11  * Returns a list organized in an intermediate format suited
15 __attribute__((nonnull(2,3,4)))
17 				struct list_head *a, struct list_head *b)  in merge()  argument
22 		/* if equal, take 'a' -- important for sort stability */  in merge()
23 		if (cmp(priv, a, b) <= 0) {  in merge()
24 			*tail = a;  in merge()
25 			tail = &a->next;  in merge()
26 			a = a->next;  in merge()
27 			if (!a) {  in merge()
36 				*tail = a;  in merge()
47  * runs faster than the tidier alternatives of either a separate final
51 __attribute__((nonnull(2,3,4,5)))
53 			struct list_head *a, struct list_head *b)  in merge_final()  argument
59 		/* if equal, take 'a' -- important for sort stability */  in merge_final()
60 		if (cmp(priv, a, b) <= 0) {  in merge_final()
61 			tail->next = a;  in merge_final()
62 			a->prev = tail;  in merge_final()
63 			tail = a;  in merge_final()
64 			a = a->next;  in merge_final()
65 			if (!a)  in merge_final()
73 				b = a;  in merge_final()
96 	/* And the final links to make a circular doubly-linked list */  in merge_final()
102  * list_sort - sort a list
107  * The comparison function @cmp must return > 0 if @a should sort after
108  * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
110  * always called with the element that came first in the input in @a,
111  * and list_sort is a stable sort, so it is not necessary to distinguish
112  * the @a < @b and @a == @b cases.
116  * - Returning a boolean 0/1.
117  * The latter offers a chance to save a few cycles in the comparison
120  * A good way to write a multi-word comparison is::
122  *	if (a->high != b->high)
123  *		return a->high > b->high;
124  *	if (a->middle != b->middle)
125  *		return a->middle > b->middle;
126  *	return a->low > b->low;
130  * 2:1 balanced merges.  Given two pending sublists of size 2^k, they are
131  * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
133  * Thus, it will avoid cache thrashing as long as 3*2^k elements can
134  * fit into the cache.  Not quite as good as a fully-eager bottom-up
144  * for each bit, when count increments to 2^k), we merge two lists of
145  * size 2^k into one list of size 2^(k+1).
148  * 2^k, which is when we have 2^k elements pending in smaller lists,
149  * so it's safe to merge away two lists of size 2^k.
151  * After this happens twice, we have created two lists of size 2^(k+1),
152  * which will be merged into a list of size 2^(k+2) before we create
153  * a third list of size 2^(k+1), so there are never more than two pending.
155  * The number of pending lists of size 2^k is determined by the
160  *   is count >= 2^(k+1)).
164  * 0:  00x: 0 pending of size 2^k;           x pending of sizes < 2^k
165  * 1:  01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
166  * 2: x10x: 0 pending of size 2^k; 2^k     + x pending of sizes < 2^k
167  * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
168  * 4: y00x: 1 pending of size 2^k; 2^k     + x pending of sizes < 2^k
169  * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
170  * (merge and loop back to state 2)
172  * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
174  * merge them away in the 5->2 transition.  Note in particular that just
175  * before the 5->2 transition, all lower-order bits are 11 (state 3),
179  * lists, from smallest to largest.  If you work through cases 2 to
180  * 5 above, you can see that the number of elements we merge with a list
181  * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
182  * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
184 __attribute__((nonnull(2,3)))
193 	/* Convert to a null-terminated singly-linked list. */  in list_sort()
200 	 * - pending is a prev-linked "list of lists" of sorted  in list_sort()
205 	 * - A pair of pending sublists are merged as soon as the number  in list_sort()
208 	 *   That ensures each later final merge will be at worst 2:1.  in list_sort()
212 	 *   - Adding an element from the input as a size-1 sublist.  in list_sort()
223 			struct list_head *a = *tail, *b = a->prev;  in list_sort()  local
225 			a = merge(priv, cmp, b, a);  in list_sort()
227 			a->prev = b->prev;  in list_sort()
228 			*tail = a;  in list_sort()