// 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); |