * 156 * There are six states we distinguish. "x" represents some arbitrary 157 * bits, and "y" represents some arbitrary non-zero bits: 158 * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k 159 * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 160 * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k 161 * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 162 * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k 163 * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k 164 * (merge and loop back to state 2) 165 * 166 * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because 167 * bit k-1 is set while the more significant bits are non-zero) and 168 * merge them away in the 5->2 transition. Note in particular that just 169 * before the 5->2 transition, all lower-order bits are 11 (state 3), 170 * so there is one list of each smaller size. 171 * 172 * When we reach the end of the input, we merge all the pending 173 * lists, from smallest to largest. If you work through cases 2 to 174 * 5 above, you can see that the number of elements we merge with a list 175 * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to 176 * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1). 177 */ 178 __attribute__((nonnull(2,3))) 179 void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp) 180 { 181 struct list_head *list = head->next, *pending = NULL; 182 size_t count = 0; /* Count of pending */ 183 184 if (list == head->prev) /* Zero or one elements */ 185 return; 186 187 /* Convert to a null-terminated singly-linked list. */ 188 head->prev->next = NULL; 189 190 /* 191 * Data structure invariants: 192 * - All lists are singly linked and null-terminated; prev 193 * pointers are not maintained. 194 * - pending is a prev-linked "list of lists" of sorted 195 * sublists awaiting further merging. 196 * - Each of the sorted sublists is power-of-two in size. 197 * - Sublists are sorted by size and age, smallest & newest at front. 198 * - There are zero to two sublists of each size. 199 * - A pair of pending sublists are merged as soon as the number 200 * of following pending elements equals their size (i.e. 201 * each time count reaches an odd multiple of that size). 202 * That ensures each later final merge will be at worst 2:1. 203 * - Each round consists of: 204 * - Merging the two sublists selected by the highest bit 205 * which flips when count is incremented, and 206 * - Adding an element from the input as a size-1 sublist. 207 */ 208 do { 209 size_t bits; 210 struct list_head **tail = &pending; 211 212 /* Find the least-significant clear bit in count */ 213 for (bits = count; bits & 1; bits >>= 1) 214 tail = &(*tail)->prev; 215 /* Do the indicated merge */ 216 if (likely(bits)) { 217 struct list_head *a = *tail, *b = a->prev; 218 219 a = merge(priv, cmp, b, a); 220 /* Install the merged result in place of the inputs */ 221 a->prev = b->prev; 222 *tail = a; 223 } 224 225 /* Move one element from input list to pending */ 226 list->prev = pending; 227 pending = list; 228 list = list->next; 229 pending->next = NULL; 230 count++; 231 } while (list); 232 233 /* End of input; merge together all the pending lists. */ 234 list = pending; 235 pending = pending->prev; 236 for (;;) { 237 struct list_head *next = pending->prev; 238 239 if (!next) 240 break; 241 list = merge(priv, cmp, pending, list); 242 pending = next; 243 } 244 /* The final merge, rebuilding prev links */ 245 merge_final(priv, cmp, head, pending, list); 246 } 247 EXPORT_SYMBOL(list_sort); 248