lib/list_sort.c

   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  *      if (a->high != b->high)
 125  *              return a->high > b->high;
 126  *      if (a->middle != b->middle)
 127  *              return a->middle > b->middle;
 128  *      return a->low > b->low;
 129  *
 130  *
 131  * This mergesort is as eager as possible while always performing at least
 132  * 2:1 balanced merges.  Given two pending sublists of size 2^k, they are
 133  * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
 134  *
 135  * Thus, it will avoid cache thrashing as long as 3*2^k elements can
 136  * fit into the cache.  Not quite as good as a fully-eager bottom-up
 137  * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
 138  * the common case that everything fits into L1.
 139  *
 140  *
 141  * The merging is controlled by "count", the number of elements in the
 142  * pending lists.  This is beautiully simple code, but rather subtle.
 143  *
 144  * Each time we increment "count", we set one bit (bit k) and clear
 145  * bits k-1 .. 0.  Each time this happens (except the very first time
 146  * for each bit, when count increments to 2^k), we merge two lists of
 147  * size 2^k into one list of size 2^(k+1).
 148  *
 149  * This merge happens exactly when the count reaches an odd multiple of
 150  * 2^k, which is when we have 2^k elements pending in smaller lists,
 151  * so it's safe to merge away two lists of size 2^k.
 152  *
 153  * After this happens twice, we have created two lists of size 2^(k+1),
 154  * which will be merged into a list of size 2^(k+2) before we create
 155  * a third list of size 2^(k+1), so there are never more than two pending.
 156  *
 157  * The number of pending lists of size 2^k is determined by the
 158  * state of bit k of "count" plus two extra pieces of information:
 159  * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
 160  * - Whether the higher-order bits are zero or non-zero (i.e.
 161  *   is count >= 2^(k+1)).
 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,
 186                 int (*cmp)(void *priv, struct list_head *a,
 187                         struct list_head *b))
 188 {
 189         struct list_head *list = head->next, *pending = NULL;
 190         size_t count = 0;       /* Count of pending */
 191
 192         if (list == head->prev) /* Zero or one elements */
 193                 return;
 194
 195         /* Convert to a null-terminated singly-linked list. */
 196         head->prev->next = NULL;
 197
 198         /*
 199          * Data structure invariants:
 200          * - All lists are singly linked and null-terminated; prev
 201          *   pointers are not maintained.
 202          * - pending is a prev-linked "list of lists" of sorted
 203          *   sublists awaiting further merging.
 204          * - Each of the sorted sublists is power-of-two in size.
 205          * - Sublists are sorted by size and age, smallest & newest at front.
 206          * - There are zero to two sublists of each size.
 207          * - A pair of pending sublists are merged as soon as the number
 208          *   of following pending elements equals their size (i.e.
 209          *   each time count reaches an odd multiple of that size).
 210          *   That ensures each later final merge will be at worst 2:1.
 211          * - Each round consists of:
 212          *   - Merging the two sublists selected by the highest bit
 213          *     which flips when count is incremented, and
 214          *   - Adding an element from the input as a size-1 sublist.
 215          */
 216         do {
 217                 size_t bits;
 218                 struct list_head **tail = &pending;
 219
 220                 /* Find the least-significant clear bit in count */
 221                 for (bits = count; bits & 1; bits >>= 1)
 222                         tail = &(*tail)->prev;
 223                 /* Do the indicated merge */
 224                 if (likely(bits)) {
 225                         struct list_head *a = *tail, *b = a->prev;
 226
 227                         a = merge(priv, (cmp_func)cmp, b, a);
 228                         /* Install the merged result in place of the inputs */
 229                         a->prev = b->prev;
 230                         *tail = a;
 231                 }
 232
 233                 /* Move one element from input list to pending */
 234                 list->prev = pending;
 235                 pending = list;
 236                 list = list->next;
 237                 pending->next = NULL;
 238                 count++;
 239         } while (list);
 240
 241         /* End of input; merge together all the pending lists. */
 242         list = pending;
 243         pending = pending->prev;
 244         for (;;) {
 245                 struct list_head *next = pending->prev;
 246
 247                 if (!next)
 248                         break;
 249                 list = merge(priv, (cmp_func)cmp, pending, list);
 250                 pending = next;
 251         }
 252         /* The final merge, rebuilding prev links */
 253         merge_final(priv, (cmp_func)cmp, head, pending, list);
 254 }
 255 EXPORT_SYMBOL(list_sort);