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253 lines
8.2 KiB
253 lines
8.2 KiB
// 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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