lib/list_sort.c

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