// SPDX-License-Identifier: GPL-2.0 #include <linux/compiler.h> #include <linux/export.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. * * The comparison function must adhere to specific mathematical properties * to ensure correct and stable sorting: * - Antisymmetry: cmp(@a, @b) must return the opposite sign of * cmp(@b, @a). * - Transitivity: if cmp(@a, @b) <= 0 and cmp(@b, @c) <= 0, then * cmp(@a, @c) <= 0. * * 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);
