254 lines
8.2 KiB
C
254 lines
8.2 KiB
C
// SPDX-License-Identifier: GPL-2.0
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#include <linux/kernel.h>
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#include <linux/bug.h>
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#include <linux/compiler.h>
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#include <linux/export.h>
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#include <linux/string.h>
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#include <linux/list_sort.h>
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#include <linux/list.h>
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/*
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* Returns a list organized in an intermediate format suited
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* to chaining of merge() calls: null-terminated, no reserved or
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* sentinel head node, "prev" links not maintained.
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*/
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__attribute__((nonnull(2,3,4)))
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static struct list_head *merge(void *priv, list_cmp_func_t cmp,
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struct list_head *a, struct list_head *b)
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{
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struct list_head *head, **tail = &head;
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for (;;) {
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/* if equal, take 'a' -- important for sort stability */
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if (cmp(priv, a, b) <= 0) {
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*tail = a;
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tail = &a->next;
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a = a->next;
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if (!a) {
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*tail = b;
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break;
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}
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} else {
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*tail = b;
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tail = &b->next;
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b = b->next;
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if (!b) {
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*tail = a;
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break;
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}
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}
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}
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return head;
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}
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/*
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* Combine final list merge with restoration of standard doubly-linked
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* list structure. This approach duplicates code from merge(), but
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* runs faster than the tidier alternatives of either a separate final
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* prev-link restoration pass, or maintaining the prev links
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* throughout.
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*/
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__attribute__((nonnull(2,3,4,5)))
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static void merge_final(void *priv, list_cmp_func_t cmp, struct list_head *head,
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struct list_head *a, struct list_head *b)
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{
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struct list_head *tail = head;
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u8 count = 0;
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for (;;) {
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/* if equal, take 'a' -- important for sort stability */
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if (cmp(priv, a, b) <= 0) {
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tail->next = a;
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a->prev = tail;
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tail = a;
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a = a->next;
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if (!a)
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break;
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} else {
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tail->next = b;
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b->prev = tail;
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tail = b;
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b = b->next;
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if (!b) {
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b = a;
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break;
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}
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}
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}
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/* Finish linking remainder of list b on to tail */
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tail->next = b;
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do {
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/*
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* If the merge is highly unbalanced (e.g. the input is
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* already sorted), this loop may run many iterations.
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* Continue callbacks to the client even though no
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* element comparison is needed, so the client's cmp()
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* routine can invoke cond_resched() periodically.
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*/
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if (unlikely(!++count))
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cmp(priv, b, b);
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b->prev = tail;
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tail = b;
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b = b->next;
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} while (b);
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/* And the final links to make a circular doubly-linked list */
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tail->next = head;
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head->prev = tail;
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}
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/**
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* list_sort - sort a list
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* @priv: private data, opaque to list_sort(), passed to @cmp
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* @head: the list to sort
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* @cmp: the elements comparison function
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*
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* The comparison function @cmp must return > 0 if @a should sort after
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* @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
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* sort before @b *or* their original order should be preserved. It is
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* always called with the element that came first in the input in @a,
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* and list_sort is a stable sort, so it is not necessary to distinguish
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* the @a < @b and @a == @b cases.
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*
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* This is compatible with two styles of @cmp function:
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* - The traditional style which returns <0 / =0 / >0, or
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* - Returning a boolean 0/1.
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* The latter offers a chance to save a few cycles in the comparison
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* (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
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*
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* A good way to write a multi-word comparison is::
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*
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* if (a->high != b->high)
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* return a->high > b->high;
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* if (a->middle != b->middle)
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* return a->middle > b->middle;
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* return a->low > b->low;
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*
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*
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* This mergesort is as eager as possible while always performing at least
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* 2:1 balanced merges. Given two pending sublists of size 2^k, they are
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* merged to a size-2^(k+1) list as soon as we have 2^k following elements.
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*
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* Thus, it will avoid cache thrashing as long as 3*2^k elements can
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* fit into the cache. Not quite as good as a fully-eager bottom-up
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* mergesort, but it does use 0.2*n fewer comparisons, so is faster in
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* the common case that everything fits into L1.
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*
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*
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* The merging is controlled by "count", the number of elements in the
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* pending lists. This is beautifully simple code, but rather subtle.
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*
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* Each time we increment "count", we set one bit (bit k) and clear
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* bits k-1 .. 0. Each time this happens (except the very first time
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* for each bit, when count increments to 2^k), we merge two lists of
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* size 2^k into one list of size 2^(k+1).
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*
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* This merge happens exactly when the count reaches an odd multiple of
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* 2^k, which is when we have 2^k elements pending in smaller lists,
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* so it's safe to merge away two lists of size 2^k.
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*
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* After this happens twice, we have created two lists of size 2^(k+1),
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* which will be merged into a list of size 2^(k+2) before we create
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* a third list of size 2^(k+1), so there are never more than two pending.
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*
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* The number of pending lists of size 2^k is determined by the
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* state of bit k of "count" plus two extra pieces of information:
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*
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* - The state of bit k-1 (when k == 0, consider bit -1 always set), and
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* - Whether the higher-order bits are zero or non-zero (i.e.
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* is count >= 2^(k+1)).
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*
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* There are six states we distinguish. "x" represents some arbitrary
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* bits, and "y" represents some arbitrary non-zero bits:
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* 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k
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* 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
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* 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k
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* 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
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* 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k
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* 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
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* (merge and loop back to state 2)
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*
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* We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
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* bit k-1 is set while the more significant bits are non-zero) and
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* merge them away in the 5->2 transition. Note in particular that just
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* before the 5->2 transition, all lower-order bits are 11 (state 3),
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* so there is one list of each smaller size.
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*
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* When we reach the end of the input, we merge all the pending
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* lists, from smallest to largest. If you work through cases 2 to
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* 5 above, you can see that the number of elements we merge with a list
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* of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
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* 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
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*/
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__attribute__((nonnull(2,3)))
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void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
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{
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struct list_head *list = head->next, *pending = NULL;
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size_t count = 0; /* Count of pending */
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if (list == head->prev) /* Zero or one elements */
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return;
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/* Convert to a null-terminated singly-linked list. */
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head->prev->next = NULL;
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/*
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* Data structure invariants:
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* - All lists are singly linked and null-terminated; prev
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* pointers are not maintained.
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* - pending is a prev-linked "list of lists" of sorted
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* sublists awaiting further merging.
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* - Each of the sorted sublists is power-of-two in size.
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* - Sublists are sorted by size and age, smallest & newest at front.
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* - There are zero to two sublists of each size.
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* - A pair of pending sublists are merged as soon as the number
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* of following pending elements equals their size (i.e.
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* each time count reaches an odd multiple of that size).
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* That ensures each later final merge will be at worst 2:1.
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* - Each round consists of:
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* - Merging the two sublists selected by the highest bit
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* which flips when count is incremented, and
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* - Adding an element from the input as a size-1 sublist.
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*/
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do {
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size_t bits;
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struct list_head **tail = &pending;
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/* Find the least-significant clear bit in count */
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for (bits = count; bits & 1; bits >>= 1)
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tail = &(*tail)->prev;
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/* Do the indicated merge */
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if (likely(bits)) {
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struct list_head *a = *tail, *b = a->prev;
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a = merge(priv, cmp, b, a);
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/* Install the merged result in place of the inputs */
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a->prev = b->prev;
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*tail = a;
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}
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/* Move one element from input list to pending */
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list->prev = pending;
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pending = list;
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list = list->next;
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pending->next = NULL;
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count++;
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} while (list);
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/* End of input; merge together all the pending lists. */
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list = pending;
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pending = pending->prev;
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for (;;) {
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struct list_head *next = pending->prev;
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if (!next)
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break;
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list = merge(priv, cmp, pending, list);
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pending = next;
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}
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/* The final merge, rebuilding prev links */
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merge_final(priv, cmp, head, pending, list);
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}
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EXPORT_SYMBOL(list_sort);
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