* 'prev' pointer of a doubly-linked list node is _not_ updated). Any
* invariant would require a post-processing pass to fix matters if
* necessary.
- *
- * Note: We refer to a list fragment as a "digit" because the code for
- * maintaining the invariants of the core data structure parallels the
- * code for incrementing the binary representation of a number.
*/
typedef list_node *digit;
* = 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 "digit" is at least 2 nodes long: we can reduce the depth by 1
+ * 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_DIGITS ((sizeof (size_t) * 8) - FLOOR_LOG2(sizeof (list_node)) - 1)
+#define MAX_RANKS ((sizeof (size_t) * 8) - FLOOR_LOG2(sizeof (list_node)) - 1)
-static inline digit
-add_digits (digit first, digit second, GCompareFunc func)
+struct sort_info
+{
+ int min_rank, n_ranks;
+ GCompareFunc 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, GCompareFunc 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, GCompareFunc func)
{
/* merge the two lists */
- digit list = NULL;
- digit *pos = &list;
+ list_node *list = NULL;
+ list_node **pos = &list;
while (first && second) {
if (func (first->data, second->data) > 0) {
*pos = second;
return list;
}
-static inline digit
-combine_digits (digit *digits, digit list, int n_digits, GCompareFunc func)
+/* Pre-condition: upto <= si->n_ranks, list == NULL || length(list) == 1 */
+static inline list_node *
+sweep_up (struct sort_info *si, list_node *list, int 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
+
int i;
- for (i = 0; i < n_digits; ++i)
- list = add_digits (digits [i], list, func);
+ 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
}
/*
- * Given: length(list) == k
- * Invariant: digit[i] == NULL || length(digit[i]) == k * 2**i
+ * 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.
*/
-static inline int
-increment (digit *digits, digit list, int n_digits, GCompareFunc func)
+
+#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, int 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
+
int i;
- for (i = 0; i < n_digits && digits [i]; i++) {
- list = add_digits (digits [i], list, func);
- digits [i] = NULL;
+
+ if (rank > si->n_ranks) {
+ if (rank > MAX_RANKS) {
+ g_warning ("Rank '%d' should not exceed " stringify (MAX_RANKS), rank);
+ rank = 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 == MAX_DIGITS) /* Will _never_ happen: so we can just devolve into quadratic ;-) */
+
+ if (i == 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 (i == n_digits)
- ++n_digits;
- digits [i] = list;
- return n_digits;
+#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 406)
+#pragma GCC diagnostic pop
+#endif
}
-/*
- * A mergesort that avoids recursion. The 'digits' array essentially
- * captures the recursion stack. The actual merge tree is built in a
- * bottom-up manner. It's "counting", since we "increment" a set of
- * "digit"s.
- */
+#undef stringify2
+#undef stringify
+#undef MAX_RANKS
+#undef FLOOR_LOG2
+
+/* A non-recursive mergesort */
static inline digit
-do_sort (digit list, GCompareFunc func)
+do_sort (list_node* list, GCompareFunc func)
{
- int n_digits = 0;
- digit digits [MAX_DIGITS]; /* ~ 128 bytes on 32bit, ~ 512 bytes on 64bit */
+ struct sort_info si;
+
+ init_sort_info (&si, func);
while (list && list->next) {
- digit next = list->next;
- digit tail = next->next;
+ list_node* next = list->next;
+ list_node* tail = next->next;
if (func (list->data, next->data) > 0) {
next->next = list;
}
next->next = NULL;
- n_digits = increment (digits, list, n_digits, func);
+ insert_list (&si, list, 0);
list = tail;
}
- return combine_digits (digits, list, n_digits, func);
+ return sweep_up (&si, list, si.n_ranks);
}
-
-#undef MAX_DIGITS
-#undef FLOOR_LOG2
projects / mono.git / blobdiff