From 3d1d75d570579c402f9462f7b3048560651ac582 Mon Sep 17 00:00:00 2001 From: David Robillard Date: Wed, 6 Jun 2018 20:35:46 +0200 Subject: Add zix data structures for use in model --- src/zix/btree.c | 785 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 785 insertions(+) create mode 100644 src/zix/btree.c (limited to 'src/zix/btree.c') diff --git a/src/zix/btree.c b/src/zix/btree.c new file mode 100644 index 00000000..4c15e07c --- /dev/null +++ b/src/zix/btree.c @@ -0,0 +1,785 @@ +/* + Copyright 2011-2014 David Robillard + + Permission to use, copy, modify, and/or distribute this software for any + purpose with or without fee is hereby granted, provided that the above + copyright notice and this permission notice appear in all copies. + + THIS 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. +*/ + +#include "zix/btree.h" + +#include +#include +#include +#include + +// #define ZIX_BTREE_DEBUG 1 + +#ifndef ZIX_BTREE_PAGE_SIZE +# define ZIX_BTREE_PAGE_SIZE 4096 +#endif + +#define ZIX_BTREE_NODE_SPACE (ZIX_BTREE_PAGE_SIZE - 2 * sizeof(uint16_t)) +#define ZIX_BTREE_LEAF_VALS ((ZIX_BTREE_NODE_SPACE / sizeof(void*)) - 1) +#define ZIX_BTREE_INODE_VALS (ZIX_BTREE_LEAF_VALS / 2) + +struct ZixBTreeImpl { + ZixBTreeNode* root; + ZixDestroyFunc destroy; + ZixComparator cmp; + const void* cmp_data; + size_t size; + unsigned height; ///< Number of levels, i.e. root only has height 1 +}; + +struct ZixBTreeNodeImpl { + uint16_t is_leaf; + uint16_t n_vals; + // On 64-bit we rely on some padding here to get page-sized nodes + void* vals[ZIX_BTREE_INODE_VALS]; // ZIX_BTREE_LEAF_VALS for leaves + ZixBTreeNode* children[ZIX_BTREE_INODE_VALS + 1]; // Nonexistent for leaves +}; + +typedef struct { + ZixBTreeNode* node; + unsigned index; +} ZixBTreeIterFrame; + +struct ZixBTreeIterImpl { + unsigned n_levels; ///< Maximum depth of stack + unsigned level; ///< Current level in stack + ZixBTreeIterFrame stack[]; ///< Position stack +}; + +#ifdef ZIX_BTREE_DEBUG + +ZIX_PRIVATE void +print_node(const ZixBTreeNode* n, const char* prefix) +{ + printf("%s[", prefix); + for (uint16_t v = 0; v < n->n_vals; ++v) { + printf(" %lu", (uintptr_t)n->vals[v]); + } + printf(" ]\n"); +} + +ZIX_PRIVATE void +print_tree(const ZixBTreeNode* parent, const ZixBTreeNode* node, int level) +{ + if (node) { + if (!parent) { + printf("TREE {\n"); + } + for (int i = 0; i < level + 1; ++i) { + printf(" "); + } + print_node(node, ""); + if (!node->is_leaf) { + for (uint16_t i = 0; i < node->n_vals + 1; ++i) { + print_tree(node, node->children[i], level + 1); + } + } + if (!parent) { + printf("}\n"); + } + } +} + +#endif // ZIX_BTREE_DEBUG + +ZIX_PRIVATE ZixBTreeNode* +zix_btree_node_new(const bool leaf) +{ + assert(sizeof(ZixBTreeNode) == ZIX_BTREE_PAGE_SIZE); + ZixBTreeNode* node = (ZixBTreeNode*)malloc(sizeof(ZixBTreeNode)); + if (node) { + node->is_leaf = leaf; + node->n_vals = 0; + } + return node; +} + +ZIX_API ZixBTree* +zix_btree_new(const ZixComparator cmp, + const void* const cmp_data, + const ZixDestroyFunc destroy) +{ + ZixBTree* t = (ZixBTree*)malloc(sizeof(ZixBTree)); + if (t) { + t->root = zix_btree_node_new(true); + t->destroy = destroy; + t->cmp = cmp; + t->cmp_data = cmp_data; + t->size = 0; + t->height = 1; + if (!t->root) { + free(t); + return NULL; + } + } + return t; +} + +ZIX_PRIVATE void +zix_btree_free_rec(ZixBTree* const t, ZixBTreeNode* const n) +{ + if (n) { + if (t->destroy) { + for (uint16_t i = 0; i < n->n_vals; ++i) { + t->destroy(n->vals[i]); + } + } + if (!n->is_leaf) { + for (uint16_t i = 0; i < n->n_vals + 1; ++i) { + zix_btree_free_rec(t, n->children[i]); + } + } + free(n); + } +} + +ZIX_API void +zix_btree_free(ZixBTree* const t) +{ + if (t) { + zix_btree_free_rec(t, t->root); + free(t); + } +} + +ZIX_API size_t +zix_btree_size(const ZixBTree* const t) +{ + return t->size; +} + +ZIX_PRIVATE uint16_t +zix_btree_max_vals(const ZixBTreeNode* const node) +{ + return node->is_leaf ? ZIX_BTREE_LEAF_VALS : ZIX_BTREE_INODE_VALS; +} + +ZIX_PRIVATE uint16_t +zix_btree_min_vals(const ZixBTreeNode* const node) +{ + return ((zix_btree_max_vals(node) + 1U) / 2U) - 1U; +} + +/** Shift pointers in `array` of length `n` right starting at `i`. */ +ZIX_PRIVATE void +zix_btree_ainsert(void** const array, + const unsigned n, + const unsigned i, + void* const e) +{ + memmove(array + i + 1, array + i, (n - i) * sizeof(e)); + array[i] = e; +} + +/** Erase element `i` in `array` of length `n` and return erased element. */ +ZIX_PRIVATE void* +zix_btree_aerase(void** const array, const unsigned n, const unsigned i) +{ + void* const ret = array[i]; + memmove(array + i, array + i + 1, (n - i) * sizeof(ret)); + return ret; +} + +/** Split lhs, the i'th child of `n`, into two nodes. */ +ZIX_PRIVATE ZixBTreeNode* +zix_btree_split_child(ZixBTreeNode* const n, + const unsigned i, + ZixBTreeNode* const lhs) +{ + assert(lhs->n_vals == zix_btree_max_vals(lhs)); + assert(n->n_vals < ZIX_BTREE_INODE_VALS); + assert(i < n->n_vals + 1U); + assert(n->children[i] == lhs); + + const uint16_t max_n_vals = zix_btree_max_vals(lhs); + ZixBTreeNode* rhs = zix_btree_node_new(lhs->is_leaf); + if (!rhs) { + return NULL; + } + + // LHS and RHS get roughly half, less the middle value which moves up + lhs->n_vals = max_n_vals / 2U; + rhs->n_vals = max_n_vals - lhs->n_vals - 1U; + + // Copy large half of values from LHS to new RHS node + memcpy(rhs->vals, + lhs->vals + lhs->n_vals + 1, + rhs->n_vals * sizeof(void*)); + + // Copy large half of children from LHS to new RHS node + if (!lhs->is_leaf) { + memcpy(rhs->children, + lhs->children + lhs->n_vals + 1, + (rhs->n_vals + 1) * sizeof(ZixBTreeNode*)); + } + + // Move middle value up to parent + zix_btree_ainsert(n->vals, n->n_vals, i, lhs->vals[lhs->n_vals]); + + // Insert new RHS node in parent at position i + zix_btree_ainsert((void**)n->children, ++n->n_vals, i + 1U, rhs); + + return rhs; +} + +/** Find the first value in `n` that is not less than `e` (lower bound). */ +ZIX_PRIVATE unsigned +zix_btree_node_find(const ZixBTree* const t, + const ZixBTreeNode* const n, + const void* const e, + bool* const equal) +{ + uint16_t first = 0; + uint16_t len = n->n_vals; + while (len > 0) { + const unsigned half = len >> 1U; + const unsigned i = first + half; + const int cmp = t->cmp(n->vals[i], e, t->cmp_data); + if (cmp == 0) { + *equal = true; + len = half; // Keep searching for wildcard matches + } else if (cmp < 0) { + const unsigned chop = half + 1U; + first += chop; + len -= chop; + } else { + len = half; + } + } + assert(!*equal || t->cmp(n->vals[first], e, t->cmp_data) == 0); + return first; +} + +ZIX_API ZixStatus +zix_btree_insert(ZixBTree* const t, void* const e) +{ + ZixBTreeNode* parent = NULL; // Parent of n + ZixBTreeNode* n = t->root; // Current node + unsigned i = 0; // Index of n in parent + while (n) { + if (n->n_vals == zix_btree_max_vals(n)) { + // Node is full, split to ensure there is space for a leaf split + if (!parent) { + // Root is full, grow tree upwards + if (!(parent = zix_btree_node_new(false))) { + return ZIX_STATUS_NO_MEM; + } + t->root = parent; + parent->children[0] = n; + ++t->height; + } + + ZixBTreeNode* const rhs = zix_btree_split_child(parent, i, n); + if (!rhs) { + return ZIX_STATUS_NO_MEM; + } + + const int cmp = t->cmp(parent->vals[i], e, t->cmp_data); + if (cmp == 0) { + return ZIX_STATUS_EXISTS; + } else if (cmp < 0) { + // Move to new RHS + n = rhs; + ++i; + } + } + + assert(!parent || parent->children[i] == n); + + bool equal = false; + i = zix_btree_node_find(t, n, e, &equal); + if (equal) { + return ZIX_STATUS_EXISTS; + } else if (!n->is_leaf) { + // Descend to child node left of value + parent = n; + n = n->children[i]; + } else { + // Insert into internal node + zix_btree_ainsert(n->vals, n->n_vals++, i, e); + break; + } + } + + ++t->size; + + return ZIX_STATUS_SUCCESS; +} + +ZIX_PRIVATE ZixBTreeIter* +zix_btree_iter_new(const ZixBTree* const t) +{ + const size_t s = t->height * sizeof(ZixBTreeIterFrame); + + ZixBTreeIter* i = (ZixBTreeIter*)calloc(1, sizeof(ZixBTreeIter) + s); + if (i) { + i->n_levels = t->height; + } + return i; +} + +ZIX_PRIVATE void +zix_btree_iter_set_frame(ZixBTreeIter* const ti, + ZixBTreeNode* const n, + const unsigned i) +{ + if (ti) { + ti->stack[ti->level].node = n; + ti->stack[ti->level].index = i; + } +} + +ZIX_PRIVATE bool +zix_btree_node_is_minimal(ZixBTreeNode* const n) +{ + assert(n->n_vals >= zix_btree_min_vals(n)); + return n->n_vals == zix_btree_min_vals(n); +} + +/** Enlarge left child by stealing a value from its right sibling. */ +ZIX_PRIVATE ZixBTreeNode* +zix_btree_rotate_left(ZixBTreeNode* const parent, const unsigned i) +{ + ZixBTreeNode* const lhs = parent->children[i]; + ZixBTreeNode* const rhs = parent->children[i + 1]; + + // Move parent value to end of LHS + lhs->vals[lhs->n_vals++] = parent->vals[i]; + + // Move first child pointer from RHS to end of LHS + if (!lhs->is_leaf) { + lhs->children[lhs->n_vals] = (ZixBTreeNode*)zix_btree_aerase( + (void**)rhs->children, rhs->n_vals, 0); + } + + // Move first value in RHS to parent + parent->vals[i] = zix_btree_aerase(rhs->vals, --rhs->n_vals, 0); + + return lhs; +} + +/** Enlarge right child by stealing a value from its left sibling. */ +ZIX_PRIVATE ZixBTreeNode* +zix_btree_rotate_right(ZixBTreeNode* const parent, const unsigned i) +{ + ZixBTreeNode* const lhs = parent->children[i - 1]; + ZixBTreeNode* const rhs = parent->children[i]; + + // Prepend parent value to RHS + zix_btree_ainsert(rhs->vals, rhs->n_vals++, 0, parent->vals[i - 1]); + + // Move last child pointer from LHS and prepend to RHS + if (!lhs->is_leaf) { + zix_btree_ainsert((void**)rhs->children, + rhs->n_vals, + 0, + lhs->children[lhs->n_vals]); + } + + // Move last value from LHS to parent + parent->vals[i - 1] = lhs->vals[--lhs->n_vals]; + + return rhs; +} + +/** Move n[i] down, merge the left and right child, return the merged node. */ +ZIX_PRIVATE ZixBTreeNode* +zix_btree_merge(ZixBTree* const t, ZixBTreeNode* const n, const unsigned i) +{ + ZixBTreeNode* const lhs = n->children[i]; + ZixBTreeNode* const rhs = n->children[i + 1]; + + assert(zix_btree_node_is_minimal(n->children[i])); + assert(lhs->n_vals + rhs->n_vals < zix_btree_max_vals(lhs)); + + // Move parent value to end of LHS + lhs->vals[lhs->n_vals++] = zix_btree_aerase(n->vals, n->n_vals, i); + + // Erase corresponding child pointer (to RHS) in parent + zix_btree_aerase((void**)n->children, n->n_vals, i + 1U); + + // Add everything from RHS to end of LHS + memcpy(lhs->vals + lhs->n_vals, rhs->vals, rhs->n_vals * sizeof(void*)); + if (!lhs->is_leaf) { + memcpy(lhs->children + lhs->n_vals, + rhs->children, + (rhs->n_vals + 1) * sizeof(void*)); + } + lhs->n_vals += rhs->n_vals; + + if (--n->n_vals == 0) { + // Root is now empty, replace it with its only child + assert(n == t->root); + t->root = lhs; + free(n); + } + + free(rhs); + return lhs; +} + +/** Remove and return the min value from the subtree rooted at `n`. */ +ZIX_PRIVATE void* +zix_btree_remove_min(ZixBTree* const t, ZixBTreeNode* n) +{ + while (!n->is_leaf) { + if (zix_btree_node_is_minimal(n->children[0])) { + // Leftmost child is minimal, must expand + if (!zix_btree_node_is_minimal(n->children[1])) { + // Child's right sibling has at least one key to steal + n = zix_btree_rotate_left(n, 0); + } else { + // Both child and right sibling are minimal, merge + n = zix_btree_merge(t, n, 0); + } + } else { + n = n->children[0]; + } + } + + return zix_btree_aerase(n->vals, --n->n_vals, 0); +} + +/** Remove and return the max value from the subtree rooted at `n`. */ +ZIX_PRIVATE void* +zix_btree_remove_max(ZixBTree* const t, ZixBTreeNode* n) +{ + while (!n->is_leaf) { + if (zix_btree_node_is_minimal(n->children[n->n_vals])) { + // Leftmost child is minimal, must expand + if (!zix_btree_node_is_minimal(n->children[n->n_vals - 1])) { + // Child's left sibling has at least one key to steal + n = zix_btree_rotate_right(n, n->n_vals); + } else { + // Both child and left sibling are minimal, merge + n = zix_btree_merge(t, n, n->n_vals - 1U); + } + } else { + n = n->children[n->n_vals]; + } + } + + return n->vals[--n->n_vals]; +} + +ZIX_API ZixStatus +zix_btree_remove(ZixBTree* const t, + const void* const e, + void** const out, + ZixBTreeIter** const next) +{ + ZixBTreeNode* n = t->root; + ZixBTreeIter* ti = NULL; + const bool user_iter = next && *next; + if (next) { + if (!*next && !(*next = zix_btree_iter_new(t))) { + return ZIX_STATUS_NO_MEM; + } + ti = *next; + ti->level = 0; + } + + while (true) { + /* To remove in a single walk down, the tree is adjusted along the way + so that the current node always has at least one more value than the + minimum required in general. Thus, there is always room to remove + without adjusting on the way back up. */ + assert(n == t->root || !zix_btree_node_is_minimal(n)); + + bool equal = false; + const unsigned i = zix_btree_node_find(t, n, e, &equal); + zix_btree_iter_set_frame(ti, n, i); + if (n->is_leaf) { + if (equal) { + // Found in leaf node + *out = zix_btree_aerase(n->vals, --n->n_vals, i); + if (ti && i == n->n_vals) { + if (i == 0) { + ti->stack[ti->level = 0].node = NULL; + } else { + --ti->stack[ti->level].index; + zix_btree_iter_increment(ti); + } + } + --t->size; + return ZIX_STATUS_SUCCESS; + } else { + // Not found in leaf node, or tree + if (ti && !user_iter) { + zix_btree_iter_free(ti); + *next = NULL; + } + return ZIX_STATUS_NOT_FOUND; + } + } else if (equal) { + // Found in internal node + const size_t l_size = n->children[i]->n_vals; + const size_t r_size = n->children[i + 1]->n_vals; + if (zix_btree_node_is_minimal(n->children[i]) && + zix_btree_node_is_minimal(n->children[i + 1])) { + // Both preceding and succeeding child are minimal + n = zix_btree_merge(t, n, i); + } else if (l_size >= r_size) { + // Left child can remove without merge + assert(!zix_btree_node_is_minimal(n->children[i])); + *out = n->vals[i]; + n->vals[i] = zix_btree_remove_max(t, n->children[i]); + --t->size; + return ZIX_STATUS_SUCCESS; + } else { + // Right child can remove without merge + assert(!zix_btree_node_is_minimal(n->children[i + 1])); + *out = n->vals[i]; + n->vals[i] = zix_btree_remove_min(t, n->children[i + 1]); + --t->size; + return ZIX_STATUS_SUCCESS; + } + } else { + // Not found in internal node, key is in/under children[i] + if (zix_btree_node_is_minimal(n->children[i])) { + if (i > 0 && !zix_btree_node_is_minimal(n->children[i - 1])) { + // Steal a key from child's left sibling + n = zix_btree_rotate_right(n, i); + } else if (i < n->n_vals && + !zix_btree_node_is_minimal(n->children[i + 1])) { + // Steal a key from child's right sibling + n = zix_btree_rotate_left(n, i); + } else { + // Both child's siblings are minimal, merge them + if (i < n->n_vals) { + n = zix_btree_merge(t, n, i); + } else { + n = zix_btree_merge(t, n, i - 1U); + if (ti) { + --ti->stack[ti->level].index; + } + } + } + } else { + n = n->children[i]; + } + } + if (ti) { + ++ti->level; + } + } + + assert(false); // Not reached + return ZIX_STATUS_ERROR; +} + +ZIX_API ZixStatus +zix_btree_find(const ZixBTree* const t, + const void* const e, + ZixBTreeIter** const ti) +{ + ZixBTreeNode* n = t->root; + if (!(*ti = zix_btree_iter_new(t))) { + return ZIX_STATUS_NO_MEM; + } + + while (n) { + bool equal = false; + const unsigned i = zix_btree_node_find(t, n, e, &equal); + + zix_btree_iter_set_frame(*ti, n, i); + + if (equal) { + return ZIX_STATUS_SUCCESS; + } else if (n->is_leaf) { + break; + } else { + ++(*ti)->level; + n = n->children[i]; + } + } + + zix_btree_iter_free(*ti); + *ti = NULL; + return ZIX_STATUS_NOT_FOUND; +} + +ZIX_API ZixStatus +zix_btree_lower_bound(const ZixBTree* const t, + const void* const e, + ZixBTreeIter** const ti) +{ + if (!t) { + *ti = NULL; + return ZIX_STATUS_BAD_ARG; + } + + ZixBTreeNode* n = t->root; + bool found = false; + unsigned found_level = 0; + if (!(*ti = zix_btree_iter_new(t))) { + return ZIX_STATUS_NO_MEM; + } + + while (n) { + bool equal = false; + const unsigned i = zix_btree_node_find(t, n, e, &equal); + + zix_btree_iter_set_frame(*ti, n, i); + + if (equal) { + found_level = (*ti)->level; + found = true; + } + + if (n->is_leaf) { + break; + } else { + ++(*ti)->level; + n = n->children[i]; + assert(n); + } + } + + const ZixBTreeIterFrame* const frame = &(*ti)->stack[(*ti)->level]; + assert(frame->node); + if (frame->index == frame->node->n_vals) { + if (found) { + // Found on a previous level but went too far + (*ti)->level = found_level; + } else { + // Reached end (key is greater than everything in tree) + (*ti)->stack[0].node = NULL; + } + } + + return ZIX_STATUS_SUCCESS; +} + +ZIX_API void* +zix_btree_get(const ZixBTreeIter* const ti) +{ + const ZixBTreeIterFrame* const frame = &ti->stack[ti->level]; + assert(frame->node); + assert(frame->index < frame->node->n_vals); + return frame->node->vals[frame->index]; +} + +ZIX_API ZixBTreeIter* +zix_btree_begin(const ZixBTree* const t) +{ + ZixBTreeIter* const i = zix_btree_iter_new(t); + if (!i) { + return NULL; + } else if (t->size == 0) { + i->stack[0].node = NULL; + } else { + ZixBTreeNode* n = t->root; + i->stack[0].node = n; + i->stack[0].index = 0; + while (!n->is_leaf) { + n = n->children[0]; + ++i->level; + i->stack[i->level].node = n; + i->stack[i->level].index = 0; + } + } + return i; +} + +ZIX_API ZixBTreeIter* +zix_btree_end(const ZixBTree* const t) +{ + return zix_btree_iter_new(t); +} + +ZIX_API ZixBTreeIter* +zix_btree_iter_copy(const ZixBTreeIter* const i) +{ + if (!i) { + return NULL; + } + + const size_t s = i->n_levels * sizeof(ZixBTreeIterFrame); + ZixBTreeIter* j = (ZixBTreeIter*)calloc(1, sizeof(ZixBTreeIter) + s); + if (j) { + memcpy(j, i, sizeof(ZixBTreeIter) + s); + } + return j; +} + +ZIX_API bool +zix_btree_iter_is_end(const ZixBTreeIter* const i) +{ + return !i || i->stack[0].node == NULL; +} + +ZIX_API bool +zix_btree_iter_equals(const ZixBTreeIter* const lhs, const ZixBTreeIter* const rhs) +{ + if (zix_btree_iter_is_end(lhs) && zix_btree_iter_is_end(rhs)) { + return true; + } else if (!lhs || !rhs || lhs->n_levels != rhs->n_levels) { + return false; + } + + return !memcmp(lhs, + rhs, + sizeof(ZixBTreeIter) + + lhs->n_levels * sizeof(ZixBTreeIterFrame)); +} + +ZIX_API void +zix_btree_iter_increment(ZixBTreeIter* const i) +{ + ZixBTreeIterFrame* f = &i->stack[i->level]; + if (f->node->is_leaf) { + // Leaf, move right + assert(f->index < f->node->n_vals); + if (++f->index == f->node->n_vals) { + // Reached end of leaf, move up + f = &i->stack[i->level]; + while (i->level > 0 && f->index == f->node->n_vals) { + f = &i->stack[--i->level]; + assert(f->index <= f->node->n_vals); + } + + if (f->index == f->node->n_vals) { + // Reached end of tree + assert(i->level == 0); + f->node = NULL; + f->index = 0; + } + } + } else { + // Internal node, move down to next child + assert(f->index < f->node->n_vals); + ZixBTreeNode* child = f->node->children[++f->index]; + + f = &i->stack[++i->level]; + f->node = child; + f->index = 0; + + // Move down and left until we hit a leaf + while (!f->node->is_leaf) { + child = f->node->children[0]; + f = &i->stack[++i->level]; + f->node = child; + f->index = 0; + } + } +} + +ZIX_API void +zix_btree_iter_free(ZixBTreeIter* const i) +{ + free(i); +} -- cgit v1.2.1