linux/lib/list_sort.c

// SPDX-License-Identifier: GPL-2.0
#include <linux/kernel.h>
#include <linux/bug.h>
#include <linux/compiler.h>
#include <linux/export.h>
#include <linux/string.h>
#include <linux/list_sort.h>
#include <linux/list.h>

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.
 */
__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;

	for (;;) {
		/* if equal, take 'a' -- important for sort stability */
		if (cmp(priv, a, b) <= 0) {
			*tail = a;
			tail = &a->next;
			a = a->next;
			if (!a) {
				*tail = b;
				break;
			}
		} else {
			*tail = b;
			tail = &b->next;
			b = b->next;
			if (!b) {
				*tail = a;
				break;
			}
		}
	}
	return head;
}

/*
 * Combine final list merge with restoration of standard doubly-linked
 * list structure.  This approach duplicates code from merge(), but
 * runs faster than the tidier alternatives of either a separate final
 * prev-link restoration pass, or maintaining the prev links
 * throughout.
 */
__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;

	for (;;) {
		/* if equal, take 'a' -- important for sort stability */
		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;
			}
		}
	}

	/* Finish linking remainder of list b on to tail */
	tail->next = b;
	do {
		/*
		 * 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, 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;
}

/**
 * list_sort - sort a list
 * @priv: private data, opaque to list_sort(), passed to @cmp
 * @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
 * 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;
 */
__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 *list = head->next, *pending = NULL;
	size_t count = 0;	/* Count of pending */

	if (list == head->prev)	/* Zero or one elements */
		return;

	/* Convert to a null-terminated singly-linked list. */
	head->prev->next = NULL;

	/*
	 * 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,
	 *   corresponding to bits set in "count".
	 * - Sublists are sorted by size and age, smallest & newest at front.
	 */
	do {
		size_t bits;
		struct list_head *cur = list;

		/* Extract the head of "list" as a single-element list "cur" */
		list = list->next;
		cur->next = NULL;

		/* 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() */
		}
		/* And place the result at the head of "pending" */
		cur->prev = pending;
		pending = cur;
		count++;
	} while (list->next);

	/* Now merge together last element with all pending lists */
	while (pending->prev) {
		list = merge(priv, (cmp_func)cmp, pending, list);
		pending = pending->prev;
	}
	/* The final merge, rebuilding prev links */
	merge_final(priv, (cmp_func)cmp, head, pending, list);
}
EXPORT_SYMBOL(list_sort);