💿🐜 Antkeeper source code
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482 lines
14 KiB
482 lines
14 KiB
/*
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* Copyright (C) 2021 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_GEOM_HYPEROCTREE_HPP
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#define ANTKEEPER_GEOM_HYPEROCTREE_HPP
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#include <cstdint>
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#include <limits>
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#include <type_traits>
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#include <unordered_set>
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#include <stack>
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namespace geom {
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/**
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* Hashed linear hyperoctree.
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*
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* @see http://codervil.blogspot.com/2015/10/octree-node-identifiers.html
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* @see https://geidav.wordpress.com/2014/08/18/advanced-octrees-2-node-representations/
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*
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* @tparam N Number of dimensions.
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* @tparam D Max depth.
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*
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* Max depth can likely be determined by a generalized formula. 2D and 3D cases are given below:
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*
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* 2D:
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* 8 bit ( 1 byte) = max depth 1 ( 4 loc bits, 1 depth bits, 1 divider bit) = 6 bits
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* 16 bit ( 2 byte) = max depth 5 ( 12 loc bits, 3 depth bits, 1 divider bit) = 16 bits
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* 32 bit ( 4 byte) = max depth 12 ( 26 loc bits, 4 depth bits, 1 divider bit) = 31 bits
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* 64 bit ( 8 byte) = max depth 28 ( 58 loc bits, 5 depth bits, 1 divider bit) = 64 bits
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* 128 bit (16 byte) = max depth 59 (120 loc bits, 6 depth bits, 1 divider bit) = 127 bits
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* 256 bit (32 byte) = max depth 123 (248 loc bits, 7 depth bits, 1 divider bit) = 256 bits
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*
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* @see https://oeis.org/A173009
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*
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* 3D:
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* 8 bit ( 1 byte) = max depth 1 ( 6 loc bits, 1 depth bits, 1 divider bit) = 8 bits
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* 16 bit ( 2 byte) = max depth 3 ( 12 loc bits, 2 depth bits, 1 divider bit) = 15 bits
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* 32 bit ( 4 byte) = max depth 8 ( 27 loc bits, 4 depth bits, 1 divider bit) = 32 bits
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* 64 bit ( 8 byte) = max depth 18 ( 57 loc bits, 5 depth bits, 1 divider bit) = 63 bits
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* 128 bit (16 byte) = max depth 39 (120 loc bits, 6 depth bits, 1 divider bit) = 127 bits
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* 256 bit (32 byte) = max depth 81 (243 loc bits, 7 depth bits, 1 divider bit) = 251 bits
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*
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* @see https://oeis.org/A178420
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*
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* @tparam T Integer node type.
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*/
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template <std::size_t N, std::size_t D, class T>
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class hyperoctree
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{
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private:
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/// Compile-time calculation of the minimum bits required to represent `n` state changes.
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static constexpr T ceil_log2(T n);
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public:
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/// Integral node type.
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typedef T node_type;
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/// Ensure the node type is integral
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static_assert(std::is_integral<T>::value, "Node type must be integral.");
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/// Maximum node depth.
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static constexpr std::size_t max_depth = D;
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/// Number of bits required to encode the depth of a node.
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static constexpr T depth_bits = ceil_log2(max_depth + 1);
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/// Number of bits required to encode the location of a node.
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static constexpr T location_bits = (max_depth + 1) * N;
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/// Number of bits in the node type.
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static constexpr T node_bits = sizeof(node_type) * 8;
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// Ensure the node type has enough bits
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static_assert(depth_bits + location_bits + 1 <= node_bits, "Size of hyperoctree node type is insufficient to encode the maximum depth");
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/// Number of children per node.
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static constexpr T children_per_node = (N) ? (2 << (N - 1)) : 1;
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/// Number of siblings per node.
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static constexpr T siblings_per_node = children_per_node - 1;
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/// Root node which is always guaranteed to exist.
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static constexpr node_type root = 0;
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/**
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* Accesses nodes in their internal hashmap order.
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*/
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struct unordered_iterator
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{
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inline unordered_iterator(const unordered_iterator& other): set_iterator(other.set_iterator) {};
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inline unordered_iterator& operator=(const unordered_iterator& other) { this->set_iterator = other.set_iterator; return *this; };
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inline unordered_iterator& operator++() { ++(this->set_iterator); return *this; };
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inline unordered_iterator& operator--() { --(this->set_iterator); return *this; };
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inline bool operator==(const unordered_iterator& other) const { return this->set_iterator == other.set_iterator; };
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inline bool operator!=(const unordered_iterator& other) const { return this->set_iterator != other.set_iterator; };
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inline node_type operator*() const { return *this->set_iterator; };
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private:
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friend class hyperoctree;
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inline explicit unordered_iterator(const typename std::unordered_set<node_type>::const_iterator& it): set_iterator(it) {};
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typename std::unordered_set<node_type>::const_iterator set_iterator;
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};
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/**
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* Accesses nodes in z-order.
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*
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* @TODO Can this be implemented without a stack?
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*/
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struct iterator
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{
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inline iterator(const iterator& other): hyperoctree(other.hyperoctree), stack(other.stack) {};
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inline iterator& operator=(const iterator& other) { this->hyperoctree = other.hyperoctree; this->stack = other.stack; return *this; };
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iterator& operator++();
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inline bool operator==(const iterator& other) const { return **this == *other; };
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inline bool operator!=(const iterator& other) const { return **this != *other; };
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inline node_type operator*() const { return stack.top(); };
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private:
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friend class hyperoctree;
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inline explicit iterator(const hyperoctree* hyperoctree, node_type node): hyperoctree(hyperoctree), stack({node}) {};
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const hyperoctree* hyperoctree;
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std::stack<node_type> stack;
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};
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/**
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* Returns the depth of a node.
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*
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* @param node Node.
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* @return Depth of the node.
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*/
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static T depth(node_type node);
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/**
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* Returns the Morton code location of a node.
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*
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* @param node Node.
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* @return Morton code location of the node.
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*/
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static T location(node_type node);
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/**
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* Returns the node at the given depth and location.
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*
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* @param depth Node depth.
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* @param location Node Morton code location.
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*/
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static node_type node(T depth, T location);
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/**
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* Returns the ancestor of a node at the specified depth.
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*
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* @param node Node whose ancestor will be located.
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* @param depth Absolute depth of the ancestors.
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* @return Ancestral node.
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*/
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static node_type ancestor(node_type node, T depth);
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/**
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* Returns the parent of a node.
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*
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* @param node Node.
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* @return Parent node.
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*/
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static node_type parent(node_type node);
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/**
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* Returns the nth sibling of a node.
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*
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* @param node Node.
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* @param n Offset to next sibling. (Automatically wraps to `[0, siblings_per_node]`)
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* @return Next sibling node.
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*/
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static node_type sibling(node_type node, T n);
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/**
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* Returns the nth child of a node.
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*
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* @param node Parent node.
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* @param n Offset to the nth sibling of the first child node. (Automatically wraps to 0..7)
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* @return nth child node.
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*/
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static node_type child(node_type node, T n);
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/**
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* Calculates the first common ancestor of two nodes.
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*
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* @param a First node.
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* @param b Second node.
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* @return First common ancestor of the two nodes.
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*/
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static node_type common_ancestor(node_type a, node_type b);
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/// Creates an hyperoctree with a single root node.
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hyperoctree();
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/// Returns a z-order iterator to the root node.
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iterator begin() const;
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/// Returns a z-order iterator indicating the end of a traversal.
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iterator end() const;
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/// Returns an iterator to the specified node.
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iterator find(node_type node) const;
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/// Returns an unordered iterator indicating the beginning of a traversal.
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unordered_iterator unordered_begin() const;
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/// Returns an unordered iterator indicating the end of a traversal.
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unordered_iterator unordered_end() const;
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/**
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* Inserts a node and its siblings into the hyperoctree, creating its ancestors as necessary. Note: The root node is persistent and cannot be inserted.
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*
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* @param node Node to insert.
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*/
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void insert(node_type node);
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/**
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* Erases a node along with its siblings and descendants. Note: The root node is persistent and cannot be erased.
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*
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* @param node Node to erase.
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*/
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void erase(node_type node);
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/**
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* Erases all nodes except the root.
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*/
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void clear();
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/// Returns `true` if the node is contained within the hyperoctree, and `false` otherwise.
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bool contains(node_type node) const;
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/// Returns `true` if the node has no children, and `false` otherwise.
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bool is_leaf(node_type node) const;
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/// Returns the number of nodes in the hyperoctree.
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std::size_t size() const;
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private:
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/// Compile-time pow()
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static constexpr T pow(T x, T exponent);
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/// Count leading zeros
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static T clz(T x);
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std::unordered_set<node_type> nodes;
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};
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template <std::size_t N, std::size_t D, class T>
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typename hyperoctree<N, D, T>::iterator& hyperoctree<N, D, T>::iterator::operator++()
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{
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// Get next node from top of stack
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node_type node = stack.top();
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stack.pop();
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// If the node has children
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if (!hyperoctree->is_leaf(node))
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{
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// Push first child onto the stack
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for (T i = 0; i < children_per_node; ++i)
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stack.push(child(node, siblings_per_node - i));
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}
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if (stack.empty())
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stack.push(std::numeric_limits<T>::max());
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return *this;
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}
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template <std::size_t N, std::size_t D, class T>
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constexpr T hyperoctree<N, D, T>::ceil_log2(T n)
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{
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return (n <= 1) ? 0 : ceil_log2((n + 1) / 2) + 1;
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}
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template <std::size_t N, std::size_t D, class T>
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inline T hyperoctree<N, D, T>::depth(node_type node)
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{
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// Extract depth using a bit mask
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constexpr T mask = pow(2, depth_bits) - 1;
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return node & mask;
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}
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template <std::size_t N, std::size_t D, class T>
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inline T hyperoctree<N, D, T>::location(node_type node)
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{
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return node >> ((node_bits - 1) - depth(node) * N);
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}
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template <std::size_t N, std::size_t D, class T>
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inline typename hyperoctree<N, D, T>::node_type hyperoctree<N, D, T>::node(T depth, T location)
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{
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return (location << ((node_bits - 1) - depth * N)) | depth;
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}
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template <std::size_t N, std::size_t D, class T>
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inline typename hyperoctree<N, D, T>::node_type hyperoctree<N, D, T>::ancestor(node_type node, T depth)
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{
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const T mask = std::numeric_limits<T>::max() << ((node_bits - 1) - depth * N);
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return (node & mask) | depth;
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}
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template <std::size_t N, std::size_t D, class T>
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inline typename hyperoctree<N, D, T>::node_type hyperoctree<N, D, T>::parent(node_type node)
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{
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return ancestor(node, depth(node) - 1);
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}
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template <std::size_t N, std::size_t D, class T>
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inline typename hyperoctree<N, D, T>::node_type hyperoctree<N, D, T>::sibling(node_type node, T n)
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{
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constexpr T mask = (1 << N) - 1;
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T depth = hyperoctree::depth(node);
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T location = node >> ((node_bits - 1) - depth * N);
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return hyperoctree::node(depth, (location & (~mask)) | ((location + n) & mask));
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}
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template <std::size_t N, std::size_t D, class T>
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inline typename hyperoctree<N, D, T>::node_type hyperoctree<N, D, T>::child(node_type node, T n)
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{
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return sibling(node + 1, n);
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}
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template <std::size_t N, std::size_t D, class T>
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inline typename hyperoctree<N, D, T>::node_type hyperoctree<N, D, T>::common_ancestor(node_type a, node_type b)
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{
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T bits = std::min<T>(depth(a), depth(b)) * N;
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T marker = (T(1) << (node_bits - 1)) >> bits;
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T depth = clz((a ^ b) | marker) / N;
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return ancestor(a, depth);
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}
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template <std::size_t N, std::size_t D, class T>
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inline hyperoctree<N, D, T>::hyperoctree():
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nodes({0})
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{}
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template <std::size_t N, std::size_t D, class T>
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void hyperoctree<N, D, T>::insert(node_type node)
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{
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if (contains(node))
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return;
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// Insert node
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nodes.emplace(node);
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// Insert siblings
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for (T i = 1; i < children_per_node; ++i)
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nodes.emplace(sibling(node, i));
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// Insert parent as necessary
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node_type parent = hyperoctree::parent(node);
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if (!contains(parent))
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insert(parent);
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}
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template <std::size_t N, std::size_t D, class T>
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void hyperoctree<N, D, T>::erase(node_type node)
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{
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// Don't erase the root!
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if (node == root)
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return;
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for (T i = 0; i < children_per_node; ++i)
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{
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// Erase node
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nodes.erase(node);
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// Erase descendants
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if (!is_leaf(node))
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{
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for (T j = 0; j < children_per_node; ++j)
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erase(child(node, j));
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}
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// Go to next sibling
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if (i < siblings_per_node)
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node = sibling(node, i);
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}
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}
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template <std::size_t N, std::size_t D, class T>
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void hyperoctree<N, D, T>::clear()
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{
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nodes = {0};
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}
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template <std::size_t N, std::size_t D, class T>
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inline bool hyperoctree<N, D, T>::contains(node_type node) const
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{
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return (nodes.find(node) != nodes.end());
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}
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template <std::size_t N, std::size_t D, class T>
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inline bool hyperoctree<N, D, T>::is_leaf(node_type node) const
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{
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return !contains(child(node, 0));
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}
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template <std::size_t N, std::size_t D, class T>
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inline std::size_t hyperoctree<N, D, T>::size() const
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{
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return nodes.size();
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}
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template <std::size_t N, std::size_t D, class T>
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typename hyperoctree<N, D, T>::iterator hyperoctree<N, D, T>::begin() const
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{
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return iterator(this, hyperoctree::root);
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}
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template <std::size_t N, std::size_t D, class T>
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typename hyperoctree<N, D, T>::iterator hyperoctree<N, D, T>::end() const
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{
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return iterator(this, std::numeric_limits<T>::max());
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}
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template <std::size_t N, std::size_t D, class T>
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typename hyperoctree<N, D, T>::iterator hyperoctree<N, D, T>::find(node_type node) const
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{
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return contains(node) ? iterator(node) : end();
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}
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template <std::size_t N, std::size_t D, class T>
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typename hyperoctree<N, D, T>::unordered_iterator hyperoctree<N, D, T>::unordered_begin() const
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{
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return unordered_iterator(nodes.begin());
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}
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template <std::size_t N, std::size_t D, class T>
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typename hyperoctree<N, D, T>::unordered_iterator hyperoctree<N, D, T>::unordered_end() const
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{
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return unordered_iterator(nodes.end());
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}
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template <std::size_t N, std::size_t D, class T>
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constexpr T hyperoctree<N, D, T>::pow(T x, T exponent)
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{
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return (exponent == 0) ? 1 : x * pow(x, exponent - 1);
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}
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template <std::size_t N, std::size_t D, class T>
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T hyperoctree<N, D, T>::clz(T x)
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{
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if (!x)
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return sizeof(T) * 8;
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#if defined(__GNU__)
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return __builtin_clz(x);
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#else
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T n = 0;
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while ((x & (T(1) << (8 * sizeof(x) - 1))) == 0)
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{
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x <<= 1;
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++n;
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}
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return n;
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#endif
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}
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} // namespace geom
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#endif // ANTKEEPER_GEOM_HYPEROCTREE_HPP
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