From 4fec3a816193ff28fbbe37836e3282330206d453 Mon Sep 17 00:00:00 2001 From: ed Date: Tue, 22 Dec 2015 18:12:11 +0000 Subject: Let tsearch()/tdelete() use an AVL tree. The existing implementations of POSIX tsearch() and tdelete() don't attempt to perform any balancing at all. Testing reveals that inserting 100k nodes into a tree sequentially takes approximately one minute on my system. Though most other BSDs also don't use any balanced tree internally, C libraries like glibc and musl do provide better implementations. glibc uses a red-black tree and musl uses an AVL tree. Red-black trees have the advantage over AVL trees that they only require O(1) rotations after insertion and deletion, but have the disadvantage that the tree has a maximum depth of 2*log2(n) instead of 1.44*log2(n). My take is that it's better to focus on having a lower maximum depth, for the reason that in the case of tsearch() the invocation of the comparator likely dominates the running time. This change replaces the tsearch() and tdelete() functions by versions that create an AVL tree. Compared to musl's implementation, this version is different in two different ways: - We don't keep track of heights; just balances. This is sufficient. This has the advantage that it reduces the number of nodes that are being accessed. Storing heights requires us to also access all of the siblings along the path. - Don't use any recursion at all. We know that the tree cannot 2^64 elements in size, so the height of the tree can never be larger than 96. Use a 128-bit bitmask to keep track of the path that is computed. This allows us to iterate over the same path twice, meaning we can apply rotations from top to bottom. Inserting 100k nodes into a tree now only takes 0.015 seconds. Insertion seems to be twice as fast as glibc, whereas deletion has about the same performance. Unlike glibc, it uses a fixed amount of memory. I also experimented with both recursive and iterative bottom-up implementations of the same algorithm. This iterative top-down version performs similar to the recursive bottom-up version in terms of speed and code size. For some reason, the iterative bottom-up algorithm was actually 30% faster for deletion, but has a quadratic memory complexity to keep track of all the parent pointers. Reviewed by: jilles Obtained from: https://github.com/NuxiNL/cloudlibc Differential Revision: https://reviews.freebsd.org/D4412 --- lib/libc/stdlib/tdelete.c | 241 ++++++++++++++++++++++++++++++++++++---------- 1 file changed, 191 insertions(+), 50 deletions(-) (limited to 'lib/libc/stdlib/tdelete.c') diff --git a/lib/libc/stdlib/tdelete.c b/lib/libc/stdlib/tdelete.c index bef187e..7799f35 100644 --- a/lib/libc/stdlib/tdelete.c +++ b/lib/libc/stdlib/tdelete.c @@ -1,72 +1,213 @@ -/* $NetBSD: tdelete.c,v 1.2 1999/09/16 11:45:37 lukem Exp $ */ - -/* - * Tree search generalized from Knuth (6.2.2) Algorithm T just like - * the AT&T man page says. +/*- + * Copyright (c) 2015 Nuxi, https://nuxi.nl/ * - * The node_t structure is for internal use only, lint doesn't grok it. + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. * - * Written by reading the System V Interface Definition, not the code. - * - * Totally public domain. + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. */ #include -#if 0 -#if defined(LIBC_SCCS) && !defined(lint) -__RCSID("$NetBSD: tdelete.c,v 1.6 2012/06/25 22:32:45 abs Exp $"); -#endif /* LIBC_SCCS and not lint */ -#endif __FBSDID("$FreeBSD$"); -#define _SEARCH_PRIVATE +#define _SEARCH_PRIVATE #include +#include #include +#include "tsearch_path.h" /* - * find a node with given key - * - * vkey: key to be found - * vrootp: address of the root of the tree - * compar: function to carry out node comparisons - */ + * Makes a step to the left along the binary search tree. This step is + * also saved, so it can be replayed while rebalancing. +*/ +#define GO_LEFT() do { \ + if ((*leaf)->balance == 0 || \ + ((*leaf)->balance < 0 && (*leaf)->rlink->balance == 0)) { \ + /* \ + * If we reach a node that is balanced, or has a child \ + * in the opposite direction that is balanced, we know \ + * that we won't need to perform any rotations above \ + * this point. In this case rotations are always \ + * capable of keeping the subtree in balance. Make \ + * this the base node and reset the path. \ + */ \ + base = leaf; \ + path_init(&path); \ + } \ + path_taking_left(&path); \ + leaf = &(*leaf)->llink; \ +} while (0) + +/* Makes a step to the right along the binary search tree. */ +#define GO_RIGHT() do { \ + if ((*leaf)->balance == 0 || \ + ((*leaf)->balance > 0 && (*leaf)->llink->balance == 0)) { \ + base = leaf; \ + path_init(&path); \ + } \ + result = &(*leaf)->key; \ + path_taking_right(&path); \ + leaf = &(*leaf)->rlink; \ +} while (0) + void * -tdelete(const void * __restrict vkey, void ** __restrict vrootp, +tdelete(const void *restrict key, void **restrict rootp, int (*compar)(const void *, const void *)) { - node_t **rootp = (node_t **)vrootp; - node_t *p, *q, *r; + struct path path; + node_t *root, **base, **leaf, *old, **n, *x, *y, *z; + void *result; int cmp; - if (rootp == NULL || (p = *rootp) == NULL) - return NULL; + /* POSIX requires that tdelete() returns NULL if rootp is NULL. */ + if (rootp == NULL) + return (NULL); + root = *rootp; + + /* + * Find the leaf that needs to be removed. Return if we cannot + * find an existing entry. Keep track of the path that is taken + * to get to the node, as we will need it to adjust the + * balances. + */ + result = (void *)1; + path_init(&path); + base = &root; + leaf = &root; + for (;;) { + if (*leaf == NULL) + return (NULL); + cmp = compar(key, (*leaf)->key); + if (cmp < 0) { + result = &(*leaf)->key; + GO_LEFT(); + } else if (cmp > 0) { + result = &(*leaf)->key; + GO_RIGHT(); + } else { + break; + } + } - while ((cmp = (*compar)(vkey, (*rootp)->key)) != 0) { - p = *rootp; - rootp = (cmp < 0) ? - &(*rootp)->llink : /* follow llink branch */ - &(*rootp)->rlink; /* follow rlink branch */ - if (*rootp == NULL) - return NULL; /* key not found */ + /* Found a matching key in the tree. Remove the node. */ + if ((*leaf)->llink == NULL) { + /* Node has no left children. Replace by its right subtree. */ + old = *leaf; + *leaf = old->rlink; + free(old); + } else { + /* + * Node has left children. Replace this node's key by + * its predecessor's and remove that node instead. + */ + void **keyp = &(*leaf)->key; + GO_LEFT(); + while ((*leaf)->rlink != NULL) + GO_RIGHT(); + old = *leaf; + *keyp = old->key; + *leaf = old->llink; + free(old); } - r = (*rootp)->rlink; /* D1: */ - if ((q = (*rootp)->llink) == NULL) /* Left NULL? */ - q = r; - else if (r != NULL) { /* Right link is NULL? */ - if (r->llink == NULL) { /* D2: Find successor */ - r->llink = q; - q = r; - } else { /* D3: Find NULL link */ - for (q = r->llink; q->llink != NULL; q = r->llink) - r = q; - r->llink = q->rlink; - q->llink = (*rootp)->llink; - q->rlink = (*rootp)->rlink; + + /* + * Walk along the same path a second time and adjust the + * balances. Though this code looks similar to the rebalancing + * performed in tsearch(), it is not identical. We now also need + * to consider the case of outward imbalance in the right-right + * and left-left case that only exists when deleting. Hence the + * duplication of code. + */ + for (n = base; n != leaf;) { + if (path_took_left(&path)) { + x = *n; + if (x->balance < 0) { + y = x->rlink; + if (y->balance > 0) { + /* Right-left case. */ + z = y->llink; + x->rlink = z->llink; + z->llink = x; + y->llink = z->rlink; + z->rlink = y; + *n = z; + + x->balance = z->balance < 0 ? 1 : 0; + y->balance = z->balance > 0 ? -1 : 0; + z->balance = 0; + } else { + /* Right-right case. */ + x->rlink = y->llink; + y->llink = x; + *n = y; + + if (y->balance < 0) { + x->balance = 0; + y->balance = 0; + } else { + x->balance = -1; + y->balance = 1; + } + } + } else { + --x->balance; + } + n = &x->llink; + } else { + x = *n; + if (x->balance > 0) { + y = x->llink; + if (y->balance < 0) { + /* Left-right case. */ + z = y->rlink; + y->rlink = z->llink; + z->llink = y; + x->llink = z->rlink; + z->rlink = x; + *n = z; + + x->balance = z->balance > 0 ? -1 : 0; + y->balance = z->balance < 0 ? 1 : 0; + z->balance = 0; + } else { + /* Left-left case. */ + x->llink = y->rlink; + y->rlink = x; + *n = y; + + if (y->balance > 0) { + x->balance = 0; + y->balance = 0; + } else { + x->balance = 1; + y->balance = -1; + } + } + } else { + ++x->balance; + } + n = &x->rlink; } } - if (p != *rootp) - free(*rootp); /* D4: Free node */ - *rootp = q; /* link parent to new node */ - return p; + + /* Return the parent of the old entry. */ + *rootp = root; + return (result); } -- cgit v1.1