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+/****************************************************************************
+ * bfs *
+ * Copyright (C) 2019 Tavian Barnes <tavianator@tavianator.com> *
+ * *
+ * 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 <assert.h>
+#include <limits.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+
+#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);
+ }
+}
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