459d04a5ee
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
98 lines
2.8 KiB
C
98 lines
2.8 KiB
C
/*-
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* Copyright (c) 2015 Nuxi, https://nuxi.nl/
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* $FreeBSD$
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*/
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#ifndef TSEARCH_PATH_H
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#define TSEARCH_PATH_H
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#include <limits.h>
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#include <stdbool.h>
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#include <stdint.h>
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/*
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* Bookkeeping for storing a path in a balanced binary search tree from
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* the root to a leaf node.
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*
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* For an AVL tree we know that its maximum height of a tree is bounded
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* by approximately 1.44 * log2(n) - 0.328. Given that the number of
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* entries of the tree is constrained by the size of the address space,
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* two uintptr_t's provide sufficient space to store the path from the
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* root to any leaf.
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*/
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struct path {
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uintptr_t steps[2];
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unsigned int nsteps;
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};
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/* Initializes the path structure with a zero-length path. */
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static inline void
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path_init(struct path *p)
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{
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p->nsteps = 0;
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}
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#define STEPS_BIT (sizeof(uintptr_t) * CHAR_BIT)
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/* Pushes a step to the left to the end of the path. */
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static inline void
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path_taking_left(struct path *p)
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{
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p->steps[p->nsteps / STEPS_BIT] |=
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(uintptr_t)1 << (p->nsteps % STEPS_BIT);
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++p->nsteps;
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}
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/* Pushes a step to the right to the end of the path. */
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static inline void
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path_taking_right(struct path *p)
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{
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p->steps[p->nsteps / STEPS_BIT] &=
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~((uintptr_t)1 << (p->nsteps % STEPS_BIT));
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++p->nsteps;
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}
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/*
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* Pops the first step from the path and returns whether it was a step
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* to the left.
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*/
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static inline bool
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path_took_left(struct path *p)
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{
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bool result;
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result = p->steps[0] & 0x1;
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p->steps[0] = (p->steps[0] >> 1) | (p->steps[1] << (STEPS_BIT - 1));
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p->steps[1] >>= 1;
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return (result);
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}
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#undef STEPS_BIT
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#endif
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