// 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>

  typedef int __attribute__((nonnull(2,3))) (*cmp_func)(void *,

  		struct list_head *, struct list_head *);

  
  /*
   * 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, cmp_func 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, cmp_func 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 beautiully 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,

  		int (*cmp)(void *priv, struct list_head *a,
  			struct list_head *b))

  {

  	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);