[v2,1/2] stdlib: Optimize number of calls to comparison function in qsort
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Commit Message
The current heapsort implementation in the siftdown function follows
the standard textbook version, necessitating two comparisons at each
level. Transitioning to the Bottom-up heapsort version allows us to
decrease the required comparisons to just one per level. On average,
this modification significantly reduces the comparison count from
2nlog2(n) - 3n + O(n) to nlog2(n) + 0.37*n + O(n).
Refs:
BOTTOM-UP-HEAPSORT, a new variant of HEAPSORT beating, on an average,
QUICKSORT (if n is not very small)
Ingo Wegener
Theoretical Computer Science, 118(1); Pages 81-98, 13 September 1993
https://doi.org/10.1016/0304-3975(93)90364-Y
Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com>
---
Changes from v1:
* Use a more concise title.
* Correct the error in asymptotic notation from little-o to big-O.
stdlib/qsort.c | 36 ++++++++++++++++++------------------
1 file changed, 18 insertions(+), 18 deletions(-)
@@ -132,26 +132,26 @@ static inline void
siftdown (void *base, size_t size, size_t k, size_t n,
enum swap_type_t swap_type, __compar_d_fn_t cmp, void *arg)
{
- /* There can only be a heap condition violation if there are
- children. */
- while (2 * k + 1 <= n)
- {
- /* Left child. */
- size_t j = 2 * k + 1;
- /* If the right child is larger, use it. */
- if (j < n && cmp (base + (j * size), base + ((j + 1) * size), arg) < 0)
- j++;
-
- /* If k is already >= to its children, we are done. */
- if (j == k || cmp (base + (k * size), base + (j * size), arg) >= 0)
- break;
+ size_t i, j;
+
+ /* Find the sift-down path all the way to the leaves. */
+ for (i = k; j = 2 * i + 1, j + 1 <= n;)
+ i = cmp (base + j * size, base + (j + 1) * size, arg) >= 0 ? j : (j + 1);
- /* Heal the violation. */
- do_swap (base + (size * j), base + (k * size), size, swap_type);
+ /* Special case for the last leaf with no sibling. */
+ if (j == n)
+ i = j;
- /* Swapping with j may have introduced a violation at j. Fix
- it in the next loop iteration. */
- k = j;
+ /* Backtrack to the correct location. */
+ while (i != k && cmp (base + k * size, base + i * size, arg) > 0)
+ i = (i - 1) / 2;
+
+ /* Shift the element into its correct place. */
+ j = i;
+ while (i != k)
+ {
+ i = (i - 1) / 2;
+ do_swap (base + i * size, base + j * size, size, swap_type);
}
}