// 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 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.
*
* 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);
