Move bundled copy of sqlite one level deeper to better separate it...

third_party/sqlite/ext/rtree/rtree.c

-/*
-** 2001 September 15
-**
-** The author disclaims copyright to this source code.  In place of
-** a legal notice, here is a blessing:
-**
-**    May you do good and not evil.
-**    May you find forgiveness for yourself and forgive others.
-**    May you share freely, never taking more than you give.
-**
-*************************************************************************
-** This file contains code for implementations of the r-tree and r*-tree
-** algorithms packaged as an SQLite virtual table module.
-**
-** $Id: rtree.c,v 1.14 2009/08/06 18:36:47 danielk1977 Exp $
-*/
-
-#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RTREE)
-
-/*
-** This file contains an implementation of a couple of different variants
-** of the r-tree algorithm. See the README file for further details. The 
-** same data-structure is used for all, but the algorithms for insert and
-** delete operations vary. The variants used are selected at compile time 
-** by defining the following symbols:
-*/
-
-/* Either, both or none of the following may be set to activate 
-** r*tree variant algorithms.
-*/
-#define VARIANT_RSTARTREE_CHOOSESUBTREE 0
-#define VARIANT_RSTARTREE_REINSERT      1
-
-/* 
-** Exactly one of the following must be set to 1.
-*/
-#define VARIANT_GUTTMAN_QUADRATIC_SPLIT 0
-#define VARIANT_GUTTMAN_LINEAR_SPLIT    0
-#define VARIANT_RSTARTREE_SPLIT         1
-
-#define VARIANT_GUTTMAN_SPLIT \
-        (VARIANT_GUTTMAN_LINEAR_SPLIT||VARIANT_GUTTMAN_QUADRATIC_SPLIT)
-
-#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
-  #define PickNext QuadraticPickNext
-  #define PickSeeds QuadraticPickSeeds
-  #define AssignCells splitNodeGuttman
-#endif
-#if VARIANT_GUTTMAN_LINEAR_SPLIT
-  #define PickNext LinearPickNext
-  #define PickSeeds LinearPickSeeds
-  #define AssignCells splitNodeGuttman
-#endif
-#if VARIANT_RSTARTREE_SPLIT
-  #define AssignCells splitNodeStartree
-#endif
-
-
-#ifndef SQLITE_CORE
-  #include "sqlite3ext.h"
-  SQLITE_EXTENSION_INIT1
-#else
-  #include "sqlite3.h"
-#endif
-
-#include <string.h>
-#include <assert.h>
-
-#ifndef SQLITE_AMALGAMATION
-typedef sqlite3_int64 i64;
-typedef unsigned char u8;
-typedef unsigned int u32;
-#endif
-
-typedef struct Rtree Rtree;
-typedef struct RtreeCursor RtreeCursor;
-typedef struct RtreeNode RtreeNode;
-typedef struct RtreeCell RtreeCell;
-typedef struct RtreeConstraint RtreeConstraint;
-typedef union RtreeCoord RtreeCoord;
-
-/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */
-#define RTREE_MAX_DIMENSIONS 5
-
-/* Size of hash table Rtree.aHash. This hash table is not expected to
-** ever contain very many entries, so a fixed number of buckets is 
-** used.
-*/
-#define HASHSIZE 128
-
-/* 
-** An rtree virtual-table object.
-*/
-struct Rtree {
-  sqlite3_vtab base;
-  sqlite3 *db;                /* Host database connection */
-  int iNodeSize;              /* Size in bytes of each node in the node table */
-  int nDim;                   /* Number of dimensions */
-  int nBytesPerCell;          /* Bytes consumed per cell */
-  int iDepth;                 /* Current depth of the r-tree structure */
-  char *zDb;                  /* Name of database containing r-tree table */
-  char *zName;                /* Name of r-tree table */ 
-  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ 
-  int nBusy;                  /* Current number of users of this structure */
-
-  /* List of nodes removed during a CondenseTree operation. List is
-  ** linked together via the pointer normally used for hash chains -
-  ** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree 
-  ** headed by the node (leaf nodes have RtreeNode.iNode==0).
-  */
-  RtreeNode *pDeleted;
-  int iReinsertHeight;        /* Height of sub-trees Reinsert() has run on */
-
-  /* Statements to read/write/delete a record from xxx_node */
-  sqlite3_stmt *pReadNode;
-  sqlite3_stmt *pWriteNode;
-  sqlite3_stmt *pDeleteNode;
-
-  /* Statements to read/write/delete a record from xxx_rowid */
-  sqlite3_stmt *pReadRowid;
-  sqlite3_stmt *pWriteRowid;
-  sqlite3_stmt *pDeleteRowid;
-
-  /* Statements to read/write/delete a record from xxx_parent */
-  sqlite3_stmt *pReadParent;
-  sqlite3_stmt *pWriteParent;
-  sqlite3_stmt *pDeleteParent;
-
-  int eCoordType;
-};
-
-/* Possible values for eCoordType: */
-#define RTREE_COORD_REAL32 0
-#define RTREE_COORD_INT32  1
-
-/*
-** The minimum number of cells allowed for a node is a third of the 
-** maximum. In Gutman's notation:
-**
-**     m = M/3
-**
-** If an R*-tree "Reinsert" operation is required, the same number of
-** cells are removed from the overfull node and reinserted into the tree.
-*/
-#define RTREE_MINCELLS(p) ((((p)->iNodeSize-4)/(p)->nBytesPerCell)/3)
-#define RTREE_REINSERT(p) RTREE_MINCELLS(p)
-#define RTREE_MAXCELLS 51
-
-/* 
-** An rtree cursor object.
-*/
-struct RtreeCursor {
-  sqlite3_vtab_cursor base;
-  RtreeNode *pNode;                 /* Node cursor is currently pointing at */
-  int iCell;                        /* Index of current cell in pNode */
-  int iStrategy;                    /* Copy of idxNum search parameter */
-  int nConstraint;                  /* Number of entries in aConstraint */
-  RtreeConstraint *aConstraint;     /* Search constraints. */
-};
-
-union RtreeCoord {
-  float f;
-  int i;
-};
-
-/*
-** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
-** formatted as a double. This macro assumes that local variable pRtree points
-** to the Rtree structure associated with the RtreeCoord.
-*/
-#define DCOORD(coord) (                           \
-  (pRtree->eCoordType==RTREE_COORD_REAL32) ?      \
-    ((double)coord.f) :                           \
-    ((double)coord.i)                             \
-)
-
-/*
-** A search constraint.
-*/
-struct RtreeConstraint {
-  int iCoord;                       /* Index of constrained coordinate */
-  int op;                           /* Constraining operation */
-  double rValue;                    /* Constraint value. */
-};
-
-/* Possible values for RtreeConstraint.op */
-#define RTREE_EQ 0x41
-#define RTREE_LE 0x42
-#define RTREE_LT 0x43
-#define RTREE_GE 0x44
-#define RTREE_GT 0x45
-
-/* 
-** An rtree structure node.
-**
-** Data format (RtreeNode.zData):
-**
-**   1. If the node is the root node (node 1), then the first 2 bytes
-**      of the node contain the tree depth as a big-endian integer.
-**      For non-root nodes, the first 2 bytes are left unused.
-**
-**   2. The next 2 bytes contain the number of entries currently 
-**      stored in the node.
-**
-**   3. The remainder of the node contains the node entries. Each entry
-**      consists of a single 8-byte integer followed by an even number
-**      of 4-byte coordinates. For leaf nodes the integer is the rowid
-**      of a record. For internal nodes it is the node number of a
-**      child page.
-*/
-struct RtreeNode {
-  RtreeNode *pParent;               /* Parent node */
-  i64 iNode;
-  int nRef;
-  int isDirty;
-  u8 *zData;
-  RtreeNode *pNext;                 /* Next node in this hash chain */
-};
-#define NCELL(pNode) readInt16(&(pNode)->zData[2])
-
-/* 
-** Structure to store a deserialized rtree record.
-*/
-struct RtreeCell {
-  i64 iRowid;
-  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];
-};
-
-#ifndef MAX
-# define MAX(x,y) ((x) < (y) ? (y) : (x))
-#endif
-#ifndef MIN
-# define MIN(x,y) ((x) > (y) ? (y) : (x))
-#endif
-
-/*
-** Functions to deserialize a 16 bit integer, 32 bit real number and
-** 64 bit integer. The deserialized value is returned.
-*/
-static int readInt16(u8 *p){
-  return (p[0]<<8) + p[1];
-}
-static void readCoord(u8 *p, RtreeCoord *pCoord){
-  u32 i = (
-    (((u32)p[0]) << 24) + 
-    (((u32)p[1]) << 16) + 
-    (((u32)p[2]) <<  8) + 
-    (((u32)p[3]) <<  0)
-  );
-  *(u32 *)pCoord = i;
-}
-static i64 readInt64(u8 *p){
-  return (
-    (((i64)p[0]) << 56) + 
-    (((i64)p[1]) << 48) + 
-    (((i64)p[2]) << 40) + 
-    (((i64)p[3]) << 32) + 
-    (((i64)p[4]) << 24) + 
-    (((i64)p[5]) << 16) + 
-    (((i64)p[6]) <<  8) + 
-    (((i64)p[7]) <<  0)
-  );
-}
-
-/*
-** Functions to serialize a 16 bit integer, 32 bit real number and
-** 64 bit integer. The value returned is the number of bytes written
-** to the argument buffer (always 2, 4 and 8 respectively).
-*/
-static int writeInt16(u8 *p, int i){
-  p[0] = (i>> 8)&0xFF;
-  p[1] = (i>> 0)&0xFF;
-  return 2;
-}
-static int writeCoord(u8 *p, RtreeCoord *pCoord){
-  u32 i;
-  assert( sizeof(RtreeCoord)==4 );
-  assert( sizeof(u32)==4 );
-  i = *(u32 *)pCoord;
-  p[0] = (i>>24)&0xFF;
-  p[1] = (i>>16)&0xFF;
-  p[2] = (i>> 8)&0xFF;
-  p[3] = (i>> 0)&0xFF;
-  return 4;
-}
-static int writeInt64(u8 *p, i64 i){
-  p[0] = (i>>56)&0xFF;
-  p[1] = (i>>48)&0xFF;
-  p[2] = (i>>40)&0xFF;
-  p[3] = (i>>32)&0xFF;
-  p[4] = (i>>24)&0xFF;
-  p[5] = (i>>16)&0xFF;
-  p[6] = (i>> 8)&0xFF;
-  p[7] = (i>> 0)&0xFF;
-  return 8;
-}
-
-/*
-** Increment the reference count of node p.
-*/
-static void nodeReference(RtreeNode *p){
-  if( p ){
-    p->nRef++;
-  }
-}
-
-/*
-** Clear the content of node p (set all bytes to 0x00).
-*/
-static void nodeZero(Rtree *pRtree, RtreeNode *p){
-  if( p ){
-    memset(&p->zData[2], 0, pRtree->iNodeSize-2);
-    p->isDirty = 1;
-  }
-}
-
-/*
-** Given a node number iNode, return the corresponding key to use
-** in the Rtree.aHash table.
-*/
-static int nodeHash(i64 iNode){
-  return (
-    (iNode>>56) ^ (iNode>>48) ^ (iNode>>40) ^ (iNode>>32) ^ 
-    (iNode>>24) ^ (iNode>>16) ^ (iNode>> 8) ^ (iNode>> 0)
-  ) % HASHSIZE;
-}
-
-/*
-** Search the node hash table for node iNode. If found, return a pointer
-** to it. Otherwise, return 0.
-*/
-static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
-  RtreeNode *p;
-  assert( iNode!=0 );
-  for(p=pRtree->aHash[nodeHash(iNode)]; p && p->iNode!=iNode; p=p->pNext);
-  return p;
-}
-
-/*
-** Add node pNode to the node hash table.
-*/
-static void nodeHashInsert(Rtree *pRtree, RtreeNode *pNode){
-  if( pNode ){
-    int iHash;
-    assert( pNode->pNext==0 );
-    iHash = nodeHash(pNode->iNode);
-    pNode->pNext = pRtree->aHash[iHash];
-    pRtree->aHash[iHash] = pNode;
-  }
-}
-
-/*
-** Remove node pNode from the node hash table.
-*/
-static void nodeHashDelete(Rtree *pRtree, RtreeNode *pNode){
-  RtreeNode **pp;
-  if( pNode->iNode!=0 ){
-    pp = &pRtree->aHash[nodeHash(pNode->iNode)];
-    for( ; (*pp)!=pNode; pp = &(*pp)->pNext){ assert(*pp); }
-    *pp = pNode->pNext;
-    pNode->pNext = 0;
-  }
-}
-
-/*
-** Allocate and return new r-tree node. Initially, (RtreeNode.iNode==0),
-** indicating that node has not yet been assigned a node number. It is
-** assigned a node number when nodeWrite() is called to write the
-** node contents out to the database.
-*/
-static RtreeNode *nodeNew(Rtree *pRtree, RtreeNode *pParent, int zero){
-  RtreeNode *pNode;
-  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
-  if( pNode ){
-    memset(pNode, 0, sizeof(RtreeNode) + (zero?pRtree->iNodeSize:0));
-    pNode->zData = (u8 *)&pNode[1];
-    pNode->nRef = 1;
-    pNode->pParent = pParent;
-    pNode->isDirty = 1;
-    nodeReference(pParent);
-  }
-  return pNode;
-}
-
-/*
-** Obtain a reference to an r-tree node.
-*/
-static int
-nodeAcquire(
-  Rtree *pRtree,             /* R-tree structure */
-  i64 iNode,                 /* Node number to load */
-  RtreeNode *pParent,        /* Either the parent node or NULL */
-  RtreeNode **ppNode         /* OUT: Acquired node */
-){
-  int rc;
-  RtreeNode *pNode;
-
-  /* Check if the requested node is already in the hash table. If so,
-  ** increase its reference count and return it.
-  */
-  if( (pNode = nodeHashLookup(pRtree, iNode)) ){
-    assert( !pParent || !pNode->pParent || pNode->pParent==pParent );
-    if( pParent && !pNode->pParent ){
-      nodeReference(pParent);
-      pNode->pParent = pParent;
-    }
-    pNode->nRef++;
-    *ppNode = pNode;
-    return SQLITE_OK;
-  }
-
-  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
-  if( !pNode ){
-    *ppNode = 0;
-    return SQLITE_NOMEM;
-  }
-  pNode->pParent = pParent;
-  pNode->zData = (u8 *)&pNode[1];
-  pNode->nRef = 1;
-  pNode->iNode = iNode;
-  pNode->isDirty = 0;
-  pNode->pNext = 0;
-
-  sqlite3_bind_int64(pRtree->pReadNode, 1, iNode);
-  rc = sqlite3_step(pRtree->pReadNode);
-  if( rc==SQLITE_ROW ){
-    const u8 *zBlob = sqlite3_column_blob(pRtree->pReadNode, 0);
-    memcpy(pNode->zData, zBlob, pRtree->iNodeSize);
-    nodeReference(pParent);
-  }else{
-    sqlite3_free(pNode);
-    pNode = 0;
-  }
-
-  *ppNode = pNode;
-  rc = sqlite3_reset(pRtree->pReadNode);
-
-  if( rc==SQLITE_OK && iNode==1 ){
-    pRtree->iDepth = readInt16(pNode->zData);
-  }
-
-  assert( (rc==SQLITE_OK && pNode) || (pNode==0 && rc!=SQLITE_OK) );
-  nodeHashInsert(pRtree, pNode);
-
-  return rc;
-}
-
-/*
-** Overwrite cell iCell of node pNode with the contents of pCell.
-*/
-static void nodeOverwriteCell(
-  Rtree *pRtree, 
-  RtreeNode *pNode,  
-  RtreeCell *pCell, 
-  int iCell
-){
-  int ii;
-  u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
-  p += writeInt64(p, pCell->iRowid);
-  for(ii=0; ii<(pRtree->nDim*2); ii++){
-    p += writeCoord(p, &pCell->aCoord[ii]);
-  }
-  pNode->isDirty = 1;
-}
-
-/*
-** Remove cell the cell with index iCell from node pNode.
-*/
-static void nodeDeleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell){
-  u8 *pDst = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
-  u8 *pSrc = &pDst[pRtree->nBytesPerCell];
-  int nByte = (NCELL(pNode) - iCell - 1) * pRtree->nBytesPerCell;
-  memmove(pDst, pSrc, nByte);
-  writeInt16(&pNode->zData[2], NCELL(pNode)-1);
-  pNode->isDirty = 1;
-}
-
-/*
-** Insert the contents of cell pCell into node pNode. If the insert
-** is successful, return SQLITE_OK.
-**
-** If there is not enough free space in pNode, return SQLITE_FULL.
-*/
-static int
-nodeInsertCell(
-  Rtree *pRtree, 
-  RtreeNode *pNode, 
-  RtreeCell *pCell 
-){
-  int nCell;                    /* Current number of cells in pNode */
-  int nMaxCell;                 /* Maximum number of cells for pNode */
-
-  nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;
-  nCell = NCELL(pNode);
-
-  assert(nCell<=nMaxCell);
-
-  if( nCell<nMaxCell ){
-    nodeOverwriteCell(pRtree, pNode, pCell, nCell);
-    writeInt16(&pNode->zData[2], nCell+1);
-    pNode->isDirty = 1;
-  }
-
-  return (nCell==nMaxCell);
-}
-
-/*
-** If the node is dirty, write it out to the database.
-*/
-static int
-nodeWrite(Rtree *pRtree, RtreeNode *pNode){
-  int rc = SQLITE_OK;
-  if( pNode->isDirty ){
-    sqlite3_stmt *p = pRtree->pWriteNode;
-    if( pNode->iNode ){
-      sqlite3_bind_int64(p, 1, pNode->iNode);
-    }else{
-      sqlite3_bind_null(p, 1);
-    }
-    sqlite3_bind_blob(p, 2, pNode->zData, pRtree->iNodeSize, SQLITE_STATIC);
-    sqlite3_step(p);
-    pNode->isDirty = 0;
-    rc = sqlite3_reset(p);
-    if( pNode->iNode==0 && rc==SQLITE_OK ){
-      pNode->iNode = sqlite3_last_insert_rowid(pRtree->db);
-      nodeHashInsert(pRtree, pNode);
-    }
-  }
-  return rc;
-}
-
-/*
-** Release a reference to a node. If the node is dirty and the reference
-** count drops to zero, the node data is written to the database.
-*/
-static int
-nodeRelease(Rtree *pRtree, RtreeNode *pNode){
-  int rc = SQLITE_OK;
-  if( pNode ){
-    assert( pNode->nRef>0 );
-    pNode->nRef--;
-    if( pNode->nRef==0 ){
-      if( pNode->iNode==1 ){
-        pRtree->iDepth = -1;
-      }
-      if( pNode->pParent ){
-        rc = nodeRelease(pRtree, pNode->pParent);
-      }
-      if( rc==SQLITE_OK ){
-        rc = nodeWrite(pRtree, pNode);
-      }
-      nodeHashDelete(pRtree, pNode);
-      sqlite3_free(pNode);
-    }
-  }
-  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;
-}
-
-/* 
-** Rtree virtual table module xClose method.
-*/
-static int rtreeClose(sqlite3_vtab_cursor *cur){
-  Rtree *pRtree = (Rtree *)(cur->pVtab);
-  int rc;
-  RtreeCursor *pCsr = (RtreeCursor *)cur;
-  sqlite3_free(pCsr->aConstraint);
-  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);
-}
-
-/* 
-** Cursor pCursor currently points to a cell in a non-leaf page.
-** Return true if the sub-tree headed by the cell is filtered
-** (excluded) by the constraints in the pCursor->aConstraint[] 
-** array, or false otherwise.
-*/
-static int testRtreeCell(Rtree *pRtree, RtreeCursor *pCursor){
-  RtreeCell cell;
-  int ii;
-  int bRes = 0;
-
-  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
-  for(ii=0; bRes==0 && ii<pCursor->nConstraint; ii++){
-    RtreeConstraint *p = &pCursor->aConstraint[ii];
-    double cell_min = DCOORD(cell.aCoord[(p->iCoord>>1)*2]);
-    double 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
-    );
-
-    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;
-    }
-  }
-
-  return bRes;
-}
-
-/* 
-** Return true if the cell that cursor pCursor currently points to
-** would be filtered (excluded) by the constraints in the 
-** pCursor->aConstraint[] array, or false otherwise.
-**
-** This function assumes that the cell is part of a leaf node.
-*/
-static int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor){
-  RtreeCell cell;
-  int ii;
-
-  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
-  for(ii=0; ii<pCursor->nConstraint; ii++){
-    RtreeConstraint *p = &pCursor->aConstraint[ii];
-    double 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
-    );
-    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;
-    }
-
-    if( !res ) return 1;
-  }
-
-  return 0;
-}
-
-/*
-** 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 ){
-    isEof = testRtreeEntry(pRtree, pCursor);
-  }else{
-    isEof = testRtreeCell(pRtree, pCursor);
-  }
-  if( isEof || iHeight==0 ){
-    *pEof = isEof;
-    return SQLITE_OK;
-  }
-
-  iRowid = nodeGetRowid(pRtree, pCursor->pNode, pCursor->iCell);
-  rc = nodeAcquire(pRtree, iRowid, pCursor->pNode, &pChild);
-  if( rc!=SQLITE_OK ){
-    return rc;
-  }
-
-  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 ){
-      return rc;
-    }
-  }
-
-  if( isEof ){
-    assert( pCursor->pNode==pChild );
-    nodeReference(pSavedNode);
-    nodeRelease(pRtree, pChild);
-    pCursor->pNode = pSavedNode;
-    pCursor->iCell = iSavedCell;
-  }
-
-  *pEof = isEof;
-  return SQLITE_OK;
-}
-
-/*
-** 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 ii;
-  for(ii=0; nodeGetRowid(pRtree, pNode, ii)!=iRowid; ii++){
-    assert( ii<(NCELL(pNode)-1) );
-  }
-  return ii;
-}
-
-/*
-** 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){
-  RtreeNode *pParent = pNode->pParent;
-  if( pParent ){
-    return nodeRowidIndex(pRtree, pParent, pNode->iNode);
-  }
-  return -1;
-}
-
-/* 
-** 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;
-
-  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 if( pCsr->pNode ){
-    /* 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;
-      pCsr->iCell = nodeParentIndex(pRtree, pNode);
-      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);
-    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
-      sqlite3_result_double(ctx, c.f);
-    }else{
-      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;
-}
-
-
-/* 
-** 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);
-
-  sqlite3_free(pCsr->aConstraint);
-  pCsr->aConstraint = 0;
-  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 && rc==SQLITE_OK ){
-      pCsr->iCell = nodeRowidIndex(pRtree, pLeaf, iRowid);
-    }
-  }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{
-        assert( (idxStr==0 && argc==0) || 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';
-          p->rValue = sqlite3_value_double(argv[ii]);
-        }
-      }
-    }
-  
-    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.
-**     3        Unused        Full table scan.
-**   ------------------------------------------------
-**
-** If strategy 1 or 3 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')
-**   ----------------------
-**
-** 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, cCol;
-
-  int iIdx = 0;
-  char zIdxStr[RTREE_MAX_DIMENSIONS*8+1];
-  memset(zIdxStr, 0, sizeof(zIdxStr));
-
-  assert( pIdxInfo->idxStr==0 );
-  for(ii=0; ii<pIdxInfo->nConstraint; 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 ){
-      u8 op = 0;
-      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;
-      }
-      if( op ){
-        /* Make sure this particular constraint has not been used before.
-        ** If it has been used before, ignore it.
-        **
-        ** A <= or < can be used if there is a prior >= or >.
-        ** A >= or > can be used if there is a prior < or <=.
-        ** A <= or < is disqualified if there is a prior <=, <, or ==.
-        ** A >= or > is disqualified if there is a prior >=, >, or ==.
-        ** A == is disqualifed if there is any prior constraint.
-        */
-        int j, opmsk;
-        static const unsigned char compatible[] = { 0, 0, 1, 1, 2, 2 };
-        assert( compatible[RTREE_EQ & 7]==0 );
-        assert( compatible[RTREE_LT & 7]==1 );
-        assert( compatible[RTREE_LE & 7]==1 );
-        assert( compatible[RTREE_GT & 7]==2 );
-        assert( compatible[RTREE_GE & 7]==2 );
-        cCol = p->iColumn - 1 + 'a';
-        opmsk = compatible[op & 7];
-        for(j=0; j<iIdx; j+=2){
-          if( zIdxStr[j+1]==cCol && (compatible[zIdxStr[j] & 7] & opmsk)!=0 ){
-            op = 0;
-            break;
-          }
-        }
-      }
-      if( op ){
-        assert( iIdx<sizeof(zIdxStr)-1 );
-        zIdxStr[iIdx++] = op;
-        zIdxStr[iIdx++] = cCol;
-        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 float cellArea(Rtree *pRtree, RtreeCell *p){
-  float area = 1.0;
-  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 float cellMargin(Rtree *pRtree, RtreeCell *p){
-  float margin = 0.0;
-  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 float cellGrowth(Rtree *pRtree, RtreeCell *p, RtreeCell *pCell){
-  float 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 float cellOverlap(
-  Rtree *pRtree, 
-  RtreeCell *p, 
-  RtreeCell *aCell, 
-  int nCell, 
-  int iExclude
-){
-  int ii;
-  float overlap = 0.0;
-  for(ii=0; ii<nCell; ii++){
-    if( ii!=iExclude ){
-      int jj;
-      float o = 1.0;
-      for(jj=0; jj<(pRtree->nDim*2); jj+=2){
-        double x1;
-        double 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 float cellOverlapEnlargement(
-  Rtree *pRtree, 
-  RtreeCell *p, 
-  RtreeCell *pInsert, 
-  RtreeCell *aCell, 
-  int nCell, 
-  int iExclude
-){
-  float before;
-  float 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;
-
-    float fMinGrowth;
-    float fMinArea;
-    float fMinOverlap;
-
-    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++){
-      float growth;
-      float area;
-      float overlap = 0.0;
-      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);
-      }
-#endif
-      if( (iCell==0) 
-       || (overlap<fMinOverlap) 
-       || (overlap==fMinOverlap && growth<fMinGrowth)
-       || (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
-      ){
-        fMinOverlap = overlap;
-        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
-** all ancestor elements.
-*/
-static void AdjustTree(
-  Rtree *pRtree,                    /* Rtree table */
-  RtreeNode *pNode,                 /* Adjust ancestry of this node. */
-  RtreeCell *pCell                  /* This cell was just inserted */
-){
-  RtreeNode *p = pNode;
-  while( p->pParent ){
-    RtreeCell cell;
-    RtreeNode *pParent = p->pParent;
-    int iCell = nodeParentIndex(pRtree, p);
-
-    nodeGetCell(pRtree, pParent, iCell, &cell);
-    if( !cellContains(pRtree, &cell, pCell) ){
-      cellUnion(pRtree, &cell, pCell);
-      nodeOverwriteCell(pRtree, pParent, &cell, iCell);
-    }
- 
-    p = pParent;
-  }
-}
-
-/*
-** Write mapping (iRowid->iNode) to the <rtree>_rowid table.
-*/
-static int rowidWrite(Rtree *pRtree, sqlite3_int64 iRowid, sqlite3_int64 iNode){
-  sqlite3_bind_int64(pRtree->pWriteRowid, 1, iRowid);
-  sqlite3_bind_int64(pRtree->pWriteRowid, 2, iNode);
-  sqlite3_step(pRtree->pWriteRowid);
-  return sqlite3_reset(pRtree->pWriteRowid);
-}
-
-/*
-** Write mapping (iNode->iPar) to the <rtree>_parent table.
-*/
-static int parentWrite(Rtree *pRtree, sqlite3_int64 iNode, sqlite3_int64 iPar){
-  sqlite3_bind_int64(pRtree->pWriteParent, 1, iNode);
-  sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
-  sqlite3_step(pRtree->pWriteParent);
-  return sqlite3_reset(pRtree->pWriteParent);
-}
-
-static int rtreeInsertCell(Rtree *, RtreeNode *, RtreeCell *, int);
-
-#if VARIANT_GUTTMAN_LINEAR_SPLIT
-/*
-** Implementation of the linear variant of the PickNext() function from
-** Guttman[84].
-*/
-static RtreeCell *LinearPickNext(
-  Rtree *pRtree,
-  RtreeCell *aCell, 
-  int nCell, 
-  RtreeCell *pLeftBox, 
-  RtreeCell *pRightBox,
-  int *aiUsed
-){
-  int ii;
-  for(ii=0; aiUsed[ii]; ii++);
-  aiUsed[ii] = 1;
-  return &aCell[ii];
-}
-
-/*
-** Implementation of the linear variant of the PickSeeds() function from
-** Guttman[84].
-*/
-static void LinearPickSeeds(
-  Rtree *pRtree,
-  RtreeCell *aCell, 
-  int nCell, 
-  int *piLeftSeed, 
-  int *piRightSeed
-){
-  int i;
-  int iLeftSeed = 0;
-  int iRightSeed = 1;
-  float maxNormalInnerWidth = 0.0;
-
-  /* Pick two "seed" cells from the array of cells. The algorithm used
-  ** here is the LinearPickSeeds algorithm from Gutman[1984]. The 
-  ** indices of the two seed cells in the array are stored in local
-  ** variables iLeftSeek and iRightSeed.
-  */
-  for(i=0; i<pRtree->nDim; i++){
-    float x1 = aCell[0].aCoord[i*2];
-    float x2 = aCell[0].aCoord[i*2+1];
-    float x3 = x1;
-    float x4 = x2;
-    int jj;
-
-    int iCellLeft = 0;
-    int iCellRight = 0;
-
-    for(jj=1; jj<nCell; jj++){
-      float left = aCell[jj].aCoord[i*2];
-      float right = aCell[jj].aCoord[i*2+1];
-
-      if( left<x1 ) x1 = left;
-      if( right>x4 ) x4 = right;
-      if( left>x3 ){
-        x3 = left;
-        iCellRight = jj;
-      }
-      if( right<x2 ){
-        x2 = right;
-        iCellLeft = jj;
-      }
-    }
-
-    if( x4!=x1 ){
-      float normalwidth = (x3 - x2) / (x4 - x1);
-      if( normalwidth>maxNormalInnerWidth ){
-        iLeftSeed = iCellLeft;
-        iRightSeed = iCellRight;
-      }
-    }
-  }
-
-  *piLeftSeed = iLeftSeed;
-  *piRightSeed = iRightSeed;
-}
-#endif /* VARIANT_GUTTMAN_LINEAR_SPLIT */
-
-#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
-/*
-** Implementation of the quadratic variant of the PickNext() function from
-** Guttman[84].
-*/
-static RtreeCell *QuadraticPickNext(
-  Rtree *pRtree,
-  RtreeCell *aCell, 
-  int nCell, 
-  RtreeCell *pLeftBox, 
-  RtreeCell *pRightBox,
-  int *aiUsed
-){
-  #define FABS(a) ((a)<0.0?-1.0*(a):(a))
-
-  int iSelect = -1;
-  float fDiff;
-  int ii;
-  for(ii=0; ii<nCell; ii++){
-    if( aiUsed[ii]==0 ){
-      float left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
-      float right = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
-      float diff = FABS(right-left);
-      if( iSelect<0 || diff>fDiff ){
-        fDiff = diff;
-        iSelect = ii;
-      }
-    }
-  }
-  aiUsed[iSelect] = 1;
-  return &aCell[iSelect];
-}
-
-/*
-** Implementation of the quadratic variant of the PickSeeds() function from
-** Guttman[84].
-*/
-static void QuadraticPickSeeds(
-  Rtree *pRtree,
-  RtreeCell *aCell, 
-  int nCell, 
-  int *piLeftSeed, 
-  int *piRightSeed
-){
-  int ii;
-  int jj;
-
-  int iLeftSeed = 0;
-  int iRightSeed = 1;
-  float fWaste = 0.0;
-
-  for(ii=0; ii<nCell; ii++){
-    for(jj=ii+1; jj<nCell; jj++){
-      float right = cellArea(pRtree, &aCell[jj]);
-      float growth = cellGrowth(pRtree, &aCell[ii], &aCell[jj]);
-      float waste = growth - right;
-
-      if( waste>fWaste ){
-        iLeftSeed = ii;
-        iRightSeed = jj;
-        fWaste = waste;
-      }
-    }
-  }
-
-  *piLeftSeed = iLeftSeed;
-  *piRightSeed = iRightSeed;
-}
-#endif /* VARIANT_GUTTMAN_QUADRATIC_SPLIT */
-
-/*
-** Arguments aIdx, aDistance and aSpare all point to arrays of size
-** nIdx. The aIdx array contains the set of integers from 0 to 
-** (nIdx-1) in no particular order. This function sorts the values
-** in aIdx according to the indexed values in aDistance. For
-** example, assuming the inputs:
-**
-**   aIdx      = { 0,   1,   2,   3 }
-**   aDistance = { 5.0, 2.0, 7.0, 6.0 }
-**
-** this function sets the aIdx array to contain:
-**
-**   aIdx      = { 0,   1,   2,   3 }
-**
-** The aSpare array is used as temporary working space by the
-** sorting algorithm.
-*/
-static void SortByDistance(
-  int *aIdx, 
-  int nIdx, 
-  float *aDistance, 
-  int *aSpare
-){
-  if( nIdx>1 ){
-    int iLeft = 0;
-    int iRight = 0;
-
-    int nLeft = nIdx/2;
-    int nRight = nIdx-nLeft;
-    int *aLeft = aIdx;
-    int *aRight = &aIdx[nLeft];
-
-    SortByDistance(aLeft, nLeft, aDistance, aSpare);
-    SortByDistance(aRight, nRight, aDistance, aSpare);
-
-    memcpy(aSpare, aLeft, sizeof(int)*nLeft);
-    aLeft = aSpare;
-
-    while( iLeft<nLeft || iRight<nRight ){
-      if( iLeft==nLeft ){
-        aIdx[iLeft+iRight] = aRight[iRight];
-        iRight++;
-      }else if( iRight==nRight ){
-        aIdx[iLeft+iRight] = aLeft[iLeft];
-        iLeft++;
-      }else{
-        float fLeft = aDistance[aLeft[iLeft]];
-        float fRight = aDistance[aRight[iRight]];
-        if( fLeft<fRight ){
-          aIdx[iLeft+iRight] = aLeft[iLeft];
-          iLeft++;
-        }else{
-          aIdx[iLeft+iRight] = aRight[iRight];
-          iRight++;
-        }
-      }
-    }
-
-#if 0
-    /* Check that the sort worked */
-    {
-      int jj;
-      for(jj=1; jj<nIdx; jj++){
-        float left = aDistance[aIdx[jj-1]];
-        float right = aDistance[aIdx[jj]];
-        assert( left<=right );
-      }
-    }
-#endif
-  }
-}
-
-/*
-** Arguments aIdx, aCell and aSpare all point to arrays of size
-** nIdx. The aIdx array contains the set of integers from 0 to 
-** (nIdx-1) in no particular order. This function sorts the values
-** in aIdx according to dimension iDim of the cells in aCell. The
-** minimum value of dimension iDim is considered first, the
-** maximum used to break ties.
-**
-** The aSpare array is used as temporary working space by the
-** sorting algorithm.
-*/
-static void SortByDimension(
-  Rtree *pRtree,
-  int *aIdx, 
-  int nIdx, 
-  int iDim, 
-  RtreeCell *aCell, 
-  int *aSpare
-){
-  if( nIdx>1 ){
-
-    int iLeft = 0;
-    int iRight = 0;
-
-    int nLeft = nIdx/2;
-    int nRight = nIdx-nLeft;
-    int *aLeft = aIdx;
-    int *aRight = &aIdx[nLeft];
-
-    SortByDimension(pRtree, aLeft, nLeft, iDim, aCell, aSpare);
-    SortByDimension(pRtree, aRight, nRight, iDim, aCell, aSpare);
-
-    memcpy(aSpare, aLeft, sizeof(int)*nLeft);
-    aLeft = aSpare;
-    while( iLeft<nLeft || iRight<nRight ){
-      double xleft1 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2]);
-      double xleft2 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2+1]);
-      double xright1 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2]);
-      double xright2 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2+1]);
-      if( (iLeft!=nLeft) && ((iRight==nRight)
-       || (xleft1<xright1)
-       || (xleft1==xright1 && xleft2<xright2)
-      )){
-        aIdx[iLeft+iRight] = aLeft[iLeft];
-        iLeft++;
-      }else{
-        aIdx[iLeft+iRight] = aRight[iRight];
-        iRight++;
-      }
-    }
-
-#if 0
-    /* Check that the sort worked */
-    {
-      int jj;
-      for(jj=1; jj<nIdx; jj++){
-        float xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
-        float xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
-        float xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
-        float xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
-        assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
-      }
-    }
-#endif
-  }
-}
-
-#if VARIANT_RSTARTREE_SPLIT
-/*
-** Implementation of the R*-tree variant of SplitNode from Beckman[1990].
-*/
-static int splitNodeStartree(
-  Rtree *pRtree,
-  RtreeCell *aCell,
-  int nCell,
-  RtreeNode *pLeft,
-  RtreeNode *pRight,
-  RtreeCell *pBboxLeft,
-  RtreeCell *pBboxRight
-){
-  int **aaSorted;
-  int *aSpare;
-  int ii;
-
-  int iBestDim;
-  int iBestSplit;
-  float fBestMargin;
-
-  int nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));
-
-  aaSorted = (int **)sqlite3_malloc(nByte);
-  if( !aaSorted ){
-    return SQLITE_NOMEM;
-  }
-
-  aSpare = &((int *)&aaSorted[pRtree->nDim])[pRtree->nDim*nCell];
-  memset(aaSorted, 0, nByte);
-  for(ii=0; ii<pRtree->nDim; ii++){
-    int jj;
-    aaSorted[ii] = &((int *)&aaSorted[pRtree->nDim])[ii*nCell];
-    for(jj=0; jj<nCell; jj++){
-      aaSorted[ii][jj] = jj;
-    }
-    SortByDimension(pRtree, aaSorted[ii], nCell, ii, aCell, aSpare);
-  }
-
-  for(ii=0; ii<pRtree->nDim; ii++){
-    float margin = 0.0;
-    float fBestOverlap;
-    float fBestArea;
-    int iBestLeft;
-    int nLeft;
-
-    for(
-      nLeft=RTREE_MINCELLS(pRtree); 
-      nLeft<=(nCell-RTREE_MINCELLS(pRtree)); 
-      nLeft++
-    ){
-      RtreeCell left;
-      RtreeCell right;
-      int kk;
-      float overlap;
-      float area;
-
-      memcpy(&left, &aCell[aaSorted[ii][0]], sizeof(RtreeCell));
-      memcpy(&right, &aCell[aaSorted[ii][nCell-1]], sizeof(RtreeCell));
-      for(kk=1; kk<(nCell-1); kk++){
-        if( kk<nLeft ){
-          cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
-        }else{
-          cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);
-        }
-      }
-      margin += cellMargin(pRtree, &left);
-      margin += cellMargin(pRtree, &right);
-      overlap = cellOverlap(pRtree, &left, &right, 1, -1);
-      area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
-      if( (nLeft==RTREE_MINCELLS(pRtree))
-       || (overlap<fBestOverlap)
-       || (overlap==fBestOverlap && area<fBestArea)
-      ){
-        iBestLeft = nLeft;
-        fBestOverlap = overlap;
-        fBestArea = area;
-      }
-    }
-
-    if( ii==0 || margin<fBestMargin ){
-      iBestDim = ii;
-      fBestMargin = margin;
-      iBestSplit = iBestLeft;
-    }
-  }
-
-  memcpy(pBboxLeft, &aCell[aaSorted[iBestDim][0]], sizeof(RtreeCell));
-  memcpy(pBboxRight, &aCell[aaSorted[iBestDim][iBestSplit]], sizeof(RtreeCell));
-  for(ii=0; ii<nCell; ii++){
-    RtreeNode *pTarget = (ii<iBestSplit)?pLeft:pRight;
-    RtreeCell *pBbox = (ii<iBestSplit)?pBboxLeft:pBboxRight;
-    RtreeCell *pCell = &aCell[aaSorted[iBestDim][ii]];
-    nodeInsertCell(pRtree, pTarget, pCell);
-    cellUnion(pRtree, pBbox, pCell);
-  }
-
-  sqlite3_free(aaSorted);
-  return SQLITE_OK;
-}
-#endif
-
-#if VARIANT_GUTTMAN_SPLIT
-/*
-** Implementation of the regular R-tree SplitNode from Guttman[1984].
-*/
-static int splitNodeGuttman(
-  Rtree *pRtree,
-  RtreeCell *aCell,
-  int nCell,
-  RtreeNode *pLeft,
-  RtreeNode *pRight,
-  RtreeCell *pBboxLeft,
-  RtreeCell *pBboxRight
-){
-  int iLeftSeed = 0;
-  int iRightSeed = 1;
-  int *aiUsed;
-  int i;
-
-  aiUsed = sqlite3_malloc(sizeof(int)*nCell);
-  memset(aiUsed, 0, sizeof(int)*nCell);
-
-  PickSeeds(pRtree, aCell, nCell, &iLeftSeed, &iRightSeed);
-
-  memcpy(pBboxLeft, &aCell[iLeftSeed], sizeof(RtreeCell));
-  memcpy(pBboxRight, &aCell[iRightSeed], sizeof(RtreeCell));
-  nodeInsertCell(pRtree, pLeft, &aCell[iLeftSeed]);
-  nodeInsertCell(pRtree, pRight, &aCell[iRightSeed]);
-  aiUsed[iLeftSeed] = 1;
-  aiUsed[iRightSeed] = 1;
-
-  for(i=nCell-2; i>0; i--){
-    RtreeCell *pNext;
-    pNext = PickNext(pRtree, aCell, nCell, pBboxLeft, pBboxRight, aiUsed);
-    float diff =  
-      cellGrowth(pRtree, pBboxLeft, pNext) - 
-      cellGrowth(pRtree, pBboxRight, pNext)
-    ;
-    if( (RTREE_MINCELLS(pRtree)-NCELL(pRight)==i)
-     || (diff>0.0 && (RTREE_MINCELLS(pRtree)-NCELL(pLeft)!=i))
-    ){
-      nodeInsertCell(pRtree, pRight, pNext);
-      cellUnion(pRtree, pBboxRight, pNext);
-    }else{
-      nodeInsertCell(pRtree, pLeft, pNext);
-      cellUnion(pRtree, pBboxLeft, pNext);
-    }
-  }
-
-  sqlite3_free(aiUsed);
-  return SQLITE_OK;
-}
-#endif
-
-static int updateMapping(
-  Rtree *pRtree, 
-  i64 iRowid, 
-  RtreeNode *pNode, 
-  int iHeight
-){
-  int (*xSetMapping)(Rtree *, sqlite3_int64, sqlite3_int64);
-  xSetMapping = ((iHeight==0)?rowidWrite:parentWrite);
-  if( iHeight>0 ){
-    RtreeNode *pChild = nodeHashLookup(pRtree, iRowid);
-    if( pChild ){
-      nodeRelease(pRtree, pChild->pParent);
-      nodeReference(pNode);
-      pChild->pParent = pNode;
-    }
-  }
-  return xSetMapping(pRtree, iRowid, pNode->iNode);
-}
-
-static int SplitNode(
-  Rtree *pRtree,
-  RtreeNode *pNode,
-  RtreeCell *pCell,
-  int iHeight
-){
-  int i;
-  int newCellIsRight = 0;
-
-  int rc = SQLITE_OK;
-  int nCell = NCELL(pNode);
-  RtreeCell *aCell;
-  int *aiUsed;
-
-  RtreeNode *pLeft = 0;
-  RtreeNode *pRight = 0;
-
-  RtreeCell leftbbox;
-  RtreeCell rightbbox;
-
-  /* Allocate an array and populate it with a copy of pCell and 
-  ** all cells from node pLeft. Then zero the original node.
-  */
-  aCell = sqlite3_malloc((sizeof(RtreeCell)+sizeof(int))*(nCell+1));
-  if( !aCell ){
-    rc = SQLITE_NOMEM;
-    goto splitnode_out;
-  }
-  aiUsed = (int *)&aCell[nCell+1];
-  memset(aiUsed, 0, sizeof(int)*(nCell+1));
-  for(i=0; i<nCell; i++){
-    nodeGetCell(pRtree, pNode, i, &aCell[i]);
-  }
-  nodeZero(pRtree, pNode);
-  memcpy(&aCell[nCell], pCell, sizeof(RtreeCell));
-  nCell++;
-
-  if( pNode->iNode==1 ){
-    pRight = nodeNew(pRtree, pNode, 1);
-    pLeft = nodeNew(pRtree, pNode, 1);
-    pRtree->iDepth++;
-    pNode->isDirty = 1;
-    writeInt16(pNode->zData, pRtree->iDepth);
-  }else{
-    pLeft = pNode;
-    pRight = nodeNew(pRtree, pLeft->pParent, 1);
-    nodeReference(pLeft);
-  }
-
-  if( !pLeft || !pRight ){
-    rc = SQLITE_NOMEM;
-    goto splitnode_out;
-  }
-
-  memset(pLeft->zData, 0, pRtree->iNodeSize);
-  memset(pRight->zData, 0, pRtree->iNodeSize);
-
-  rc = AssignCells(pRtree, aCell, nCell, pLeft, pRight, &leftbbox, &rightbbox);
-  if( rc!=SQLITE_OK ){
-    goto splitnode_out;
-  }
-
-  /* Ensure both child nodes have node numbers assigned to them. */
-  if( (0==pRight->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pRight)))
-   || (0==pLeft->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pLeft)))
-  ){
-    goto splitnode_out;
-  }
-
-  rightbbox.iRowid = pRight->iNode;
-  leftbbox.iRowid = pLeft->iNode;
-
-  if( pNode->iNode==1 ){
-    rc = rtreeInsertCell(pRtree, pLeft->pParent, &leftbbox, iHeight+1);
-    if( rc!=SQLITE_OK ){
-      goto splitnode_out;
-    }
-  }else{
-    RtreeNode *pParent = pLeft->pParent;
-    int iCell = nodeParentIndex(pRtree, pLeft);
-    nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);
-    AdjustTree(pRtree, pParent, &leftbbox);
-  }
-  if( (rc = rtreeInsertCell(pRtree, pRight->pParent, &rightbbox, iHeight+1)) ){
-    goto splitnode_out;
-  }
-
-  for(i=0; i<NCELL(pRight); i++){
-    i64 iRowid = nodeGetRowid(pRtree, pRight, i);
-    rc = updateMapping(pRtree, iRowid, pRight, iHeight);
-    if( iRowid==pCell->iRowid ){
-      newCellIsRight = 1;
-    }
-    if( rc!=SQLITE_OK ){
-      goto splitnode_out;
-    }
-  }
-  if( pNode->iNode==1 ){
-    for(i=0; i<NCELL(pLeft); i++){
-      i64 iRowid = nodeGetRowid(pRtree, pLeft, i);
-      rc = updateMapping(pRtree, iRowid, pLeft, iHeight);
-      if( rc!=SQLITE_OK ){
-        goto splitnode_out;
-      }
-    }
-  }else if( newCellIsRight==0 ){
-    rc = updateMapping(pRtree, pCell->iRowid, pLeft, iHeight);
-  }
-
-  if( rc==SQLITE_OK ){
-    rc = nodeRelease(pRtree, pRight);
-    pRight = 0;
-  }
-  if( rc==SQLITE_OK ){
-    rc = nodeRelease(pRtree, pLeft);
-    pLeft = 0;
-  }
-
-splitnode_out:
-  nodeRelease(pRtree, pRight);
-  nodeRelease(pRtree, pLeft);
-  sqlite3_free(aCell);
-  return rc;
-}
-
-static int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){
-  int rc = SQLITE_OK;
-  if( pLeaf->iNode!=1 && pLeaf->pParent==0 ){
-    sqlite3_bind_int64(pRtree->pReadParent, 1, pLeaf->iNode);
-    if( sqlite3_step(pRtree->pReadParent)==SQLITE_ROW ){
-      i64 iNode = sqlite3_column_int64(pRtree->pReadParent, 0);
-      rc = nodeAcquire(pRtree, iNode, 0, &pLeaf->pParent);
-    }else{
-      rc = SQLITE_ERROR;
-    }
-    sqlite3_reset(pRtree->pReadParent);
-    if( rc==SQLITE_OK ){
-      rc = fixLeafParent(pRtree, pLeaf->pParent);
-    }
-  }
-  return rc;
-}
-
-static int deleteCell(Rtree *, RtreeNode *, int, int);
-
-static int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){
-  int rc;
-  RtreeNode *pParent;
-  int iCell;
-
-  assert( pNode->nRef==1 );
-
-  /* Remove the entry in the parent cell. */
-  iCell = nodeParentIndex(pRtree, pNode);
-  pParent = pNode->pParent;
-  pNode->pParent = 0;
-  if( SQLITE_OK!=(rc = deleteCell(pRtree, pParent, iCell, iHeight+1)) 
-   || SQLITE_OK!=(rc = nodeRelease(pRtree, pParent))
-  ){
-    return rc;
-  }
-
-  /* Remove the xxx_node entry. */
-  sqlite3_bind_int64(pRtree->pDeleteNode, 1, pNode->iNode);
-  sqlite3_step(pRtree->pDeleteNode);
-  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteNode)) ){
-    return rc;
-  }
-
-  /* Remove the xxx_parent entry. */
-  sqlite3_bind_int64(pRtree->pDeleteParent, 1, pNode->iNode);
-  sqlite3_step(pRtree->pDeleteParent);
-  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteParent)) ){
-    return rc;
-  }
-  
-  /* Remove the node from the in-memory hash table and link it into
-  ** the Rtree.pDeleted list. Its contents will be re-inserted later on.
-  */
-  nodeHashDelete(pRtree, pNode);
-  pNode->iNode = iHeight;
-  pNode->pNext = pRtree->pDeleted;
-  pNode->nRef++;
-  pRtree->pDeleted = pNode;
-
-  return SQLITE_OK;
-}
-
-static void fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){
-  RtreeNode *pParent = pNode->pParent;
-  if( pParent ){
-    int ii; 
-    int nCell = NCELL(pNode);
-    RtreeCell box;                            /* Bounding box for pNode */
-    nodeGetCell(pRtree, pNode, 0, &box);
-    for(ii=1; ii<nCell; ii++){
-      RtreeCell cell;
-      nodeGetCell(pRtree, pNode, ii, &cell);
-      cellUnion(pRtree, &box, &cell);
-    }
-    box.iRowid = pNode->iNode;
-    ii = nodeParentIndex(pRtree, pNode);
-    nodeOverwriteCell(pRtree, pParent, &box, ii);
-    fixBoundingBox(pRtree, pParent);
-  }
-}
-
-/*
-** Delete the cell at index iCell of node pNode. After removing the
-** cell, adjust the r-tree data structure if required.
-*/
-static int deleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell, int iHeight){
-  int rc;
-
-  if( SQLITE_OK!=(rc = fixLeafParent(pRtree, pNode)) ){
-    return rc;
-  }
-
-  /* Remove the cell from the node. This call just moves bytes around
-  ** the in-memory node image, so it cannot fail.
-  */
-  nodeDeleteCell(pRtree, pNode, iCell);
-
-  /* If the node is not the tree root and now has less than the minimum
-  ** number of cells, remove it from the tree. Otherwise, update the
-  ** cell in the parent node so that it tightly contains the updated
-  ** node.
-  */
-  if( pNode->iNode!=1 ){
-    RtreeNode *pParent = pNode->pParent;
-    if( (pParent->iNode!=1 || NCELL(pParent)!=1) 
-     && (NCELL(pNode)<RTREE_MINCELLS(pRtree))
-    ){
-      rc = removeNode(pRtree, pNode, iHeight);
-    }else{
-      fixBoundingBox(pRtree, pNode);
-    }
-  }
-
-  return rc;
-}
-
-static int Reinsert(
-  Rtree *pRtree, 
-  RtreeNode *pNode, 
-  RtreeCell *pCell, 
-  int iHeight
-){
-  int *aOrder;
-  int *aSpare;
-  RtreeCell *aCell;
-  float *aDistance;
-  int nCell;
-  float aCenterCoord[RTREE_MAX_DIMENSIONS];
-  int iDim;
-  int ii;
-  int rc = SQLITE_OK;
-
-  memset(aCenterCoord, 0, sizeof(float)*RTREE_MAX_DIMENSIONS);
-
-  nCell = NCELL(pNode)+1;
-
-  /* Allocate the buffers used by this operation. The allocation is
-  ** relinquished before this function returns.
-  */
-  aCell = (RtreeCell *)sqlite3_malloc(nCell * (
-    sizeof(RtreeCell) +         /* aCell array */
-    sizeof(int)       +         /* aOrder array */
-    sizeof(int)       +         /* aSpare array */
-    sizeof(float)               /* aDistance array */
-  ));
-  if( !aCell ){
-    return SQLITE_NOMEM;
-  }
-  aOrder    = (int *)&aCell[nCell];
-  aSpare    = (int *)&aOrder[nCell];
-  aDistance = (float *)&aSpare[nCell];
-
-  for(ii=0; ii<nCell; ii++){
-    if( ii==(nCell-1) ){
-      memcpy(&aCell[ii], pCell, sizeof(RtreeCell));
-    }else{
-      nodeGetCell(pRtree, pNode, ii, &aCell[ii]);
-    }
-    aOrder[ii] = ii;
-    for(iDim=0; iDim<pRtree->nDim; iDim++){
-      aCenterCoord[iDim] += DCOORD(aCell[ii].aCoord[iDim*2]);
-      aCenterCoord[iDim] += DCOORD(aCell[ii].aCoord[iDim*2+1]);
-    }
-  }
-  for(iDim=0; iDim<pRtree->nDim; iDim++){
-    aCenterCoord[iDim] = aCenterCoord[iDim]/((float)nCell*2.0);
-  }
-
-  for(ii=0; ii<nCell; ii++){
-    aDistance[ii] = 0.0;
-    for(iDim=0; iDim<pRtree->nDim; iDim++){
-      float coord = DCOORD(aCell[ii].aCoord[iDim*2+1]) - 
-          DCOORD(aCell[ii].aCoord[iDim*2]);
-      aDistance[ii] += (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);
-    }
-  }
-
-  SortByDistance(aOrder, nCell, aDistance, aSpare);
-  nodeZero(pRtree, pNode);
-
-  for(ii=0; rc==SQLITE_OK && ii<(nCell-(RTREE_MINCELLS(pRtree)+1)); ii++){
-    RtreeCell *p = &aCell[aOrder[ii]];
-    nodeInsertCell(pRtree, pNode, p);
-    if( p->iRowid==pCell->iRowid ){
-      if( iHeight==0 ){
-        rc = rowidWrite(pRtree, p->iRowid, pNode->iNode);
-      }else{
-        rc = parentWrite(pRtree, p->iRowid, pNode->iNode);
-      }
-    }
-  }
-  if( rc==SQLITE_OK ){
-    fixBoundingBox(pRtree, pNode);
-  }
-  for(; rc==SQLITE_OK && ii<nCell; ii++){
-    /* Find a node to store this cell in. pNode->iNode currently contains
-    ** the height of the sub-tree headed by the cell.
-    */
-    RtreeNode *pInsert;
-    RtreeCell *p = &aCell[aOrder[ii]];
-    rc = ChooseLeaf(pRtree, p, iHeight, &pInsert);
-    if( rc==SQLITE_OK ){
-      int rc2;
-      rc = rtreeInsertCell(pRtree, pInsert, p, iHeight);
-      rc2 = nodeRelease(pRtree, pInsert);
-      if( rc==SQLITE_OK ){
-        rc = rc2;
-      }
-    }
-  }
-
-  sqlite3_free(aCell);
-  return rc;
-}
-
-/*
-** Insert cell pCell into node pNode. Node pNode is the head of a 
-** subtree iHeight high (leaf nodes have iHeight==0).
-*/
-static int rtreeInsertCell(
-  Rtree *pRtree,
-  RtreeNode *pNode,
-  RtreeCell *pCell,
-  int iHeight
-){
-  int rc = SQLITE_OK;
-  if( iHeight>0 ){
-    RtreeNode *pChild = nodeHashLookup(pRtree, pCell->iRowid);
-    if( pChild ){
-      nodeRelease(pRtree, pChild->pParent);
-      nodeReference(pNode);
-      pChild->pParent = pNode;
-    }
-  }
-  if( nodeInsertCell(pRtree, pNode, pCell) ){
-#if VARIANT_RSTARTREE_REINSERT
-    if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
-      rc = SplitNode(pRtree, pNode, pCell, iHeight);
-    }else{
-      pRtree->iReinsertHeight = iHeight;
-      rc = Reinsert(pRtree, pNode, pCell, iHeight);
-    }
-#else
-    rc = SplitNode(pRtree, pNode, pCell, iHeight);
-#endif
-  }else{
-    AdjustTree(pRtree, pNode, pCell);
-    if( iHeight==0 ){
-      rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
-    }else{
-      rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
-    }
-  }
-  return rc;
-}
-
-static int reinsertNodeContent(Rtree *pRtree, RtreeNode *pNode){
-  int ii;
-  int rc = SQLITE_OK;
-  int nCell = NCELL(pNode);
-
-  for(ii=0; rc==SQLITE_OK && ii<nCell; ii++){
-    RtreeNode *pInsert;
-    RtreeCell cell;
-    nodeGetCell(pRtree, pNode, ii, &cell);
-
-    /* Find a node to store this cell in. pNode->iNode currently contains
-    ** the height of the sub-tree headed by the cell.
-    */
-    rc = ChooseLeaf(pRtree, &cell, pNode->iNode, &pInsert);
-    if( rc==SQLITE_OK ){
-      int rc2;
-      rc = rtreeInsertCell(pRtree, pInsert, &cell, pNode->iNode);
-      rc2 = nodeRelease(pRtree, pInsert);
-      if( rc==SQLITE_OK ){
-        rc = rc2;
-      }
-    }
-  }
-  return rc;
-}
-
-/*
-** Select a currently unused rowid for a new r-tree record.
-*/
-static int newRowid(Rtree *pRtree, i64 *piRowid){
-  int rc;
-  sqlite3_bind_null(pRtree->pWriteRowid, 1);
-  sqlite3_bind_null(pRtree->pWriteRowid, 2);
-  sqlite3_step(pRtree->pWriteRowid);
-  rc = sqlite3_reset(pRtree->pWriteRowid);
-  *piRowid = sqlite3_last_insert_rowid(pRtree->db);
-  return rc;
-}
-
-#ifndef NDEBUG
-static int hashIsEmpty(Rtree *pRtree){
-  int ii;
-  for(ii=0; ii<HASHSIZE; ii++){
-    assert( !pRtree->aHash[ii] );
-  }
-  return 1;
-}
-#endif
-
-/*
-** The xUpdate method for rtree module virtual tables.
-*/
-static int rtreeUpdate(
-  sqlite3_vtab *pVtab, 
-  int nData, 
-  sqlite3_value **azData, 
-  sqlite_int64 *pRowid
-){
-  Rtree *pRtree = (Rtree *)pVtab;
-  int rc = SQLITE_OK;
-
-  rtreeReference(pRtree);
-
-  assert(nData>=1);
-  assert(hashIsEmpty(pRtree));
-
-  /* If azData[0] is not an SQL NULL value, it is the rowid of a
-  ** record to delete from the r-tree table. The following block does
-  ** just that.
-  */
-  if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){
-    i64 iDelete;                /* The rowid to delete */
-    RtreeNode *pLeaf;           /* Leaf node containing record iDelete */
-    int iCell;                  /* Index of iDelete cell in pLeaf */
-    RtreeNode *pRoot;
-
-    /* Obtain a reference to the root node to initialise Rtree.iDepth */
-    rc = nodeAcquire(pRtree, 1, 0, &pRoot);
-
-    /* Obtain a reference to the leaf node that contains the entry 
-    ** about to be deleted. 
-    */
-    if( rc==SQLITE_OK ){
-      iDelete = sqlite3_value_int64(azData[0]);
-      rc = findLeafNode(pRtree, iDelete, &pLeaf);
-    }
-
-    /* Delete the cell in question from the leaf node. */
-    if( rc==SQLITE_OK ){
-      int rc2;
-      iCell = nodeRowidIndex(pRtree, pLeaf, iDelete);
-      rc = deleteCell(pRtree, pLeaf, iCell, 0);
-      rc2 = nodeRelease(pRtree, pLeaf);
-      if( rc==SQLITE_OK ){
-        rc = rc2;
-      }
-    }
-
-    /* Delete the corresponding entry in the <rtree>_rowid table. */
-    if( rc==SQLITE_OK ){
-      sqlite3_bind_int64(pRtree->pDeleteRowid, 1, iDelete);
-      sqlite3_step(pRtree->pDeleteRowid);
-      rc = sqlite3_reset(pRtree->pDeleteRowid);
-    }
-
-    /* Check if the root node now has exactly one child. If so, remove
-    ** it, schedule the contents of the child for reinsertion and 
-    ** reduce the tree height by one.
-    **
-    ** This is equivalent to copying the contents of the child into
-    ** the root node (the operation that Gutman's paper says to perform 
-    ** in this scenario).
-    */
-    if( rc==SQLITE_OK && pRtree->iDepth>0 ){
-      if( rc==SQLITE_OK && NCELL(pRoot)==1 ){
-        RtreeNode *pChild;
-        i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
-        rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);
-        if( rc==SQLITE_OK ){
-          rc = removeNode(pRtree, pChild, pRtree->iDepth-1);
-        }
-        if( rc==SQLITE_OK ){
-          pRtree->iDepth--;
-          writeInt16(pRoot->zData, pRtree->iDepth);
-          pRoot->isDirty = 1;
-        }
-      }
-    }
-
-    /* Re-insert the contents of any underfull nodes removed from the tree. */
-    for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){
-      if( rc==SQLITE_OK ){
-        rc = reinsertNodeContent(pRtree, pLeaf);
-      }
-      pRtree->pDeleted = pLeaf->pNext;
-      sqlite3_free(pLeaf);
-    }
-
-    /* Release the reference to the root node. */
-    if( rc==SQLITE_OK ){
-      rc = nodeRelease(pRtree, pRoot);
-    }else{
-      nodeRelease(pRtree, pRoot);
-    }
-  }
-
-  /* If the azData[] array contains more than one element, elements
-  ** (azData[2]..azData[argc-1]) contain a new record to insert into
-  ** the r-tree structure.
-  */
-  if( rc==SQLITE_OK && nData>1 ){
-    /* Insert a new record into the r-tree */
-    RtreeCell cell;
-    int ii;
-    RtreeNode *pLeaf;
-
-    /* Populate the cell.aCoord[] array. The first coordinate is azData[3]. */
-    assert( nData==(pRtree->nDim*2 + 3) );
-    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
-      for(ii=0; ii<(pRtree->nDim*2); ii+=2){
-        cell.aCoord[ii].f = (float)sqlite3_value_double(azData[ii+3]);
-        cell.aCoord[ii+1].f = (float)sqlite3_value_double(azData[ii+4]);
-        if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
-          rc = SQLITE_CONSTRAINT;
-          goto constraint;
-        }
-      }
-    }else{
-      for(ii=0; ii<(pRtree->nDim*2); ii+=2){
-        cell.aCoord[ii].i = sqlite3_value_int(azData[ii+3]);
-        cell.aCoord[ii+1].i = sqlite3_value_int(azData[ii+4]);
-        if( cell.aCoord[ii].i>cell.aCoord[ii+1].i ){
-          rc = SQLITE_CONSTRAINT;
-          goto constraint;
-        }
-      }
-    }
-
-    /* Figure out the rowid of the new row. */
-    if( sqlite3_value_type(azData[2])==SQLITE_NULL ){
-      rc = newRowid(pRtree, &cell.iRowid);
-    }else{
-      cell.iRowid = sqlite3_value_int64(azData[2]);
-      sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
-      if( SQLITE_ROW==sqlite3_step(pRtree->pReadRowid) ){
-        sqlite3_reset(pRtree->pReadRowid);
-        rc = SQLITE_CONSTRAINT;
-        goto constraint;
-      }
-      rc = sqlite3_reset(pRtree->pReadRowid);
-    }
-
-    if( rc==SQLITE_OK ){
-      rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);
-    }
-    if( rc==SQLITE_OK ){
-      int rc2;
-      pRtree->iReinsertHeight = -1;
-      rc = rtreeInsertCell(pRtree, pLeaf, &cell, 0);
-      rc2 = nodeRelease(pRtree, pLeaf);
-      if( rc==SQLITE_OK ){
-        rc = rc2;
-      }
-    }
-  }
-
-constraint:
-  rtreeRelease(pRtree);
-  return rc;
-}
-
-/*
-** The xRename method for rtree module virtual tables.
-*/
-static int rtreeRename(sqlite3_vtab *pVtab, const char *zNewName){
-  Rtree *pRtree = (Rtree *)pVtab;
-  int rc = SQLITE_NOMEM;
-  char *zSql = sqlite3_mprintf(
-    "ALTER TABLE %Q.'%q_node'   RENAME TO \"%w_node\";"
-    "ALTER TABLE %Q.'%q_parent' RENAME TO \"%w_parent\";"
-    "ALTER TABLE %Q.'%q_rowid'  RENAME TO \"%w_rowid\";"
-    , pRtree->zDb, pRtree->zName, zNewName 
-    , pRtree->zDb, pRtree->zName, zNewName 
-    , pRtree->zDb, pRtree->zName, zNewName
-  );
-  if( zSql ){
-    rc = sqlite3_exec(pRtree->db, zSql, 0, 0, 0);
-    sqlite3_free(zSql);
-  }
-  return rc;
-}
-
-static sqlite3_module rtreeModule = {
-  0,                         /* iVersion */
-  rtreeCreate,                /* xCreate - create a table */
-  rtreeConnect,               /* xConnect - connect to an existing table */
-  rtreeBestIndex,             /* xBestIndex - Determine search strategy */
-  rtreeDisconnect,            /* xDisconnect - Disconnect from a table */
-  rtreeDestroy,               /* xDestroy - Drop a table */
-  rtreeOpen,                  /* xOpen - open a cursor */
-  rtreeClose,                 /* xClose - close a cursor */
-  rtreeFilter,                /* xFilter - configure scan constraints */
-  rtreeNext,                  /* xNext - advance a cursor */
-  rtreeEof,                   /* xEof */
-  rtreeColumn,                /* xColumn - read data */
-  rtreeRowid,                 /* xRowid - read data */
-  rtreeUpdate,                /* xUpdate - write data */
-  0,                          /* xBegin - begin transaction */
-  0,                          /* xSync - sync transaction */
-  0,                          /* xCommit - commit transaction */
-  0,                          /* xRollback - rollback transaction */
-  0,                          /* xFindFunction - function overloading */
-  rtreeRename                 /* xRename - rename the table */
-};
-
-static int rtreeSqlInit(
-  Rtree *pRtree, 
-  sqlite3 *db, 
-  const char *zDb, 
-  const char *zPrefix, 
-  int isCreate
-){
-  int rc = SQLITE_OK;
-
-  #define N_STATEMENT 9
-  static const char *azSql[N_STATEMENT] = {
-    /* Read and write the xxx_node table */
-    "SELECT data FROM '%q'.'%q_node' WHERE nodeno = :1",
-    "INSERT OR REPLACE INTO '%q'.'%q_node' VALUES(:1, :2)",
-    "DELETE FROM '%q'.'%q_node' WHERE nodeno = :1",
-
-    /* Read and write the xxx_rowid table */
-    "SELECT nodeno FROM '%q'.'%q_rowid' WHERE rowid = :1",
-    "INSERT OR REPLACE INTO '%q'.'%q_rowid' VALUES(:1, :2)",
-    "DELETE FROM '%q'.'%q_rowid' WHERE rowid = :1",
-
-    /* Read and write the xxx_parent table */
-    "SELECT parentnode FROM '%q'.'%q_parent' WHERE nodeno = :1",
-    "INSERT OR REPLACE INTO '%q'.'%q_parent' VALUES(:1, :2)",
-    "DELETE FROM '%q'.'%q_parent' WHERE nodeno = :1"
-  };
-  sqlite3_stmt **appStmt[N_STATEMENT];
-  int i;
-
-  pRtree->db = db;
-
-  if( isCreate ){
-    char *zCreate = sqlite3_mprintf(
-"CREATE TABLE \"%w\".\"%w_node\"(nodeno INTEGER PRIMARY KEY, data BLOB);"
-"CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY, nodeno INTEGER);"
-"CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY, parentnode INTEGER);"
-"INSERT INTO '%q'.'%q_node' VALUES(1, zeroblob(%d))",
-      zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, pRtree->iNodeSize
-    );
-    if( !zCreate ){
-      return SQLITE_NOMEM;
-    }
-    rc = sqlite3_exec(db, zCreate, 0, 0, 0);
-    sqlite3_free(zCreate);
-    if( rc!=SQLITE_OK ){
-      return rc;
-    }
-  }
-
-  appStmt[0] = &pRtree->pReadNode;
-  appStmt[1] = &pRtree->pWriteNode;
-  appStmt[2] = &pRtree->pDeleteNode;
-  appStmt[3] = &pRtree->pReadRowid;
-  appStmt[4] = &pRtree->pWriteRowid;
-  appStmt[5] = &pRtree->pDeleteRowid;
-  appStmt[6] = &pRtree->pReadParent;
-  appStmt[7] = &pRtree->pWriteParent;
-  appStmt[8] = &pRtree->pDeleteParent;
-
-  for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){
-    char *zSql = sqlite3_mprintf(azSql[i], zDb, zPrefix);
-    if( zSql ){
-      rc = sqlite3_prepare_v2(db, zSql, -1, appStmt[i], 0); 
-    }else{
-      rc = SQLITE_NOMEM;
-    }
-    sqlite3_free(zSql);
-  }
-
-  return rc;
-}
-
-/*
-** This routine queries database handle db for the page-size used by
-** database zDb. If successful, the page-size in bytes is written to
-** *piPageSize and SQLITE_OK returned. Otherwise, and an SQLite error 
-** code is returned.
-*/
-static int getPageSize(sqlite3 *db, const char *zDb, int *piPageSize){
-  int rc = SQLITE_NOMEM;
-  char *zSql;
-  sqlite3_stmt *pStmt = 0;
-
-  zSql = sqlite3_mprintf("PRAGMA %Q.page_size", zDb);
-  if( !zSql ){
-    return SQLITE_NOMEM;
-  }
-
-  rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);
-  sqlite3_free(zSql);
-  if( rc!=SQLITE_OK ){
-    return rc;
-  }
-
-  if( SQLITE_ROW==sqlite3_step(pStmt) ){
-    *piPageSize = sqlite3_column_int(pStmt, 0);
-  }
-  return sqlite3_finalize(pStmt);
-}
-
-/* 
-** This function is the implementation of both the xConnect and xCreate
-** methods of the r-tree virtual table.
-**
-**   argv[0]   -> module name
-**   argv[1]   -> database name
-**   argv[2]   -> table name
-**   argv[...] -> column names...
-*/
-static int rtreeInit(
-  sqlite3 *db,                        /* Database connection */
-  void *pAux,                         /* One of the RTREE_COORD_* constants */
-  int argc, const char *const*argv,   /* Parameters to CREATE TABLE statement */
-  sqlite3_vtab **ppVtab,              /* OUT: New virtual table */
-  char **pzErr,                       /* OUT: Error message, if any */
-  int isCreate                        /* True for xCreate, false for xConnect */
-){
-  int rc = SQLITE_OK;
-  int iPageSize = 0;
-  Rtree *pRtree;
-  int nDb;              /* Length of string argv[1] */
-  int nName;            /* Length of string argv[2] */
-  int eCoordType = (int)pAux;
-
-  const char *aErrMsg[] = {
-    0,                                                    /* 0 */
-    "Wrong number of columns for an rtree table",         /* 1 */
-    "Too few columns for an rtree table",                 /* 2 */
-    "Too many columns for an rtree table"                 /* 3 */
-  };
-
-  int iErr = (argc<6) ? 2 : argc>(RTREE_MAX_DIMENSIONS*2+4) ? 3 : argc%2;
-  if( aErrMsg[iErr] ){
-    *pzErr = sqlite3_mprintf("%s", aErrMsg[iErr]);
-    return SQLITE_ERROR;
-  }
-
-  rc = getPageSize(db, argv[1], &iPageSize);
-  if( rc!=SQLITE_OK ){
-    return rc;
-  }
-
-  /* Allocate the sqlite3_vtab structure */
-  nDb = strlen(argv[1]);
-  nName = strlen(argv[2]);
-  pRtree = (Rtree *)sqlite3_malloc(sizeof(Rtree)+nDb+nName+2);
-  if( !pRtree ){
-    return SQLITE_NOMEM;
-  }
-  memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);
-  pRtree->nBusy = 1;
-  pRtree->base.pModule = &rtreeModule;
-  pRtree->zDb = (char *)&pRtree[1];
-  pRtree->zName = &pRtree->zDb[nDb+1];
-  pRtree->nDim = (argc-4)/2;
-  pRtree->nBytesPerCell = 8 + pRtree->nDim*4*2;
-  pRtree->eCoordType = eCoordType;
-  memcpy(pRtree->zDb, argv[1], nDb);
-  memcpy(pRtree->zName, argv[2], nName);
-
-  /* Figure out the node size to use. By default, use 64 bytes less than
-  ** the database page-size. This ensures that each node is stored on
-  ** a single database page.
-  **
-  ** If the databasd page-size is so large that more than RTREE_MAXCELLS
-  ** entries would fit in a single node, use a smaller node-size.
-  */
-  pRtree->iNodeSize = iPageSize-64;
-  if( (4+pRtree->nBytesPerCell*RTREE_MAXCELLS)<pRtree->iNodeSize ){
-    pRtree->iNodeSize = 4+pRtree->nBytesPerCell*RTREE_MAXCELLS;
-  }
-
-  /* Create/Connect to the underlying relational database schema. If
-  ** that is successful, call sqlite3_declare_vtab() to configure
-  ** the r-tree table schema.
-  */
-  if( (rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate)) ){
-    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
-  }else{
-    char *zSql = sqlite3_mprintf("CREATE TABLE x(%s", argv[3]);
-    char *zTmp;
-    int ii;
-    for(ii=4; zSql && ii<argc; ii++){
-      zTmp = zSql;
-      zSql = sqlite3_mprintf("%s, %s", zTmp, argv[ii]);
-      sqlite3_free(zTmp);
-    }
-    if( zSql ){
-      zTmp = zSql;
-      zSql = sqlite3_mprintf("%s);", zTmp);
-      sqlite3_free(zTmp);
-    }
-    if( !zSql ){
-      rc = SQLITE_NOMEM;
-    }else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){
-      *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
-    }
-    sqlite3_free(zSql);
-  }
-
-  if( rc==SQLITE_OK ){
-    *ppVtab = (sqlite3_vtab *)pRtree;
-  }else{
-    rtreeRelease(pRtree);
-  }
-  return rc;
-}
-
-
-/*
-** Implementation of a scalar function that decodes r-tree nodes to
-** human readable strings. This can be used for debugging and analysis.
-**
-** The scalar function takes two arguments, a blob of data containing
-** an r-tree node, and the number of dimensions the r-tree indexes.
-** For a two-dimensional r-tree structure called "rt", to deserialize
-** all nodes, a statement like:
-**
-**   SELECT rtreenode(2, data) FROM rt_node;
-**
-** The human readable string takes the form of a Tcl list with one
-** entry for each cell in the r-tree node. Each entry is itself a
-** list, containing the 8-byte rowid/pageno followed by the 
-** <num-dimension>*2 coordinates.
-*/
-static void rtreenode(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
-  char *zText = 0;
-  RtreeNode node;
-  Rtree tree;
-  int ii;
-
-  memset(&node, 0, sizeof(RtreeNode));
-  memset(&tree, 0, sizeof(Rtree));
-  tree.nDim = sqlite3_value_int(apArg[0]);
-  tree.nBytesPerCell = 8 + 8 * tree.nDim;
-  node.zData = (u8 *)sqlite3_value_blob(apArg[1]);
-
-  for(ii=0; ii<NCELL(&node); ii++){
-    char zCell[512];
-    int nCell = 0;
-    RtreeCell cell;
-    int jj;
-
-    nodeGetCell(&tree, &node, ii, &cell);
-    sqlite3_snprintf(512-nCell,&zCell[nCell],"%d", cell.iRowid);
-    nCell = strlen(zCell);
-    for(jj=0; jj<tree.nDim*2; jj++){
-      sqlite3_snprintf(512-nCell,&zCell[nCell]," %f",(double)cell.aCoord[jj].f);
-      nCell = strlen(zCell);
-    }
-
-    if( zText ){
-      char *zTextNew = sqlite3_mprintf("%s {%s}", zText, zCell);
-      sqlite3_free(zText);
-      zText = zTextNew;
-    }else{
-      zText = sqlite3_mprintf("{%s}", zCell);
-    }
-  }
-  
-  sqlite3_result_text(ctx, zText, -1, sqlite3_free);
-}
-
-static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
-  if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB 
-   || sqlite3_value_bytes(apArg[0])<2
-  ){
-    sqlite3_result_error(ctx, "Invalid argument to rtreedepth()", -1); 
-  }else{
-    u8 *zBlob = (u8 *)sqlite3_value_blob(apArg[0]);
-    sqlite3_result_int(ctx, readInt16(zBlob));
-  }
-}
-
-/*
-** Register the r-tree module with database handle db. This creates the
-** virtual table module "rtree" and the debugging/analysis scalar 
-** function "rtreenode".
-*/
-int sqlite3RtreeInit(sqlite3 *db){
-  int rc = SQLITE_OK;
-
-  if( rc==SQLITE_OK ){
-    int utf8 = SQLITE_UTF8;
-    rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);
-  }
-  if( rc==SQLITE_OK ){
-    int utf8 = SQLITE_UTF8;
-    rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
-  }
-  if( rc==SQLITE_OK ){
-    void *c = (void *)RTREE_COORD_REAL32;
-    rc = sqlite3_create_module_v2(db, "rtree", &rtreeModule, c, 0);
-  }
-  if( rc==SQLITE_OK ){
-    void *c = (void *)RTREE_COORD_INT32;
-    rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
-  }
-
-  return rc;
-}
-
-#if !SQLITE_CORE
-int sqlite3_extension_init(
-  sqlite3 *db,
-  char **pzErrMsg,
-  const sqlite3_api_routines *pApi
-){
-  SQLITE_EXTENSION_INIT2(pApi)
-  return sqlite3RtreeInit(db);
-}
-#endif
-
-#endif