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