linux-kernel - [PATCH 2/2] min_heap: Optimize number of comparisons in min

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Message-Id: <20231220083224.3712113-3-visitorckw@gmail.com>
Date: Wed, 20 Dec 2023 16:32:24 +0800
From: Kuan-Wei Chiu <visitorckw@...il.com>
To: akpm@...ux-foundation.org
Cc: irogers@...gle.com,
	linux-kernel@...r.kernel.org,
	Kuan-Wei Chiu <visitorckw@...il.com>
Subject: [PATCH 2/2] min_heap: Optimize number of comparisons in min_heapify()

This patch optimizes the min_heapify() function, resulting in a
significant reduction of approximately 50% in the number of comparisons
for large random inputs, while maintaining identical results.

The current implementation performs two comparisons per level to
identify the minimum among three elements. In contrast, the proposed
bottom-up variation uses only one comparison per level to assess two
children until reaching the leaves. Then, it sifts up until the correct
position is determined.

Typically, the process of sifting down proceeds to the leaf level,
resulting in O(1) secondary comparisons instead of log2(n). This
optimization significantly reduces the number of costly indirect
function calls and improves overall performance.

Signed-off-by: Kuan-Wei Chiu <visitorckw@...il.com>
---
 include/linux/min_heap.h | 42 +++++++++++++++++++++-------------------
 1 file changed, 22 insertions(+), 20 deletions(-)

diff --git a/include/linux/min_heap.h b/include/linux/min_heap.h
index 18a581310eb3..d52daf45861b 100644
--- a/include/linux/min_heap.h
+++ b/include/linux/min_heap.h
@@ -35,31 +35,33 @@ static __always_inline
 void min_heapify(struct min_heap *heap, int pos,
 		const struct min_heap_callbacks *func)
 {
-	void *left, *right, *parent, *smallest;
+	void *left, *right;
 	void *data = heap->data;
+	void *root = data + pos * func->elem_size;
+	int i = pos, j;
 
+	/* Find the sift-down path all the way to the leaves. */
 	for (;;) {
-		if (pos * 2 + 1 >= heap->nr)
+		if (i * 2 + 2 >= heap->nr)
 			break;
+		left = data + (i * 2 + 1) * func->elem_size;
+		right = data + (i * 2 + 2) * func->elem_size;
+		i = func->less(left, right) ? i * 2 + 1 : i * 2 + 2;
+	}
 
-		left = data + ((pos * 2 + 1) * func->elem_size);
-		parent = data + (pos * func->elem_size);
-		smallest = parent;
-		if (func->less(left, smallest))
-			smallest = left;
-
-		if (pos * 2 + 2 < heap->nr) {
-			right = data + ((pos * 2 + 2) * func->elem_size);
-			if (func->less(right, smallest))
-				smallest = right;
-		}
-		if (smallest == parent)
-			break;
-		func->swp(smallest, parent);
-		if (smallest == left)
-			pos = (pos * 2) + 1;
-		else
-			pos = (pos * 2) + 2;
+	/* Special case for the last leaf with no sibling. */
+	if (i * 2 + 2 == heap->nr)
+		i = i * 2 + 1;
+
+	/* Backtrack to the correct location. */
+	while (i != pos && func->less(root, data + i * func->elem_size))
+		i = (i - 1) / 2;
+
+	/* Shift the element into its correct place. */
+	j = i;
+	while (i != pos) {
+		i = (i - 1) / 2;
+		func->swp(data + i * func->elem_size, data + j * func->elem_size);
 	}
 }
 
-- 
2.25.1