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- // 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 *, struct list_head *);
- /*
- * 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
- *
- * 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.
- *
- * 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 *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.
- * - 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;
- }
- /* 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;
- }
- /* The final merge, rebuilding prev links */
- merge_final(priv, cmp, head, pending, list);
- }
- EXPORT_SYMBOL(list_sort);
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