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-rw-r--r--src/zix/btree.c290
1 files changed, 194 insertions, 96 deletions
diff --git a/src/zix/btree.c b/src/zix/btree.c
index 3dc2d57..ba2ad0d 100644
--- a/src/zix/btree.c
+++ b/src/zix/btree.c
@@ -1,5 +1,5 @@
/*
- Copyright 2011-2019 David Robillard <http://drobilla.net>
+ Copyright 2011-2020 David Robillard <http://drobilla.net>
Permission to use, copy, modify, and/or distribute this software for any
purpose with or without fee is hereby granted, provided that the above
@@ -45,10 +45,23 @@ 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
+ union {
+ struct {
+ void* vals[ZIX_BTREE_LEAF_VALS];
+ } leaf;
+
+ struct {
+ void* vals[ZIX_BTREE_INODE_VALS];
+ ZixBTreeNode* children[ZIX_BTREE_INODE_VALS + 1];
+ } inode;
+ } data;
};
+#if (defined(__STDC_VERSION__) && __STDC_VERSION__ >= 201112l) || \
+ (defined(__cplusplus) && __cplusplus >= 201103L)
+static_assert(sizeof(ZixBTreeNode) == ZIX_BTREE_PAGE_SIZE, "");
+#endif
+
typedef struct {
ZixBTreeNode* node;
unsigned index;
@@ -85,7 +98,7 @@ print_tree(const ZixBTreeNode* parent, const ZixBTreeNode* node, int level)
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);
+ print_tree(node, node->data.inode.children[i], level + 1);
}
}
if (!parent) {
@@ -99,7 +112,11 @@ print_tree(const ZixBTreeNode* parent, const ZixBTreeNode* node, int level)
ZIX_PRIVATE ZixBTreeNode*
zix_btree_node_new(const bool leaf)
{
+#if !((defined(__STDC_VERSION__) && __STDC_VERSION__ >= 201112l) || \
+ (defined(__cplusplus) && __cplusplus >= 201103L))
assert(sizeof(ZixBTreeNode) == ZIX_BTREE_PAGE_SIZE);
+#endif
+
ZixBTreeNode* node = (ZixBTreeNode*)malloc(sizeof(ZixBTreeNode));
if (node) {
node->is_leaf = leaf;
@@ -108,6 +125,23 @@ zix_btree_node_new(const bool leaf)
return node;
}
+ZIX_PRIVATE
+void*
+zix_btree_value(const ZixBTreeNode* const node, const unsigned i)
+{
+ assert(i < node->n_vals);
+ return node->is_leaf ? node->data.leaf.vals[i] : node->data.inode.vals[i];
+}
+
+ZIX_PRIVATE
+ZixBTreeNode*
+zix_btree_child(const ZixBTreeNode* const node, const unsigned i)
+{
+ assert(!node->is_leaf);
+ assert(i <= ZIX_BTREE_INODE_VALS);
+ return node->data.inode.children[i];
+}
+
ZixBTree*
zix_btree_new(const ZixComparator cmp,
const void* const cmp_data,
@@ -133,14 +167,21 @@ 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) {
+ if (t->destroy) {
+ for (uint16_t i = 0; i < n->n_vals; ++i) {
+ t->destroy(n->data.leaf.vals[i]);
+ }
}
- }
- if (!n->is_leaf) {
+ } else {
+ if (t->destroy) {
+ for (uint16_t i = 0; i < n->n_vals; ++i) {
+ t->destroy(n->data.inode.vals[i]);
+ }
+ }
+
for (uint16_t i = 0; i < n->n_vals + 1; ++i) {
- zix_btree_free_rec(t, n->children[i]);
+ zix_btree_free_rec(t, zix_btree_child(n, i));
}
}
free(n);
@@ -203,7 +244,7 @@ zix_btree_split_child(ZixBTreeNode* const n,
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);
+ assert(zix_btree_child(n, i) == lhs);
const uint16_t max_n_vals = zix_btree_max_vals(lhs);
ZixBTreeNode* rhs = zix_btree_node_new(lhs->is_leaf);
@@ -215,23 +256,35 @@ zix_btree_split_child(ZixBTreeNode* const n,
lhs->n_vals = max_n_vals / 2U;
rhs->n_vals = (uint16_t)(max_n_vals - lhs->n_vals - 1);
- // 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,
+ if (lhs->is_leaf) {
+ // Copy large half from LHS to new RHS node
+ memcpy(rhs->data.leaf.vals,
+ lhs->data.leaf.vals + lhs->n_vals + 1,
+ rhs->n_vals * sizeof(void*));
+
+ // Move middle value up to parent
+ zix_btree_ainsert(n->data.inode.vals,
+ n->n_vals,
+ i,
+ lhs->data.leaf.vals[lhs->n_vals]);
+ } else {
+ // Copy large half from LHS to new RHS node
+ memcpy(rhs->data.inode.vals,
+ lhs->data.inode.vals + lhs->n_vals + 1,
+ rhs->n_vals * sizeof(void*));
+ memcpy(rhs->data.inode.children,
+ lhs->data.inode.children + lhs->n_vals + 1,
(rhs->n_vals + 1U) * sizeof(ZixBTreeNode*));
- }
- // Move middle value up to parent
- zix_btree_ainsert(n->vals, n->n_vals, i, lhs->vals[lhs->n_vals]);
+ // Move middle value up to parent
+ zix_btree_ainsert(n->data.inode.vals,
+ n->n_vals,
+ i,
+ lhs->data.inode.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);
+ zix_btree_ainsert((void**)n->data.inode.children, ++n->n_vals, i + 1U, rhs);
return rhs;
}
@@ -247,10 +300,11 @@ zix_btree_node_is_sorted_with_respect_to(const ZixBTree* const t,
return true;
}
- int cmp = t->cmp(n->vals[0], e, t->cmp_data);
+ int cmp = t->cmp(zix_btree_value(n, 0), e, t->cmp_data);
for (uint16_t i = 1; i < n->n_vals; ++i) {
- const int next_cmp = t->cmp(n->vals[i], e, t->cmp_data);
- if ((cmp >= 0 && next_cmp < 0)) {
+ const int next_cmp = t->cmp(zix_btree_value(n, i), e, t->cmp_data);
+ if ((cmp >= 0 && next_cmp < 0) ||
+ (cmp > 0 && next_cmp <= 0)) {
return false;
}
cmp = next_cmp;
@@ -276,7 +330,7 @@ zix_btree_node_find(const ZixBTree* const t,
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);
+ const int cmp = t->cmp(zix_btree_value(n, i), e, t->cmp_data);
if (cmp == 0) {
*equal = true;
len = half; // Keep searching for wildcard matches
@@ -288,7 +342,7 @@ zix_btree_node_find(const ZixBTree* const t,
len = half;
}
}
- assert(!*equal || t->cmp(n->vals[first], e, t->cmp_data) == 0);
+ assert(!*equal || t->cmp(zix_btree_value(n, first), e, t->cmp_data) == 0);
return first;
}
@@ -306,8 +360,8 @@ zix_btree_insert(ZixBTree* const t, void* const e)
if (!(parent = zix_btree_node_new(false))) {
return ZIX_STATUS_NO_MEM;
}
- t->root = parent;
- parent->children[0] = n;
+ t->root = parent;
+ parent->data.inode.children[0] = n;
++t->height;
}
@@ -316,7 +370,7 @@ zix_btree_insert(ZixBTree* const t, void* const e)
return ZIX_STATUS_NO_MEM;
}
- const int cmp = t->cmp(parent->vals[i], e, t->cmp_data);
+ const int cmp = t->cmp(parent->data.inode.vals[i], e, t->cmp_data);
if (cmp == 0) {
return ZIX_STATUS_EXISTS;
} else if (cmp < 0) {
@@ -326,7 +380,7 @@ zix_btree_insert(ZixBTree* const t, void* const e)
}
}
- assert(!parent || parent->children[i] == n);
+ assert(!parent || zix_btree_child(parent, i) == n);
bool equal = false;
i = zix_btree_node_find(t, n, e, &equal);
@@ -335,10 +389,10 @@ zix_btree_insert(ZixBTree* const t, void* const e)
} else if (!n->is_leaf) {
// Descend to child node left of value
parent = n;
- n = n->children[i];
+ n = zix_btree_child(n, i);
} else {
// Insert into internal node
- zix_btree_ainsert(n->vals, n->n_vals++, i, e);
+ zix_btree_ainsert(n->data.leaf.vals, n->n_vals++, i, e);
break;
}
}
@@ -382,20 +436,32 @@ zix_btree_node_is_minimal(ZixBTreeNode* const n)
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];
+ ZixBTreeNode* const lhs = zix_btree_child(parent, i);
+ ZixBTreeNode* const rhs = zix_btree_child(parent, i + 1);
- // Move parent value to end of LHS
- lhs->vals[lhs->n_vals++] = parent->vals[i];
+ assert(lhs->is_leaf == rhs->is_leaf);
+
+ if (lhs->is_leaf) {
+ // Move parent value to end of LHS
+ lhs->data.leaf.vals[lhs->n_vals++] = parent->data.inode.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->data.inode.vals[i] =
+ zix_btree_aerase(rhs->data.leaf.vals, rhs->n_vals, 0);
+ } else {
+ // Move parent value to end of LHS
+ lhs->data.inode.vals[lhs->n_vals++] = parent->data.inode.vals[i];
+
+ // Move first value in RHS to parent
+ parent->data.inode.vals[i] =
+ zix_btree_aerase(rhs->data.inode.vals, rhs->n_vals, 0);
+
+ // Move first child pointer from RHS to end of LHS
+ lhs->data.inode.children[lhs->n_vals] = (ZixBTreeNode*)zix_btree_aerase(
+ (void**)rhs->data.inode.children, rhs->n_vals, 0);
}
- // Move first value in RHS to parent
- parent->vals[i] = zix_btree_aerase(rhs->vals, --rhs->n_vals, 0);
+ --rhs->n_vals;
return lhs;
}
@@ -404,22 +470,36 @@ zix_btree_rotate_left(ZixBTreeNode* const parent, const unsigned i)
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];
+ ZixBTreeNode* const lhs = zix_btree_child(parent, i - 1);
+ ZixBTreeNode* const rhs = zix_btree_child(parent, i);
- // Prepend parent value to RHS
- zix_btree_ainsert(rhs->vals, rhs->n_vals++, 0, parent->vals[i - 1]);
+ assert(lhs->is_leaf == rhs->is_leaf);
+
+ if (lhs->is_leaf) {
+ // Prepend parent value to RHS
+ zix_btree_ainsert(rhs->data.leaf.vals,
+ rhs->n_vals++,
+ 0,
+ parent->data.inode.vals[i - 1]);
- // Move last child pointer from LHS and prepend to RHS
- if (!lhs->is_leaf) {
- zix_btree_ainsert((void**)rhs->children,
+ // Move last value from LHS to parent
+ parent->data.inode.vals[i - 1] = lhs->data.leaf.vals[--lhs->n_vals];
+ } else {
+ // Prepend parent value to RHS
+ zix_btree_ainsert(rhs->data.inode.vals,
+ rhs->n_vals++,
+ 0,
+ parent->data.inode.vals[i - 1]);
+
+ // Move last child pointer from LHS and prepend to RHS
+ zix_btree_ainsert((void**)rhs->data.inode.children,
rhs->n_vals,
0,
- lhs->children[lhs->n_vals]);
- }
+ lhs->data.inode.children[lhs->n_vals]);
- // Move last value from LHS to parent
- parent->vals[i - 1] = lhs->vals[--lhs->n_vals];
+ // Move last value from LHS to parent
+ parent->data.inode.vals[i - 1] = lhs->data.inode.vals[--lhs->n_vals];
+ }
return rhs;
}
@@ -428,25 +508,39 @@ zix_btree_rotate_right(ZixBTreeNode* const parent, const unsigned i)
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];
+ ZixBTreeNode* const lhs = zix_btree_child(n, i);
+ ZixBTreeNode* const rhs = zix_btree_child(n, i + 1);
- assert(zix_btree_node_is_minimal(n->children[i]));
+ assert(lhs->is_leaf == rhs->is_leaf);
+ assert(zix_btree_node_is_minimal(lhs));
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);
+ if (lhs->is_leaf) {
+ lhs->data.leaf.vals[lhs->n_vals++] =
+ zix_btree_aerase(n->data.inode.vals, n->n_vals, i);
+ } else {
+ lhs->data.inode.vals[lhs->n_vals++] =
+ zix_btree_aerase(n->data.inode.vals, n->n_vals, i);
+ }
// Erase corresponding child pointer (to RHS) in parent
- zix_btree_aerase((void**)n->children, n->n_vals, i + 1U);
+ zix_btree_aerase((void**)n->data.inode.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,
+ if (lhs->is_leaf) {
+ memcpy(lhs->data.leaf.vals + lhs->n_vals,
+ rhs->data.leaf.vals,
+ rhs->n_vals * sizeof(void*));
+ } else {
+ memcpy(lhs->data.inode.vals + lhs->n_vals,
+ rhs->data.inode.vals,
+ rhs->n_vals * sizeof(void*));
+ memcpy(lhs->data.inode.children + lhs->n_vals,
+ rhs->data.inode.children,
(rhs->n_vals + 1U) * sizeof(void*));
}
+
lhs->n_vals = (uint16_t)(lhs->n_vals + rhs->n_vals);
if (--n->n_vals == 0) {
@@ -465,9 +559,9 @@ 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])) {
+ if (zix_btree_node_is_minimal(zix_btree_child(n, 0))) {
// Leftmost child is minimal, must expand
- if (!zix_btree_node_is_minimal(n->children[1])) {
+ if (!zix_btree_node_is_minimal(zix_btree_child(n, 1))) {
// Child's right sibling has at least one key to steal
n = zix_btree_rotate_left(n, 0);
} else {
@@ -475,11 +569,11 @@ zix_btree_remove_min(ZixBTree* const t, ZixBTreeNode* n)
n = zix_btree_merge(t, n, 0);
}
} else {
- n = n->children[0];
+ n = zix_btree_child(n, 0);
}
}
- return zix_btree_aerase(n->vals, --n->n_vals, 0);
+ return zix_btree_aerase(n->data.leaf.vals, --n->n_vals, 0);
}
/** Remove and return the max value from the subtree rooted at `n`. */
@@ -487,9 +581,9 @@ 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])) {
+ if (zix_btree_node_is_minimal(zix_btree_child(n, n->n_vals))) {
// Leftmost child is minimal, must expand
- if (!zix_btree_node_is_minimal(n->children[n->n_vals - 1])) {
+ if (!zix_btree_node_is_minimal(zix_btree_child(n, 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 {
@@ -497,11 +591,11 @@ zix_btree_remove_max(ZixBTree* const t, ZixBTreeNode* n)
n = zix_btree_merge(t, n, n->n_vals - 1U);
}
} else {
- n = n->children[n->n_vals];
+ n = zix_btree_child(n, n->n_vals);
}
}
- return n->vals[--n->n_vals];
+ return n->data.leaf.vals[--n->n_vals];
}
ZixStatus
@@ -534,7 +628,7 @@ zix_btree_remove(ZixBTree* const t,
if (n->is_leaf) {
if (equal) {
// Found in leaf node
- *out = zix_btree_aerase(n->vals, --n->n_vals, i);
+ *out = zix_btree_aerase(n->data.leaf.vals, --n->n_vals, i);
if (ti && i == n->n_vals) {
if (i == 0) {
ti->level = 0;
@@ -556,42 +650,46 @@ zix_btree_remove(ZixBTree* const t,
}
} 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])) {
+ ZixBTreeNode* const lhs = zix_btree_child(n, i);
+ ZixBTreeNode* const rhs = zix_btree_child(n, i + 1);
+ const size_t l_size = lhs->n_vals;
+ const size_t r_size = rhs->n_vals;
+ if (zix_btree_node_is_minimal(lhs) &&
+ zix_btree_node_is_minimal(rhs)) {
// 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]);
+ assert(!zix_btree_node_is_minimal(lhs));
+ *out = n->data.inode.vals[i];
+ n->data.inode.vals[i] = zix_btree_remove_max(t, lhs);
--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]);
+ assert(!zix_btree_node_is_minimal(rhs));
+ *out = n->data.inode.vals[i];
+ n->data.inode.vals[i] = zix_btree_remove_min(t, rhs);
--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])) {
+ if (zix_btree_node_is_minimal(zix_btree_child(n, i))) {
+ if (i > 0 &&
+ !zix_btree_node_is_minimal(zix_btree_child(n, 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])) {
+ !zix_btree_node_is_minimal(
+ zix_btree_child(n, i + 1))) {
// Steal a key from child's right sibling
n = zix_btree_rotate_left(n, i);
} else if (n == t->root && n->n_vals == 1) {
// Root has two children, both minimal, delete it
assert(i == 0 || i == 1);
- const uint16_t counts[2] = {n->children[0]->n_vals,
- n->children[1]->n_vals};
+ const uint16_t counts[2] = {zix_btree_child(n, 0)->n_vals,
+ zix_btree_child(n, 1)->n_vals};
n = zix_btree_merge(t, n, 0);
if (ti) {
@@ -610,7 +708,7 @@ zix_btree_remove(ZixBTree* const t,
}
}
} else {
- n = n->children[i];
+ n = zix_btree_child(n, i);
}
}
if (ti) {
@@ -644,7 +742,7 @@ zix_btree_find(const ZixBTree* const t,
break;
} else {
++(*ti)->level;
- n = n->children[i];
+ n = zix_btree_child(n, i);
}
}
@@ -688,7 +786,7 @@ zix_btree_lower_bound(const ZixBTree* const t,
break;
} else {
++(*ti)->level;
- n = n->children[i];
+ n = zix_btree_child(n, i);
assert(n);
}
}
@@ -715,7 +813,7 @@ 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];
+ return zix_btree_value(frame->node, frame->index);
}
ZixBTreeIter*
@@ -732,7 +830,7 @@ zix_btree_begin(const ZixBTree* const t)
i->stack[0].node = n;
i->stack[0].index = 0;
while (!n->is_leaf) {
- n = n->children[0];
+ n = zix_btree_child(n, 0);
++i->level;
i->stack[i->level].node = n;
i->stack[i->level].index = 0;
@@ -809,7 +907,7 @@ zix_btree_iter_increment(ZixBTreeIter* const i)
} else {
// Internal node, move down to next child
assert(f->index < f->node->n_vals);
- ZixBTreeNode* child = f->node->children[++f->index];
+ ZixBTreeNode* child = zix_btree_child(f->node, ++f->index);
f = &i->stack[++i->level];
f->node = child;
@@ -817,7 +915,7 @@ zix_btree_iter_increment(ZixBTreeIter* const i)
// Move down and left until we hit a leaf
while (!f->node->is_leaf) {
- child = f->node->children[0];
+ child = zix_btree_child(f->node, 0);
f = &i->stack[++i->level];
f->node = child;
f->index = 0;