/*
  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 "zix/btree.h"

#include <assert.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>

// #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) + 1) / 2) - 1;
}

/** Shift pointers in `array` of length `n` right starting at `i`. */
ZIX_PRIVATE void
zix_btree_ainsert(void** const   array,
                  const uint16_t n,
                  const uint16_t 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 uint16_t n, const uint16_t 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 uint16_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 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 / 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 uint16_t
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 uint16_t half = len >> 1;
		const uint16_t 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 uint16_t 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
	uint16_t      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 uint16_t      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 uint16_t 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 uint16_t 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 uint16_t 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_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 uint16_t 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 - 1);
						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 uint16_t 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 uint16_t 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);
}