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-rw-r--r--lib/list_sort.c113
1 files changed, 91 insertions, 22 deletions
diff --git a/lib/list_sort.c b/lib/list_sort.c
index ba9431bcac0b..06e900c5587b 100644
--- a/lib/list_sort.c
+++ b/lib/list_sort.c
@@ -107,11 +107,6 @@ static void merge_final(void *priv, cmp_func cmp, struct list_head *head,
* @head: the list to sort
* @cmp: the elements comparison function
*
- * This function implements a bottom-up merge sort, which has O(nlog(n))
- * complexity. We use depth-first order to take advantage of cacheing.
- * (E.g. when we get to the fourth element, we immediately merge the
- * first two 2-element lists.)
- *
* The comparison funtion @cmp must return > 0 if @a should sort after
* @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
* sort before @b *or* their original order should be preserved. It is
@@ -131,6 +126,60 @@ static void merge_final(void *priv, cmp_func cmp, struct list_head *head,
* if (a->middle != b->middle)
* return a->middle > b->middle;
* return a->low > b->low;
+ *
+ *
+ * This mergesort is as eager as possible while always performing at least
+ * 2:1 balanced merges. Given two pending sublists of size 2^k, they are
+ * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
+ *
+ * Thus, it will avoid cache thrashing as long as 3*2^k elements can
+ * fit into the cache. Not quite as good as a fully-eager bottom-up
+ * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
+ * the common case that everything fits into L1.
+ *
+ *
+ * The merging is controlled by "count", the number of elements in the
+ * pending lists. This is beautiully simple code, but rather subtle.
+ *
+ * Each time we increment "count", we set one bit (bit k) and clear
+ * bits k-1 .. 0. Each time this happens (except the very first time
+ * for each bit, when count increments to 2^k), we merge two lists of
+ * size 2^k into one list of size 2^(k+1).
+ *
+ * This merge happens exactly when the count reaches an odd multiple of
+ * 2^k, which is when we have 2^k elements pending in smaller lists,
+ * so it's safe to merge away two lists of size 2^k.
+ *
+ * After this happens twice, we have created two lists of size 2^(k+1),
+ * which will be merged into a list of size 2^(k+2) before we create
+ * a third list of size 2^(k+1), so there are never more than two pending.
+ *
+ * The number of pending lists of size 2^k is determined by the
+ * state of bit k of "count" plus two extra pieces of information:
+ * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
+ * - Whether the higher-order bits are zero or non-zero (i.e.
+ * is count >= 2^(k+1)).
+ * There are six states we distinguish. "x" represents some arbitrary
+ * bits, and "y" represents some arbitrary non-zero bits:
+ * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k
+ * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
+ * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k
+ * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
+ * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k
+ * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
+ * (merge and loop back to state 2)
+ *
+ * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
+ * bit k-1 is set while the more significant bits are non-zero) and
+ * merge them away in the 5->2 transition. Note in particular that just
+ * before the 5->2 transition, all lower-order bits are 11 (state 3),
+ * so there is one list of each smaller size.
+ *
+ * When we reach the end of the input, we merge all the pending
+ * lists, from smallest to largest. If you work through cases 2 to
+ * 5 above, you can see that the number of elements we merge with a list
+ * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
+ * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
*/
__attribute__((nonnull(2,3)))
void list_sort(void *priv, struct list_head *head,
@@ -152,33 +201,53 @@ void list_sort(void *priv, struct list_head *head,
* pointers are not maintained.
* - pending is a prev-linked "list of lists" of sorted
* sublists awaiting further merging.
- * - Each of the sorted sublists is power-of-two in size,
- * corresponding to bits set in "count".
+ * - Each of the sorted sublists is power-of-two in size.
* - Sublists are sorted by size and age, smallest & newest at front.
+ * - There are zero to two sublists of each size.
+ * - A pair of pending sublists are merged as soon as the number
+ * of following pending elements equals their size (i.e.
+ * each time count reaches an odd multiple of that size).
+ * That ensures each later final merge will be at worst 2:1.
+ * - Each round consists of:
+ * - Merging the two sublists selected by the highest bit
+ * which flips when count is incremented, and
+ * - Adding an element from the input as a size-1 sublist.
*/
do {
size_t bits;
- struct list_head *cur = list;
+ struct list_head **tail = &pending;
- /* Extract the head of "list" as a single-element list "cur" */
- list = list->next;
- cur->next = NULL;
+ /* Find the least-significant clear bit in count */
+ for (bits = count; bits & 1; bits >>= 1)
+ tail = &(*tail)->prev;
+ /* Do the indicated merge */
+ if (likely(bits)) {
+ struct list_head *a = *tail, *b = a->prev;
- /* Do merges corresponding to set lsbits in count */
- for (bits = count; bits & 1; bits >>= 1) {
- cur = merge(priv, (cmp_func)cmp, pending, cur);
- pending = pending->prev; /* Untouched by merge() */
+ a = merge(priv, (cmp_func)cmp, b, a);
+ /* Install the merged result in place of the inputs */
+ a->prev = b->prev;
+ *tail = a;
}
- /* And place the result at the head of "pending" */
- cur->prev = pending;
- pending = cur;
+
+ /* Move one element from input list to pending */
+ list->prev = pending;
+ pending = list;
+ list = list->next;
+ pending->next = NULL;
count++;
- } while (list->next);
+ } while (list);
+
+ /* End of input; merge together all the pending lists. */
+ list = pending;
+ pending = pending->prev;
+ for (;;) {
+ struct list_head *next = pending->prev;
- /* Now merge together last element with all pending lists */
- while (pending->prev) {
+ if (!next)
+ break;
list = merge(priv, (cmp_func)cmp, pending, list);
- pending = pending->prev;
+ pending = next;
}
/* The final merge, rebuilding prev links */
merge_final(priv, (cmp_func)cmp, head, pending, list);