10  * Returns a list organized in an intermediate format suited
14 __attribute__((nonnull(2,3,4)))
16 				struct list_head *a, struct list_head *b)  in merge()  argument
21 		/* if equal, take 'a' -- important for sort stability */  in merge()
22 		if (cmp(priv, a, b) <= 0) {  in merge()
23 			*tail = a;  in merge()
24 			tail = &a->next;  in merge()
25 			a = a->next;  in merge()
26 			if (!a) {  in merge()
35 				*tail = a;  in merge()
46  * runs faster than the tidier alternatives of either a separate final
50 __attribute__((nonnull(2,3,4,5)))
52 			struct list_head *a, struct list_head *b)  in merge_final()  argument
57 		/* if equal, take 'a' -- important for sort stability */  in merge_final()
58 		if (cmp(priv, a, b) <= 0) {  in merge_final()
59 			tail->next = a;  in merge_final()
60 			a->prev = tail;  in merge_final()
61 			tail = a;  in merge_final()
62 			a = a->next;  in merge_final()
63 			if (!a)  in merge_final()
71 				b = a;  in merge_final()
85 	/* And the final links to make a circular doubly-linked list */  in merge_final()
91  * list_sort - sort a list
96  * The comparison function @cmp must return > 0 if @a should sort after
97  * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
99  * always called with the element that came first in the input in @a,
100  * and list_sort is a stable sort, so it is not necessary to distinguish
101  * the @a < @b and @a == @b cases.
105  * - Returning a boolean 0/1.
106  * The latter offers a chance to save a few cycles in the comparison
109  * A good way to write a multi-word comparison is::
111  *	if (a->high != b->high)
112  *		return a->high > b->high;
113  *	if (a->middle != b->middle)
114  *		return a->middle > b->middle;
115  *	return a->low > b->low;
119  * 2:1 balanced merges.  Given two pending sublists of size 2^k, they are
120  * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
122  * Thus, it will avoid cache thrashing as long as 3*2^k elements can
123  * fit into the cache.  Not quite as good as a fully-eager bottom-up
133  * for each bit, when count increments to 2^k), we merge two lists of
134  * size 2^k into one list of size 2^(k+1).
137  * 2^k, which is when we have 2^k elements pending in smaller lists,
138  * so it's safe to merge away two lists of size 2^k.
140  * After this happens twice, we have created two lists of size 2^(k+1),
141  * which will be merged into a list of size 2^(k+2) before we create
142  * a third list of size 2^(k+1), so there are never more than two pending.
144  * The number of pending lists of size 2^k is determined by the
149  *   is count >= 2^(k+1)).
153  * 0:  00x: 0 pending of size 2^k;           x pending of sizes < 2^k
154  * 1:  01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
155  * 2: x10x: 0 pending of size 2^k; 2^k     + x pending of sizes < 2^k
156  * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
157  * 4: y00x: 1 pending of size 2^k; 2^k     + x pending of sizes < 2^k
158  * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
159  * (merge and loop back to state 2)
161  * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
163  * merge them away in the 5->2 transition.  Note in particular that just
164  * before the 5->2 transition, all lower-order bits are 11 (state 3),
168  * lists, from smallest to largest.  If you work through cases 2 to
169  * 5 above, you can see that the number of elements we merge with a list
170  * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
171  * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
173 __attribute__((nonnull(2,3)))
182 	/* Convert to a null-terminated singly-linked list. */  in list_sort()
189 	 * - pending is a prev-linked "list of lists" of sorted  in list_sort()
194 	 * - A pair of pending sublists are merged as soon as the number  in list_sort()
197 	 *   That ensures each later final merge will be at worst 2:1.  in list_sort()
201 	 *   - Adding an element from the input as a size-1 sublist.  in list_sort()
212 			struct list_head *a = *tail, *b = a->prev;  in list_sort()  local
214 			a = merge(priv, cmp, b, a);  in list_sort()
216 			a->prev = b->prev;  in list_sort()
217 			*tail = a;  in list_sort()