Ian Rogers | 92ec3cc | 2021-10-15 10:21:12 -0700 | [diff] [blame] | 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); |