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-rw-r--r--src/zix/btree.c702
1 files changed, 702 insertions, 0 deletions
diff --git a/src/zix/btree.c b/src/zix/btree.c
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--- /dev/null
+++ b/src/zix/btree.c
@@ -0,0 +1,702 @@
+/*
+ Copyright 2011-2014 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
+ 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 <assert.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "zix/btree.h"
+
+// #define ZIX_BTREE_DEBUG 1
+
+#define ZIX_BTREE_PAGE_SIZE 4096
+#define ZIX_BTREE_NODE_SPACE (ZIX_BTREE_PAGE_SIZE - 2 * sizeof(uint32_t))
+#define ZIX_BTREE_LEAF_VALS (ZIX_BTREE_NODE_SPACE / sizeof(void*))
+#define ZIX_BTREE_INODE_VALS (ZIX_BTREE_LEAF_VALS / 2)
+
+struct ZixBTreeImpl {
+ ZixBTreeNode* root;
+ ZixDestroyFunc destroy;
+ ZixComparator cmp;
+ void* cmp_data;
+ size_t size;
+ unsigned height; ///< Number of levels, i.e. root only has height 1
+};
+
+struct ZixBTreeNodeImpl {
+ uint32_t is_leaf;
+ uint32_t n_vals;
+ 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 level; ///< Current level in pos
+ ZixBTreeIterFrame stack[]; ///< Position stack
+};
+
+#ifdef ZIX_BTREE_DEBUG
+
+ZIX_PRIVATE void
+print_node(const ZixBTreeNode* n, const char* prefix)
+{
+ printf("%s[", prefix);
+ for (unsigned 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 (unsigned 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,
+ 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 (unsigned i = 0; i < n->n_vals; ++i) {
+ t->destroy(n->vals[i]);
+ }
+ }
+ if (!n->is_leaf) {
+ for (unsigned 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 unsigned
+zix_btree_max_vals(const ZixBTreeNode* const node)
+{
+ return node->is_leaf ? ZIX_BTREE_LEAF_VALS : ZIX_BTREE_INODE_VALS;
+}
+
+ZIX_PRIVATE unsigned
+zix_btree_min_vals(const ZixBTreeNode* const node)
+{
+ return ((zix_btree_max_vals(node) + 1) / 2) - 1;
+}
+
+/** 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 uint32_t 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 + 1);
+ assert(n->children[i] == lhs);
+
+ const unsigned 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 / 2;
+ rhs->n_vals = 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,
+ (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 + 1, 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)
+{
+ unsigned first = 0;
+ unsigned len = n->n_vals;
+ while (len > 0) {
+ const unsigned half = len >> 1;
+ 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 + 1;
+ 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;
+ }
+ }
+
+ ++n->n_vals;
+ ++t->size;
+
+ return ZIX_STATUS_SUCCESS;
+}
+
+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] = 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 + 1);
+
+ // 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 - 1);
+ }
+ } else {
+ n = n->children[n->n_vals];
+ }
+ }
+
+ return n->vals[--n->n_vals];
+}
+
+ZIX_PRIVATE ZixStatus
+zix_btree_remove_rec(ZixBTree* const t,
+ ZixBTreeNode* const n,
+ const void* const e,
+ void** const removed)
+{
+ /* 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);
+
+ if (n->is_leaf) {
+ if (equal) {
+ // Found in leaf node
+ *removed = zix_btree_aerase(n->vals, --n->n_vals, i);
+ return ZIX_STATUS_SUCCESS;
+ } else {
+ // Not found in leaf node, or tree
+ return ZIX_STATUS_NOT_FOUND;
+ }
+ } else if (equal) {
+ // Found in internal node
+ if (!zix_btree_node_is_minimal(n->children[i])) {
+ // Left child can remove without merge
+ *removed = n->vals[i];
+ n->vals[i] = zix_btree_remove_max(t, n->children[i]);
+ return ZIX_STATUS_SUCCESS;
+ } else if (!zix_btree_node_is_minimal(n->children[i + 1])) {
+ // Right child can remove without merge
+ *removed = n->vals[i];
+ n->vals[i] = zix_btree_remove_min(t, n->children[i + 1]);
+ return ZIX_STATUS_SUCCESS;
+ } else {
+ // Both preceding and succeeding child are minimal
+ ZixBTreeNode* const merged = zix_btree_merge(t, n, i);
+ return zix_btree_remove_rec(t, merged, e, removed);
+ }
+ } 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])) {
+ // Child's left sibling has at least one key to steal
+ ZixBTreeNode* const rhs = zix_btree_rotate_right(n, i);
+ return zix_btree_remove_rec(t, rhs, e, removed);
+ } else if (i < n->n_vals &&
+ !zix_btree_node_is_minimal(n->children[i + 1])) {
+ // Child's right sibling has at least one key to steal
+ ZixBTreeNode* const lhs = zix_btree_rotate_left(n, i);
+ return zix_btree_remove_rec(t, lhs, e, removed);
+ } else {
+ // Both child's siblings are minimal, merge them
+ const unsigned m = (i < n->n_vals) ? i : i - 1;
+ ZixBTreeNode* const merged = zix_btree_merge(t, n, m);
+ return zix_btree_remove_rec(t, merged, e, removed);
+ }
+ } else {
+ return zix_btree_remove_rec(t, n->children[i], e, removed);
+ }
+ }
+
+ assert(false); // Not reached
+ return ZIX_STATUS_ERROR;
+}
+
+ZIX_API ZixStatus
+zix_btree_remove(ZixBTree* const t, const void* const e, void** const removed)
+{
+ const ZixStatus st = zix_btree_remove_rec(t, t->root, e, removed);
+ if (!st) {
+ --t->size;
+ }
+ return st;
+}
+
+ZIX_PRIVATE ZixBTreeIter*
+zix_btree_iter_new(const ZixBTree* const t)
+{
+ const size_t s = t->height * sizeof(ZixBTreeIterFrame);
+ ZixBTreeIter* const i = (ZixBTreeIter*)malloc(sizeof(ZixBTreeIter) + s);
+ if (i) {
+ i->level = 0;
+ }
+ return i;
+}
+
+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);
+
+ // Update iterator stack
+ (*ti)->stack[(*ti)->level].node = n;
+ (*ti)->stack[(*ti)->level].index = 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)
+{
+ 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);
+
+ // Update iterator stack
+ (*ti)->stack[(*ti)->level].node = n;
+ (*ti)->stack[(*ti)->level].index = i;
+
+ if (equal) {
+ found_level = (*ti)->level;
+ found = true;
+ }
+
+ if (n->is_leaf) {
+ break;
+ } else {
+ ++(*ti)->level;
+ n = n->children[i];
+ }
+ }
+
+ const ZixBTreeIterFrame* const frame = &(*ti)->stack[(*ti)->level];
+ 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->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 bool
+zix_btree_iter_is_end(const ZixBTreeIter* const i)
+{
+ return !i || i->stack[0].node == NULL;
+}
+
+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);
+}
generated by cgit v1.2.1 (git 2.18.0) at 2024-11-09 04:28:59 +0000