lib/sort: optimize heapsort with double-pop variation

Instead of popping only the maximum element from the heap during each
iteration, we now pop the two largest elements at once.  Although this
introduces an additional comparison to determine the second largest
element, it enables a reduction in the height of the tree by one during
the heapify operations starting from root's left/right child.  This
reduction in tree height by one leads to a decrease of one comparison and
one swap.

This optimization results in saving approximately 0.5 * n swaps without
increasing the number of comparisons.  Additionally, the heap size during
heapify is now one less than the original size, offering a chance for
further reduction in comparisons and swaps.

The following experimental data is based on the array generated using
get_random_u32().

| N     | swaps (old) | swaps (new) | comparisons (old) | comparisons (new) |
|-------|-------------|-------------|-------------------|-------------------|
| 1000  | 9054        | 8569        | 10328             | 10320             |
| 2000  | 20137       | 19182       | 22634             | 22587             |
| 3000  | 32062       | 30623       | 35833             | 35752             |
| 4000  | 44274       | 42282       | 49332             | 49306             |
| 5000  | 57195       | 54676       | 63300             | 63294             |
| 6000  | 70205       | 67202       | 77599             | 77557             |
| 7000  | 83276       | 79831       | 92113             | 92032             |
| 8000  | 96630       | 92678       | 106635            | 106617            |
| 9000  | 110349      | 105883      | 121505            | 121404            |
| 10000 | 124165      | 119202      | 136628            | 136617            |


Link: https://lkml.kernel.org/r/20240113031352.2395118-3-visitorckw@gmail.com
Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com>
Cc: Ching-Chun (Jim) Huang <jserv@ccns.ncku.edu.tw>
Cc: George Spelvin <lkml@sdf.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>

lib/sort.c

@@ -215,6 +215,7 @@ void sort_r(void *base, size_t num, size_t size,
 	/* pre-scale counters for performance */
 	size_t n = num * size, a = (num/2) * size;
 	const unsigned int lsbit = size & -size;  /* Used to find parent */
+	size_t shift = 0;
 
 	if (!a)		/* num < 2 || size == 0 */
 		return;
@@ -242,12 +243,21 @@ void sort_r(void *base, size_t num, size_t size,
 	for (;;) {
 		size_t b, c, d;
 
-		if (a)			/* Building heap: sift down --a */
-			a -= size;
-		else if (n -= size)	/* Sorting: Extract root to --n */
+		if (a)			/* Building heap: sift down a */
+			a -= size << shift;
+		else if (n > 3 * size) { /* Sorting: Extract two largest elements */
+			n -= size;
 			do_swap(base, base + n, size, swap_func, priv);
-		else			/* Sort complete */
+			shift = do_cmp(base + size, base + 2 * size, cmp_func, priv) <= 0;
+			a = size << shift;
+			n -= size;
+			do_swap(base + a, base + n, size, swap_func, priv);
+		} else if (n > size) {	/* Sorting: Extract root */
+			n -= size;
+			do_swap(base, base + n, size, swap_func, priv);
+		} else	{		/* Sort complete */
 			break;
+		}
 
 		/*
 		 * Sift element at "a" down into heap.  This is the