/* Copyright (c) 2002, 2021, Oracle and/or its affiliates.
   
   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License, version 2.0,
   as published by the Free Software Foundation.

   This program is also distributed with certain software (including
   but not limited to OpenSSL) that is licensed under separate terms,
   as designated in a particular file or component or in included license
   documentation.  The authors of MySQL hereby grant you an additional
   permission to link the program and your derivative works with the
   separately licensed software that they have included with MySQL.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License, version 2.0, for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA */

#include "myisamdef.h"
#include "rt_index.h"
#include "rt_key.h"
#include "rt_mbr.h"

#define REINSERT_BUFFER_INC 10
#define PICK_BY_AREA
/*#define PICK_BY_PERIMETER*/

typedef struct st_page_level
{
  uint level;
  my_off_t offs;
} stPageLevel;

typedef struct st_page_list
{   
  ulong n_pages;
  ulong m_pages;
  stPageLevel *pages;
} stPageList;


/* 
   Find next key in r-tree according to search_flag recursively

   NOTES
     Used in rtree_find_first() and rtree_find_next()

   RETURN
     -1	 Error
     0   Found
     1   Not found 
*/

static int rtree_find_req(MI_INFO *info, MI_KEYDEF *keyinfo, uint search_flag,
			  uint nod_cmp_flag, my_off_t page, int level)
{
  uchar *k;
  uchar *last;
  uint nod_flag;
  int res;
  uchar *page_buf;
  int k_len;
  uint *saved_key = (uint*) (info->rtree_recursion_state) + level;
  
  if (!(page_buf = (uchar*)my_alloca((uint)keyinfo->block_length)))
  {
    set_my_errno(HA_ERR_OUT_OF_MEM);
    return -1;
  }
  if (!_mi_fetch_keypage(info, keyinfo, page, DFLT_INIT_HITS, page_buf, 0))
    goto err1;
  nod_flag = mi_test_if_nod(page_buf);

  k_len = keyinfo->keylength - info->s->base.rec_reflength;
  
  if(info->rtree_recursion_depth >= level)
  {
    k = page_buf + *saved_key;
  }
  else
  {
    k = rt_PAGE_FIRST_KEY(page_buf, nod_flag);
  }
  last = rt_PAGE_END(page_buf);

  for (; k < last; k = rt_PAGE_NEXT_KEY(k, k_len, nod_flag))
  {
    if (nod_flag) 
    { 
      /* this is an internal node in the tree */
      if (!(res = rtree_key_cmp(keyinfo->seg, info->first_mbr_key, k, 
                            info->last_rkey_length, nod_cmp_flag)))
      {
        switch ((res = rtree_find_req(info, keyinfo, search_flag, nod_cmp_flag,
                                      _mi_kpos(nod_flag, k), level + 1)))
        {
          case 0: /* found - exit from recursion */
            *saved_key = (uint) (k - page_buf);
            goto ok;
          case 1: /* not found - continue searching */
            info->rtree_recursion_depth = level;
            break;
          default: /* error */
          case -1:
            goto err1;
        }
      }
    }
    else 
    { 
      /* this is a leaf */
      if (!rtree_key_cmp(keyinfo->seg, info->first_mbr_key, k, 
                         info->last_rkey_length, search_flag))
      {
        uchar *after_key = rt_PAGE_NEXT_KEY(k, k_len, nod_flag);
        info->lastpos = _mi_dpos(info, 0, after_key);
        info->lastkey_length = k_len + info->s->base.rec_reflength;
        memcpy(info->lastkey, k, info->lastkey_length);
        info->rtree_recursion_depth = level;
        *saved_key = (uint) (last - page_buf);

        if (after_key < last)
        {
          info->int_keypos = info->buff;
          info->int_maxpos = info->buff + (last - after_key);
          memcpy(info->buff, after_key, last - after_key);
          info->buff_used = 0;
        }
        else
        {
	  info->buff_used = 1;
        }

        res = 0;
        goto ok;
      }
    }
  }
  info->lastpos = HA_OFFSET_ERROR;
  set_my_errno(HA_ERR_KEY_NOT_FOUND);
  res = 1;

ok:
  return res;

err1:
  info->lastpos = HA_OFFSET_ERROR;
  return -1;
}


/*
  Find first key in r-tree according to search_flag condition

  SYNOPSIS
   rtree_find_first()
   info			Handler to MyISAM file
   uint keynr		Key number to use
   key			Key to search for
   key_length		Length of 'key' 
   search_flag		Bitmap of flags how to do the search

  RETURN
    -1  Error
    0   Found
    1   Not found
*/

int rtree_find_first(MI_INFO *info, uint keynr, uchar *key, uint key_length, 
                    uint search_flag)
{
  my_off_t root;
  uint nod_cmp_flag;
  MI_KEYDEF *keyinfo = info->s->keyinfo + keynr;

  if ((root = info->s->state.key_root[keynr]) == HA_OFFSET_ERROR)
  {
    // This is assumed to happen only when the index is empty. If that
    // doesn't hold, the code in mi_rkey() that checks the record
    // count has to be changed.
    assert(info->s->state.state.records == 0);
    set_my_errno(HA_ERR_END_OF_FILE);
    return -1;
  }

  // All empty indexes should be caught above. Negative record counts
  // should never occur.
  assert(info->s->state.state.records > 0);

  /*
    Save searched key, include data pointer.
    The data pointer is required if the search_flag contains MBR_DATA.
    (minimum bounding rectangle)
  */
  memcpy(info->first_mbr_key, key, keyinfo->keylength);
  info->last_rkey_length = key_length;

  info->rtree_recursion_depth = -1;
  info->buff_used = 1;
  
  nod_cmp_flag = ((search_flag & (MBR_EQUAL | MBR_WITHIN)) ? 
        MBR_WITHIN : MBR_INTERSECT);
  return rtree_find_req(info, keyinfo, search_flag, nod_cmp_flag, root, 0);
}


/* 
   Find next key in r-tree according to search_flag condition

  SYNOPSIS
   rtree_find_next()
   info			Handler to MyISAM file
   uint keynr		Key number to use
   search_flag		Bitmap of flags how to do the search

   RETURN
     -1  Error
     0   Found
     1   Not found
*/

int rtree_find_next(MI_INFO *info, uint keynr, uint search_flag)
{
  my_off_t root;
  uint nod_cmp_flag;
  MI_KEYDEF *keyinfo = info->s->keyinfo + keynr;

  if (info->update & HA_STATE_DELETED)
    return rtree_find_first(info, keynr, info->lastkey, info->lastkey_length,
			    search_flag);

  if (!info->buff_used)
  {
    uchar *key= info->int_keypos;

    while (key < info->int_maxpos)
    {
      if (!rtree_key_cmp(keyinfo->seg, info->first_mbr_key, key, 
                         info->last_rkey_length, search_flag))
      {
        uchar *after_key = key + keyinfo->keylength;

        info->lastpos= _mi_dpos(info, 0, after_key);
        memcpy(info->lastkey, key, info->lastkey_length);

        if (after_key < info->int_maxpos)
	  info->int_keypos= after_key;
        else
	  info->buff_used= 1;
        return 0;
      }
      key+= keyinfo->keylength;
    }
  }
  if ((root = info->s->state.key_root[keynr]) == HA_OFFSET_ERROR)
  {
    set_my_errno(HA_ERR_END_OF_FILE);
    return -1;
  }
  
  nod_cmp_flag = ((search_flag & (MBR_EQUAL | MBR_WITHIN)) ? 
        MBR_WITHIN : MBR_INTERSECT);
  return rtree_find_req(info, keyinfo, search_flag, nod_cmp_flag, root, 0);
}


/*
  Get next key in r-tree recursively

  NOTES
    Used in rtree_get_first() and rtree_get_next()

  RETURN
    -1  Error
    0   Found
    1   Not found
*/

static int rtree_get_req(MI_INFO *info, MI_KEYDEF *keyinfo, uint key_length, 
                         my_off_t page, int level)
{
  uchar *k;
  uchar *last;
  uint nod_flag;
  int res;
  uchar *page_buf;
  uint k_len;
  uint *saved_key = (uint*) (info->rtree_recursion_state) + level;
  
  if (!(page_buf = (uchar*)my_alloca((uint)keyinfo->block_length)))
    return -1;
  if (!_mi_fetch_keypage(info, keyinfo, page, DFLT_INIT_HITS, page_buf, 0))
    goto err1;
  nod_flag = mi_test_if_nod(page_buf);

  k_len = keyinfo->keylength - info->s->base.rec_reflength;

  if(info->rtree_recursion_depth >= level)
  {
    k = page_buf + *saved_key;
    if (!nod_flag)
    {
      /* Only leaf pages contain data references. */
      /* Need to check next key with data reference. */
      k = rt_PAGE_NEXT_KEY(k, k_len, nod_flag);
    }
  }
  else
  {
    k = rt_PAGE_FIRST_KEY(page_buf, nod_flag);
  }
  last = rt_PAGE_END(page_buf);

  for (; k < last; k = rt_PAGE_NEXT_KEY(k, k_len, nod_flag))
  {
    if (nod_flag) 
    { 
      /* this is an internal node in the tree */
      switch ((res = rtree_get_req(info, keyinfo, key_length, 
                                  _mi_kpos(nod_flag, k), level + 1)))
      {
        case 0: /* found - exit from recursion */
          *saved_key = (uint) (k - page_buf);
          goto ok;
        case 1: /* not found - continue searching */
          info->rtree_recursion_depth = level;
          break;
        default:
        case -1: /* error */
          goto err1;
      }
    }
    else 
    { 
      /* this is a leaf */
      uchar *after_key = rt_PAGE_NEXT_KEY(k, k_len, nod_flag);
      info->lastpos = _mi_dpos(info, 0, after_key);
      info->lastkey_length = k_len + info->s->base.rec_reflength;
      memcpy(info->lastkey, k, info->lastkey_length);

      info->rtree_recursion_depth = level;
      *saved_key = (uint) (k - page_buf);

      if (after_key < last)
      {
        info->int_keypos = (uchar*)saved_key;
        memcpy(info->buff, page_buf, keyinfo->block_length);
        info->int_maxpos = rt_PAGE_END(info->buff);
        info->buff_used = 0;
      }
      else
      {
	info->buff_used = 1;
      }

      res = 0;
      goto ok;
    }
  }
  info->lastpos = HA_OFFSET_ERROR;
  set_my_errno(HA_ERR_KEY_NOT_FOUND);
  res = 1;

ok:
  return res;

err1:
  info->lastpos = HA_OFFSET_ERROR;
  return -1;
}


/*
  Get first key in r-tree

  RETURN
    -1	Error
    0	Found
    1	Not found
*/

int rtree_get_first(MI_INFO *info, uint keynr, uint key_length)
{
  my_off_t root;
  MI_KEYDEF *keyinfo = info->s->keyinfo + keynr;

  if ((root = info->s->state.key_root[keynr]) == HA_OFFSET_ERROR)
  {
    set_my_errno(HA_ERR_END_OF_FILE);
    return -1;
  }

  info->rtree_recursion_depth = -1;
  info->buff_used = 1;
  
  return rtree_get_req(info, keyinfo, key_length, root, 0);
}


/* 
  Get next key in r-tree

  RETURN
    -1	Error
    0	Found
    1	Not found
*/

int rtree_get_next(MI_INFO *info, uint keynr, uint key_length)
{
  my_off_t root= info->s->state.key_root[keynr];
  MI_KEYDEF *keyinfo = info->s->keyinfo + keynr;

  if (root == HA_OFFSET_ERROR)
  {
    set_my_errno(HA_ERR_END_OF_FILE);
    return -1;
  }
  
  if (!info->buff_used && !info->page_changed)
  {
    uint k_len = keyinfo->keylength - info->s->base.rec_reflength;
    /* rt_PAGE_NEXT_KEY(info->int_keypos) */
    uchar *key = info->buff + *(int*)info->int_keypos + k_len + 
                 info->s->base.rec_reflength;
    /* rt_PAGE_NEXT_KEY(key) */
    uchar *after_key = key + k_len + info->s->base.rec_reflength; 

    info->lastpos = _mi_dpos(info, 0, after_key);
    info->lastkey_length = k_len + info->s->base.rec_reflength;
    memcpy(info->lastkey, key, k_len + info->s->base.rec_reflength);

    *(uint*)info->int_keypos = (uint) (key - info->buff);
    if (after_key >= info->int_maxpos)
    {
      info->buff_used = 1;
    }

    return 0;
  }

  return rtree_get_req(info, keyinfo, key_length, root, 0);
}


/*
  Choose non-leaf better key for insertion
*/

#ifdef PICK_BY_PERIMETER
static uchar *rtree_pick_key(MI_INFO *info, MI_KEYDEF *keyinfo, uchar *key, 
			     uint key_length, uchar *page_buf, uint nod_flag)
{
  double increase;
  double best_incr = DBL_MAX;
  double perimeter;
  double best_perimeter= 0.0;
  uchar *best_key= NULL;
  uchar *k = rt_PAGE_FIRST_KEY(page_buf, nod_flag);
  uchar *last = rt_PAGE_END(page_buf);

  for (; k < last; k = rt_PAGE_NEXT_KEY(k, key_length, nod_flag))
  {
    if ((increase = rtree_perimeter_increase(keyinfo->seg, k, key, key_length,
					     &perimeter)) == -1)
      return NULL;
    if ((increase < best_incr)||
	(increase == best_incr && perimeter < best_perimeter))
    {
      best_key = k;
      best_perimeter= perimeter;
      best_incr = increase;
    }
  }
  return best_key;
}

#endif /*PICK_BY_PERIMETER*/

#ifdef PICK_BY_AREA
static uchar *rtree_pick_key(MI_INFO *info, MI_KEYDEF *keyinfo, uchar *key, 
			     uint key_length, uchar *page_buf, uint nod_flag)
{
  double increase;
  double best_incr= 0.0;
  double area;
  double best_area= 0.0;
  uchar *best_key= NULL;
  uchar *k = rt_PAGE_FIRST_KEY(page_buf, nod_flag);
  uchar *last = rt_PAGE_END(page_buf);

  for (; k < last; k = rt_PAGE_NEXT_KEY(k, key_length, nod_flag))
  {
    /* The following is safe as -1.0 is an exact number */
    if ((increase = rtree_area_increase(keyinfo->seg, k, key, key_length, 
                                        &area)) == -1.0)
      return NULL;
    /* The following should be safe, even if we compare doubles */
    if (!best_key || increase < best_incr ||
        ((increase == best_incr) && (area < best_area)))
    {
      best_key = k;
      best_area = area;
      best_incr = increase;
    }
  }
  return best_key;
}

#endif /*PICK_BY_AREA*/

/*
  Go down and insert key into tree

  RETURN
    -1	Error
    0	Child was not split
    1	Child was split
*/

static int rtree_insert_req(MI_INFO *info, MI_KEYDEF *keyinfo, uchar *key, 
                            uint key_length, my_off_t page, my_off_t *new_page, 
                            int ins_level, int level)
{
  uchar *k;
  uint nod_flag;
  uchar *page_buf;
  int res;
  DBUG_ENTER("rtree_insert_req");

  if (!(page_buf = (uchar*)my_alloca((uint)keyinfo->block_length + 
                                     MI_MAX_KEY_BUFF)))
  {
    set_my_errno(HA_ERR_OUT_OF_MEM);
    DBUG_RETURN(-1); /* purecov: inspected */
  }
  if (!_mi_fetch_keypage(info, keyinfo, page, DFLT_INIT_HITS, page_buf, 0))
    goto err1;
  nod_flag = mi_test_if_nod(page_buf);
  DBUG_PRINT("rtree", ("page: %lu  level: %d  ins_level: %d  nod_flag: %u",
                       (ulong) page, level, ins_level, nod_flag));

  if ((ins_level == -1 && nod_flag) ||       /* key: go down to leaf */
      (ins_level > -1 && ins_level > level)) /* branch: go down to ins_level */
  { 
    if ((k = rtree_pick_key(info, keyinfo, key, key_length, page_buf, 
                             nod_flag)) == NULL)
      goto err1;
    switch ((res = rtree_insert_req(info, keyinfo, key, key_length, 
                     _mi_kpos(nod_flag, k), new_page, ins_level, level + 1)))
    {
      case 0: /* child was not split */
      {
        rtree_combine_rect(keyinfo->seg, k, key, k, key_length);
        if (_mi_write_keypage(info, keyinfo, page, DFLT_INIT_HITS, page_buf))
          goto err1;
        goto ok;
      }
      case 1: /* child was split */
      {
        uchar *new_key = page_buf + keyinfo->block_length + nod_flag;
        /* set proper MBR for key */
        if (rtree_set_key_mbr(info, keyinfo, k, key_length, 
                            _mi_kpos(nod_flag, k)))
          goto err1;
        /* add new key for new page */
        _mi_kpointer(info, new_key - nod_flag, *new_page);
        if (rtree_set_key_mbr(info, keyinfo, new_key, key_length, *new_page))
          goto err1;
        res = rtree_add_key(info, keyinfo, new_key, key_length, 
                           page_buf, new_page);
        if (_mi_write_keypage(info, keyinfo, page, DFLT_INIT_HITS, page_buf))
          goto err1;
        goto ok;
      }
      default:
      case -1: /* error */
      {
        goto err1;
      }
    }
  }
  else
  { 
    res = rtree_add_key(info, keyinfo, key, key_length, page_buf, new_page);
    if (_mi_write_keypage(info, keyinfo, page, DFLT_INIT_HITS, page_buf))
      goto err1;
    goto ok;
  }

ok:
  DBUG_RETURN(res);

err1:
  DBUG_RETURN(-1); /* purecov: inspected */
}


/*
  Insert key into the tree

  RETURN
    -1	Error
    0	Root was not split
    1	Root was split
*/

static int rtree_insert_level(MI_INFO *info, uint keynr, uchar *key, 
                             uint key_length, int ins_level)
{
  my_off_t old_root;
  MI_KEYDEF *keyinfo = info->s->keyinfo + keynr;
  int res;
  my_off_t new_page;
  DBUG_ENTER("rtree_insert_level");

  if ((old_root = info->s->state.key_root[keynr]) == HA_OFFSET_ERROR)
  {
    if ((old_root = _mi_new(info, keyinfo, DFLT_INIT_HITS)) == HA_OFFSET_ERROR)
      DBUG_RETURN(-1);
    info->buff_used = 1;
    mi_putint(info->buff, 2, 0);
    res = rtree_add_key(info, keyinfo, key, key_length, info->buff, NULL);
    if (_mi_write_keypage(info, keyinfo, old_root, DFLT_INIT_HITS, info->buff))
      DBUG_RETURN(1);
    info->s->state.key_root[keynr] = old_root;
    DBUG_RETURN(res);
  }

  switch ((res = rtree_insert_req(info, keyinfo, key, key_length, 
                                  old_root, &new_page, ins_level, 0)))
  {
    case 0: /* root was not split */
    {
      break;
    }
    case 1: /* root was split, grow a new root */
    { 
      uchar *new_root_buf= info->buff + info->s->base.max_key_block_length;
      my_off_t new_root;
      uchar *new_key;
      uint nod_flag = info->s->base.key_reflength;

      DBUG_PRINT("rtree", ("root was split, grow a new root"));

      mi_putint(new_root_buf, 2, nod_flag);
      if ((new_root = _mi_new(info, keyinfo, DFLT_INIT_HITS)) ==
	  HA_OFFSET_ERROR)
        goto err1;

      new_key = new_root_buf + keyinfo->block_length + nod_flag;

      _mi_kpointer(info, new_key - nod_flag, old_root);
      if (rtree_set_key_mbr(info, keyinfo, new_key, key_length, old_root))
        goto err1;
      if (rtree_add_key(info, keyinfo, new_key, key_length, new_root_buf, NULL) 
          == -1)
        goto err1;
      _mi_kpointer(info, new_key - nod_flag, new_page);
      if (rtree_set_key_mbr(info, keyinfo, new_key, key_length, new_page))
        goto err1;
      if (rtree_add_key(info, keyinfo, new_key, key_length, new_root_buf, NULL) 
          == -1)
        goto err1;
      if (_mi_write_keypage(info, keyinfo, new_root,
                            DFLT_INIT_HITS, new_root_buf))
        goto err1;
      info->s->state.key_root[keynr] = new_root;
      DBUG_PRINT("rtree", ("new root page: %lu  level: %d  nod_flag: %u",
                           (ulong) new_root, 0, mi_test_if_nod(new_root_buf)));

      break;
err1:
      DBUG_RETURN(-1); /* purecov: inspected */
    }
    default:
    case -1: /* error */
    {
      break;
    }
  }
  DBUG_RETURN(res);
}


/*
  Insert key into the tree - interface function

  RETURN
    -1	Error
    0	OK
*/

int rtree_insert(MI_INFO *info, uint keynr, uchar *key, uint key_length)
{
  DBUG_ENTER("rtree_insert");
  DBUG_RETURN((!key_length ||
               (rtree_insert_level(info, keynr, key, key_length, -1) == -1)) ?
              -1 : 0);
}


/* 
  Fill reinsert page buffer 

  RETURN
    -1	Error
    0	OK
*/

static int rtree_fill_reinsert_list(stPageList *ReinsertList, my_off_t page, 
                                    int level)
{
  DBUG_ENTER("rtree_fill_reinsert_list");
  DBUG_PRINT("rtree", ("page: %lu  level: %d", (ulong) page, level));
  if (ReinsertList->n_pages == ReinsertList->m_pages)
  {
    ReinsertList->m_pages += REINSERT_BUFFER_INC;
    if (!(ReinsertList->pages = (stPageLevel*)my_realloc(mi_key_memory_stPageList_pages,
                                                         (uchar*)ReinsertList->pages, 
      ReinsertList->m_pages * sizeof(stPageLevel), MYF(MY_ALLOW_ZERO_PTR))))
      goto err1;
  }
  /* save page to ReinsertList */
  ReinsertList->pages[ReinsertList->n_pages].offs = page;
  ReinsertList->pages[ReinsertList->n_pages].level = level;
  ReinsertList->n_pages++;
  DBUG_RETURN(0);

err1:
  DBUG_RETURN(-1); /* purecov: inspected */
}


/*
  Go down and delete key from the tree

  RETURN
    -1	Error
    0	Deleted
    1	Not found
    2	Empty leaf
*/

static int rtree_delete_req(MI_INFO *info, MI_KEYDEF *keyinfo, uchar *key, 
                           uint key_length, my_off_t page, uint *page_size, 
                           stPageList *ReinsertList, int level)
{
  uchar *k;
  uchar *last;
  ulong i;
  uint nod_flag;
  uchar *page_buf;
  int res;
  DBUG_ENTER("rtree_delete_req");

  if (!(page_buf = (uchar*)my_alloca((uint)keyinfo->block_length)))
  {
    set_my_errno(HA_ERR_OUT_OF_MEM);
    DBUG_RETURN(-1); /* purecov: inspected */
  }
  if (!_mi_fetch_keypage(info, keyinfo, page, DFLT_INIT_HITS, page_buf, 0))
    goto err1;
  nod_flag = mi_test_if_nod(page_buf);
  DBUG_PRINT("rtree", ("page: %lu  level: %d  nod_flag: %u",
                       (ulong) page, level, nod_flag));

  k = rt_PAGE_FIRST_KEY(page_buf, nod_flag);
  last = rt_PAGE_END(page_buf);

  for (i = 0; k < last; k = rt_PAGE_NEXT_KEY(k, key_length, nod_flag), ++i)
  {
    if (nod_flag)
    { 
      /* not leaf */
      if (!rtree_key_cmp(keyinfo->seg, key, k, key_length, MBR_WITHIN))
      {
        switch ((res = rtree_delete_req(info, keyinfo, key, key_length, 
                  _mi_kpos(nod_flag, k), page_size, ReinsertList, level + 1)))
        {
          case 0: /* deleted */
          { 
            /* test page filling */
            if (*page_size + key_length >= rt_PAGE_MIN_SIZE(keyinfo->block_length)) 
            { 
              /* OK */
              /* Calculate a new key value (MBR) for the shrinked block. */
              if (rtree_set_key_mbr(info, keyinfo, k, key_length, 
                                  _mi_kpos(nod_flag, k)))
                goto err1;
              if (_mi_write_keypage(info, keyinfo, page,
                                    DFLT_INIT_HITS, page_buf))
                goto err1;
            }
            else
            { 
              /*
                Too small: delete key & add it descendant to reinsert list.
                Store position and level of the block so that it can be
                accessed later for inserting the remaining keys.
              */
              DBUG_PRINT("rtree", ("too small. move block to reinsert list"));
              if (rtree_fill_reinsert_list(ReinsertList, _mi_kpos(nod_flag, k),
                                           level + 1))
                goto err1;
              /*
                Delete the key that references the block. This makes the
                block disappear from the index. Hence we need to insert
                its remaining keys later. Note: if the block is a branch
                block, we do not only remove this block, but the whole
                subtree. So we need to re-insert its keys on the same
                level later to reintegrate the subtrees.
              */
              rtree_delete_key(info, page_buf, k, key_length, nod_flag);
              if (_mi_write_keypage(info, keyinfo, page,
                                    DFLT_INIT_HITS, page_buf))
                goto err1;
              *page_size = mi_getint(page_buf);
            }
            
            goto ok;
          }
          case 1: /* not found - continue searching */
          {
            break;
          }
          case 2: /* vacuous case: last key in the leaf */
          {
            rtree_delete_key(info, page_buf, k, key_length, nod_flag);
            if (_mi_write_keypage(info, keyinfo, page,
                                  DFLT_INIT_HITS, page_buf))
              goto err1;
            *page_size = mi_getint(page_buf);
            res = 0;
            goto ok;
          }
          default: /* error */
          case -1:
          {
            goto err1;
          }
        }
      }
    }
    else  
    {
      /* leaf */
      if (!rtree_key_cmp(keyinfo->seg, key, k, key_length, MBR_EQUAL | MBR_DATA))
      {
        rtree_delete_key(info, page_buf, k, key_length, nod_flag);
        *page_size = mi_getint(page_buf);
        if (*page_size == 2) 
        {
          /* last key in the leaf */
          res = 2;
          if (_mi_dispose(info, keyinfo, page, DFLT_INIT_HITS))
            goto err1;
        }
        else
        {
          res = 0;
          if (_mi_write_keypage(info, keyinfo, page, DFLT_INIT_HITS, page_buf))
            goto err1;
        }
        goto ok;
      }
    }
  }
  res = 1;

ok:
  DBUG_RETURN(res);

err1:
  DBUG_RETURN(-1); /* purecov: inspected */
}


/*
  Delete key - interface function

  RETURN
    -1	Error
    0	Deleted
*/

int rtree_delete(MI_INFO *info, uint keynr, uchar *key, uint key_length)
{
  uint page_size;
  stPageList ReinsertList;
  my_off_t old_root;
  MI_KEYDEF *keyinfo = info->s->keyinfo + keynr;
  DBUG_ENTER("rtree_delete");

  if ((old_root = info->s->state.key_root[keynr]) == HA_OFFSET_ERROR)
  {
    set_my_errno(HA_ERR_END_OF_FILE);
    DBUG_RETURN(-1); /* purecov: inspected */
  }
  DBUG_PRINT("rtree", ("starting deletion at root page: %lu",
                       (ulong) old_root));

  ReinsertList.pages = NULL;
  ReinsertList.n_pages = 0;
  ReinsertList.m_pages = 0;
  
  switch (rtree_delete_req(info, keyinfo, key, key_length, old_root, 
                                 &page_size, &ReinsertList, 0))
  {
    case 2: /* empty */
    {
      info->s->state.key_root[keynr] = HA_OFFSET_ERROR;
      DBUG_RETURN(0);
    }
    case 0: /* deleted */
    {
      uint nod_flag;
      ulong i;
      for (i = 0; i < ReinsertList.n_pages; ++i)
      {
        uchar *page_buf;
        uchar *k;
        uchar *last;

        if (!(page_buf = (uchar*)my_alloca((uint)keyinfo->block_length)))
        {
          set_my_errno(HA_ERR_OUT_OF_MEM);
          goto err1;
        }
        if (!_mi_fetch_keypage(info, keyinfo, ReinsertList.pages[i].offs, 
                               DFLT_INIT_HITS, page_buf, 0))
          goto err1;
        nod_flag = mi_test_if_nod(page_buf);
        DBUG_PRINT("rtree", ("reinserting keys from "
                             "page: %lu  level: %d  nod_flag: %u",
                             (ulong) ReinsertList.pages[i].offs,
                             ReinsertList.pages[i].level, nod_flag));

        k = rt_PAGE_FIRST_KEY(page_buf, nod_flag);
        last = rt_PAGE_END(page_buf);
        for (; k < last; k = rt_PAGE_NEXT_KEY(k, key_length, nod_flag))
        {
          int res;
          if ((res= rtree_insert_level(info, keynr, k, key_length,
                                       ReinsertList.pages[i].level)) == -1)
          {
            goto err1;
          }
          if (res)
          {
            ulong j;
            DBUG_PRINT("rtree", ("root has been split, adjust levels"));
            for (j= i; j < ReinsertList.n_pages; j++)
            {
              ReinsertList.pages[j].level++;
              DBUG_PRINT("rtree", ("keys from page: %lu  now level: %d",
                                   (ulong) ReinsertList.pages[i].offs,
                                   ReinsertList.pages[i].level));
            }
          }
        }
        if (_mi_dispose(info, keyinfo, ReinsertList.pages[i].offs,
            DFLT_INIT_HITS))
          goto err1;
      }
      if (ReinsertList.pages)
        my_free(ReinsertList.pages);

      /* check for redundant root (not leaf, 1 child) and eliminate */
      if ((old_root = info->s->state.key_root[keynr]) == HA_OFFSET_ERROR)
        goto err1;
      if (!_mi_fetch_keypage(info, keyinfo, old_root, DFLT_INIT_HITS,
                             info->buff, 0))
        goto err1;
      nod_flag = mi_test_if_nod(info->buff);
      page_size = mi_getint(info->buff);
      if (nod_flag && (page_size == 2 + key_length + nod_flag))
      {
        my_off_t new_root = _mi_kpos(nod_flag,
                                     rt_PAGE_FIRST_KEY(info->buff, nod_flag));
        if (_mi_dispose(info, keyinfo, old_root, DFLT_INIT_HITS))
          goto err1;
        info->s->state.key_root[keynr] = new_root;
      }
      info->update= HA_STATE_DELETED;
      DBUG_RETURN(0);

err1:
      DBUG_RETURN(-1); /* purecov: inspected */
    }
    case 1: /* not found */
    {
      set_my_errno(HA_ERR_KEY_NOT_FOUND);
      DBUG_RETURN(-1); /* purecov: inspected */
    }
    default:
    case -1: /* error */
    {
      DBUG_RETURN(-1); /* purecov: inspected */
    }
  }
}


/* 
  Estimate number of suitable keys in the tree 

  RETURN
    estimated value
*/

ha_rows rtree_estimate(MI_INFO *info, uint keynr, uchar *key, 
                       uint key_length, uint flag)
{
  MI_KEYDEF *keyinfo = info->s->keyinfo + keynr;
  my_off_t root;
  uint i = 0;
  uchar *k;
  uchar *last;
  uint nod_flag;
  uchar *page_buf;
  uint k_len;
  double area = 0;
  ha_rows res = 0;

  if (flag & MBR_DISJOINT)
    return info->state->records;

  if ((root = info->s->state.key_root[keynr]) == HA_OFFSET_ERROR)
    return HA_POS_ERROR;
  if (!(page_buf = (uchar*)my_alloca((uint)keyinfo->block_length)))
    return HA_POS_ERROR;
  if (!_mi_fetch_keypage(info, keyinfo, root, DFLT_INIT_HITS, page_buf, 0))
    goto err1;
  nod_flag = mi_test_if_nod(page_buf);

  k_len = keyinfo->keylength - info->s->base.rec_reflength;

  k = rt_PAGE_FIRST_KEY(page_buf, nod_flag);
  last = rt_PAGE_END(page_buf);

  for (; k < last; k = rt_PAGE_NEXT_KEY(k, k_len, nod_flag), ++i)
  {
    if (nod_flag)
    {
      double k_area = rtree_rect_volume(keyinfo->seg, k, key_length);

      /* The following should be safe, even if we compare doubles */
      if (k_area == 0)
      {
        if (flag & (MBR_CONTAIN | MBR_INTERSECT))
        {
          area += 1;
        }
        else if (flag & (MBR_WITHIN | MBR_EQUAL))
        {
          if (!rtree_key_cmp(keyinfo->seg, key, k, key_length, MBR_WITHIN))
            area += 1;
        }
        else
          goto err1;
      }
      else
      {
        if (flag & (MBR_CONTAIN | MBR_INTERSECT))
        {
          area += rtree_overlapping_area(keyinfo->seg, key, k, key_length) / 
                  k_area;
        }
        else if (flag & (MBR_WITHIN | MBR_EQUAL))
        {
          if (!rtree_key_cmp(keyinfo->seg, key, k, key_length, MBR_WITHIN))
            area += rtree_rect_volume(keyinfo->seg, key, key_length) /
                    k_area;
        }
        else
          goto err1;
      }
    }
    else
    {
      if (!rtree_key_cmp(keyinfo->seg, key, k, key_length, flag))
        ++res;
    }
  }
  if (nod_flag)
  {
    if (i)
      res = (ha_rows) (area / i * info->state->records);
    else 
      res = HA_POS_ERROR;
  }

  return res;

err1:
  return HA_POS_ERROR;
}
