#include <linux/list_sort.h>
#include <linux/list.h>
-#define MAX_LIST_LENGTH_BITS 20
+typedef int __attribute__((nonnull(2,3))) (*cmp_func)(void *,
+ struct list_head const *, struct list_head const *);
/*
* Returns a list organized in an intermediate format suited
* to chaining of merge() calls: null-terminated, no reserved or
* sentinel head node, "prev" links not maintained.
*/
-static struct list_head *merge(void *priv,
- int (*cmp)(void *priv, struct list_head *a,
- struct list_head *b),
+__attribute__((nonnull(2,3,4)))
+static struct list_head *merge(void *priv, cmp_func cmp,
struct list_head *a, struct list_head *b)
{
- struct list_head head, *tail = &head;
+ struct list_head *head, **tail = &head;
- while (a && b) {
+ for (;;) {
/* if equal, take 'a' -- important for sort stability */
- if ((*cmp)(priv, a, b) <= 0) {
- tail->next = a;
+ if (cmp(priv, a, b) <= 0) {
+ *tail = a;
+ tail = &a->next;
a = a->next;
+ if (!a) {
+ *tail = b;
+ break;
+ }
} else {
- tail->next = b;
+ *tail = b;
+ tail = &b->next;
b = b->next;
+ if (!b) {
+ *tail = a;
+ break;
+ }
}
- tail = tail->next;
}
- tail->next = a?:b;
- return head.next;
+ return head;
}
/*
* prev-link restoration pass, or maintaining the prev links
* throughout.
*/
-static void merge_and_restore_back_links(void *priv,
- int (*cmp)(void *priv, struct list_head *a,
- struct list_head *b),
- struct list_head *head,
- struct list_head *a, struct list_head *b)
+__attribute__((nonnull(2,3,4,5)))
+static void merge_final(void *priv, cmp_func cmp, struct list_head *head,
+ struct list_head *a, struct list_head *b)
{
struct list_head *tail = head;
u8 count = 0;
- while (a && b) {
+ for (;;) {
/* if equal, take 'a' -- important for sort stability */
- if ((*cmp)(priv, a, b) <= 0) {
+ if (cmp(priv, a, b) <= 0) {
tail->next = a;
a->prev = tail;
+ tail = a;
a = a->next;
+ if (!a)
+ break;
} else {
tail->next = b;
b->prev = tail;
+ tail = b;
b = b->next;
+ if (!b) {
+ b = a;
+ break;
+ }
}
- tail = tail->next;
}
- tail->next = a ? : b;
+ /* Finish linking remainder of list b on to tail */
+ tail->next = b;
do {
/*
- * In worst cases this loop may run many iterations.
+ * If the merge is highly unbalanced (e.g. the input is
+ * already sorted), this loop may run many iterations.
* Continue callbacks to the client even though no
* element comparison is needed, so the client's cmp()
* routine can invoke cond_resched() periodically.
*/
- if (unlikely(!(++count)))
- (*cmp)(priv, tail->next, tail->next);
-
- tail->next->prev = tail;
- tail = tail->next;
- } while (tail->next);
-
+ if (unlikely(!++count))
+ cmp(priv, b, b);
+ b->prev = tail;
+ tail = b;
+ b = b->next;
+ } while (b);
+
+ /* And the final links to make a circular doubly-linked list */
tail->next = head;
head->prev = tail;
}
* @head: the list to sort
* @cmp: the elements comparison function
*
- * This function implements "merge sort", which has O(nlog(n))
- * complexity.
+ * 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
+ * always called with the element that came first in the input in @a,
+ * and list_sort is a stable sort, so it is not necessary to distinguish
+ * the @a < @b and @a == @b cases.
+ *
+ * This is compatible with two styles of @cmp function:
+ * - The traditional style which returns <0 / =0 / >0, or
+ * - Returning a boolean 0/1.
+ * The latter offers a chance to save a few cycles in the comparison
+ * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
+ *
+ * A good way to write a multi-word comparison is
+ * if (a->high != b->high)
+ * return a->high > b->high;
+ * 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.
*
- * The comparison function @cmp must return a negative value if @a
- * should sort before @b, and a positive value if @a should sort after
- * @b. If @a and @b are equivalent, and their original relative
- * ordering is to be preserved, @cmp must return 0.
+ * 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,
int (*cmp)(void *priv, struct list_head *a,
struct list_head *b))
{
- struct list_head *part[MAX_LIST_LENGTH_BITS+1]; /* sorted partial lists
- -- last slot is a sentinel */
- int lev; /* index into part[] */
- int max_lev = 0;
- struct list_head *list;
+ struct list_head *list = head->next, *pending = NULL;
+ size_t count = 0; /* Count of pending */
- if (list_empty(head))
+ if (list == head->prev) /* Zero or one elements */
return;
- memset(part, 0, sizeof(part));
-
+ /* Convert to a null-terminated singly-linked list. */
head->prev->next = NULL;
- list = head->next;
-
- while (list) {
- struct list_head *cur = list;
- list = list->next;
- cur->next = NULL;
- for (lev = 0; part[lev]; lev++) {
- cur = merge(priv, cmp, part[lev], cur);
- part[lev] = NULL;
- }
- if (lev > max_lev) {
- if (unlikely(lev >= ARRAY_SIZE(part)-1)) {
- printk_once(KERN_DEBUG "list too long for efficiency\n");
- lev--;
- }
- max_lev = lev;
+ /*
+ * Data structure invariants:
+ * - All lists are singly linked and null-terminated; prev
+ * 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.
+ * - 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 **tail = &pending;
+
+ /* 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;
+
+ a = merge(priv, (cmp_func)cmp, b, a);
+ /* Install the merged result in place of the inputs */
+ a->prev = b->prev;
+ *tail = a;
}
- part[lev] = cur;
- }
- for (lev = 0; lev < max_lev; lev++)
- if (part[lev])
- list = merge(priv, cmp, part[lev], list);
-
- merge_and_restore_back_links(priv, cmp, head, part[max_lev], list);
+ /* Move one element from input list to pending */
+ list->prev = pending;
+ pending = list;
+ list = list->next;
+ pending->next = NULL;
+ count++;
+ } while (list);
+
+ /* End of input; merge together all the pending lists. */
+ list = pending;
+ pending = pending->prev;
+ for (;;) {
+ struct list_head *next = pending->prev;
+
+ if (!next)
+ break;
+ list = merge(priv, (cmp_func)cmp, pending, list);
+ pending = next;
+ }
+ /* The final merge, rebuilding prev links */
+ merge_final(priv, (cmp_func)cmp, head, pending, list);
}
EXPORT_SYMBOL(list_sort);
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