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dn-sort-frag.inc
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dn-sort-frag.inc
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/* (C) 2006 Novell, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
/*
* This code requires a typedef named 'list_node' for the list node. It
* is assumed that the list type is the type of a pointer to a list
* node, and that the node has a field named 'next' that implements to
* the linked list. No additional invariant is maintained (e.g. the
* 'prev' pointer of a doubly-linked list node is _not_ updated). Any
* invariant would require a post-processing pass to fix matters if
* necessary.
*/
typedef list_node *digit;
/*
* The maximum possible depth of the merge tree
* = ceiling (log2 (maximum number of list nodes))
* = ceiling (log2 (maximum possible memory size/size of each list node))
* = number of bits in 'size_t' - floor (log2 (sizeof digit))
* Also, each list in sort_info is at least 2 nodes long: we can reduce the depth by 1
*/
#define FLOOR_LOG2(x) (((x)>=2) + ((x)>=4) + ((x)>=8) + ((x)>=16) + ((x)>=32) + ((x)>=64) + ((x)>=128))
#define MAX_RANKS ((sizeof (size_t) * 8) - FLOOR_LOG2(sizeof (list_node)) - 1)
struct sort_info
{
int32_t min_rank, n_ranks;
compare_func_t func;
/* Invariant: ranks[i] == NULL || length(ranks[i]) >= 2**(i+1) */
list_node *ranks [MAX_RANKS]; /* ~ 128 bytes on 32bit, ~ 512 bytes on 64bit */
};
static inline void
init_sort_info (struct sort_info *si, compare_func_t func)
{
si->min_rank = si->n_ranks = 0;
si->func = func;
/* we don't need to initialize si->ranks, since we never lookup past si->n_ranks. */
}
static inline list_node *
merge_lists (list_node *first, list_node *second, compare_func_t func)
{
/* merge the two lists */
list_node *list = NULL;
list_node **pos = &list;
while (first && second) {
if (func (first->data, second->data) > 0) {
*pos = second;
second = second->next;
} else {
*pos = first;
first = first->next;
}
pos = &((*pos)->next);
}
*pos = first ? first : second;
return list;
}
/* Pre-condition: upto <= si->n_ranks, list == NULL || length(list) == 1 */
static inline list_node *
sweep_up (struct sort_info *si, list_node *list, int32_t upto)
{
#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 406)
/*
* GCC incorrectly thinks we're writing below si->ranks array bounds.
*/
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Warray-bounds"
#endif
int32_t i;
for (i = si->min_rank; i < upto; ++i) {
list = merge_lists (si->ranks [i], list, si->func);
si->ranks [i] = NULL;
}
return list;
#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 406)
#pragma GCC diagnostic pop
#endif
}
/*
* The 'ranks' array essentially captures the recursion stack of a mergesort.
* The merge tree is built in a bottom-up manner. The control loop for
* updating the 'ranks' array is analogous to incrementing a binary integer,
* and the O(n) time for counting upto n translates to O(n) merges when
* inserting rank-0 lists. When we plug in the sizes of the lists involved in
* those merges, we get the O(n log n) time for the sort.
*
* Inserting higher-ranked lists reduce the height of the merge tree, and also
* eliminate a lot of redundant comparisons when merging two lists that would've
* been part of the same run. Adding a rank-i list is analogous to incrementing
* a binary integer by 2**i in one operation, thus sharing a similar speedup.
*
* When inserting higher-ranked lists, we choose to clear out the lower ranks
* in the interests of keeping the sort stable, but this makes analysis harder.
* Note that clearing the lower-ranked lists is O(length(list))-- thus it
* shouldn't affect the O(n log n) behaviour. IOW, inserting one rank-i list
* is equivalent to inserting 2**i rank-0 lists, thus even if we do i additional
* merges in the clearing-out (taking at most 2**i time) we are still fine.
*/
#define stringify2(x) #x
#define stringify(x) stringify2(x)
/* Pre-condition: 2**(rank+1) <= length(list) < 2**(rank+2) (therefore: length(list) >= 2) */
static inline void
insert_list (struct sort_info *si, list_node* list, int32_t rank)
{
#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 406)
/*
* GCC incorrectly thinks we're writing below si->ranks array bounds.
*/
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Warray-bounds"
#endif
int32_t i;
if (rank > si->n_ranks) {
if (rank > (int32_t)MAX_RANKS) {
rank = (int32_t)MAX_RANKS;
}
list = merge_lists (sweep_up (si, NULL, si->n_ranks), list, si->func);
for (i = si->n_ranks; i < rank; ++i)
si->ranks [i] = NULL;
} else {
if (rank)
list = merge_lists (sweep_up (si, NULL, rank), list, si->func);
for (i = rank; i < si->n_ranks && si->ranks [i]; ++i) {
list = merge_lists (si->ranks [i], list, si->func);
si->ranks [i] = NULL;
}
}
if (i == (int32_t)MAX_RANKS) /* Will _never_ happen: so we can just devolve into quadratic ;-) */
--i;
if (i >= si->n_ranks)
si->n_ranks = i + 1;
si->min_rank = i;
si->ranks [i] = list;
#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 406)
#pragma GCC diagnostic pop
#endif
}
#undef stringify2
#undef stringify
#undef MAX_RANKS
#undef FLOOR_LOG2
/* A non-recursive mergesort */
static inline digit
do_sort (list_node* list, compare_func_t func)
{
struct sort_info si;
init_sort_info (&si, func);
while (list && list->next) {
list_node* next = list->next;
list_node* tail = next->next;
if (func (list->data, next->data) > 0) {
next->next = list;
next = list;
list = list->next;
}
next->next = NULL;
insert_list (&si, list, 0);
list = tail;
}
return sweep_up (&si, list, si.n_ranks);
}