sqlite3.c

  return rc;
}

/*
** Return the 64-bit integer value associated with cell iCell of
** node pNode. If pNode is a leaf node, this is a rowid. If it is
** an internal node, then the 64-bit integer is a child page number.
*/
static i64 nodeGetRowid(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  int iCell
){
  assert( iCell<NCELL(pNode) );
  return readInt64(&pNode->zData[4 + pRtree->nBytesPerCell*iCell]);
}

/*
** Return coordinate iCoord from cell iCell in node pNode.
*/
static void nodeGetCoord(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  int iCell,
  int iCoord,
  RtreeCoord *pCoord           /* Space to write result to */
){
  readCoord(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord], pCoord);
}

/*
** Deserialize cell iCell of node pNode. Populate the structure pointed
** to by pCell with the results.
*/
static void nodeGetCell(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  int iCell,
  RtreeCell *pCell
){
  int ii;
  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
  for(ii=0; ii<pRtree->nDim*2; ii++){
    nodeGetCoord(pRtree, pNode, iCell, ii, &pCell->aCoord[ii]);
  }
}


/* Forward declaration for the function that does the work of
** the virtual table module xCreate() and xConnect() methods.
*/
static int rtreeInit(
  sqlite3 *, void *, int, const char *const*, sqlite3_vtab **, char **, int
);

/* 
** Rtree virtual table module xCreate method.
*/
static int rtreeCreate(
  sqlite3 *db,
  void *pAux,
  int argc, const char *const*argv,
  sqlite3_vtab **ppVtab,
  char **pzErr
){
  return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 1);
}

/* 
** Rtree virtual table module xConnect method.
*/
static int rtreeConnect(
  sqlite3 *db,
  void *pAux,
  int argc, const char *const*argv,
  sqlite3_vtab **ppVtab,
  char **pzErr
){
  return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 0);
}

/*
** Increment the r-tree reference count.
*/
static void rtreeReference(Rtree *pRtree){
  pRtree->nBusy++;
}

/*
** Decrement the r-tree reference count. When the reference count reaches
** zero the structure is deleted.
*/
static void rtreeRelease(Rtree *pRtree){
  pRtree->nBusy--;
  if( pRtree->nBusy==0 ){
    sqlite3_finalize(pRtree->pReadNode);
    sqlite3_finalize(pRtree->pWriteNode);
    sqlite3_finalize(pRtree->pDeleteNode);
    sqlite3_finalize(pRtree->pReadRowid);
    sqlite3_finalize(pRtree->pWriteRowid);
    sqlite3_finalize(pRtree->pDeleteRowid);
    sqlite3_finalize(pRtree->pReadParent);
    sqlite3_finalize(pRtree->pWriteParent);
    sqlite3_finalize(pRtree->pDeleteParent);
    sqlite3_free(pRtree);
  }
}

/* 
** Rtree virtual table module xDisconnect method.
*/
static int rtreeDisconnect(sqlite3_vtab *pVtab){
  rtreeRelease((Rtree *)pVtab);
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xDestroy method.
*/
static int rtreeDestroy(sqlite3_vtab *pVtab){
  Rtree *pRtree = (Rtree *)pVtab;
  int rc;
  char *zCreate = sqlite3_mprintf(
    "DROP TABLE '%q'.'%q_node';"
    "DROP TABLE '%q'.'%q_rowid';"
    "DROP TABLE '%q'.'%q_parent';",
    pRtree->zDb, pRtree->zName, 
    pRtree->zDb, pRtree->zName,
    pRtree->zDb, pRtree->zName
  );
  if( !zCreate ){
    rc = SQLITE_NOMEM;
  }else{
    rc = sqlite3_exec(pRtree->db, zCreate, 0, 0, 0);
    sqlite3_free(zCreate);
  }
  if( rc==SQLITE_OK ){
    rtreeRelease(pRtree);
  }

  return rc;
}

/* 
** Rtree virtual table module xOpen method.
*/
static int rtreeOpen(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor){
  int rc = SQLITE_NOMEM;
  RtreeCursor *pCsr;

  pCsr = (RtreeCursor *)sqlite3_malloc(sizeof(RtreeCursor));
  if( pCsr ){
    memset(pCsr, 0, sizeof(RtreeCursor));
    pCsr->base.pVtab = pVTab;
    rc = SQLITE_OK;
  }
  *ppCursor = (sqlite3_vtab_cursor *)pCsr;

  return rc;
}


/*
** Free the RtreeCursor.aConstraint[] array and its contents.
*/
static void freeCursorConstraints(RtreeCursor *pCsr){
  if( pCsr->aConstraint ){
    int i;                        /* Used to iterate through constraint array */
    for(i=0; i<pCsr->nConstraint; i++){
      sqlite3_rtree_geometry *pGeom = pCsr->aConstraint[i].pGeom;
      if( pGeom ){
        if( pGeom->xDelUser ) pGeom->xDelUser(pGeom->pUser);
        sqlite3_free(pGeom);
      }
    }
    sqlite3_free(pCsr->aConstraint);
    pCsr->aConstraint = 0;
  }
}

/* 
** Rtree virtual table module xClose method.
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
  Rtree *pRtree = (Rtree *)(cur->pVtab);
  int rc;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  freeCursorConstraints(pCsr);
  rc = nodeRelease(pRtree, pCsr->pNode);
  sqlite3_free(pCsr);
  return rc;
}

/*
** Rtree virtual table module xEof method.
**
** Return non-zero if the cursor does not currently point to a valid 
** record (i.e if the scan has finished), or zero otherwise.
*/
static int rtreeEof(sqlite3_vtab_cursor *cur){
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  return (pCsr->pNode==0);
}

/*
** The r-tree constraint passed as the second argument to this function is
** guaranteed to be a MATCH constraint.
*/
static int testRtreeGeom(
  Rtree *pRtree,                  /* R-Tree object */
  RtreeConstraint *pConstraint,   /* MATCH constraint to test */
  RtreeCell *pCell,               /* Cell to test */
  int *pbRes                      /* OUT: Test result */
){
  int i;
  RtreeDValue aCoord[RTREE_MAX_DIMENSIONS*2];
  int nCoord = pRtree->nDim*2;

  assert( pConstraint->op==RTREE_MATCH );
  assert( pConstraint->pGeom );

  for(i=0; i<nCoord; i++){
    aCoord[i] = DCOORD(pCell->aCoord[i]);
  }
  return pConstraint->xGeom(pConstraint->pGeom, nCoord, aCoord, pbRes);
}

/* 
** Cursor pCursor currently points to a cell in a non-leaf page.
** Set *pbEof to true if the sub-tree headed by the cell is filtered
** (excluded) by the constraints in the pCursor->aConstraint[] 
** array, or false otherwise.
**
** Return SQLITE_OK if successful or an SQLite error code if an error
** occurs within a geometry callback.
*/
static int testRtreeCell(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
  RtreeCell cell;
  int ii;
  int bRes = 0;
  int rc = SQLITE_OK;

  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; bRes==0 && ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    RtreeDValue cell_min = DCOORD(cell.aCoord[(p->iCoord>>1)*2]);
    RtreeDValue cell_max = DCOORD(cell.aCoord[(p->iCoord>>1)*2+1]);

    assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
        || p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_MATCH
    );

    switch( p->op ){
      case RTREE_LE: case RTREE_LT: 
        bRes = p->rValue<cell_min; 
        break;

      case RTREE_GE: case RTREE_GT: 
        bRes = p->rValue>cell_max; 
        break;

      case RTREE_EQ:
        bRes = (p->rValue>cell_max || p->rValue<cell_min);
        break;

      default: {
        assert( p->op==RTREE_MATCH );
        rc = testRtreeGeom(pRtree, p, &cell, &bRes);
        bRes = !bRes;
        break;
      }
    }
  }

  *pbEof = bRes;
  return rc;
}

/* 
** Test if the cell that cursor pCursor currently points to
** would be filtered (excluded) by the constraints in the 
** pCursor->aConstraint[] array. If so, set *pbEof to true before
** returning. If the cell is not filtered (excluded) by the constraints,
** set pbEof to zero.
**
** Return SQLITE_OK if successful or an SQLite error code if an error
** occurs within a geometry callback.
**
** This function assumes that the cell is part of a leaf node.
*/
static int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
  RtreeCell cell;
  int ii;
  *pbEof = 0;

  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    RtreeDValue coord = DCOORD(cell.aCoord[p->iCoord]);
    int res;
    assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
        || p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_MATCH
    );
    switch( p->op ){
      case RTREE_LE: res = (coord<=p->rValue); break;
      case RTREE_LT: res = (coord<p->rValue);  break;
      case RTREE_GE: res = (coord>=p->rValue); break;
      case RTREE_GT: res = (coord>p->rValue);  break;
      case RTREE_EQ: res = (coord==p->rValue); break;
      default: {
        int rc;
        assert( p->op==RTREE_MATCH );
        rc = testRtreeGeom(pRtree, p, &cell, &res);
        if( rc!=SQLITE_OK ){
          return rc;
        }
        break;
      }
    }

    if( !res ){
      *pbEof = 1;
      return SQLITE_OK;
    }
  }

  return SQLITE_OK;
}

/*
** Cursor pCursor currently points at a node that heads a sub-tree of
** height iHeight (if iHeight==0, then the node is a leaf). Descend
** to point to the left-most cell of the sub-tree that matches the 
** configured constraints.
*/
static int descendToCell(
  Rtree *pRtree, 
  RtreeCursor *pCursor, 
  int iHeight,
  int *pEof                 /* OUT: Set to true if cannot descend */
){
  int isEof;
  int rc;
  int ii;
  RtreeNode *pChild;
  sqlite3_int64 iRowid;

  RtreeNode *pSavedNode = pCursor->pNode;
  int iSavedCell = pCursor->iCell;

  assert( iHeight>=0 );

  if( iHeight==0 ){
    rc = testRtreeEntry(pRtree, pCursor, &isEof);
  }else{
    rc = testRtreeCell(pRtree, pCursor, &isEof);
  }
  if( rc!=SQLITE_OK || isEof || iHeight==0 ){
    goto descend_to_cell_out;
  }

  iRowid = nodeGetRowid(pRtree, pCursor->pNode, pCursor->iCell);
  rc = nodeAcquire(pRtree, iRowid, pCursor->pNode, &pChild);
  if( rc!=SQLITE_OK ){
    goto descend_to_cell_out;
  }

  nodeRelease(pRtree, pCursor->pNode);
  pCursor->pNode = pChild;
  isEof = 1;
  for(ii=0; isEof && ii<NCELL(pChild); ii++){
    pCursor->iCell = ii;
    rc = descendToCell(pRtree, pCursor, iHeight-1, &isEof);
    if( rc!=SQLITE_OK ){
      goto descend_to_cell_out;
    }
  }

  if( isEof ){
    assert( pCursor->pNode==pChild );
    nodeReference(pSavedNode);
    nodeRelease(pRtree, pChild);
    pCursor->pNode = pSavedNode;
    pCursor->iCell = iSavedCell;
  }

descend_to_cell_out:
  *pEof = isEof;
  return rc;
}

/*
** One of the cells in node pNode is guaranteed to have a 64-bit 
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  i64 iRowid,
  int *piIndex
){
  int ii;
  int nCell = NCELL(pNode);
  for(ii=0; ii<nCell; ii++){
    if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){
      *piIndex = ii;
      return SQLITE_OK;
    }
  }
  return SQLITE_CORRUPT_VTAB;
}

/*
** Return the index of the cell containing a pointer to node pNode
** in its parent. If pNode is the root node, return -1.
*/
static int nodeParentIndex(Rtree *pRtree, RtreeNode *pNode, int *piIndex){
  RtreeNode *pParent = pNode->pParent;
  if( pParent ){
    return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);
  }
  *piIndex = -1;
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xNext method.
*/
static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
  Rtree *pRtree = (Rtree *)(pVtabCursor->pVtab);
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
  int rc = SQLITE_OK;

  /* RtreeCursor.pNode must not be NULL. If is is NULL, then this cursor is
  ** already at EOF. It is against the rules to call the xNext() method of
  ** a cursor that has already reached EOF.
  */
  assert( pCsr->pNode );

  if( pCsr->iStrategy==1 ){
    /* This "scan" is a direct lookup by rowid. There is no next entry. */
    nodeRelease(pRtree, pCsr->pNode);
    pCsr->pNode = 0;
  }else{
    /* Move to the next entry that matches the configured constraints. */
    int iHeight = 0;
    while( pCsr->pNode ){
      RtreeNode *pNode = pCsr->pNode;
      int nCell = NCELL(pNode);
      for(pCsr->iCell++; pCsr->iCell<nCell; pCsr->iCell++){
        int isEof;
        rc = descendToCell(pRtree, pCsr, iHeight, &isEof);
        if( rc!=SQLITE_OK || !isEof ){
          return rc;
        }
      }
      pCsr->pNode = pNode->pParent;
      rc = nodeParentIndex(pRtree, pNode, &pCsr->iCell);
      if( rc!=SQLITE_OK ){
        return rc;
      }
      nodeReference(pCsr->pNode);
      nodeRelease(pRtree, pNode);
      iHeight++;
    }
  }

  return rc;
}

/* 
** Rtree virtual table module xRowid method.
*/
static int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){
  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;

  assert(pCsr->pNode);
  *pRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);

  return SQLITE_OK;
}

/* 
** Rtree virtual table module xColumn method.
*/
static int rtreeColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){
  Rtree *pRtree = (Rtree *)cur->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)cur;

  if( i==0 ){
    i64 iRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
    sqlite3_result_int64(ctx, iRowid);
  }else{
    RtreeCoord c;
    nodeGetCoord(pRtree, pCsr->pNode, pCsr->iCell, i-1, &c);
#ifndef SQLITE_RTREE_INT_ONLY
    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
      sqlite3_result_double(ctx, c.f);
    }else
#endif
    {
      assert( pRtree->eCoordType==RTREE_COORD_INT32 );
      sqlite3_result_int(ctx, c.i);
    }
  }

  return SQLITE_OK;
}

/* 
** Use nodeAcquire() to obtain the leaf node containing the record with 
** rowid iRowid. If successful, set *ppLeaf to point to the node and
** return SQLITE_OK. If there is no such record in the table, set
** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf
** to zero and return an SQLite error code.
*/
static int findLeafNode(Rtree *pRtree, i64 iRowid, RtreeNode **ppLeaf){
  int rc;
  *ppLeaf = 0;
  sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);
  if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){
    i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);
    rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);
    sqlite3_reset(pRtree->pReadRowid);
  }else{
    rc = sqlite3_reset(pRtree->pReadRowid);
  }
  return rc;
}

/*
** This function is called to configure the RtreeConstraint object passed
** as the second argument for a MATCH constraint. The value passed as the
** first argument to this function is the right-hand operand to the MATCH
** operator.
*/
static int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){
  RtreeMatchArg *p;
  sqlite3_rtree_geometry *pGeom;
  int nBlob;

  /* Check that value is actually a blob. */
  if( sqlite3_value_type(pValue)!=SQLITE_BLOB ) return SQLITE_ERROR;

  /* Check that the blob is roughly the right size. */
  nBlob = sqlite3_value_bytes(pValue);
  if( nBlob<(int)sizeof(RtreeMatchArg) 
   || ((nBlob-sizeof(RtreeMatchArg))%sizeof(RtreeDValue))!=0
  ){
    return SQLITE_ERROR;
  }

  pGeom = (sqlite3_rtree_geometry *)sqlite3_malloc(
      sizeof(sqlite3_rtree_geometry) + nBlob
  );
  if( !pGeom ) return SQLITE_NOMEM;
  memset(pGeom, 0, sizeof(sqlite3_rtree_geometry));
  p = (RtreeMatchArg *)&pGeom[1];

  memcpy(p, sqlite3_value_blob(pValue), nBlob);
  if( p->magic!=RTREE_GEOMETRY_MAGIC 
   || nBlob!=(int)(sizeof(RtreeMatchArg) + (p->nParam-1)*sizeof(RtreeDValue))
  ){
    sqlite3_free(pGeom);
    return SQLITE_ERROR;
  }

  pGeom->pContext = p->pContext;
  pGeom->nParam = p->nParam;
  pGeom->aParam = p->aParam;

  pCons->xGeom = p->xGeom;
  pCons->pGeom = pGeom;
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xFilter method.
*/
static int rtreeFilter(
  sqlite3_vtab_cursor *pVtabCursor, 
  int idxNum, const char *idxStr,
  int argc, sqlite3_value **argv
){
  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;

  RtreeNode *pRoot = 0;
  int ii;
  int rc = SQLITE_OK;

  rtreeReference(pRtree);

  freeCursorConstraints(pCsr);
  pCsr->iStrategy = idxNum;

  if( idxNum==1 ){
    /* Special case - lookup by rowid. */
    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
    i64 iRowid = sqlite3_value_int64(argv[0]);
    rc = findLeafNode(pRtree, iRowid, &pLeaf);
    pCsr->pNode = pLeaf; 
    if( pLeaf ){
      assert( rc==SQLITE_OK );
      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &pCsr->iCell);
    }
  }else{
    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
    ** with the configured constraints. 
    */
    if( argc>0 ){
      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
      pCsr->nConstraint = argc;
      if( !pCsr->aConstraint ){
        rc = SQLITE_NOMEM;
      }else{
        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);
        assert( (idxStr==0 && argc==0)
                || (idxStr && (int)strlen(idxStr)==argc*2) );
        for(ii=0; ii<argc; ii++){
          RtreeConstraint *p = &pCsr->aConstraint[ii];
          p->op = idxStr[ii*2];
          p->iCoord = idxStr[ii*2+1]-'a';
          if( p->op==RTREE_MATCH ){
            /* A MATCH operator. The right-hand-side must be a blob that
            ** can be cast into an RtreeMatchArg object. One created using
            ** an sqlite3_rtree_geometry_callback() SQL user function.
            */
            rc = deserializeGeometry(argv[ii], p);
            if( rc!=SQLITE_OK ){
              break;
            }
          }else{
#ifdef SQLITE_RTREE_INT_ONLY
            p->rValue = sqlite3_value_int64(argv[ii]);
#else
            p->rValue = sqlite3_value_double(argv[ii]);
#endif
          }
        }
      }
    }
  
    if( rc==SQLITE_OK ){
      pCsr->pNode = 0;
      rc = nodeAcquire(pRtree, 1, 0, &pRoot);
    }
    if( rc==SQLITE_OK ){
      int isEof = 1;
      int nCell = NCELL(pRoot);
      pCsr->pNode = pRoot;
      for(pCsr->iCell=0; rc==SQLITE_OK && pCsr->iCell<nCell; pCsr->iCell++){
        assert( pCsr->pNode==pRoot );
        rc = descendToCell(pRtree, pCsr, pRtree->iDepth, &isEof);
        if( !isEof ){
          break;
        }
      }
      if( rc==SQLITE_OK && isEof ){
        assert( pCsr->pNode==pRoot );
        nodeRelease(pRtree, pRoot);
        pCsr->pNode = 0;
      }
      assert( rc!=SQLITE_OK || !pCsr->pNode || pCsr->iCell<NCELL(pCsr->pNode) );
    }
  }

  rtreeRelease(pRtree);
  return rc;
}

/*
** Rtree virtual table module xBestIndex method. There are three
** table scan strategies to choose from (in order from most to 
** least desirable):
**
**   idxNum     idxStr        Strategy
**   ------------------------------------------------
**     1        Unused        Direct lookup by rowid.
**     2        See below     R-tree query or full-table scan.
**   ------------------------------------------------
**
** If strategy 1 is used, then idxStr is not meaningful. If strategy
** 2 is used, idxStr is formatted to contain 2 bytes for each 
** constraint used. The first two bytes of idxStr correspond to 
** the constraint in sqlite3_index_info.aConstraintUsage[] with
** (argvIndex==1) etc.
**
** The first of each pair of bytes in idxStr identifies the constraint
** operator as follows:
**
**   Operator    Byte Value
**   ----------------------
**      =        0x41 ('A')
**     <=        0x42 ('B')
**      <        0x43 ('C')
**     >=        0x44 ('D')
**      >        0x45 ('E')
**   MATCH       0x46 ('F')
**   ----------------------
**
** The second of each pair of bytes identifies the coordinate column
** to which the constraint applies. The leftmost coordinate column
** is 'a', the second from the left 'b' etc.
*/
static int rtreeBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
  int rc = SQLITE_OK;
  int ii;

  int iIdx = 0;
  char zIdxStr[RTREE_MAX_DIMENSIONS*8+1];
  memset(zIdxStr, 0, sizeof(zIdxStr));
  UNUSED_PARAMETER(tab);

  assert( pIdxInfo->idxStr==0 );
  for(ii=0; ii<pIdxInfo->nConstraint && iIdx<(int)(sizeof(zIdxStr)-1); ii++){
    struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[ii];

    if( p->usable && p->iColumn==0 && p->op==SQLITE_INDEX_CONSTRAINT_EQ ){
      /* We have an equality constraint on the rowid. Use strategy 1. */
      int jj;
      for(jj=0; jj<ii; jj++){
        pIdxInfo->aConstraintUsage[jj].argvIndex = 0;
        pIdxInfo->aConstraintUsage[jj].omit = 0;
      }
      pIdxInfo->idxNum = 1;
      pIdxInfo->aConstraintUsage[ii].argvIndex = 1;
      pIdxInfo->aConstraintUsage[jj].omit = 1;

      /* This strategy involves a two rowid lookups on an B-Tree structures
      ** and then a linear search of an R-Tree node. This should be 
      ** considered almost as quick as a direct rowid lookup (for which 
      ** sqlite uses an internal cost of 0.0).
      */ 
      pIdxInfo->estimatedCost = 10.0;
      return SQLITE_OK;
    }

    if( p->usable && (p->iColumn>0 || p->op==SQLITE_INDEX_CONSTRAINT_MATCH) ){
      u8 op;
      switch( p->op ){
        case SQLITE_INDEX_CONSTRAINT_EQ: op = RTREE_EQ; break;
        case SQLITE_INDEX_CONSTRAINT_GT: op = RTREE_GT; break;
        case SQLITE_INDEX_CONSTRAINT_LE: op = RTREE_LE; break;
        case SQLITE_INDEX_CONSTRAINT_LT: op = RTREE_LT; break;
        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;
        default:
          assert( p->op==SQLITE_INDEX_CONSTRAINT_MATCH );
          op = RTREE_MATCH; 
          break;
      }
      zIdxStr[iIdx++] = op;
      zIdxStr[iIdx++] = p->iColumn - 1 + 'a';
      pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
      pIdxInfo->aConstraintUsage[ii].omit = 1;
    }
  }

  pIdxInfo->idxNum = 2;
  pIdxInfo->needToFreeIdxStr = 1;
  if( iIdx>0 && 0==(pIdxInfo->idxStr = sqlite3_mprintf("%s", zIdxStr)) ){
    return SQLITE_NOMEM;
  }
  assert( iIdx>=0 );
  pIdxInfo->estimatedCost = (2000000.0 / (double)(iIdx + 1));
  return rc;
}

/*
** Return the N-dimensional volumn of the cell stored in *p.
*/
static RtreeDValue cellArea(Rtree *pRtree, RtreeCell *p){
  RtreeDValue area = (RtreeDValue)1;
  int ii;
  for(ii=0; ii<(pRtree->nDim*2); ii+=2){
    area = (area * (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii])));
  }
  return area;
}

/*
** Return the margin length of cell p. The margin length is the sum
** of the objects size in each dimension.
*/
static RtreeDValue cellMargin(Rtree *pRtree, RtreeCell *p){
  RtreeDValue margin = (RtreeDValue)0;
  int ii;
  for(ii=0; ii<(pRtree->nDim*2); ii+=2){
    margin += (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));
  }
  return margin;
}

/*
** Store the union of cells p1 and p2 in p1.
*/
static void cellUnion(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){
  int ii;
  if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
    for(ii=0; ii<(pRtree->nDim*2); ii+=2){
      p1->aCoord[ii].f = MIN(p1->aCoord[ii].f, p2->aCoord[ii].f);
      p1->aCoord[ii+1].f = MAX(p1->aCoord[ii+1].f, p2->aCoord[ii+1].f);
    }
  }else{
    for(ii=0; ii<(pRtree->nDim*2); ii+=2){
      p1->aCoord[ii].i = MIN(p1->aCoord[ii].i, p2->aCoord[ii].i);
      p1->aCoord[ii+1].i = MAX(p1->aCoord[ii+1].i, p2->aCoord[ii+1].i);
    }
  }
}

/*
** Return true if the area covered by p2 is a subset of the area covered
** by p1. False otherwise.
*/
static int cellContains(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){
  int ii;
  int isInt = (pRtree->eCoordType==RTREE_COORD_INT32);
  for(ii=0; ii<(pRtree->nDim*2); ii+=2){
    RtreeCoord *a1 = &p1->aCoord[ii];
    RtreeCoord *a2 = &p2->aCoord[ii];
    if( (!isInt && (a2[0].f<a1[0].f || a2[1].f>a1[1].f)) 
     || ( isInt && (a2[0].i<a1[0].i || a2[1].i>a1[1].i)) 
    ){
      return 0;
    }
  }
  return 1;
}

/*
** Return the amount cell p would grow by if it were unioned with pCell.
*/
static RtreeDValue cellGrowth(Rtree *pRtree, RtreeCell *p, RtreeCell *pCell){
  RtreeDValue area;
  RtreeCell cell;
  memcpy(&cell, p, sizeof(RtreeCell));
  area = cellArea(pRtree, &cell);
  cellUnion(pRtree, &cell, pCell);
  return (cellArea(pRtree, &cell)-area);
}

#if VARIANT_RSTARTREE_CHOOSESUBTREE || VARIANT_RSTARTREE_SPLIT
static RtreeDValue cellOverlap(
  Rtree *pRtree, 
  RtreeCell *p, 
  RtreeCell *aCell, 
  int nCell, 
  int iExclude
){
  int ii;
  RtreeDValue overlap = 0.0;
  for(ii=0; ii<nCell; ii++){
#if VARIANT_RSTARTREE_CHOOSESUBTREE
    if( ii!=iExclude )
#else
    assert( iExclude==-1 );
    UNUSED_PARAMETER(iExclude);
#endif
    {
      int jj;
      RtreeDValue o = (RtreeDValue)1;
      for(jj=0; jj<(pRtree->nDim*2); jj+=2){
        RtreeDValue x1, x2;

        x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));
        x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));

        if( x2<x1 ){
          o = 0.0;
          break;
        }else{
          o = o * (x2-x1);
        }
      }
      overlap += o;
    }
  }
  return overlap;
}
#endif

#if VARIANT_RSTARTREE_CHOOSESUBTREE
static RtreeDValue cellOverlapEnlargement(
  Rtree *pRtree, 
  RtreeCell *p, 
  RtreeCell *pInsert, 
  RtreeCell *aCell, 
  int nCell, 
  int iExclude
){
  RtreeDValue before, after;
  before = cellOverlap(pRtree, p, aCell, nCell, iExclude);
  cellUnion(pRtree, p, pInsert);
  after = cellOverlap(pRtree, p, aCell, nCell, iExclude);
  return (after-before);
}
#endif


/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
  Rtree *pRtree,               /* Rtree table */
  RtreeCell *pCell,            /* Cell to insert into rtree */
  int iHeight,                 /* Height of sub-tree rooted at pCell */
  RtreeNode **ppLeaf           /* OUT: Selected leaf page */
){
  int rc;
  int ii;
  RtreeNode *pNode;
  rc = nodeAcquire(pRtree, 1, 0, &pNode);

  for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
    int iCell;
    sqlite3_int64 iBest = 0;

    RtreeDValue fMinGrowth = 0.0;
    RtreeDValue fMinArea = 0.0;
#if VARIANT_RSTARTREE_CHOOSESUBTREE
    RtreeDValue fMinOverlap = 0.0;
    RtreeDValue overlap;
#endif

    int nCell = NCELL(pNode);
    RtreeCell cell;
    RtreeNode *pChild;

    RtreeCell *aCell = 0;

#if VARIANT_RSTARTREE_CHOOSESUBTREE
    if( ii==(pRtree->iDepth-1) ){
      int jj;
      aCell = sqlite3_malloc(sizeof(RtreeCell)*nCell);
      if( !aCell ){
        rc = SQLITE_NOMEM;
        nodeRelease(pRtree, pNode);
        pNode = 0;
        continue;
      }
      for(jj=0; jj<nCell; jj++){
        nodeGetCell(pRtree, pNode, jj, &aCell[jj]);
      }
    }
#endif

    /* Select the child node which will be enlarged the least if pCell
    ** is inserted into it. Resolve ties by choosing the entry with
    ** the smallest area.
    */
    for(iCell=0; iCell<nCell; iCell++){
      int bBest = 0;
      RtreeDValue growth;
      RtreeDValue area;
      nodeGetCell(pRtree, pNode, iCell, &cell);
      growth = cellGrowth(pRtree, &cell, pCell);
      area = cellArea(pRtree, &cell);

#if VARIANT_RSTARTREE_CHOOSESUBTREE
      if( ii==(pRtree->iDepth-1) ){
        overlap = cellOverlapEnlargement(pRtree,&cell,pCell,aCell,nCell,iCell);
      }else{
        overlap = 0.0;
      }
      if( (iCell==0) 
       || (overlap<fMinOverlap) 
       || (overlap==fMinOverlap && growth<fMinGrowth)
       || (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
      ){
        bBest = 1;
        fMinOverlap = overlap;
      }
#else
      if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
        bBest = 1;
      }
#endif
      if( bBest ){
        fMinGrowth = growth;
        fMinArea = area;
        iBest = cell.iRowid;
      }
    }

    sqlite3_free(aCell);
    rc = nodeAcquire(pRtree, iBest, pNode, &pChild);
    nodeRelease(pRtree, pNode);
    pNode = pChild;
  }

  *ppLeaf = pNode;
  return rc;
}

/*
** A cell with the same content as pCell has just been inserted into
** the node pNode. This function updates the bounding box cells in