/* Abstract AVL Tree Generic C Package.
** Implementation generation header file.
**
** This code is in the public domain.  See cavl_tree.html for interface
** documentation.
**
** Version: 1.5  Author: Walt Karas
*/

#undef L__
#undef L__EST_LONG_BIT
#undef L__SIZE
#undef L__tree
#undef L__MASK_HIGH_BIT
#undef L__LONG_BIT
#undef L__BIT_ARR_DEFN
#undef L__BIT_ARR_VAL
#undef L__BIT_ARR_0
#undef L__BIT_ARR_1
#undef L__BIT_ARR_ALL
#undef L__BIT_ARR_LONGS
#undef L__IMPL_MASK
#undef L__CHECK_READ_ERROR
#undef L__CHECK_READ_ERROR_INV_DEPTH
#undef L__SC
#undef L__BALANCE_PARAM_PREFIX

#ifdef AVL_UNIQUE

#define L__ AVL_UNIQUE

#else

#define L__(X) X

#endif

/* Determine correct storage class for functions */
#ifdef AVL_PRIVATE

#define L__SC static

#else

#define L__SC

#endif

#ifdef AVL_SIZE

#define L__SIZE AVL_SIZE

#else

#define L__SIZE unsigned long

#endif

#define L__MASK_HIGH_BIT ((int) ~ ((~ (unsigned) 0) >> 1))

/* ANSI C/ISO C++ require that a long have at least 32 bits.  Set
** L__EST_LONG_BIT to be the greatest multiple of 8 in the range
** 32 - 64 (inclusive) that is less than or equal to the number of
** bits in a long.
*/

#if (((LONG_MAX >> 31) >> 7) == 0)

#define L__EST_LONG_BIT 32

#elif (((LONG_MAX >> 31) >> 15) == 0)

#define L__EST_LONG_BIT 40

#elif (((LONG_MAX >> 31) >> 23) == 0)

#define L__EST_LONG_BIT 48

#elif (((LONG_MAX >> 31) >> 31) == 0)

#define L__EST_LONG_BIT 56

#else

#define L__EST_LONG_BIT 64

#endif

#define L__LONG_BIT (sizeof(long) * CHAR_BIT)

#if ((AVL_MAX_DEPTH) > L__EST_LONG_BIT)

/* The maximum depth may be greater than the number of bits in a long,
** so multiple longs are needed to hold a bit array indexed by node
** depth. */

#define L__BIT_ARR_LONGS (((AVL_MAX_DEPTH) + L__LONG_BIT - 1) / L__LONG_BIT)

#define L__BIT_ARR_DEFN(NAME) unsigned long NAME[L__BIT_ARR_LONGS];

#define L__BIT_ARR_VAL(BIT_ARR, BIT_NUM) \
  ((BIT_ARR)[(BIT_NUM) / L__LONG_BIT] & (1L << ((BIT_NUM) % L__LONG_BIT)))

#define L__BIT_ARR_0(BIT_ARR, BIT_NUM) \
  (BIT_ARR)[(BIT_NUM) / L__LONG_BIT] &= ~(1L << ((BIT_NUM) % L__LONG_BIT));

#define L__BIT_ARR_1(BIT_ARR, BIT_NUM) \
  (BIT_ARR)[(BIT_NUM) / L__LONG_BIT] |= 1L << ((BIT_NUM) % L__LONG_BIT);

#define L__BIT_ARR_ALL(BIT_ARR, BIT_VAL) \
  { int i = L__BIT_ARR_LONGS; do (BIT_ARR)[--i] = 0L - (BIT_VAL); while(i); }

#else /* The bit array can definitely fit in one long */

#define L__BIT_ARR_DEFN(NAME) unsigned long NAME;

#define L__BIT_ARR_VAL(BIT_ARR, BIT_NUM) ((BIT_ARR) & (1L << (BIT_NUM)))

#define L__BIT_ARR_0(BIT_ARR, BIT_NUM) (BIT_ARR) &= ~(1L << (BIT_NUM));

#define L__BIT_ARR_1(BIT_ARR, BIT_NUM) (BIT_ARR) |= 1L << (BIT_NUM);

#define L__BIT_ARR_ALL(BIT_ARR, BIT_VAL) (BIT_ARR) = 0L - (BIT_VAL);

#endif

#ifdef AVL_READ_ERRORS_HAPPEN

#define L__CHECK_READ_ERROR(ERROR_RETURN) \
{ if (AVL_READ_ERROR) return(ERROR_RETURN); }

#else

#define L__CHECK_READ_ERROR(ERROR_RETURN)

#endif

/* The presumed reason that an instantiation places additional fields
** inside the AVL tree structure is that the SET_ and GET_ macros
** need these fields.  The "balance" function does not explicitly use
** any fields in the AVL tree structure, so only pass an AVL tree
** structure pointer to "balance" if it has instantiation-specific
** fields that are (presumably) needed by the SET_/GET_ calls within
** "balance".
*/
#ifdef AVL_INSIDE_STRUCT

#define L__BALANCE_PARAM_CALL_PREFIX L__tree,
#define L__BALANCE_PARAM_DECL_PREFIX L__(avl) *L__tree,

#else

#define L__BALANCE_PARAM_CALL_PREFIX
#define L__BALANCE_PARAM_DECL_PREFIX

#endif

#ifdef AVL_IMPL_MASK

#define L__IMPL_MASK (AVL_IMPL_MASK)

#else

/* Define all functions. */
#define L__IMPL_MASK AVL_IMPL_ALL

#endif

#if (L__IMPL_MASK & AVL_IMPL_INIT)

L__SC void L__(init)(L__(avl) *L__tree) { L__tree->root = AVL_NULL; }

#endif

#if (L__IMPL_MASK & AVL_IMPL_IS_EMPTY)

L__SC int L__(is_empty)(L__(avl) *L__tree)
  { return(L__tree->root == AVL_NULL); }

#endif

/* Put the private balance function in the same compilation module as
** the insert function.  */
#if (L__IMPL_MASK & AVL_IMPL_INSERT)

/* Balances subtree, returns handle of root node of subtree after balancing.
*/
L__SC AVL_HANDLE L__(balance)(L__BALANCE_PARAM_DECL_PREFIX AVL_HANDLE bal_h)
  {
    AVL_HANDLE deep_h;

    /* Either the "greater than" or the "less than" subtree of
    ** this node has to be 2 levels deeper (or else it wouldn't
    ** need balancing).
    */
    if (AVL_GET_BALANCE_FACTOR(bal_h) > 0)
      {
	/* "Greater than" subtree is deeper. */

	deep_h = AVL_GET_GREATER(bal_h, 1);

	L__CHECK_READ_ERROR(AVL_NULL)

	if (AVL_GET_BALANCE_FACTOR(deep_h) < 0)
	  {
	    int bf;

	    AVL_HANDLE old_h = bal_h;
	    bal_h = AVL_GET_LESS(deep_h, 1);
	    L__CHECK_READ_ERROR(AVL_NULL)
	    AVL_SET_GREATER(old_h, AVL_GET_LESS(bal_h, 1))
	    AVL_SET_LESS(deep_h, AVL_GET_GREATER(bal_h, 1))
	    AVL_SET_LESS(bal_h, old_h)
	    AVL_SET_GREATER(bal_h, deep_h)

	    bf = AVL_GET_BALANCE_FACTOR(bal_h);
	    if (bf != 0)
	      {
		if (bf > 0)
		  {
		    AVL_SET_BALANCE_FACTOR(old_h, -1)
		    AVL_SET_BALANCE_FACTOR(deep_h, 0)
		  }
		else
		  {
		    AVL_SET_BALANCE_FACTOR(deep_h, 1)
		    AVL_SET_BALANCE_FACTOR(old_h, 0)
		  }
		AVL_SET_BALANCE_FACTOR(bal_h, 0)
	      }
	    else
	      {
		AVL_SET_BALANCE_FACTOR(old_h, 0)
		AVL_SET_BALANCE_FACTOR(deep_h, 0)
	      }
	  }
	else
	  {
	    AVL_SET_GREATER(bal_h, AVL_GET_LESS(deep_h, 0))
	    AVL_SET_LESS(deep_h, bal_h)
	    if (AVL_GET_BALANCE_FACTOR(deep_h) == 0)
	      {
		AVL_SET_BALANCE_FACTOR(deep_h, -1)
		AVL_SET_BALANCE_FACTOR(bal_h, 1)
	      }
	    else
	      {
		AVL_SET_BALANCE_FACTOR(deep_h, 0)
		AVL_SET_BALANCE_FACTOR(bal_h, 0)
	      }
	    bal_h = deep_h;
	  }
      }
    else
      {
	/* "Less than" subtree is deeper. */

	deep_h = AVL_GET_LESS(bal_h, 1);
	L__CHECK_READ_ERROR(AVL_NULL)

	if (AVL_GET_BALANCE_FACTOR(deep_h) > 0)
	  {
	    int bf;
	    AVL_HANDLE old_h = bal_h;
	    bal_h = AVL_GET_GREATER(deep_h, 1);
	    L__CHECK_READ_ERROR(AVL_NULL)
	    AVL_SET_LESS(old_h, AVL_GET_GREATER(bal_h, 0))
	    AVL_SET_GREATER(deep_h, AVL_GET_LESS(bal_h, 0))
	    AVL_SET_GREATER(bal_h, old_h)
	    AVL_SET_LESS(bal_h, deep_h)

	    bf = AVL_GET_BALANCE_FACTOR(bal_h);
	    if (bf != 0)
	      {
		if (bf < 0)
		  {
		    AVL_SET_BALANCE_FACTOR(old_h, 1)
		    AVL_SET_BALANCE_FACTOR(deep_h, 0)
		  }
		else
		  {
		    AVL_SET_BALANCE_FACTOR(deep_h, -1)
		    AVL_SET_BALANCE_FACTOR(old_h, 0)
		  }
		AVL_SET_BALANCE_FACTOR(bal_h, 0)
	      }
	    else
	      {
		AVL_SET_BALANCE_FACTOR(old_h, 0)
		AVL_SET_BALANCE_FACTOR(deep_h, 0)
	      }
	  }
	else
	  {
	    AVL_SET_LESS(bal_h, AVL_GET_GREATER(deep_h, 0))
	    AVL_SET_GREATER(deep_h, bal_h)
	    if (AVL_GET_BALANCE_FACTOR(deep_h) == 0)
	      {
		AVL_SET_BALANCE_FACTOR(deep_h, 1)
		AVL_SET_BALANCE_FACTOR(bal_h, -1)
	      }
	    else
	      {
		AVL_SET_BALANCE_FACTOR(deep_h, 0)
		AVL_SET_BALANCE_FACTOR(bal_h, 0)
	      }
	    bal_h = deep_h;
	  }
      }

    return(bal_h);
  }

L__SC AVL_HANDLE L__(insert)(L__(avl) *L__tree, AVL_HANDLE h)
  {
    AVL_SET_LESS(h, AVL_NULL)
    AVL_SET_GREATER(h, AVL_NULL)
    AVL_SET_BALANCE_FACTOR(h, 0)

    if (L__tree->root == AVL_NULL)
      L__tree->root = h;
    else
      {
	/* Last unbalanced node encountered in search for insertion point. */
	AVL_HANDLE unbal = AVL_NULL;
	/* Parent of last unbalanced node. */
	AVL_HANDLE parent_unbal = AVL_NULL;
	/* Balance factor of last unbalanced node. */
	int unbal_bf;

	/* Zero-based depth in tree. */
	unsigned depth = 0, unbal_depth = 0;

	/* Records a path into the tree.  If bit n is true, indicates
	** take greater branch from the nth node in the path, otherwise
	** take the less branch.  bit 0 gives branch from root, and
	** so on. */
	L__BIT_ARR_DEFN(branch)

	AVL_HANDLE hh = L__tree->root;
	AVL_HANDLE parent = AVL_NULL;
	int cmp;

	do
 	  {
	    if (AVL_GET_BALANCE_FACTOR(hh) != 0)
	      {
		unbal = hh;
		parent_unbal = parent;
		unbal_depth = depth;
	      }
	    cmp = AVL_COMPARE_NODE_NODE(h, hh);
	    if (cmp == 0)
	      /* Duplicate key. */
	      return(hh);
	    parent = hh;
	    if (cmp > 0)
	      {
		hh = AVL_GET_GREATER(hh, 1);
		L__BIT_ARR_1(branch, depth)
	      }
	    else
	      {
		hh = AVL_GET_LESS(hh, 1);
		L__BIT_ARR_0(branch, depth)
	      }
	    L__CHECK_READ_ERROR(AVL_NULL)
	    depth++;
	  }
	while (hh != AVL_NULL);

	/*  Add node to insert as leaf of tree. */
	if (cmp < 0)
	  AVL_SET_LESS(parent, h)
	else
	  AVL_SET_GREATER(parent, h)

	depth = unbal_depth;

	if (unbal == AVL_NULL)
	  hh = L__tree->root;
	else
	  {
	    cmp = L__BIT_ARR_VAL(branch, depth) ? 1 : -1;
	    depth++;
	    unbal_bf = AVL_GET_BALANCE_FACTOR(unbal);
	    if (cmp < 0)
	      unbal_bf--;
	    else  /* cmp > 0 */
	      unbal_bf++;
	    hh = cmp < 0 ? AVL_GET_LESS(unbal, 1) : AVL_GET_GREATER(unbal, 1);
	    L__CHECK_READ_ERROR(AVL_NULL)
	    if ((unbal_bf != -2) && (unbal_bf != 2))
	      {
		/* No rebalancing of tree is necessary. */
		AVL_SET_BALANCE_FACTOR(unbal, unbal_bf)
		unbal = AVL_NULL;
	      }
	  }

	if (hh != AVL_NULL)
	  while (h != hh)
	    {
	      cmp = L__BIT_ARR_VAL(branch, depth) ? 1 : -1;
	      depth++;
	      if (cmp < 0)
		{
		  AVL_SET_BALANCE_FACTOR(hh, -1)
		  hh = AVL_GET_LESS(hh, 1);
		}
	      else /* cmp > 0 */
		{
		  AVL_SET_BALANCE_FACTOR(hh, 1)
		  hh = AVL_GET_GREATER(hh, 1);
		}
	      L__CHECK_READ_ERROR(AVL_NULL)
	    }

	if (unbal != AVL_NULL)
	  {
	    unbal = L__(balance)(L__BALANCE_PARAM_CALL_PREFIX unbal);
	    L__CHECK_READ_ERROR(AVL_NULL)
	    if (parent_unbal == AVL_NULL)
	      L__tree->root = unbal;
	    else
	      {
		depth = unbal_depth - 1;
		cmp = L__BIT_ARR_VAL(branch, depth) ? 1 : -1;
		if (cmp < 0)
		  AVL_SET_LESS(parent_unbal, unbal)
		else  /* cmp > 0 */
		  AVL_SET_GREATER(parent_unbal, unbal)
	      }
	  }

      }

    return(h);
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_SEARCH)

L__SC AVL_HANDLE L__(search)(L__(avl) *L__tree, AVL_KEY k, avl_search_type st)
  {
    int cmp, target_cmp;
    AVL_HANDLE match_h = AVL_NULL;
    AVL_HANDLE h = L__tree->root;

    if (st & AVL_LESS)
      target_cmp = 1;
    else if (st & AVL_GREATER)
      target_cmp = -1;
    else
      target_cmp = 0;

    while (h != AVL_NULL)
      {
	cmp = AVL_COMPARE_KEY_NODE(k, h);
	if (cmp == 0)
	  {
	    if (st & AVL_EQUAL)
	      {
		match_h = h;
		break;
	      }
	    cmp = -target_cmp;
	  }
	else if (target_cmp != 0)
	  if (!((cmp ^ target_cmp) & L__MASK_HIGH_BIT))
	    /* cmp and target_cmp are both positive or both negative. */
	    match_h = h;
	h = cmp < 0 ? AVL_GET_LESS(h, 1) : AVL_GET_GREATER(h, 1);
	L__CHECK_READ_ERROR(AVL_NULL)
      }

    return(match_h);
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_SEARCH_LEAST)

L__SC AVL_HANDLE L__(search_least)(L__(avl) *L__tree)
  {
    AVL_HANDLE h = L__tree->root;
    AVL_HANDLE parent = AVL_NULL;

    while (h != AVL_NULL)
      {
	parent = h;
	h = AVL_GET_LESS(h, 1);
	L__CHECK_READ_ERROR(AVL_NULL)
      }

    return(parent);
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_SEARCH_GREATEST)

L__SC AVL_HANDLE L__(search_greatest)(L__(avl) *L__tree)
  {
    AVL_HANDLE h = L__tree->root;
    AVL_HANDLE parent = AVL_NULL;

    while (h != AVL_NULL)
      {
	parent = h;
	h = AVL_GET_GREATER(h, 1);
	L__CHECK_READ_ERROR(AVL_NULL)
      }

    return(parent);
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_REMOVE)

/* Prototype of balance function (called by remove) in case not in
** same compilation unit.
*/
L__SC AVL_HANDLE L__(balance)(L__BALANCE_PARAM_DECL_PREFIX AVL_HANDLE bal_h);

L__SC AVL_HANDLE L__(remove)(L__(avl) *L__tree, AVL_KEY k)
  {
    /* Zero-based depth in tree. */
    unsigned depth = 0, rm_depth;

    /* Records a path into the tree.  If bit n is true, indicates
    ** take greater branch from the nth node in the path, otherwise
    ** take the less branch.  bit 0 gives branch from root, and
    ** so on. */
    L__BIT_ARR_DEFN(branch)

    AVL_HANDLE h = L__tree->root;
    AVL_HANDLE parent = AVL_NULL;
    AVL_HANDLE child;
    AVL_HANDLE path;
    int cmp, cmp_shortened_sub_with_path;
    int reduced_depth;
    int bf;
    AVL_HANDLE rm;
    AVL_HANDLE parent_rm;

    for ( ; ; )
      {
	if (h == AVL_NULL)
	  /* No node in tree with given key. */
	  return(AVL_NULL);
	cmp = AVL_COMPARE_KEY_NODE(k, h);
	if (cmp == 0)
	  /* Found node to remove. */
	  break;
	parent = h;
	if (cmp > 0)
	  {
	    h = AVL_GET_GREATER(h, 1);
	    L__BIT_ARR_1(branch, depth)
	  }
	else
	  {
	    h = AVL_GET_LESS(h, 1);
	    L__BIT_ARR_0(branch, depth)
	  }
	L__CHECK_READ_ERROR(AVL_NULL)
	depth++;
	cmp_shortened_sub_with_path = cmp;
      }
    rm = h;
    parent_rm = parent;
    rm_depth = depth;

    /* If the node to remove is not a leaf node, we need to get a
    ** leaf node, or a node with a single leaf as its child, to put
    ** in the place of the node to remove.  We will get the greatest
    ** node in the less subtree (of the node to remove), or the least
    ** node in the greater subtree.  We take the leaf node from the
    ** deeper subtree, if there is one. */

    if (AVL_GET_BALANCE_FACTOR(h) < 0)
      {
	child = AVL_GET_LESS(h, 1);
	L__BIT_ARR_0(branch, depth)
	cmp = -1;
      }
    else
      {
	child = AVL_GET_GREATER(h, 1);
	L__BIT_ARR_1(branch, depth)
	cmp = 1;
      }
    L__CHECK_READ_ERROR(AVL_NULL)
    depth++;

    if (child != AVL_NULL)
      {
	cmp = -cmp;
	do
	  {
	    parent = h;
	    h = child;
	    if (cmp < 0)
	      {
		child = AVL_GET_LESS(h, 1);
		L__BIT_ARR_0(branch, depth)
	      }
	    else
	      {
		child = AVL_GET_GREATER(h, 1);
		L__BIT_ARR_1(branch, depth)
	      }
	    L__CHECK_READ_ERROR(AVL_NULL)
	    depth++;
	  }
	while (child != AVL_NULL);

	if (parent == rm)
	  /* Only went through do loop once.  Deleted node will be replaced
	  ** in the tree structure by one of its immediate children. */
	  cmp_shortened_sub_with_path = -cmp;
        else
	  cmp_shortened_sub_with_path = cmp;

	/* Get the handle of the opposite child, which may not be null. */
	child = cmp > 0 ? AVL_GET_LESS(h, 0) : AVL_GET_GREATER(h, 0);
      }

    if (parent == AVL_NULL)
      /* There were only 1 or 2 nodes in this tree. */
      L__tree->root = child;
    else if (cmp_shortened_sub_with_path < 0)
      AVL_SET_LESS(parent, child)
    else
      AVL_SET_GREATER(parent, child)

    /* "path" is the parent of the subtree being eliminated or reduced
    ** from a depth of 2 to 1.  If "path" is the node to be removed, we
    ** set path to the node we're about to poke into the position of the
    ** node to be removed. */
    path = parent == rm ? h : parent;

    if (h != rm)
      {
	/* Poke in the replacement for the node to be removed. */
	AVL_SET_LESS(h, AVL_GET_LESS(rm, 0))
	AVL_SET_GREATER(h, AVL_GET_GREATER(rm, 0))
	AVL_SET_BALANCE_FACTOR(h, AVL_GET_BALANCE_FACTOR(rm))
	if (parent_rm == AVL_NULL)
	  L__tree->root = h;
	else
	  {
	    depth = rm_depth - 1;
	    if (L__BIT_ARR_VAL(branch, depth))
	      AVL_SET_GREATER(parent_rm, h)
	    else
	      AVL_SET_LESS(parent_rm, h)
	  }
      }

    if (path != AVL_NULL)
      {
	/* Create a temporary linked list from the parent of the path node
	** to the root node. */
	h = L__tree->root;
	parent = AVL_NULL;
	depth = 0;
	while (h != path)
	  {
	    if (L__BIT_ARR_VAL(branch, depth))
	      {
	        child = AVL_GET_GREATER(h, 1);
		AVL_SET_GREATER(h, parent)
	      }
	    else
	      {
	        child = AVL_GET_LESS(h, 1);
		AVL_SET_LESS(h, parent)
	      }
	    L__CHECK_READ_ERROR(AVL_NULL)
	    depth++;
	    parent = h;
	    h = child;
	  }

	/* Climb from the path node to the root node using the linked
	** list, restoring the tree structure and rebalancing as necessary.
	*/
	reduced_depth = 1;
	cmp = cmp_shortened_sub_with_path;
	for ( ; ; )
	  {
	    if (reduced_depth)
	      {
		bf = AVL_GET_BALANCE_FACTOR(h);
		if (cmp < 0)
		  bf++;
		else  /* cmp > 0 */
		  bf--;
		if ((bf == -2) || (bf == 2))
		  {
		    h = L__(balance)(L__BALANCE_PARAM_CALL_PREFIX h);
		    L__CHECK_READ_ERROR(AVL_NULL)
		    bf = AVL_GET_BALANCE_FACTOR(h);
		  }
		else
		  AVL_SET_BALANCE_FACTOR(h, bf)
		reduced_depth = (bf == 0);
	      }
	    if (parent == AVL_NULL)
	      break;
	    child = h;
	    h = parent;
	    depth--;
	    cmp = L__BIT_ARR_VAL(branch, depth) ? 1 : -1;
	    if (cmp < 0)
	      {
		parent = AVL_GET_LESS(h, 1);
		AVL_SET_LESS(h, child)
	      }
	    else
	      {
		parent = AVL_GET_GREATER(h, 1);
		AVL_SET_GREATER(h, child)
	      }
	    L__CHECK_READ_ERROR(AVL_NULL)
	  }
	L__tree->root = h;
      }

    return(rm);
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_SUBST)

L__SC AVL_HANDLE L__(subst)(L__(avl) *L__tree, AVL_HANDLE new_node)
  {
    AVL_HANDLE h = L__tree->root;
    AVL_HANDLE parent = AVL_NULL;
    int cmp, last_cmp;

    /* Search for node already in tree with same key. */
    for ( ; ; )
      {
	if (h == AVL_NULL)
	  /* No node in tree with same key as new node. */
	  return(AVL_NULL);
	cmp = AVL_COMPARE_NODE_NODE(new_node, h);
	if (cmp == 0)
	  /* Found the node to substitute new one for. */
	  break;
	last_cmp = cmp;
	parent = h;
	h = cmp < 0 ? AVL_GET_LESS(h, 1) : AVL_GET_GREATER(h, 1);
	L__CHECK_READ_ERROR(AVL_NULL)
      }

    /* Copy tree housekeeping fields from node in tree to new node. */
    AVL_SET_LESS(new_node, AVL_GET_LESS(h, 0))
    AVL_SET_GREATER(new_node, AVL_GET_GREATER(h, 0))
    AVL_SET_BALANCE_FACTOR(new_node, AVL_GET_BALANCE_FACTOR(h))

    if (parent == AVL_NULL)
      /* New node is also new root. */
      L__tree->root = new_node;
    else
      {
	/* Make parent point to new node. */
	if (last_cmp < 0)
	  AVL_SET_LESS(parent, new_node)
	else
	  AVL_SET_GREATER(parent, new_node)
      }

    return(h);
  }

#endif

#ifdef AVL_BUILD_ITER_TYPE

#if (L__IMPL_MASK & AVL_IMPL_BUILD)

L__SC int L__(build)(
  L__(avl) *L__tree, AVL_BUILD_ITER_TYPE p, L__SIZE num_nodes)
  {
    /* Gives path to subtree being built.  If bit n is false, branch
    ** less from the node at depth n, if true branch greater. */
    L__BIT_ARR_DEFN(branch)

    /* If bit n is true, then for the current subtree at depth n, its
    ** greater subtree has one more node than its less subtree. */
    L__BIT_ARR_DEFN(rem)

    /* Depth of root node of current subtree. */
    unsigned depth = 0;

    /* Number of nodes in current subtree. */
    L__SIZE num_sub = num_nodes;

    /* The algorithm relies on a stack of nodes whose less subtree has
    ** been built, but whose greater subtree has not yet been built.
    ** The stack is implemented as linked list.  The nodes are linked
    ** together by having the "greater" handle of a node set to the
    ** next node in the list.  "less_parent" is the handle of the first
    ** node in the list. */
    AVL_HANDLE less_parent = AVL_NULL;

    /* h is root of current subtree, child is one of its children. */
    AVL_HANDLE h;
    AVL_HANDLE child;

    if (num_nodes == 0)
      {
	L__tree->root = AVL_NULL;
	return(1);
      }

    for ( ; ; )
      {
	while (num_sub > 2)
	  {
	    /* Subtract one for root of subtree. */
	    num_sub--;
	    if (num_sub & 1)
	      L__BIT_ARR_1(rem, depth)
	    else
	      L__BIT_ARR_0(rem, depth)
	    L__BIT_ARR_0(branch, depth)
	    depth++;
	    num_sub >>= 1;
	  }

	if (num_sub == 2)
	  {
	    /* Build a subtree with two nodes, slanting to greater.
	    ** I arbitrarily chose to always have the extra node in the
	    ** greater subtree when there is an odd number of nodes to
	    ** split between the two subtrees. */

	    h = AVL_BUILD_ITER_VAL(p);
	    L__CHECK_READ_ERROR(0)
	    AVL_BUILD_ITER_INCR(p)
	    child = AVL_BUILD_ITER_VAL(p);
	    L__CHECK_READ_ERROR(0)
	    AVL_BUILD_ITER_INCR(p)
	    AVL_SET_LESS(child, AVL_NULL)
	    AVL_SET_GREATER(child, AVL_NULL)
	    AVL_SET_BALANCE_FACTOR(child, 0)
	    AVL_SET_GREATER(h, child)
	    AVL_SET_LESS(h, AVL_NULL)
	    AVL_SET_BALANCE_FACTOR(h, 1)
	  }
	else  /* num_sub == 1 */
	  {
	    /* Build a subtree with one node. */

	    h = AVL_BUILD_ITER_VAL(p);
	    L__CHECK_READ_ERROR(0)
	    AVL_BUILD_ITER_INCR(p)
	    AVL_SET_LESS(h, AVL_NULL)
	    AVL_SET_GREATER(h, AVL_NULL)
	    AVL_SET_BALANCE_FACTOR(h, 0)
	  }

	while (depth)
	  {
	    depth--;
	    if (!L__BIT_ARR_VAL(branch, depth))
	      /* We've completed a less subtree. */
	      break;

	    /* We've completed a greater subtree, so attach it to
	    ** its parent (that is less than it).  We pop the parent
	    ** off the stack of less parents. */
	    child = h;
	    h = less_parent;
	    less_parent = AVL_GET_GREATER(h, 1);
	    L__CHECK_READ_ERROR(0)
	    AVL_SET_GREATER(h, child)
	    /* num_sub = 2 * (num_sub - rem[depth]) + rem[depth] + 1 */
	    num_sub <<= 1;
	    num_sub += L__BIT_ARR_VAL(rem, depth) ? 0 : 1;
	    if (num_sub & (num_sub - 1))
	      /* num_sub is not a power of 2. */
	      AVL_SET_BALANCE_FACTOR(h, 0)
	    else
	      /* num_sub is a power of 2. */
	      AVL_SET_BALANCE_FACTOR(h, 1)
	  }

	if (num_sub == num_nodes)
	  /* We've completed the full tree. */
	  break;

	/* The subtree we've completed is the less subtree of the
	** next node in the sequence. */

	child = h;
	h = AVL_BUILD_ITER_VAL(p);
	L__CHECK_READ_ERROR(0)
	AVL_BUILD_ITER_INCR(p)
	AVL_SET_LESS(h, child)

	/* Put h into stack of less parents. */
	AVL_SET_GREATER(h, less_parent)
	less_parent = h;

	/* Proceed to creating greater than subtree of h. */
	L__BIT_ARR_1(branch, depth)
	num_sub += L__BIT_ARR_VAL(rem, depth) ? 1 : 0;
	depth++;

      } /* end for ( ; ; ) */

    L__tree->root = h;

    return(1);
  }

#endif

#endif

#if (L__IMPL_MASK & AVL_IMPL_INIT_ITER)

/* Initialize depth to invalid value, to indicate iterator is
** invalid.   (Depth is zero-base.)  It's not necessary to initialize
** iterators prior to passing them to the "start" function.
*/
L__SC void L__(init_iter)(L__(iter) *iter) { iter->depth = ~0; }

#endif

#ifdef AVL_READ_ERRORS_HAPPEN

#define L__CHECK_READ_ERROR_INV_DEPTH \
{ if (AVL_READ_ERROR) { iter->depth = ~0; return; } }

#else

#define L__CHECK_READ_ERROR_INV_DEPTH

#endif

#if (L__IMPL_MASK & AVL_IMPL_START_ITER)

L__SC void L__(start_iter)(
  L__(avl) *L__tree, L__(iter) *iter, AVL_KEY k, avl_search_type st)
  {
    AVL_HANDLE h = L__tree->root;
    unsigned d = 0;
    int cmp, target_cmp;

    /* Save the tree that we're going to iterate through in a
    ** member variable. */
    iter->tree_ = L__tree;

    iter->depth = ~0;

    if (h == AVL_NULL)
      /* Tree is empty. */
      return;

    if (st & AVL_LESS)
      /* Key can be greater than key of starting node. */
      target_cmp = 1;
    else if (st & AVL_GREATER)
      /* Key can be less than key of starting node. */
      target_cmp = -1;
    else
      /* Key must be same as key of starting node. */
      target_cmp = 0;

    for ( ; ; )
      {
	cmp = AVL_COMPARE_KEY_NODE(k, h);
	if (cmp == 0)
	  {
	    if (st & AVL_EQUAL)
	      {
		/* Equal node was sought and found as starting node. */
		iter->depth = d;
		break;
	      }
	    cmp = -target_cmp;
	  }
	else if (target_cmp != 0)
	  if (!((cmp ^ target_cmp) & L__MASK_HIGH_BIT))
	    /* cmp and target_cmp are both negative or both positive. */
	    iter->depth = d;
	h = cmp < 0 ? AVL_GET_LESS(h, 1) : AVL_GET_GREATER(h, 1);
	L__CHECK_READ_ERROR_INV_DEPTH
	if (h == AVL_NULL)
	  break;
	if (cmp > 0)
	  L__BIT_ARR_1(iter->branch, d)
	else
	  L__BIT_ARR_0(iter->branch, d)
	iter->path_h[d++] = h;
      }
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_START_ITER_LEAST)

L__SC void L__(start_iter_least)(L__(avl) *L__tree, L__(iter) *iter)
  {
    AVL_HANDLE h = L__tree->root;

    iter->tree_ = L__tree;

    iter->depth = ~0;

    L__BIT_ARR_ALL(iter->branch, 0)

    while (h != AVL_NULL)
      {
	if (iter->depth != ~0)
	  iter->path_h[iter->depth] = h;
	iter->depth++;
	h = AVL_GET_LESS(h, 1);
	L__CHECK_READ_ERROR_INV_DEPTH
      }
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_START_ITER_GREATEST)

L__SC void L__(start_iter_greatest)(L__(avl) *L__tree, L__(iter) *iter)
  {
    AVL_HANDLE h = L__tree->root;

    iter->tree_ = L__tree;

    iter->depth = ~0;

    L__BIT_ARR_ALL(iter->branch, 1)

    while (h != AVL_NULL)
      {
	if (iter->depth != ~0)
	  iter->path_h[iter->depth] = h;
	iter->depth++;
	h = AVL_GET_GREATER(h, 1);
	L__CHECK_READ_ERROR_INV_DEPTH
      }
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_GET_ITER)

L__SC AVL_HANDLE L__(get_iter)(L__(iter) *iter)
  {
    if (iter->depth == ~0)
      return(AVL_NULL);

    return(iter->depth == 0 ?
	     iter->tree_->root : iter->path_h[iter->depth - 1]);
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_INCR_ITER)

L__SC void L__(incr_iter)(L__(iter) *iter)
  {
    #define L__tree (iter->tree_)

    if (iter->depth != ~0)
      {
	AVL_HANDLE h =
	  AVL_GET_GREATER((iter->depth == 0 ?
	    iter->tree_->root : iter->path_h[iter->depth - 1]), 1);
	L__CHECK_READ_ERROR_INV_DEPTH

	if (h == AVL_NULL)
	  do
	    {
	      if (iter->depth == 0)
		{
		  iter->depth = ~0;
		  break;
		}
	      iter->depth--;
	    }
	  while (L__BIT_ARR_VAL(iter->branch, iter->depth));
	else
	  {
	    L__BIT_ARR_1(iter->branch, iter->depth)
	    iter->path_h[iter->depth++] = h;
	    for ( ; ; )
	      {
		h = AVL_GET_LESS(h, 1);
		L__CHECK_READ_ERROR_INV_DEPTH
		if (h == AVL_NULL)
		  break;
		L__BIT_ARR_0(iter->branch, iter->depth)
		iter->path_h[iter->depth++] = h;
	      }
	  }
      }

    #undef L__tree
  }

#endif

#if (L__IMPL_MASK & AVL_IMPL_DECR_ITER)

L__SC void L__(decr_iter)(L__(iter) *iter)
  {
    #define L__tree (iter->tree_)

    if (iter->depth != ~0)
      {
	AVL_HANDLE h =
	  AVL_GET_LESS((iter->depth == 0 ?
	    iter->tree_->root : iter->path_h[iter->depth - 1]), 1);
	L__CHECK_READ_ERROR_INV_DEPTH

	if (h == AVL_NULL)
	  do
	    {
	      if (iter->depth == 0)
		{
		  iter->depth = ~0;
		  break;
		}
	      iter->depth--;
	    }
	  while (!L__BIT_ARR_VAL(iter->branch, iter->depth));
	else
	  {
	    L__BIT_ARR_0(iter->branch, iter->depth)
	    iter->path_h[iter->depth++] = h;
	    for ( ; ; )
	      {
		h = AVL_GET_GREATER(h, 1);
		L__CHECK_READ_ERROR_INV_DEPTH
		if (h == AVL_NULL)
		  break;
		L__BIT_ARR_1(iter->branch, iter->depth)
		iter->path_h[iter->depth++] = h;
	      }
	  }
      }

    #undef L__tree
  }

#endif

/* Tidy up the preprocessor symbol name space. */
#undef L__
#undef L__EST_LONG_BIT
#undef L__SIZE
#undef L__MASK_HIGH_BIT
#undef L__LONG_BIT
#undef L__BIT_ARR_DEFN
#undef L__BIT_ARR_VAL
#undef L__BIT_ARR_0
#undef L__BIT_ARR_1
#undef L__BIT_ARR_ALL
#undef L__CHECK_READ_ERROR
#undef L__CHECK_READ_ERROR_INV_DEPTH
#undef L__BIT_ARR_LONGS
#undef L__IMPL_MASK
#undef L__CHECK_READ_ERROR
#undef L__CHECK_READ_ERROR_INV_DEPTH
#undef L__SC
#undef L__BALANCE_PARAM_CALL_PREFIX
#undef L__BALANCE_PARAM_DECL_PREFIX