254 lines
8.2 KiB
C
254 lines
8.2 KiB
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>
|
|
|
|
/*
|
|
* 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, list_cmp_func_t 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, 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;
|
|
|
|
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 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.
|
|
*
|
|
* 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, list_cmp_func_t cmp)
|
|
{
|
|
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);
|