From db946a42226052a13fbce8757ff77b3107dd2030 Mon Sep 17 00:00:00 2001 From: Kuan-Wei Chiu Date: Sat, 13 Jan 2024 11:13:51 +0800 Subject: lib/sort: optimize heapsort for equal elements in sift-down path Patch series "lib/sort: Optimize the number of swaps and comparisons". This patch series aims to optimize the heapsort algorithm, specifically targeting a reduction in the number of swaps and comparisons required. This patch (of 2): Currently, when searching for the sift-down path and encountering equal elements, the algorithm chooses the left child. However, considering that the height of the right subtree may be one less than that of the left subtree, selecting the right child in such cases can potentially reduce the number of comparisons and swaps. For instance, when sorting an array of 10,000 identical elements, the current implementation requires 247,209 comparisons. With this patch, the number of comparisons can be reduced to 227,241. Link: https://lkml.kernel.org/r/20240113031352.2395118-1-visitorckw@gmail.com Link: https://lkml.kernel.org/r/20240113031352.2395118-2-visitorckw@gmail.com Signed-off-by: Kuan-Wei Chiu Signed-off-by: Andrew Morton --- lib/sort.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'lib/sort.c') diff --git a/lib/sort.c b/lib/sort.c index b399bf10d675..fe4efd4a1410 100644 --- a/lib/sort.c +++ b/lib/sort.c @@ -262,7 +262,7 @@ void sort_r(void *base, size_t num, size_t size, * average, 3/4 worst-case.) */ for (b = a; c = 2*b + size, (d = c + size) < n;) - b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d; + b = do_cmp(base + c, base + d, cmp_func, priv) > 0 ? c : d; if (d == n) /* Special case last leaf with no sibling */ b = c; -- cgit v1.2.3 From 0e02ca29a5634dfb90fe1bad9467ee0965a1e170 Mon Sep 17 00:00:00 2001 From: Kuan-Wei Chiu Date: Sat, 13 Jan 2024 11:13:52 +0800 Subject: 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 Cc: Ching-Chun (Jim) Huang Cc: George Spelvin Signed-off-by: Andrew Morton --- lib/sort.c | 18 ++++++++++++++---- 1 file changed, 14 insertions(+), 4 deletions(-) (limited to 'lib/sort.c') diff --git a/lib/sort.c b/lib/sort.c index fe4efd4a1410..a0509088f82a 100644 --- a/lib/sort.c +++ b/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 -- cgit v1.2.3