1 files changed, 188 insertions, 222 deletions

diff --git a/lib/list_sort.c b/lib/list_sort.c
index 1183fa70a44d..a310ecb7ccc0 100644
--- a/lib/list_sort.c
+++ b/lib/list_sort.c
@@ -1,36 +1,41 @@
-#include <linux/kernel.h>
-#include <linux/module.h>
+// SPDX-License-Identifier: GPL-2.0
+#include <linux/compiler.h>
+#include <linux/export.h>
 #include <linux/list_sort.h>
-#include <linux/slab.h>
 #include <linux/list.h>
 
-#define MAX_LIST_LENGTH_BITS 20
-
 /*
  * 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, list_cmp_func_t 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;
 }
 
 /*
@@ -40,42 +45,52 @@ static struct list_head *merge(void *priv,
  * 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, list_cmp_func_t 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.
 		 */
-		(*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;
 }
@@ -86,206 +101,157 @@ static void merge_and_restore_back_links(void *priv,
  * @head: the list to sort
  * @cmp: the elements comparison function
  *
- * This function implements "merge sort", which has O(nlog(n))
- * complexity.
+ * The comparison function @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.
+ *
+ * The comparison function must adhere to specific mathematical properties
+ * to ensure correct and stable sorting:
+ * - Antisymmetry: cmp(@a, @b) must return the opposite sign of
+ * cmp(@b, @a).
+ * - Transitivity: if cmp(@a, @b) <= 0 and cmp(@b, @c) <= 0, then
+ * cmp(@a, @c) <= 0.
+ *
+ * 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 beautifully 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.
  *
- * 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.
+ * 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).
  */
-void list_sort(void *priv, struct list_head *head,
-		int (*cmp)(void *priv, struct list_head *a,
-			struct list_head *b))
+__attribute__((nonnull(2,3)))
+void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
 {
-	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 passed to"
-					" list_sort() too long for"
-					" efficiency\n");
-				lev--;
-			}
-			max_lev = lev;
-		}
-		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);
-}
-EXPORT_SYMBOL(list_sort);
-
-#ifdef CONFIG_TEST_LIST_SORT
-
-#include <linux/random.h>
-
-/*
- * The pattern of set bits in the list length determines which cases
- * are hit in list_sort().
- */
-#define TEST_LIST_LEN (512+128+2) /* not including head */
-
-#define TEST_POISON1 0xDEADBEEF
-#define TEST_POISON2 0xA324354C
-
-struct debug_el {
-	unsigned int poison1;
-	struct list_head list;
-	unsigned int poison2;
-	int value;
-	unsigned serial;
-};
-
-/* Array, containing pointers to all elements in the test list */
-static struct debug_el **elts __initdata;
-
-static int __init check(struct debug_el *ela, struct debug_el *elb)
-{
-	if (ela->serial >= TEST_LIST_LEN) {
-		printk(KERN_ERR "list_sort_test: error: incorrect serial %d\n",
-				ela->serial);
-		return -EINVAL;
-	}
-	if (elb->serial >= TEST_LIST_LEN) {
-		printk(KERN_ERR "list_sort_test: error: incorrect serial %d\n",
-				elb->serial);
-		return -EINVAL;
-	}
-	if (elts[ela->serial] != ela || elts[elb->serial] != elb) {
-		printk(KERN_ERR "list_sort_test: error: phantom element\n");
-		return -EINVAL;
-	}
-	if (ela->poison1 != TEST_POISON1 || ela->poison2 != TEST_POISON2) {
-		printk(KERN_ERR "list_sort_test: error: bad poison: %#x/%#x\n",
-				ela->poison1, ela->poison2);
-		return -EINVAL;
-	}
-	if (elb->poison1 != TEST_POISON1 || elb->poison2 != TEST_POISON2) {
-		printk(KERN_ERR "list_sort_test: error: bad poison: %#x/%#x\n",
-				elb->poison1, elb->poison2);
-		return -EINVAL;
-	}
-	return 0;
-}
-
-static int __init cmp(void *priv, struct list_head *a, struct list_head *b)
-{
-	struct debug_el *ela, *elb;
-
-	ela = container_of(a, struct debug_el, list);
-	elb = container_of(b, struct debug_el, list);
-
-	check(ela, elb);
-	return ela->value - elb->value;
-}
-
-static int __init list_sort_test(void)
-{
-	int i, count = 1, err = -EINVAL;
-	struct debug_el *el;
-	struct list_head *cur, *tmp;
-	LIST_HEAD(head);
 
-	printk(KERN_DEBUG "list_sort_test: start testing list_sort()\n");
-
-	elts = kmalloc(sizeof(void *) * TEST_LIST_LEN, GFP_KERNEL);
-	if (!elts) {
-		printk(KERN_ERR "list_sort_test: error: cannot allocate "
-				"memory\n");
-		goto exit;
-	}
-
-	for (i = 0; i < TEST_LIST_LEN; i++) {
-		el = kmalloc(sizeof(*el), GFP_KERNEL);
-		if (!el) {
-			printk(KERN_ERR "list_sort_test: error: cannot "
-					"allocate memory\n");
-			goto exit;
-		}
-		 /* force some equivalencies */
-		el->value = prandom_u32() % (TEST_LIST_LEN / 3);
-		el->serial = i;
-		el->poison1 = TEST_POISON1;
-		el->poison2 = TEST_POISON2;
-		elts[i] = el;
-		list_add_tail(&el->list, &head);
-	}
-
-	list_sort(NULL, &head, cmp);
-
-	for (cur = head.next; cur->next != &head; cur = cur->next) {
-		struct debug_el *el1;
-		int cmp_result;
-
-		if (cur->next->prev != cur) {
-			printk(KERN_ERR "list_sort_test: error: list is "
-					"corrupted\n");
-			goto exit;
-		}
-
-		cmp_result = cmp(NULL, cur, cur->next);
-		if (cmp_result > 0) {
-			printk(KERN_ERR "list_sort_test: error: list is not "
-					"sorted\n");
-			goto exit;
-		}
-
-		el = container_of(cur, struct debug_el, list);
-		el1 = container_of(cur->next, struct debug_el, list);
-		if (cmp_result == 0 && el->serial >= el1->serial) {
-			printk(KERN_ERR "list_sort_test: error: order of "
-					"equivalent elements not preserved\n");
-			goto exit;
+	/*
+	 * 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, b, a);
+			/* Install the merged result in place of the inputs */
+			a->prev = b->prev;
+			*tail = a;
 		}
 
-		if (check(el, el1)) {
-			printk(KERN_ERR "list_sort_test: error: element check "
-					"failed\n");
-			goto exit;
-		}
+		/* 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, pending, list);
+		pending = next;
 	}
-
-	if (count != TEST_LIST_LEN) {
-		printk(KERN_ERR "list_sort_test: error: bad list length %d",
-				count);
-		goto exit;
-	}
-
-	err = 0;
-exit:
-	kfree(elts);
-	list_for_each_safe(cur, tmp, &head) {
-		list_del(cur);
-		kfree(container_of(cur, struct debug_el, list));
-	}
-	return err;
+	/* The final merge, rebuilding prev links */
+	merge_final(priv, cmp, head, pending, list);
 }
-module_init(list_sort_test);
-#endif /* CONFIG_TEST_LIST_SORT */
+EXPORT_SYMBOL(list_sort);