Organize the sourcefiles

1 files changed, 800 insertions, 0 deletions

diff --git a/src/utils/btree.c b/src/utils/btree.c
new file mode 100644
index 0000000..c125564
--- /dev/null
+++ b/src/utils/btree.c
@@ -0,0 +1,800 @@
+#include <engine/btree.h>
+
+#include <stdbool.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include <sys/types.h>
+
+/* Definitions */
+typedef unsigned char byte;
+
+struct node {
+  ssize_t n; /* number of items/keys/elements */
+  ssize_t c; /* number of children */
+  byte* items;
+  struct node** children;
+};
+
+struct btree {
+  /* Memory stuffs */
+  void* (*alloc)(size_t);
+  void (*dealloc)(void*);
+
+  /* Size stuffs */
+  size_t elem_size;
+  ssize_t degree;
+
+  struct node* root;
+
+  /* comparison */
+  int (*cmp)(const void* a, const void* b);
+};
+
+struct btree_iter_t {
+  size_t head;
+  struct stack {
+    int pos;
+    struct node* node;
+  } stack[512];
+  /* This heavily relies on the assumption that a tree never grows deeper than
+   * 512 nodes */
+};
+
+/**********************/
+/* Node functionality */
+/**********************/
+#define node_leaf(node) (node->children == NULL)
+
+#define node_maxdegree(t) (2 * t - 1)
+
+#define node_mindegree(t) (t - 1)
+
+#define node_full(degree, t) (t->n >= 2 * degree - 1)
+
+/* Node memory */
+
+/* `node_new` allocates a new leaf node, children should be added and allocated
+ * when the node is no longer a leaf node */
+struct node* node_new(const ssize_t degree, const size_t elem_size) {
+  const size_t max_items = 2 * degree;
+  struct node* retval = calloc(1, sizeof(struct node));
+
+  retval->n = 0;
+  retval->c = 0;
+  retval->items = calloc(max_items, elem_size);
+  retval->children = NULL;
+
+  return retval;
+}
+
+/* `node_transition` turns a leaf node into a non-leaf. Children are not
+ * allocated.
+ * returnvalue: `false` if we we're unable to allocate space for the new
+ * children. */
+bool node_transition(struct node* node, const ssize_t degree) {
+  const int max_children = 2 * degree + 1;
+  int c;
+
+  if (!node_leaf(node)) {
+    perror("node_transition was called on an already non-leaf node?");
+    return false;
+  }
+
+  /* Allocate pointers for children */
+  node->children = calloc(max_children, sizeof(struct node*));
+
+  if (node->children == NULL) {
+    perror("could not allocate space for children pointers");
+    return false;
+  }
+
+  /* Allocate children */
+  for (c = 0; c < max_children; c++) {
+    node->children[c] = NULL;
+  }
+
+  return true;
+}
+
+void node_free(struct node** node, size_t elem_size, void (*dealloc)(void*)) {
+  if (*node == NULL) return;
+
+  if (!node_leaf((*node))) {
+    ssize_t i;
+    for (i = 0; i < (*node)->c; i++) {
+      node_free(&((*node)->children[i]), elem_size, dealloc);
+    }
+    dealloc((*node)->children);
+  }
+
+  dealloc((*node)->items);
+  (*node)->items = NULL;
+
+  dealloc(*node);
+  *node = NULL;
+}
+
+/* `node_tree_split_child` splits a _full_ node (c = 2t-1 items) into two nodes
+ * with t-1 items each.
+ * The median key/item/element moves up to the original nodes parent, to signify
+ * the split.  If the parent is full too, we need to split it before inserting
+ * the median key.
+ * This can potentially split full nodes all the way up throughout the tree. */
+/* Instead of waiting to find out wether we should split the nodes, we split the
+ * full nodes we encounter on the way down, including the leafs themselves.
+ * By doing this, we are assured that whenever we split a node, its parent has
+ * room for the median key. */
+void node_tree_split_child(const ssize_t t, const size_t elem_size,
+                           struct node* nonfull, ssize_t i) {
+  struct node* z = node_new(t, elem_size);
+  struct node* y = nonfull->children[i];
+  ssize_t j;
+
+  /* `z` should be a branching node if `y` is */
+  if (!node_leaf(y)) {
+    node_transition(z, t);
+  }
+
+  z->n = t - 1;
+
+  /* Move last `t-1` items to new node `z` */
+  /* TODO This can be done with one memcpy */
+  for (j = 0; j < t - 1; j++) {
+    const size_t offset_dst = elem_size * j;
+    const size_t offset_src = elem_size * (t + j);
+    memcpy((z->items) + offset_dst, (y->items) + offset_src, elem_size);
+  }
+  /* Set unused item-memory to zero? */
+
+  /* Move children t..2t, if applicable*/
+  if (!node_leaf(y)) {
+    for (j = 0; j < t + 1; j++) {
+      z->children[j] = y->children[j + t];
+    }
+    y->c = t;
+    z->c = t;
+  }
+
+  y->n = t - 1;
+
+  /* Move children +1 */
+  for (j = nonfull->n; j > i; j--) {
+    nonfull->children[j + 1] = nonfull->children[j];
+  }
+
+  /* new child */
+  nonfull->children[i + 1] = z;
+  nonfull->c++;
+
+  /* moving keys i..n + 1*/
+  /* TODO This can be done with one memcpy */
+  for (j = nonfull->n; j >= i; j--) {
+    const size_t offset = j * elem_size;
+    memcpy((nonfull->items) + offset + elem_size, (nonfull->items) + offset,
+           elem_size);
+  }
+
+  /* Lastly, copy the median element to nonfull-parent*/
+  memcpy((nonfull->items) + i * elem_size, (y->items) + (t - 1) * elem_size,
+         elem_size);
+
+  nonfull->n++;
+}
+
+/* `node_child_merge`: Merges two children around the key at index `i` (k)
+ * by appending k to the left child (y) followed by
+ * appending the right child (z) to y
+ *
+ * `x`: The parent node of y and z
+ * `i`: Index of the item that acts as the new median of the merged node
+ *
+ * WARNING: THIS FUNCTION ASSUMES THAT `i` IS A VALID INDEX
+ */
+void node_child_merge(struct node* x, ssize_t i, const size_t elem_size,
+                      void (*dealloc)(void*)) {
+  struct node* y = x->children[i];
+  struct node* z = x->children[i + 1];
+  int j = 0;
+
+  /* append k to y */
+  memcpy(y->items + (elem_size * y->n++), x->items + (elem_size * i),
+         elem_size);
+
+  /* append keys in z to y */
+  memcpy(y->items + (elem_size * y->n), z->items, elem_size * z->n);
+  y->n += z->n;
+
+  /* Move children from z to y */
+  for (j = 0; j < z->c; j++) {
+    y->children[y->c + j] = z->children[j];
+  }
+  y->c += z->c;
+
+  /* Remove z from x */
+  for (j = i + 1; j < x->c; j++) {
+    x->children[j] = x->children[j + 1];
+  }
+  x->c--;
+
+  /* remove k from x */
+  /* TODO check if we need to use (x->n - 1 - i) instead */
+  memmove(x->items + (elem_size * i), x->items + (elem_size * (i + 1)),
+          elem_size * (x->n - i));
+  x->n--;
+
+  dealloc(z); /* DO NOT USE THE RECURSIVE ONE AS CHILDREN WILL BE LOST!!! */
+}
+
+/* ASSUME i < x->c */
+void node_shift_left(struct node* x, ssize_t i, const size_t elem_size) {
+  struct node* y = x->children[i];
+  struct node* z = x->children[i + 1];
+  byte* x_k = x->items + (elem_size * i);
+
+  /* Append x.k[i] to y */
+  memcpy(y->items + (elem_size * y->n++), x_k, elem_size);
+
+  /* Move first element of z to x.k[i] */
+  memcpy(x_k, z->items, elem_size);
+
+  /* Shift z's items left */
+  memmove(z->items, z->items + elem_size, elem_size * (z->n - 1));
+
+  if (!node_leaf(z)) {
+    ssize_t j;
+    /* append first child of z to y */
+    y->children[y->c++] = z->children[0];
+
+    /* Shift z's children left */
+    for (j = 0; j < z->c; j++) {
+      z->children[j] = z->children[j + 1];
+    }
+    z->c--;
+  }
+
+  z->n--;
+}
+
+void node_shift_right(struct node* x, ssize_t i, const size_t elem_size) {
+  struct node* y = x->children[i];
+  struct node* z = x->children[i + 1];
+  byte* x_k = x->items + (elem_size * i);
+
+  /* Shift z's items right */
+  memmove(z->items + elem_size, z->items, elem_size * z->n);
+
+  /* Prepend x.k[i] to z */
+  memcpy(z->items, x_k, elem_size);
+
+  /* Move last element of y to x.k[i] */
+  memcpy(x_k, y->items + (elem_size * --(y->n)), elem_size);
+
+  if (!node_leaf(z)) {
+    size_t j;
+    /* Shift z's children right */
+    for (j = z->c; j > 0; j--) {
+      z->children[j] = z->children[j - 1];
+    }
+    z->c++;
+
+    /* prepend last child of y to z */
+    z->children[0] = y->children[--(y->c)];
+  }
+
+  z->n++;
+}
+
+/* return: Returns the new root, if a split happens */
+void node_insert_nonfull(struct node* root, void* elem, const ssize_t degree,
+                         const size_t elem_size,
+                         int (*cmp)(const void* a, const void* b)) {
+
+  /* TODO check correctness */
+  ssize_t i = root->n - 1;
+
+  if (node_leaf(root)) {
+    size_t offset = elem_size * i;
+    while (i >= 0 && cmp(elem, root->items + offset) < 0) {
+      /* TODO This can be done with one memcpy */
+      memcpy(root->items + offset + elem_size, root->items + offset, elem_size);
+
+      i--;
+      offset = elem_size * i;
+    }
+    offset = elem_size * (++i);
+    memcpy(root->items + offset, elem, elem_size);
+    root->n++;
+
+  } else {
+    size_t offset = elem_size * i;
+    struct node* nextchild = NULL;
+    while (i >= 0 && cmp(elem, root->items + offset) < 0) {
+      i--;
+      offset = elem_size * i;
+    }
+    i++;
+    nextchild = root->children[i];
+    if (node_full(degree, nextchild)) {
+      /* TODO Check if the root has changed */
+      node_tree_split_child(degree, elem_size, root, i);
+      if (cmp(elem, root->items + elem_size * i) > 0) {
+        nextchild = root->children[++i];
+      }
+    }
+    node_insert_nonfull(nextchild, elem, degree, elem_size, cmp);
+  }
+}
+
+/* Returns the new root, if a split occurs */
+struct node* node_insert(struct node* root, void* elem, const ssize_t degree,
+                         const size_t elem_size,
+                         int (*cmp)(const void* a, const void* b)) {
+
+  struct node* s = root;
+
+  if (node_full(degree, root)) {
+    s = node_new(degree, elem_size);
+    if (s == NULL) {
+      fputs("BTree error: Failed to allocate new node for insertion!\n",
+            stderr);
+      return NULL;
+    }
+    node_transition(s, degree);
+    s->children[s->c++] = root;
+    /* TODO Check if the root has changed */
+    node_tree_split_child(degree, elem_size, s, 0);
+    node_insert_nonfull(s, elem, degree, elem_size, cmp);
+  } else {
+    node_insert_nonfull(s, elem, degree, elem_size, cmp);
+  }
+  return s;
+}
+
+void* node_search(struct node* x, void* key,
+                  int (*cmp)(const void* a, const void* b),
+                  const size_t elem_size) {
+  /* We set to one, since we pre-emptively do a comparison with the assumption
+   * that there's already one in the items */
+  ssize_t i = 0;
+  int last_cmp_res = 0;
+
+  while (i < x->n &&
+         (last_cmp_res = cmp(key, (const void*)(x->items + (i * elem_size)))) >
+             0) {
+    i++;
+  }
+
+  if ((ssize_t)i < x->n && last_cmp_res == 0) {
+    return (void*)(x->items + (i * elem_size));
+  } else if (node_leaf(x)) {
+    return NULL;
+  }
+
+  /* Assumption: ¬node_leaf(x) → x.children is allocated */
+  return node_search(x->children[i], key, cmp, elem_size);
+}
+
+int node_delete(struct node* x, void* key,
+                int (*cmp)(const void* a, const void* b), const ssize_t degree,
+                const size_t elem_size, void* (*alloc)(size_t),
+                void (*dealloc)(void*)) {
+  /* Determine wether the key is in the node */
+  int i = 0; /* Index of `k`, if found */
+  int last_cmp_res = 0;
+
+  while (i < x->n &&
+         (last_cmp_res = cmp(key, (const void*)(x->items + (i * elem_size)))) >
+             0) {
+    i++;
+  }
+
+  if (last_cmp_res == 0) {
+
+    if (node_leaf(x)) {
+      /* 1. k ϵ x && node_leaf(x) */
+      /* Delete k from x */
+      int j = i;
+      while (j + 1 < x->n) {
+        const size_t offset_dst = elem_size * j;
+        const size_t offset_src = elem_size * (j + 1);
+        memcpy((x->items) + offset_dst, (x->items) + offset_src, elem_size);
+        j++;
+      }
+      x->n--;
+      return 1;
+    } else {
+      /* 2. k ϵ x && !node_leaf(x) */
+      /* let i be the index of k in x */
+      /* 2a: if size(child[i]) >= t; find the largest k' in child[i] */
+      /* replace k with k' */
+      if (x->children[i]->n >= degree) {
+        struct node* y = x->children[i];
+        byte* kk = alloc(elem_size);
+
+        /* Find the predecessor, k' of k in y */
+        {
+          struct node* tmp = y;
+          while (!node_leaf(tmp)) {
+            tmp = tmp->children[tmp->n - 1];
+          }
+
+          /* copy kk */
+          memcpy(kk, tmp->items + elem_size * (tmp->n - 1), elem_size);
+        }
+
+        /* Recursively delete kk from y */
+        return node_delete(y, kk, cmp, degree, elem_size, alloc, dealloc);
+
+        /* replace k with kk */
+        memcpy(x->items + (elem_size * i), kk, elem_size);
+
+        dealloc(kk);
+
+        return 1;
+
+      } else if (x->children[i + 1]->n >= degree) {
+        struct node* z = x->children[i + 1];
+        byte* kk = alloc(elem_size);
+
+        /* Find the successor, k' of k in z */
+        {
+          struct node* tmp = z->children[0];
+          while (!node_leaf(tmp)) {
+            tmp = tmp->children[0];
+          }
+
+          /* copy kk */
+          memcpy(kk, tmp->items + elem_size * (tmp->n - 1), elem_size);
+        }
+
+        /* Recursively delete kk from y */
+        return node_delete(z, kk, cmp, degree, elem_size, alloc, dealloc);
+
+        /* replace k with kk */
+        memcpy(x->items + (elem_size * i), kk, elem_size);
+
+        dealloc(kk);
+
+        return 1;
+      } else {
+        /* Merge k and z into y */
+        node_child_merge(x, i, elem_size, dealloc);
+
+        /* recurse */
+        return node_delete(x->children[i], key, cmp, degree, elem_size, alloc,
+                           dealloc);
+      }
+    }
+  } else if (node_leaf(x)) {
+    return 0;
+  } else {
+    /* 3. !(k ϵ x) */
+
+    /*  if x is a leaf, then it is not in the tree */
+
+    struct node* y;
+    int ii; /* index of x.c[i] */
+
+    /* Determine x.c[i] that must contain k */
+    /* if last cmp < 0, then the child must be in the left child of x.items[i]*/
+    if (last_cmp_res < 0) ii = i;
+    /* Otherwise, it must be the very last child */
+    else if (i < x->n)
+      ii = i + 1;
+    else
+      ii = i;
+
+    y = x->children[ii];
+
+    if (y->n < degree) {
+      /* we are left biased */
+      if (ii > 0 && x->children[ii - 1]->n >= degree) {
+        node_shift_right(x, ii - 1, elem_size);
+
+      } else if (ii < x->c - 1 && x->children[ii + 1]->n >= degree) {
+        node_shift_left(x, ii, elem_size);
+
+      } else {
+        /* We need to determine wether we merge left or right, if possible */
+        if (ii > 0) {
+          node_child_merge(x, ii - 1, elem_size, dealloc);
+          y = x->children[ii - 1];
+        } else if (ii < x->c - 1) {
+          node_child_merge(x, ii, elem_size, dealloc);
+        } else {
+          perror("Cannot merge!");
+        }
+      }
+    }
+
+    return node_delete(y, key, cmp, degree, elem_size, alloc, dealloc);
+  }
+  return 0;
+}
+
+/***********************/
+/* Btree functionality */
+/***********************/
+struct btree* btree_new(size_t elem_size, size_t t,
+                        int (*cmp)(const void* a, const void* b)) {
+  return btree_new_with_allocator(elem_size, t, cmp, malloc, free);
+}
+
+struct btree* btree_new_with_allocator(size_t elem_size, size_t t,
+                                       int (*cmp)(const void* a, const void* b),
+                                       void* (*alloc)(size_t),
+                                       void (*dealloc)(void*)) {
+  struct btree* new_tree = alloc(sizeof(struct btree));
+
+  new_tree->alloc = alloc;
+  new_tree->dealloc = dealloc;
+
+  new_tree->elem_size = elem_size;
+  new_tree->degree = t;
+
+  new_tree->root = NULL;
+
+  new_tree->cmp = cmp;
+
+  return new_tree;
+}
+
+void btree_free(struct btree** btree) {
+  node_free(&((*btree)->root), (*btree)->elem_size, (*btree)->dealloc);
+  (*btree)->dealloc(*btree);
+  *btree = NULL;
+}
+
+void btree_insert(struct btree* btree, void* elem) {
+  if (btree == NULL) {
+    fputs("BTree error: Inserting into a NULL ptr!\n", stderr);
+    return;
+  }
+  if (elem == NULL) {
+    fputs("BTree error: Inserting NULL into a tree!\n", stderr);
+    return;
+  }
+  if (btree->root == NULL) {
+    btree->root = node_new(btree->degree, btree->elem_size);
+    if (btree->root == NULL) {
+      fputs("BTree error: Failed to create new root node!\n", stderr);
+      return;
+    }
+    node_insert(btree->root, elem, btree->degree, btree->elem_size, btree->cmp);
+  } else {
+    btree->root = node_insert(btree->root, elem, btree->degree,
+                              btree->elem_size, btree->cmp);
+  }
+}
+
+void* btree_search(struct btree* btree, void* elem) {
+  return node_search(btree->root, elem, btree->cmp, btree->elem_size);
+}
+
+int btree_delete(struct btree* btree, void* elem) {
+  struct node* newroot = btree->root;
+  int res = node_delete(btree->root, elem, btree->cmp, btree->degree,
+                        btree->elem_size, btree->alloc, btree->dealloc);
+  if (newroot->n == 0) {
+    if (node_leaf(newroot)) return res;
+    /* shrink the tree */
+    struct node* newroot_p = newroot->children[0];
+    btree->dealloc(newroot);
+    btree->root = newroot_p;
+  }
+  return res;
+}
+
+void node_print(struct node* root, const size_t elem_size, const int indent,
+                void (*print_elem)(const void*)) {
+  ssize_t i;
+  int t;
+
+  for (t = 0; t < indent - 1; t++) {
+    fputs(" ┃ ", stdout);
+  }
+  if (indent > 0) {
+    fputs(" ┣┯", stdout);
+  }
+  printf("printing node \x1b[33m%0lx\x1b[0m,"
+         " c:%ld n:%ld\t\t"
+         "\x1b[30m%p\x1b[0m\n",
+         (unsigned long)((size_t)root % 0x10000), root->c, root->n,
+         (void*)root);
+
+  if (node_leaf(root)) {
+    for (i = 0; i < root->n - 1; i++) {
+      const size_t ofst = i * elem_size;
+      for (t = 0; t < indent; t++) {
+        fputs(" ┃├", stdout);
+      }
+      print_elem(root->items + ofst);
+    }
+    for (t = 0; t < indent; t++) {
+      fputs(" ┃└", stdout);
+    }
+    print_elem(root->items + i * elem_size);
+  } else {
+    size_t ofst = 0;
+    for (i = 0; i < root->c - 1; i++) {
+      node_print(root->children[i], elem_size, indent + 1, print_elem);
+      for (t = 0; t < indent; t++) {
+        fputs(" ┃ ", stdout);
+      }
+      print_elem(root->items + ofst);
+      ofst += elem_size;
+    }
+    node_print(root->children[i], elem_size, indent + 1, print_elem);
+  }
+}
+
+void btree_print(struct btree* btree, void (*print_elem)(const void*)) {
+  printf("BTRee: degree:%ld\n", btree->degree);
+  if (btree->root == NULL) return;
+  node_print(btree->root, btree->elem_size, 0, print_elem);
+}
+
+void* btree_first(struct btree* btree) {
+  struct node* root;
+  if (btree == NULL) return NULL;
+  root = btree->root;
+
+  if (root == NULL) return NULL;
+
+  while (!node_leaf(root)) root = root->children[0];
+
+  if (root->n == 0) return NULL;
+  return root->items; /* Return first element */
+}
+
+void* btree_last(struct btree* btree) {
+  struct node* root;
+
+  if (btree == NULL) return NULL;
+  root = btree->root;
+
+  if (root == NULL) return NULL;
+
+  while (!node_leaf(root)) root = root->children[root->c];
+
+  if (root->n == 0) return NULL;
+  return root->items +
+         btree->elem_size * (root->n - 1); /* Return first element */
+}
+
+size_t btree_height(struct btree* btree) {
+  struct node* root;
+  size_t height = 0;
+
+  if (btree == NULL) return 0;
+  root = btree->root;
+
+  if (root == NULL) return 0;
+
+  while (!node_leaf(root)) {
+    root = root->children[0];
+    height++;
+  }
+
+  return height;
+}
+
+size_t u32_pow(size_t base, size_t exponent) {
+  size_t res = 1;
+  while (exponent > 0) {
+    res *= base;
+    exponent--;
+  }
+  return res;
+}
+
+size_t btree_size(struct btree* btree) {
+  return u32_pow(2 * btree->degree, btree_height(btree)) - 1;
+}
+
+struct btree_iter_t* btree_iter_t_new(struct btree* tree) {
+  struct btree_iter_t* iter = NULL;
+
+  if (tree == NULL) return NULL;
+
+  iter = (struct btree_iter_t*)tree->alloc(sizeof(struct btree_iter_t));
+
+  if (tree != NULL) {
+    iter->head = 0;
+    memset(iter->stack, 0, 512 * sizeof(struct node*));
+
+    iter->stack[iter->head].pos = 0;
+    iter->stack[iter->head].node = tree->root;
+  } else {
+    perror("Cannot instantiate iterator from null-pointer tree");
+  }
+  return iter;
+}
+
+void btree_iter_t_reset(struct btree* tree, struct btree_iter_t** it) {
+  (*it)->head = 0;
+
+  (*it)->stack[0].pos = 0;
+  (*it)->stack[0].node = tree->root;
+}
+
+void* btree_iter(struct btree* tree, struct btree_iter_t* iter) {
+  register int pos = 0;
+  register ssize_t head = 0;
+  register ssize_t n = 0;
+
+  if (iter->stack[head].node == NULL) return NULL;
+
+  head = iter->head;
+  pos = iter->stack[head].pos;
+  n = iter->stack[head].node->n;
+
+#define BTREE_ITER_POP(it)                                                     \
+  {                                                                            \
+    iter->stack[head].pos = 0;                                                 \
+    iter->stack[head].node = NULL;                                             \
+    iter->head--;                                                              \
+    head--;                                                                    \
+    iter->stack[head].pos++;                                                   \
+                                                                               \
+    pos = iter->stack[head].pos;                                               \
+    n = iter->stack[head].node->n;                                             \
+  }
+
+  /* Check if we have reached the end of a node.
+   * Take note of the difference of inequality in the if statement and
+   * following while */
+
+  /* Leafs are a special case, as, if the only node is the root node, we might
+   * want to exit */
+  if (node_leaf(iter->stack[iter->head].node) && pos >= 2 * n) {
+    if (head == 0) return NULL;
+
+    /* Pop, if so */
+    else
+      BTREE_ITER_POP(iter);
+  }
+
+  /* Otherwise, pop while we have reached the end of a node */
+  while (pos > 2 * n) {
+    if (head == 0) return NULL;
+
+    /* Pop, if so */
+    else
+      BTREE_ITER_POP(iter);
+  }
+
+#undef BTREE_ITER_POP
+
+  /* On evens, we decent into children */
+  if (!node_leaf(iter->stack[head].node)) {
+    if (pos % 2 == 0) {
+      /* push child node onto iter->stack */
+      iter->stack[head + 1].pos = 0;
+      iter->stack[head + 1].node = iter->stack[head].node->children[pos / 2];
+      iter->head++;
+      head++;
+
+      /* Decent all the way to the left, if pos == 0 */
+      while (!node_leaf(iter->stack[iter->head].node)) {
+        iter->stack[head + 1].pos = 0;
+        iter->stack[head + 1].node = iter->stack[head].node->children[0];
+        iter->head++;
+        head++;
+      }
+    }
+  }
+
+  /* Finally, update index and return a value */
+  if (node_leaf(iter->stack[head].node)) {
+    iter->stack[head].pos += 2;
+    pos = iter->stack[head].pos;
+  } else {
+    iter->stack[head].pos++;
+    pos = iter->stack[head].pos;
+  }
+
+  return iter->stack[head].node->items + tree->elem_size * ((pos - 1) / 2);
+}