From 33cc3b9dd7bf3dae1c6cf86e46bb4923f96e7fff Mon Sep 17 00:00:00 2001 From: トトも <85485984+ElectronicsArchiver@users.noreply.github.com> Date: Sat, 16 Apr 2022 20:18:56 +0200 Subject: Source / Include Folder (#88) Moved Source Files Into `src` Folder --- src/trie.c | 693 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 693 insertions(+) create mode 100644 src/trie.c (limited to 'src/trie.c') diff --git a/src/trie.c b/src/trie.c new file mode 100644 index 0000000..bae9acb --- /dev/null +++ b/src/trie.c @@ -0,0 +1,693 @@ +/**************************************************************************** + * bfs * + * Copyright (C) 2019 Tavian Barnes * + * * + * Permission to use, copy, modify, and/or distribute this software for any * + * purpose with or without fee is hereby granted. * + * * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES * + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF * + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR * + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES * + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN * + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF * + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. * + ****************************************************************************/ + +/** + * This is an implementation of a "qp trie," as documented at + * https://dotat.at/prog/qp/README.html + * + * An uncompressed trie over the dataset {AAAA, AADD, ABCD, DDAA, DDDD} would + * look like + * + * A A A A + * *--->*--->*--->*--->$ + * | | | D D + * | | +--->*--->$ + * | | B C D + * | +--->*--->*--->$ + * | D D A A + * +--->*--->*--->*--->$ + * | D D + * +--->*--->$ + * + * A compressed (PATRICIA) trie collapses internal nodes that have only a single + * child, like this: + * + * A A AA + * *--->*--->*---->$ + * | | | DD + * | | +---->$ + * | | BCD + * | +----->$ + * | DD AA + * +---->*---->$ + * | DD + * +---->$ + * + * The nodes can be compressed further by dropping the actual compressed + * sequences from the nodes, storing it only in the leaves. This is the + * technique applied in QP tries, and the crit-bit trees that inspired them + * (https://cr.yp.to/critbit.html). Only the index to test, and the values to + * branch on, need to be stored in each node. + * + * A A A + * 0--->1--->2--->AAAA + * | | | D + * | | +--->AADD + * | | B + * | +--->ABCD + * | D A + * +--->2--->DDAA + * | D + * +--->DDDD + * + * Nodes are represented very compactly. Rather than a dense array of children, + * a sparse array of only the non-NULL children directly follows the node in + * memory. A bitmap is used to track which children exist; the index of a child + * i is found by counting the number of bits below bit i that are set. A tag + * bit is used to tell pointers to internal nodes apart from pointers to leaves. + * + * This implementation tests a whole nibble (half byte/hex digit) at every + * branch, so the bitmap takes up 16 bits. The remainder of a machine word is + * used to hold the offset, which severely constrains its range on 32-bit + * platforms. As a workaround, we store relative instead of absolute offsets, + * and insert intermediate singleton "jump" nodes when necessary. + */ + +#include "trie.h" +#include "util.h" +#include +#include +#include +#include +#include +#include + +#if CHAR_BIT != 8 +# error "This trie implementation assumes 8-bit bytes." +#endif + +/** Number of bits for the sparse array bitmap, aka the range of a nibble. */ +#define BITMAP_BITS 16 +/** The number of remaining bits in a word, to hold the offset. */ +#define OFFSET_BITS (sizeof(size_t)*CHAR_BIT - BITMAP_BITS) +/** The highest representable offset (only 64k on a 32-bit architecture). */ +#define OFFSET_MAX (((size_t)1 << OFFSET_BITS) - 1) + +/** + * An internal node of the trie. + */ +struct trie_node { + /** + * A bitmap that hold which indices exist in the sparse children array. + * Bit i will be set if a child exists at logical index i, and its index + * into the array will be popcount(bitmap & ((1 << i) - 1)). + */ + size_t bitmap : BITMAP_BITS; + + /** + * The offset into the key in nibbles. This is relative to the parent + * node, to support offsets larger than OFFSET_MAX. + */ + size_t offset : OFFSET_BITS; + + /** + * Flexible array of children. Each pointer uses the lowest bit as a + * tag to distinguish internal nodes from leaves. This is safe as long + * as all dynamic allocations are aligned to more than a single byte. + */ + uintptr_t children[]; +}; + +/** Check if an encoded pointer is to a leaf. */ +static bool trie_is_leaf(uintptr_t ptr) { + return ptr & 1; +} + +/** Decode a pointer to a leaf. */ +static struct trie_leaf *trie_decode_leaf(uintptr_t ptr) { + assert(trie_is_leaf(ptr)); + return (struct trie_leaf *)(ptr ^ 1); +} + +/** Encode a pointer to a leaf. */ +static uintptr_t trie_encode_leaf(const struct trie_leaf *leaf) { + uintptr_t ptr = (uintptr_t)leaf ^ 1; + assert(trie_is_leaf(ptr)); + return ptr; +} + +/** Decode a pointer to an internal node. */ +static struct trie_node *trie_decode_node(uintptr_t ptr) { + assert(!trie_is_leaf(ptr)); + return (struct trie_node *)ptr; +} + +/** Encode a pointer to an internal node. */ +static uintptr_t trie_encode_node(const struct trie_node *node) { + uintptr_t ptr = (uintptr_t)node; + assert(!trie_is_leaf(ptr)); + return ptr; +} + +void trie_init(struct trie *trie) { + trie->root = 0; +} + +/** Compute the popcount (Hamming weight) of a bitmap. */ +static unsigned int trie_popcount(unsigned int n) { +#if __POPCNT__ + // Use the x86 instruction if we have it. Otherwise, GCC generates a + // library call, so use the below implementation instead. + return __builtin_popcount(n); +#else + // See https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation + n -= (n >> 1) & 0x5555; + n = (n & 0x3333) + ((n >> 2) & 0x3333); + n = (n + (n >> 4)) & 0x0F0F; + n = (n + (n >> 8)) & 0xFF; + return n; +#endif +} + +/** Extract the nibble at a certain offset from a byte sequence. */ +static unsigned char trie_key_nibble(const void *key, size_t offset) { + const unsigned char *bytes = key; + size_t byte = offset >> 1; + + // A branchless version of + // if (offset & 1) { + // return bytes[byte] >> 4; + // } else { + // return bytes[byte] & 0xF; + // } + unsigned int shift = (offset & 1) << 2; + return (bytes[byte] >> shift) & 0xF; +} + +/** + * Finds a leaf in the trie that matches the key at every branch. If the key + * exists in the trie, the representative will match the searched key. But + * since only branch points are tested, it can be different from the key. In + * that case, the first mismatch between the key and the representative will be + * the depth at which to make a new branch to insert the key. + */ +static struct trie_leaf *trie_representative(const struct trie *trie, const void *key, size_t length) { + uintptr_t ptr = trie->root; + if (!ptr) { + return NULL; + } + + size_t offset = 0; + while (!trie_is_leaf(ptr)) { + struct trie_node *node = trie_decode_node(ptr); + offset += node->offset; + + unsigned int index = 0; + if ((offset >> 1) < length) { + unsigned char nibble = trie_key_nibble(key, offset); + unsigned int bit = 1U << nibble; + if (node->bitmap & bit) { + index = trie_popcount(node->bitmap & (bit - 1)); + } + } + ptr = node->children[index]; + } + + return trie_decode_leaf(ptr); +} + +struct trie_leaf *trie_first_leaf(const struct trie *trie) { + return trie_representative(trie, NULL, 0); +} + +struct trie_leaf *trie_find_str(const struct trie *trie, const char *key) { + return trie_find_mem(trie, key, strlen(key) + 1); +} + +struct trie_leaf *trie_find_mem(const struct trie *trie, const void *key, size_t length) { + struct trie_leaf *rep = trie_representative(trie, key, length); + if (rep && rep->length == length && memcmp(rep->key, key, length) == 0) { + return rep; + } else { + return NULL; + } +} + +struct trie_leaf *trie_find_postfix(const struct trie *trie, const char *key) { + size_t length = strlen(key); + struct trie_leaf *rep = trie_representative(trie, key, length + 1); + if (rep && rep->length >= length && memcmp(rep->key, key, length) == 0) { + return rep; + } else { + return NULL; + } +} + +/** + * Find a leaf that may end at the current node. + */ +static struct trie_leaf *trie_terminal_leaf(const struct trie_node *node) { + // Finding a terminating NUL byte may take two nibbles + for (int i = 0; i < 2; ++i) { + if (!(node->bitmap & 1)) { + break; + } + + uintptr_t ptr = node->children[0]; + if (trie_is_leaf(ptr)) { + return trie_decode_leaf(ptr); + } else { + node = trie_decode_node(ptr); + } + } + + return NULL; +} + +/** Check if a leaf is a prefix of a search key. */ +static bool trie_check_prefix(struct trie_leaf *leaf, size_t skip, const char *key, size_t length) { + if (leaf && leaf->length <= length) { + return memcmp(key + skip, leaf->key + skip, leaf->length - skip - 1) == 0; + } else { + return false; + } +} + +struct trie_leaf *trie_find_prefix(const struct trie *trie, const char *key) { + uintptr_t ptr = trie->root; + if (!ptr) { + return NULL; + } + + struct trie_leaf *best = NULL; + size_t skip = 0; + size_t length = strlen(key) + 1; + + size_t offset = 0; + while (!trie_is_leaf(ptr)) { + struct trie_node *node = trie_decode_node(ptr); + offset += node->offset; + if ((offset >> 1) >= length) { + return best; + } + + struct trie_leaf *leaf = trie_terminal_leaf(node); + if (trie_check_prefix(leaf, skip, key, length)) { + best = leaf; + skip = offset >> 1; + } + + unsigned char nibble = trie_key_nibble(key, offset); + unsigned int bit = 1U << nibble; + if (node->bitmap & bit) { + unsigned int index = trie_popcount(node->bitmap & (bit - 1)); + ptr = node->children[index]; + } else { + return best; + } + } + + struct trie_leaf *leaf = trie_decode_leaf(ptr); + if (trie_check_prefix(leaf, skip, key, length)) { + best = leaf; + } + + return best; +} + +/** Create a new leaf, holding a copy of the given key. */ +static struct trie_leaf *new_trie_leaf(const void *key, size_t length) { + struct trie_leaf *leaf = malloc(BFS_FLEX_SIZEOF(struct trie_leaf, key, length)); + if (leaf) { + leaf->value = NULL; + leaf->length = length; + memcpy(leaf->key, key, length); + } + return leaf; +} + +/** Compute the size of a trie node with a certain number of children. */ +static size_t trie_node_size(unsigned int size) { + // Empty nodes aren't supported + assert(size > 0); + // Node size must be a power of two + assert((size & (size - 1)) == 0); + + return BFS_FLEX_SIZEOF(struct trie_node, children, size); +} + +/** Find the offset of the first nibble that differs between two keys. */ +static size_t trie_key_mismatch(const void *key1, const void *key2, size_t length) { + const unsigned char *bytes1 = key1; + const unsigned char *bytes2 = key2; + size_t i = 0; + size_t offset = 0; + const size_t chunk = sizeof(size_t); + + for (; i + chunk <= length; i += chunk) { + if (memcmp(bytes1 + i, bytes2 + i, chunk) != 0) { + break; + } + } + + for (; i < length; ++i) { + unsigned char b1 = bytes1[i], b2 = bytes2[i]; + if (b1 != b2) { + offset = (b1 & 0xF) == (b2 & 0xF); + break; + } + } + + offset |= i << 1; + return offset; +} + +/** + * Insert a key into a node. The node must not have a child in that position + * already. Effectively takes a subtrie like this: + * + * ptr + * | + * v X + * *--->... + * | Z + * +--->... + * + * and transforms it to: + * + * ptr + * | + * v X + * *--->... + * | Y + * +--->key + * | Z + * +--->... + */ +static struct trie_leaf *trie_node_insert(uintptr_t *ptr, const void *key, size_t length, size_t offset) { + struct trie_node *node = trie_decode_node(*ptr); + unsigned int size = trie_popcount(node->bitmap); + + // Double the capacity every power of two + if ((size & (size - 1)) == 0) { + node = realloc(node, trie_node_size(2*size)); + if (!node) { + return NULL; + } + *ptr = trie_encode_node(node); + } + + struct trie_leaf *leaf = new_trie_leaf(key, length); + if (!leaf) { + return NULL; + } + + unsigned char nibble = trie_key_nibble(key, offset); + unsigned int bit = 1U << nibble; + + // The child must not already be present + assert(!(node->bitmap & bit)); + node->bitmap |= bit; + + unsigned int index = trie_popcount(node->bitmap & (bit - 1)); + uintptr_t *child = &node->children[index]; + if (index < size) { + memmove(child + 1, child, (size - index)*sizeof(*child)); + } + *child = trie_encode_leaf(leaf); + return leaf; +} + +/** + * When the current offset exceeds OFFSET_MAX, insert "jump" nodes that bridge + * the gap. This function takes a subtrie like this: + * + * ptr + * | + * v + * *--->rep + * + * and changes it to: + * + * ptr ret + * | | + * v v + * *--->*--->rep + * + * so that a new key can be inserted like: + * + * ptr ret + * | | + * v v X + * *--->*--->rep + * | Y + * +--->key + */ +static uintptr_t *trie_jump(uintptr_t *ptr, const char *key, size_t *offset) { + // We only ever need to jump to leaf nodes, since internal nodes are + // guaranteed to be within OFFSET_MAX anyway + assert(trie_is_leaf(*ptr)); + + struct trie_node *node = malloc(trie_node_size(1)); + if (!node) { + return NULL; + } + + *offset += OFFSET_MAX; + node->offset = OFFSET_MAX; + + unsigned char nibble = trie_key_nibble(key, *offset); + node->bitmap = 1 << nibble; + + node->children[0] = *ptr; + *ptr = trie_encode_node(node); + return node->children; +} + +/** + * Split a node in the trie. Changes a subtrie like this: + * + * ptr + * | + * v + * *...>--->rep + * + * into this: + * + * ptr + * | + * v X + * *--->*...>--->rep + * | Y + * +--->key + */ +static struct trie_leaf *trie_split(uintptr_t *ptr, const void *key, size_t length, struct trie_leaf *rep, size_t offset, size_t mismatch) { + unsigned char key_nibble = trie_key_nibble(key, mismatch); + unsigned char rep_nibble = trie_key_nibble(rep->key, mismatch); + assert(key_nibble != rep_nibble); + + struct trie_node *node = malloc(trie_node_size(2)); + if (!node) { + return NULL; + } + + struct trie_leaf *leaf = new_trie_leaf(key, length); + if (!leaf) { + free(node); + return NULL; + } + + node->bitmap = (1 << key_nibble) | (1 << rep_nibble); + + size_t delta = mismatch - offset; + if (!trie_is_leaf(*ptr)) { + struct trie_node *child = trie_decode_node(*ptr); + child->offset -= delta; + } + node->offset = delta; + + unsigned int key_index = key_nibble > rep_nibble; + node->children[key_index] = trie_encode_leaf(leaf); + node->children[key_index ^ 1] = *ptr; + *ptr = trie_encode_node(node); + return leaf; +} + +struct trie_leaf *trie_insert_str(struct trie *trie, const char *key) { + return trie_insert_mem(trie, key, strlen(key) + 1); +} + +struct trie_leaf *trie_insert_mem(struct trie *trie, const void *key, size_t length) { + struct trie_leaf *rep = trie_representative(trie, key, length); + if (!rep) { + struct trie_leaf *leaf = new_trie_leaf(key, length); + if (leaf) { + trie->root = trie_encode_leaf(leaf); + } + return leaf; + } + + size_t limit = length < rep->length ? length : rep->length; + size_t mismatch = trie_key_mismatch(key, rep->key, limit); + if ((mismatch >> 1) >= length) { + return rep; + } + + size_t offset = 0; + uintptr_t *ptr = &trie->root; + while (!trie_is_leaf(*ptr)) { + struct trie_node *node = trie_decode_node(*ptr); + if (offset + node->offset > mismatch) { + break; + } + offset += node->offset; + + unsigned char nibble = trie_key_nibble(key, offset); + unsigned int bit = 1U << nibble; + if (node->bitmap & bit) { + assert(offset < mismatch); + unsigned int index = trie_popcount(node->bitmap & (bit - 1)); + ptr = &node->children[index]; + } else { + assert(offset == mismatch); + return trie_node_insert(ptr, key, length, offset); + } + } + + while (mismatch - offset > OFFSET_MAX) { + ptr = trie_jump(ptr, key, &offset); + if (!ptr) { + return NULL; + } + } + + return trie_split(ptr, key, length, rep, offset, mismatch); +} + +/** Free a chain of singleton nodes. */ +static void trie_free_singletons(uintptr_t ptr) { + while (!trie_is_leaf(ptr)) { + struct trie_node *node = trie_decode_node(ptr); + + // Make sure the bitmap is a power of two, i.e. it has just one child + assert((node->bitmap & (node->bitmap - 1)) == 0); + + ptr = node->children[0]; + free(node); + } + + free(trie_decode_leaf(ptr)); +} + +/** + * Try to collapse a two-child node like: + * + * parent child + * | | + * v v + * *----->*----->*----->leaf + * | + * +----->other + * + * into + * + * parent + * | + * v + * other + */ +static int trie_collapse_node(uintptr_t *parent, struct trie_node *parent_node, unsigned int child_index) { + uintptr_t other = parent_node->children[child_index ^ 1]; + if (!trie_is_leaf(other)) { + struct trie_node *other_node = trie_decode_node(other); + if (other_node->offset + parent_node->offset <= OFFSET_MAX) { + other_node->offset += parent_node->offset; + } else { + return -1; + } + } + + *parent = other; + free(parent_node); + return 0; +} + +void trie_remove(struct trie *trie, struct trie_leaf *leaf) { + uintptr_t *child = &trie->root; + uintptr_t *parent = NULL; + unsigned int child_bit = 0, child_index = 0; + size_t offset = 0; + while (!trie_is_leaf(*child)) { + struct trie_node *node = trie_decode_node(*child); + offset += node->offset; + assert((offset >> 1) < leaf->length); + + unsigned char nibble = trie_key_nibble(leaf->key, offset); + unsigned int bit = 1U << nibble; + unsigned int bitmap = node->bitmap; + assert(bitmap & bit); + unsigned int index = trie_popcount(bitmap & (bit - 1)); + + // Advance the parent pointer, unless this node had only one child + if (bitmap & (bitmap - 1)) { + parent = child; + child_bit = bit; + child_index = index; + } + + child = &node->children[index]; + } + + assert(trie_decode_leaf(*child) == leaf); + + if (!parent) { + trie_free_singletons(trie->root); + trie->root = 0; + return; + } + + struct trie_node *node = trie_decode_node(*parent); + child = node->children + child_index; + trie_free_singletons(*child); + + node->bitmap ^= child_bit; + unsigned int parent_size = trie_popcount(node->bitmap); + assert(parent_size > 0); + if (parent_size == 1 && trie_collapse_node(parent, node, child_index) == 0) { + return; + } + + if (child_index < parent_size) { + memmove(child, child + 1, (parent_size - child_index)*sizeof(*child)); + } + + if ((parent_size & (parent_size - 1)) == 0) { + node = realloc(node, trie_node_size(parent_size)); + if (node) { + *parent = trie_encode_node(node); + } + } +} + +/** Free an encoded pointer to a node. */ +static void free_trie_ptr(uintptr_t ptr) { + if (trie_is_leaf(ptr)) { + free(trie_decode_leaf(ptr)); + } else { + struct trie_node *node = trie_decode_node(ptr); + size_t size = trie_popcount(node->bitmap); + for (size_t i = 0; i < size; ++i) { + free_trie_ptr(node->children[i]); + } + free(node); + } +} + +void trie_destroy(struct trie *trie) { + if (trie->root) { + free_trie_ptr(trie->root); + } +} -- cgit v1.2.3