From 0e02ca29a5634dfb90fe1bad9467ee0965a1e170 Mon Sep 17 00:00:00 2001 From: Kuan-Wei Chiu Date: Sat, 13 Jan 2024 11:13:52 +0800 Subject: [PATCH] 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(-) 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