[sql] Remove SQLite 3.10.2 reference directory.

third_party/sqlite/sqlite-src-3100200/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.
-*/
-
-/*
-** Database Format of R-Tree Tables
-** --------------------------------
-**
-** The data structure for a single virtual r-tree table is stored in three 
-** native SQLite tables declared as follows. In each case, the '%' character
-** in the table name is replaced with the user-supplied name of the r-tree
-** table.
-**
-**   CREATE TABLE %_node(nodeno INTEGER PRIMARY KEY, data BLOB)
-**   CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)
-**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER)
-**
-** The data for each node of the r-tree structure is stored in the %_node
-** table. For each node that is not the root node of the r-tree, there is
-** an entry in the %_parent table associating the node with its parent.
-** And for each row of data in the table, there is an entry in the %_rowid
-** table that maps from the entries rowid to the id of the node that it
-** is stored on.
-**
-** The root node of an r-tree always exists, even if the r-tree table is
-** empty. The nodeno of the root node is always 1. All other nodes in the
-** table must be the same size as the root node. The content of each node
-** is formatted as follows:
-**
-**   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.
-*/
-
-#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RTREE)
-
-#ifndef SQLITE_CORE
-  #include "sqlite3ext.h"
-  SQLITE_EXTENSION_INIT1
-#else
-  #include "sqlite3.h"
-#endif
-
-#include <string.h>
-#include <assert.h>
-#include <stdio.h>
-
-#ifndef SQLITE_AMALGAMATION
-#include "sqlite3rtree.h"
-typedef sqlite3_int64 i64;
-typedef unsigned char u8;
-typedef unsigned short u16;
-typedef unsigned int u32;
-#endif
-
-/*  The following macro is used to suppress compiler warnings.
-*/
-#ifndef UNUSED_PARAMETER
-# define UNUSED_PARAMETER(x) (void)(x)
-#endif
-
-typedef struct Rtree Rtree;
-typedef struct RtreeCursor RtreeCursor;
-typedef struct RtreeNode RtreeNode;
-typedef struct RtreeCell RtreeCell;
-typedef struct RtreeConstraint RtreeConstraint;
-typedef struct RtreeMatchArg RtreeMatchArg;
-typedef struct RtreeGeomCallback RtreeGeomCallback;
-typedef union RtreeCoord RtreeCoord;
-typedef struct RtreeSearchPoint RtreeSearchPoint;
-
-/* 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 97
-
-/* The xBestIndex method of this virtual table requires an estimate of
-** the number of rows in the virtual table to calculate the costs of
-** various strategies. If possible, this estimate is loaded from the
-** sqlite_stat1 table (with RTREE_MIN_ROWEST as a hard-coded minimum).
-** Otherwise, if no sqlite_stat1 entry is available, use 
-** RTREE_DEFAULT_ROWEST.
-*/
-#define RTREE_DEFAULT_ROWEST 1048576
-#define RTREE_MIN_ROWEST         100
-
-/* 
-** An rtree virtual-table object.
-*/
-struct Rtree {
-  sqlite3_vtab base;          /* Base class.  Must be first */
-  sqlite3 *db;                /* Host database connection */
-  int iNodeSize;              /* Size in bytes of each node in the node table */
-  u8 nDim;                    /* Number of dimensions */
-  u8 eCoordType;              /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */
-  u8 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 */ 
-  int nBusy;                  /* Current number of users of this structure */
-  i64 nRowEst;                /* Estimated number of rows in this table */
-
-  /* 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;
-
-  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ 
-};
-
-/* Possible values for Rtree.eCoordType: */
-#define RTREE_COORD_REAL32 0
-#define RTREE_COORD_INT32  1
-
-/*
-** If SQLITE_RTREE_INT_ONLY is defined, then this virtual table will
-** only deal with integer coordinates.  No floating point operations
-** will be done.
-*/
-#ifdef SQLITE_RTREE_INT_ONLY
-  typedef sqlite3_int64 RtreeDValue;       /* High accuracy coordinate */
-  typedef int RtreeValue;                  /* Low accuracy coordinate */
-# define RTREE_ZERO 0
-#else
-  typedef double RtreeDValue;              /* High accuracy coordinate */
-  typedef float RtreeValue;                /* Low accuracy coordinate */
-# define RTREE_ZERO 0.0
-#endif
-
-/*
-** When doing a search of an r-tree, instances of the following structure
-** record intermediate results from the tree walk.
-**
-** The id is always a node-id.  For iLevel>=1 the id is the node-id of
-** the node that the RtreeSearchPoint represents.  When iLevel==0, however,
-** the id is of the parent node and the cell that RtreeSearchPoint
-** represents is the iCell-th entry in the parent node.
-*/
-struct RtreeSearchPoint {
-  RtreeDValue rScore;    /* The score for this node.  Smallest goes first. */
-  sqlite3_int64 id;      /* Node ID */
-  u8 iLevel;             /* 0=entries.  1=leaf node.  2+ for higher */
-  u8 eWithin;            /* PARTLY_WITHIN or FULLY_WITHIN */
-  u8 iCell;              /* Cell index within the node */
-};
-
-/*
-** 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
-
-/*
-** The smallest possible node-size is (512-64)==448 bytes. And the largest
-** supported cell size is 48 bytes (8 byte rowid + ten 4 byte coordinates).
-** Therefore all non-root nodes must contain at least 3 entries. Since 
-** 2^40 is greater than 2^64, an r-tree structure always has a depth of
-** 40 or less.
-*/
-#define RTREE_MAX_DEPTH 40
-
-
-/*
-** Number of entries in the cursor RtreeNode cache.  The first entry is
-** used to cache the RtreeNode for RtreeCursor.sPoint.  The remaining
-** entries cache the RtreeNode for the first elements of the priority queue.
-*/
-#define RTREE_CACHE_SZ  5
-
-/* 
-** An rtree cursor object.
-*/
-struct RtreeCursor {
-  sqlite3_vtab_cursor base;         /* Base class.  Must be first */
-  u8 atEOF;                         /* True if at end of search */
-  u8 bPoint;                        /* True if sPoint is valid */
-  int iStrategy;                    /* Copy of idxNum search parameter */
-  int nConstraint;                  /* Number of entries in aConstraint */
-  RtreeConstraint *aConstraint;     /* Search constraints. */
-  int nPointAlloc;                  /* Number of slots allocated for aPoint[] */
-  int nPoint;                       /* Number of slots used in aPoint[] */
-  int mxLevel;                      /* iLevel value for root of the tree */
-  RtreeSearchPoint *aPoint;         /* Priority queue for search points */
-  RtreeSearchPoint sPoint;          /* Cached next search point */
-  RtreeNode *aNode[RTREE_CACHE_SZ]; /* Rtree node cache */
-  u32 anQueue[RTREE_MAX_DEPTH+1];   /* Number of queued entries by iLevel */
-};
-
-/* Return the Rtree of a RtreeCursor */
-#define RTREE_OF_CURSOR(X)   ((Rtree*)((X)->base.pVtab))
-
-/*
-** A coordinate can be either a floating point number or a integer.  All
-** coordinates within a single R-Tree are always of the same time.
-*/
-union RtreeCoord {
-  RtreeValue f;      /* Floating point value */
-  int i;             /* Integer value */
-  u32 u;             /* Unsigned for byte-order conversions */
-};
-
-/*
-** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
-** formatted as a RtreeDValue (double or int64). This macro assumes that local
-** variable pRtree points to the Rtree structure associated with the
-** RtreeCoord.
-*/
-#ifdef SQLITE_RTREE_INT_ONLY
-# define DCOORD(coord) ((RtreeDValue)coord.i)
-#else
-# define DCOORD(coord) (                           \
-    (pRtree->eCoordType==RTREE_COORD_REAL32) ?      \
-      ((double)coord.f) :                           \
-      ((double)coord.i)                             \
-  )
-#endif
-
-/*
-** A search constraint.
-*/
-struct RtreeConstraint {
-  int iCoord;                     /* Index of constrained coordinate */
-  int op;                         /* Constraining operation */
-  union {
-    RtreeDValue rValue;             /* Constraint value. */
-    int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*);
-    int (*xQueryFunc)(sqlite3_rtree_query_info*);
-  } u;
-  sqlite3_rtree_query_info *pInfo;  /* xGeom and xQueryFunc argument */
-};
-
-/* Possible values for RtreeConstraint.op */
-#define RTREE_EQ    0x41  /* A */
-#define RTREE_LE    0x42  /* B */
-#define RTREE_LT    0x43  /* C */
-#define RTREE_GE    0x44  /* D */
-#define RTREE_GT    0x45  /* E */
-#define RTREE_MATCH 0x46  /* F: Old-style sqlite3_rtree_geometry_callback() */
-#define RTREE_QUERY 0x47  /* G: New-style sqlite3_rtree_query_callback() */
-
-
-/* 
-** An rtree structure node.
-*/
-struct RtreeNode {
-  RtreeNode *pParent;         /* Parent node */
-  i64 iNode;                  /* The node number */
-  int nRef;                   /* Number of references to this node */
-  int isDirty;                /* True if the node needs to be written to disk */
-  u8 *zData;                  /* Content of the node, as should be on disk */
-  RtreeNode *pNext;           /* Next node in this hash collision chain */
-};
-
-/* Return the number of cells in a node  */
-#define NCELL(pNode) readInt16(&(pNode)->zData[2])
-
-/* 
-** A single cell from a node, deserialized
-*/
-struct RtreeCell {
-  i64 iRowid;                                 /* Node or entry ID */
-  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];  /* Bounding box coordinates */
-};
-
-
-/*
-** This object becomes the sqlite3_user_data() for the SQL functions
-** that are created by sqlite3_rtree_geometry_callback() and
-** sqlite3_rtree_query_callback() and which appear on the right of MATCH
-** operators in order to constrain a search.
-**
-** xGeom and xQueryFunc are the callback functions.  Exactly one of 
-** xGeom and xQueryFunc fields is non-NULL, depending on whether the
-** SQL function was created using sqlite3_rtree_geometry_callback() or
-** sqlite3_rtree_query_callback().
-** 
-** This object is deleted automatically by the destructor mechanism in
-** sqlite3_create_function_v2().
-*/
-struct RtreeGeomCallback {
-  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
-  int (*xQueryFunc)(sqlite3_rtree_query_info*);
-  void (*xDestructor)(void*);
-  void *pContext;
-};
-
-
-/*
-** Value for the first field of every RtreeMatchArg object. The MATCH
-** operator tests that the first field of a blob operand matches this
-** value to avoid operating on invalid blobs (which could cause a segfault).
-*/
-#define RTREE_GEOMETRY_MAGIC 0x891245AB
-
-/*
-** An instance of this structure (in the form of a BLOB) is returned by
-** the SQL functions that sqlite3_rtree_geometry_callback() and
-** sqlite3_rtree_query_callback() create, and is read as the right-hand
-** operand to the MATCH operator of an R-Tree.
-*/
-struct RtreeMatchArg {
-  u32 magic;                  /* Always RTREE_GEOMETRY_MAGIC */
-  RtreeGeomCallback cb;       /* Info about the callback functions */
-  int nParam;                 /* Number of parameters to the SQL function */
-  sqlite3_value **apSqlParam; /* Original SQL parameter values */
-  RtreeDValue aParam[1];      /* Values for parameters to the SQL function */
-};
-
-#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){
-  pCoord->u = (
-    (((u32)p[0]) << 24) + 
-    (((u32)p[1]) << 16) + 
-    (((u32)p[2]) <<  8) + 
-    (((u32)p[3]) <<  0)
-  );
-}
-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 = pCoord->u;
-  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){
-  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 % 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;
-  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){
-  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){
-  RtreeNode *pNode;
-  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
-  if( pNode ){
-    memset(pNode, 0, sizeof(RtreeNode) + pRtree->iNodeSize);
-    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;
-  int rc2 = SQLITE_OK;
-  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;
-  }
-
-  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);
-    if( pRtree->iNodeSize==sqlite3_column_bytes(pRtree->pReadNode, 0) ){
-      pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode)+pRtree->iNodeSize);
-      if( !pNode ){
-        rc2 = SQLITE_NOMEM;
-      }else{
-        pNode->pParent = pParent;
-        pNode->zData = (u8 *)&pNode[1];
-        pNode->nRef = 1;
-        pNode->iNode = iNode;
-        pNode->isDirty = 0;
-        pNode->pNext = 0;
-        memcpy(pNode->zData, zBlob, pRtree->iNodeSize);
-        nodeReference(pParent);
-      }
-    }
-  }
-  rc = sqlite3_reset(pRtree->pReadNode);
-  if( rc==SQLITE_OK ) rc = rc2;
-
-  /* If the root node was just loaded, set pRtree->iDepth to the height
-  ** of the r-tree structure. A height of zero means all data is stored on
-  ** the root node. A height of one means the children of the root node
-  ** are the leaves, and so on. If the depth as specified on the root node
-  ** is greater than RTREE_MAX_DEPTH, the r-tree structure must be corrupt.
-  */
-  if( pNode && iNode==1 ){
-    pRtree->iDepth = readInt16(pNode->zData);
-    if( pRtree->iDepth>RTREE_MAX_DEPTH ){
-      rc = SQLITE_CORRUPT_VTAB;
-    }
-  }
-
-  /* If no error has occurred so far, check if the "number of entries"
-  ** field on the node is too large. If so, set the return code to 
-  ** SQLITE_CORRUPT_VTAB.
-  */
-  if( pNode && rc==SQLITE_OK ){
-    if( NCELL(pNode)>((pRtree->iNodeSize-4)/pRtree->nBytesPerCell) ){
-      rc = SQLITE_CORRUPT_VTAB;
-    }
-  }
-
-  if( rc==SQLITE_OK ){
-    if( pNode!=0 ){
-      nodeHashInsert(pRtree, pNode);
-    }else{
-      rc = SQLITE_CORRUPT_VTAB;
-    }
-    *ppNode = pNode;
-  }else{
-    sqlite3_free(pNode);
-    *ppNode = 0;
-  }
-
-  return rc;
-}
-
-/*
-** Overwrite cell iCell of node pNode with the contents of pCell.
-*/
-static void nodeOverwriteCell(
-  Rtree *pRtree,             /* The overall R-Tree */
-  RtreeNode *pNode,          /* The node into which the cell is to be written */
-  RtreeCell *pCell,          /* The cell to write */
-  int iCell                  /* Index into pNode into which pCell is written */
-){
-  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 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,                /* The overall R-Tree */
-  RtreeNode *pNode,             /* Write new cell into this node */
-  RtreeCell *pCell              /* The cell to be inserted */
-){
-  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,       /* The overall R-Tree */
-  RtreeNode *pNode,    /* The node from which to extract the ID */
-  int iCell            /* The cell index from which to extract the ID */
-){
-  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,               /* The overall R-Tree */
-  RtreeNode *pNode,            /* The node from which to extract a coordinate */
-  int iCell,                   /* The index of the cell within the node */
-  int iCoord,                  /* Which coordinate to extract */
-  RtreeCoord *pCoord           /* OUT: 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,               /* The overall R-Tree */
-  RtreeNode *pNode,            /* The node containing the cell to be read */
-  int iCell,                   /* Index of the cell within the node */
-  RtreeCell *pCell             /* OUT: Write the cell contents here */
-){
-  u8 *pData;
-  RtreeCoord *pCoord;
-  int ii;
-  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
-  pData = pNode->zData + (12 + pRtree->nBytesPerCell*iCell);
-  pCoord = pCell->aCoord;
-  for(ii=0; ii<pRtree->nDim*2; ii++){
-    readCoord(&pData[ii*4], &pCoord[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_query_info *pInfo = pCsr->aConstraint[i].pInfo;
-      if( pInfo ){
-        if( pInfo->xDelUser ) pInfo->xDelUser(pInfo->pUser);
-        sqlite3_free(pInfo);
-      }
-    }
-    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 ii;
-  RtreeCursor *pCsr = (RtreeCursor *)cur;
-  freeCursorConstraints(pCsr);
-  sqlite3_free(pCsr->aPoint);
-  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
-  sqlite3_free(pCsr);
-  return SQLITE_OK;
-}
-
-/*
-** 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->atEOF;
-}
-
-/*
-** Convert raw bits from the on-disk RTree record into a coordinate value.
-** The on-disk format is big-endian and needs to be converted for little-
-** endian platforms.  The on-disk record stores integer coordinates if
-** eInt is true and it stores 32-bit floating point records if eInt is
-** false.  a[] is the four bytes of the on-disk record to be decoded.
-** Store the results in "r".
-**
-** There are three versions of this macro, one each for little-endian and
-** big-endian processors and a third generic implementation.  The endian-
-** specific implementations are much faster and are preferred if the
-** processor endianness is known at compile-time.  The SQLITE_BYTEORDER
-** macro is part of sqliteInt.h and hence the endian-specific
-** implementation will only be used if this module is compiled as part
-** of the amalgamation.
-*/
-#if defined(SQLITE_BYTEORDER) && SQLITE_BYTEORDER==1234
-#define RTREE_DECODE_COORD(eInt, a, r) {                        \
-    RtreeCoord c;    /* Coordinate decoded */                   \
-    memcpy(&c.u,a,4);                                           \
-    c.u = ((c.u>>24)&0xff)|((c.u>>8)&0xff00)|                   \
-          ((c.u&0xff)<<24)|((c.u&0xff00)<<8);                   \
-    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
-}
-#elif defined(SQLITE_BYTEORDER) && SQLITE_BYTEORDER==4321
-#define RTREE_DECODE_COORD(eInt, a, r) {                        \
-    RtreeCoord c;    /* Coordinate decoded */                   \
-    memcpy(&c.u,a,4);                                           \
-    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
-}
-#else
-#define RTREE_DECODE_COORD(eInt, a, r) {                        \
-    RtreeCoord c;    /* Coordinate decoded */                   \
-    c.u = ((u32)a[0]<<24) + ((u32)a[1]<<16)                     \
-           +((u32)a[2]<<8) + a[3];                              \
-    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
-}
-#endif
-
-/*
-** Check the RTree node or entry given by pCellData and p against the MATCH
-** constraint pConstraint.  
-*/
-static int rtreeCallbackConstraint(
-  RtreeConstraint *pConstraint,  /* The constraint to test */
-  int eInt,                      /* True if RTree holding integer coordinates */
-  u8 *pCellData,                 /* Raw cell content */
-  RtreeSearchPoint *pSearch,     /* Container of this cell */
-  sqlite3_rtree_dbl *prScore,    /* OUT: score for the cell */
-  int *peWithin                  /* OUT: visibility of the cell */
-){
-  int i;                                                /* Loop counter */
-  sqlite3_rtree_query_info *pInfo = pConstraint->pInfo; /* Callback info */
-  int nCoord = pInfo->nCoord;                           /* No. of coordinates */
-  int rc;                                             /* Callback return code */
-  sqlite3_rtree_dbl aCoord[RTREE_MAX_DIMENSIONS*2];   /* Decoded coordinates */
-
-  assert( pConstraint->op==RTREE_MATCH || pConstraint->op==RTREE_QUERY );
-  assert( nCoord==2 || nCoord==4 || nCoord==6 || nCoord==8 || nCoord==10 );
-
-  if( pConstraint->op==RTREE_QUERY && pSearch->iLevel==1 ){
-    pInfo->iRowid = readInt64(pCellData);
-  }
-  pCellData += 8;
-  for(i=0; i<nCoord; i++, pCellData += 4){
-    RTREE_DECODE_COORD(eInt, pCellData, aCoord[i]);
-  }
-  if( pConstraint->op==RTREE_MATCH ){
-    rc = pConstraint->u.xGeom((sqlite3_rtree_geometry*)pInfo,
-                              nCoord, aCoord, &i);
-    if( i==0 ) *peWithin = NOT_WITHIN;
-    *prScore = RTREE_ZERO;
-  }else{
-    pInfo->aCoord = aCoord;
-    pInfo->iLevel = pSearch->iLevel - 1;
-    pInfo->rScore = pInfo->rParentScore = pSearch->rScore;
-    pInfo->eWithin = pInfo->eParentWithin = pSearch->eWithin;
-    rc = pConstraint->u.xQueryFunc(pInfo);
-    if( pInfo->eWithin<*peWithin ) *peWithin = pInfo->eWithin;
-    if( pInfo->rScore<*prScore || *prScore<RTREE_ZERO ){
-      *prScore = pInfo->rScore;
-    }
-  }
-  return rc;
-}
-
-/* 
-** Check the internal RTree node given by pCellData against constraint p.
-** If this constraint cannot be satisfied by any child within the node,
-** set *peWithin to NOT_WITHIN.
-*/
-static void rtreeNonleafConstraint(
-  RtreeConstraint *p,        /* The constraint to test */
-  int eInt,                  /* True if RTree holds integer coordinates */
-  u8 *pCellData,             /* Raw cell content as appears on disk */
-  int *peWithin              /* Adjust downward, as appropriate */
-){
-  sqlite3_rtree_dbl val;     /* Coordinate value convert to a double */
-
-  /* p->iCoord might point to either a lower or upper bound coordinate
-  ** in a coordinate pair.  But make pCellData point to the lower bound.
-  */
-  pCellData += 8 + 4*(p->iCoord&0xfe);
-
-  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:
-    case RTREE_EQ:
-      RTREE_DECODE_COORD(eInt, pCellData, val);
-      /* val now holds the lower bound of the coordinate pair */
-      if( p->u.rValue>=val ) return;
-      if( p->op!=RTREE_EQ ) break;  /* RTREE_LE and RTREE_LT end here */
-      /* Fall through for the RTREE_EQ case */
-
-    default: /* RTREE_GT or RTREE_GE,  or fallthrough of RTREE_EQ */
-      pCellData += 4;
-      RTREE_DECODE_COORD(eInt, pCellData, val);
-      /* val now holds the upper bound of the coordinate pair */
-      if( p->u.rValue<=val ) return;
-  }
-  *peWithin = NOT_WITHIN;
-}
-
-/*
-** Check the leaf RTree cell given by pCellData against constraint p.
-** If this constraint is not satisfied, set *peWithin to NOT_WITHIN.
-** If the constraint is satisfied, leave *peWithin unchanged.
-**
-** The constraint is of the form:  xN op $val
-**
-** The op is given by p->op.  The xN is p->iCoord-th coordinate in
-** pCellData.  $val is given by p->u.rValue.
-*/
-static void rtreeLeafConstraint(
-  RtreeConstraint *p,        /* The constraint to test */
-  int eInt,                  /* True if RTree holds integer coordinates */
-  u8 *pCellData,             /* Raw cell content as appears on disk */
-  int *peWithin              /* Adjust downward, as appropriate */
-){
-  RtreeDValue xN;      /* Coordinate value converted to a double */
-
-  assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
-      || p->op==RTREE_GT || p->op==RTREE_EQ );
-  pCellData += 8 + p->iCoord*4;
-  RTREE_DECODE_COORD(eInt, pCellData, xN);
-  switch( p->op ){
-    case RTREE_LE: if( xN <= p->u.rValue ) return;  break;
-    case RTREE_LT: if( xN <  p->u.rValue ) return;  break;
-    case RTREE_GE: if( xN >= p->u.rValue ) return;  break;
-    case RTREE_GT: if( xN >  p->u.rValue ) return;  break;
-    default:       if( xN == p->u.rValue ) return;  break;
-  }
-  *peWithin = NOT_WITHIN;
-}
-
-/*
-** 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);
-  assert( nCell<200 );
-  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;
-}
-
-/*
-** Compare two search points.  Return negative, zero, or positive if the first
-** is less than, equal to, or greater than the second.
-**
-** The rScore is the primary key.  Smaller rScore values come first.
-** If the rScore is a tie, then use iLevel as the tie breaker with smaller
-** iLevel values coming first.  In this way, if rScore is the same for all
-** SearchPoints, then iLevel becomes the deciding factor and the result
-** is a depth-first search, which is the desired default behavior.
-*/
-static int rtreeSearchPointCompare(
-  const RtreeSearchPoint *pA,
-  const RtreeSearchPoint *pB
-){
-  if( pA->rScore<pB->rScore ) return -1;
-  if( pA->rScore>pB->rScore ) return +1;
-  if( pA->iLevel<pB->iLevel ) return -1;
-  if( pA->iLevel>pB->iLevel ) return +1;
-  return 0;
-}
-
-/*
-** Interchange to search points in a cursor.
-*/
-static void rtreeSearchPointSwap(RtreeCursor *p, int i, int j){
-  RtreeSearchPoint t = p->aPoint[i];
-  assert( i<j );
-  p->aPoint[i] = p->aPoint[j];
-  p->aPoint[j] = t;
-  i++; j++;
-  if( i<RTREE_CACHE_SZ ){
-    if( j>=RTREE_CACHE_SZ ){
-      nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);
-      p->aNode[i] = 0;
-    }else{
-      RtreeNode *pTemp = p->aNode[i];
-      p->aNode[i] = p->aNode[j];
-      p->aNode[j] = pTemp;
-    }
-  }
-}
-
-/*
-** Return the search point with the lowest current score.
-*/
-static RtreeSearchPoint *rtreeSearchPointFirst(RtreeCursor *pCur){
-  return pCur->bPoint ? &pCur->sPoint : pCur->nPoint ? pCur->aPoint : 0;
-}
-
-/*
-** Get the RtreeNode for the search point with the lowest score.
-*/
-static RtreeNode *rtreeNodeOfFirstSearchPoint(RtreeCursor *pCur, int *pRC){
-  sqlite3_int64 id;
-  int ii = 1 - pCur->bPoint;
-  assert( ii==0 || ii==1 );
-  assert( pCur->bPoint || pCur->nPoint );
-  if( pCur->aNode[ii]==0 ){
-    assert( pRC!=0 );
-    id = ii ? pCur->aPoint[0].id : pCur->sPoint.id;
-    *pRC = nodeAcquire(RTREE_OF_CURSOR(pCur), id, 0, &pCur->aNode[ii]);
-  }
-  return pCur->aNode[ii];
-}
-
-/*
-** Push a new element onto the priority queue
-*/
-static RtreeSearchPoint *rtreeEnqueue(
-  RtreeCursor *pCur,    /* The cursor */
-  RtreeDValue rScore,   /* Score for the new search point */
-  u8 iLevel             /* Level for the new search point */
-){
-  int i, j;
-  RtreeSearchPoint *pNew;
-  if( pCur->nPoint>=pCur->nPointAlloc ){
-    int nNew = pCur->nPointAlloc*2 + 8;
-    pNew = sqlite3_realloc(pCur->aPoint, nNew*sizeof(pCur->aPoint[0]));
-    if( pNew==0 ) return 0;
-    pCur->aPoint = pNew;
-    pCur->nPointAlloc = nNew;
-  }
-  i = pCur->nPoint++;
-  pNew = pCur->aPoint + i;
-  pNew->rScore = rScore;
-  pNew->iLevel = iLevel;
-  assert( iLevel<=RTREE_MAX_DEPTH );
-  while( i>0 ){
-    RtreeSearchPoint *pParent;
-    j = (i-1)/2;
-    pParent = pCur->aPoint + j;
-    if( rtreeSearchPointCompare(pNew, pParent)>=0 ) break;
-    rtreeSearchPointSwap(pCur, j, i);
-    i = j;
-    pNew = pParent;
-  }
-  return pNew;
-}
-
-/*
-** Allocate a new RtreeSearchPoint and return a pointer to it.  Return
-** NULL if malloc fails.
-*/
-static RtreeSearchPoint *rtreeSearchPointNew(
-  RtreeCursor *pCur,    /* The cursor */
-  RtreeDValue rScore,   /* Score for the new search point */
-  u8 iLevel             /* Level for the new search point */
-){
-  RtreeSearchPoint *pNew, *pFirst;
-  pFirst = rtreeSearchPointFirst(pCur);
-  pCur->anQueue[iLevel]++;
-  if( pFirst==0
-   || pFirst->rScore>rScore 
-   || (pFirst->rScore==rScore && pFirst->iLevel>iLevel)
-  ){
-    if( pCur->bPoint ){
-      int ii;
-      pNew = rtreeEnqueue(pCur, rScore, iLevel);
-      if( pNew==0 ) return 0;
-      ii = (int)(pNew - pCur->aPoint) + 1;
-      if( ii<RTREE_CACHE_SZ ){
-        assert( pCur->aNode[ii]==0 );
-        pCur->aNode[ii] = pCur->aNode[0];
-       }else{
-        nodeRelease(RTREE_OF_CURSOR(pCur), pCur->aNode[0]);
-      }
-      pCur->aNode[0] = 0;
-      *pNew = pCur->sPoint;
-    }
-    pCur->sPoint.rScore = rScore;
-    pCur->sPoint.iLevel = iLevel;
-    pCur->bPoint = 1;
-    return &pCur->sPoint;
-  }else{
-    return rtreeEnqueue(pCur, rScore, iLevel);
-  }
-}
-
-#if 0
-/* Tracing routines for the RtreeSearchPoint queue */
-static void tracePoint(RtreeSearchPoint *p, int idx, RtreeCursor *pCur){
-  if( idx<0 ){ printf(" s"); }else{ printf("%2d", idx); }
-  printf(" %d.%05lld.%02d %g %d",
-    p->iLevel, p->id, p->iCell, p->rScore, p->eWithin
-  );
-  idx++;
-  if( idx<RTREE_CACHE_SZ ){
-    printf(" %p\n", pCur->aNode[idx]);
-  }else{
-    printf("\n");
-  }
-}
-static void traceQueue(RtreeCursor *pCur, const char *zPrefix){
-  int ii;
-  printf("=== %9s ", zPrefix);
-  if( pCur->bPoint ){
-    tracePoint(&pCur->sPoint, -1, pCur);
-  }
-  for(ii=0; ii<pCur->nPoint; ii++){
-    if( ii>0 || pCur->bPoint ) printf("              ");
-    tracePoint(&pCur->aPoint[ii], ii, pCur);
-  }
-}
-# define RTREE_QUEUE_TRACE(A,B) traceQueue(A,B)
-#else
-# define RTREE_QUEUE_TRACE(A,B)   /* no-op */
-#endif
-
-/* Remove the search point with the lowest current score.
-*/
-static void rtreeSearchPointPop(RtreeCursor *p){
-  int i, j, k, n;
-  i = 1 - p->bPoint;
-  assert( i==0 || i==1 );
-  if( p->aNode[i] ){
-    nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);
-    p->aNode[i] = 0;
-  }
-  if( p->bPoint ){
-    p->anQueue[p->sPoint.iLevel]--;
-    p->bPoint = 0;
-  }else if( p->nPoint ){
-    p->anQueue[p->aPoint[0].iLevel]--;
-    n = --p->nPoint;
-    p->aPoint[0] = p->aPoint[n];
-    if( n<RTREE_CACHE_SZ-1 ){
-      p->aNode[1] = p->aNode[n+1];
-      p->aNode[n+1] = 0;
-    }
-    i = 0;
-    while( (j = i*2+1)<n ){
-      k = j+1;
-      if( k<n && rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[j])<0 ){
-        if( rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[i])<0 ){
-          rtreeSearchPointSwap(p, i, k);
-          i = k;
-        }else{
-          break;
-        }
-      }else{
-        if( rtreeSearchPointCompare(&p->aPoint[j], &p->aPoint[i])<0 ){
-          rtreeSearchPointSwap(p, i, j);
-          i = j;
-        }else{
-          break;
-        }
-      }
-    }
-  }
-}
-
-
-/*
-** Continue the search on cursor pCur until the front of the queue
-** contains an entry suitable for returning as a result-set row,
-** or until the RtreeSearchPoint queue is empty, indicating that the
-** query has completed.
-*/
-static int rtreeStepToLeaf(RtreeCursor *pCur){
-  RtreeSearchPoint *p;
-  Rtree *pRtree = RTREE_OF_CURSOR(pCur);
-  RtreeNode *pNode;
-  int eWithin;
-  int rc = SQLITE_OK;
-  int nCell;
-  int nConstraint = pCur->nConstraint;
-  int ii;
-  int eInt;
-  RtreeSearchPoint x;
-
-  eInt = pRtree->eCoordType==RTREE_COORD_INT32;
-  while( (p = rtreeSearchPointFirst(pCur))!=0 && p->iLevel>0 ){
-    pNode = rtreeNodeOfFirstSearchPoint(pCur, &rc);
-    if( rc ) return rc;
-    nCell = NCELL(pNode);
-    assert( nCell<200 );
-    while( p->iCell<nCell ){
-      sqlite3_rtree_dbl rScore = (sqlite3_rtree_dbl)-1;
-      u8 *pCellData = pNode->zData + (4+pRtree->nBytesPerCell*p->iCell);
-      eWithin = FULLY_WITHIN;
-      for(ii=0; ii<nConstraint; ii++){
-        RtreeConstraint *pConstraint = pCur->aConstraint + ii;
-        if( pConstraint->op>=RTREE_MATCH ){
-          rc = rtreeCallbackConstraint(pConstraint, eInt, pCellData, p,
-                                       &rScore, &eWithin);
-          if( rc ) return rc;
-        }else if( p->iLevel==1 ){
-          rtreeLeafConstraint(pConstraint, eInt, pCellData, &eWithin);
-        }else{
-          rtreeNonleafConstraint(pConstraint, eInt, pCellData, &eWithin);
-        }
-        if( eWithin==NOT_WITHIN ) break;
-      }
-      p->iCell++;
-      if( eWithin==NOT_WITHIN ) continue;
-      x.iLevel = p->iLevel - 1;
-      if( x.iLevel ){
-        x.id = readInt64(pCellData);
-        x.iCell = 0;
-      }else{
-        x.id = p->id;
-        x.iCell = p->iCell - 1;
-      }
-      if( p->iCell>=nCell ){
-        RTREE_QUEUE_TRACE(pCur, "POP-S:");
-        rtreeSearchPointPop(pCur);
-      }
-      if( rScore<RTREE_ZERO ) rScore = RTREE_ZERO;
-      p = rtreeSearchPointNew(pCur, rScore, x.iLevel);
-      if( p==0 ) return SQLITE_NOMEM;
-      p->eWithin = eWithin;
-      p->id = x.id;
-      p->iCell = x.iCell;
-      RTREE_QUEUE_TRACE(pCur, "PUSH-S:");
-      break;
-    }
-    if( p->iCell>=nCell ){
-      RTREE_QUEUE_TRACE(pCur, "POP-Se:");
-      rtreeSearchPointPop(pCur);
-    }
-  }
-  pCur->atEOF = p==0;
-  return SQLITE_OK;
-}
-
-/* 
-** Rtree virtual table module xNext method.
-*/
-static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
-  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
-  int rc = SQLITE_OK;
-
-  /* Move to the next entry that matches the configured constraints. */
-  RTREE_QUEUE_TRACE(pCsr, "POP-Nx:");
-  rtreeSearchPointPop(pCsr);
-  rc = rtreeStepToLeaf(pCsr);
-  return rc;
-}
-
-/* 
-** Rtree virtual table module xRowid method.
-*/
-static int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){
-  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
-  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
-  int rc = SQLITE_OK;
-  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
-  if( rc==SQLITE_OK && p ){
-    *pRowid = nodeGetRowid(RTREE_OF_CURSOR(pCsr), pNode, p->iCell);
-  }
-  return rc;
-}
-
-/* 
-** 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;
-  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
-  RtreeCoord c;
-  int rc = SQLITE_OK;
-  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
-
-  if( rc ) return rc;
-  if( p==0 ) return SQLITE_OK;
-  if( i==0 ){
-    sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));
-  }else{
-    if( rc ) return rc;
-    nodeGetCoord(pRtree, pNode, p->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,              /* RTree to search */
-  i64 iRowid,                 /* The rowid searching for */
-  RtreeNode **ppLeaf,         /* Write the node here */
-  sqlite3_int64 *piNode       /* Write the node-id here */
-){
-  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);
-    if( piNode ) *piNode = iNode;
-    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 *pBlob;              /* BLOB returned by geometry function */
-  sqlite3_rtree_query_info *pInfo;   /* Callback information */
-  int nBlob;                         /* Size of the geometry function blob */
-  int nExpected;                     /* Expected size of the BLOB */
-
-  /* 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) ){
-    return SQLITE_ERROR;
-  }
-
-  pInfo = (sqlite3_rtree_query_info*)sqlite3_malloc( sizeof(*pInfo)+nBlob );
-  if( !pInfo ) return SQLITE_NOMEM;
-  memset(pInfo, 0, sizeof(*pInfo));
-  pBlob = (RtreeMatchArg*)&pInfo[1];
-
-  memcpy(pBlob, sqlite3_value_blob(pValue), nBlob);
-  nExpected = (int)(sizeof(RtreeMatchArg) +
-                    pBlob->nParam*sizeof(sqlite3_value*) +
-                    (pBlob->nParam-1)*sizeof(RtreeDValue));
-  if( pBlob->magic!=RTREE_GEOMETRY_MAGIC || nBlob!=nExpected ){
-    sqlite3_free(pInfo);
-    return SQLITE_ERROR;
-  }
-  pInfo->pContext = pBlob->cb.pContext;
-  pInfo->nParam = pBlob->nParam;
-  pInfo->aParam = pBlob->aParam;
-  pInfo->apSqlParam = pBlob->apSqlParam;
-
-  if( pBlob->cb.xGeom ){
-    pCons->u.xGeom = pBlob->cb.xGeom;
-  }else{
-    pCons->op = RTREE_QUERY;
-    pCons->u.xQueryFunc = pBlob->cb.xQueryFunc;
-  }
-  pCons->pInfo = pInfo;
-  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;
-  int iCell = 0;
-
-  rtreeReference(pRtree);
-
-  /* Reset the cursor to the same state as rtreeOpen() leaves it in. */
-  freeCursorConstraints(pCsr);
-  sqlite3_free(pCsr->aPoint);
-  memset(pCsr, 0, sizeof(RtreeCursor));
-  pCsr->base.pVtab = (sqlite3_vtab*)pRtree;
-
-  pCsr->iStrategy = idxNum;
-  if( idxNum==1 ){
-    /* Special case - lookup by rowid. */
-    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
-    RtreeSearchPoint *p;     /* Search point for the the leaf */
-    i64 iRowid = sqlite3_value_int64(argv[0]);
-    i64 iNode = 0;
-    rc = findLeafNode(pRtree, iRowid, &pLeaf, &iNode);
-    if( rc==SQLITE_OK && pLeaf!=0 ){
-      p = rtreeSearchPointNew(pCsr, RTREE_ZERO, 0);
-      assert( p!=0 );  /* Always returns pCsr->sPoint */
-      pCsr->aNode[0] = pLeaf;
-      p->id = iNode;
-      p->eWithin = PARTLY_WITHIN;
-      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &iCell);
-      p->iCell = iCell;
-      RTREE_QUEUE_TRACE(pCsr, "PUSH-F1:");
-    }else{
-      pCsr->atEOF = 1;
-    }
-  }else{
-    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
-    ** with the configured constraints. 
-    */
-    rc = nodeAcquire(pRtree, 1, 0, &pRoot);
-    if( rc==SQLITE_OK && 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);
-        memset(pCsr->anQueue, 0, sizeof(u32)*(pRtree->iDepth + 1));
-        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]-'0';
-          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;
-            }
-            p->pInfo->nCoord = pRtree->nDim*2;
-            p->pInfo->anQueue = pCsr->anQueue;
-            p->pInfo->mxLevel = pRtree->iDepth + 1;
-          }else{
-#ifdef SQLITE_RTREE_INT_ONLY
-            p->u.rValue = sqlite3_value_int64(argv[ii]);
-#else
-            p->u.rValue = sqlite3_value_double(argv[ii]);
-#endif
-          }
-        }
-      }
-    }
-    if( rc==SQLITE_OK ){
-      RtreeSearchPoint *pNew;
-      pNew = rtreeSearchPointNew(pCsr, RTREE_ZERO, pRtree->iDepth+1);
-      if( pNew==0 ) return SQLITE_NOMEM;
-      pNew->id = 1;
-      pNew->iCell = 0;
-      pNew->eWithin = PARTLY_WITHIN;
-      assert( pCsr->bPoint==1 );
-      pCsr->aNode[0] = pRoot;
-      pRoot = 0;
-      RTREE_QUEUE_TRACE(pCsr, "PUSH-Fm:");
-      rc = rtreeStepToLeaf(pCsr);
-    }
-  }
-
-  nodeRelease(pRtree, pRoot);
-  rtreeRelease(pRtree);
-  return rc;
-}
-
-/*
-** Set the pIdxInfo->estimatedRows variable to nRow. Unless this
-** extension is currently being used by a version of SQLite too old to
-** support estimatedRows. In that case this function is a no-op.
-*/
-static void setEstimatedRows(sqlite3_index_info *pIdxInfo, i64 nRow){
-#if SQLITE_VERSION_NUMBER>=3008002
-  if( sqlite3_libversion_number()>=3008002 ){
-    pIdxInfo->estimatedRows = nRow;
-  }
-#endif
-}
-
-/*
-** 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){
-  Rtree *pRtree = (Rtree*)tab;
-  int rc = SQLITE_OK;
-  int ii;
-  int bMatch = 0;                 /* True if there exists a MATCH constraint */
-  i64 nRow;                       /* Estimated rows returned by this scan */
-
-  int iIdx = 0;
-  char zIdxStr[RTREE_MAX_DIMENSIONS*8+1];
-  memset(zIdxStr, 0, sizeof(zIdxStr));
-
-  /* Check if there exists a MATCH constraint - even an unusable one. If there
-  ** is, do not consider the lookup-by-rowid plan as using such a plan would
-  ** require the VDBE to evaluate the MATCH constraint, which is not currently
-  ** possible. */
-  for(ii=0; ii<pIdxInfo->nConstraint; ii++){
-    if( pIdxInfo->aConstraint[ii].op==SQLITE_INDEX_CONSTRAINT_MATCH ){
-      bMatch = 1;
-    }
-  }
-
-  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( bMatch==0 && 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). It is expected to return
-      ** a single row.
-      */ 
-      pIdxInfo->estimatedCost = 30.0;
-      setEstimatedRows(pIdxInfo, 1);
-      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 + '0';
-      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;
-  }
-
-  nRow = pRtree->nRowEst / (iIdx + 1);
-  pIdxInfo->estimatedCost = (double)6.0 * (double)nRow;
-  setEstimatedRows(pIdxInfo, nRow);
-
-  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);
-}
-
-static RtreeDValue cellOverlap(
-  Rtree *pRtree, 
-  RtreeCell *p, 
-  RtreeCell *aCell, 
-  int nCell
-){
-  int ii;
-  RtreeDValue overlap = RTREE_ZERO;
-  for(ii=0; ii<nCell; ii++){
-    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 = (RtreeDValue)0;
-        break;
-      }else{
-        o = o * (x2-x1);
-      }
-    }
-    overlap += o;
-  }
-  return overlap;
-}
-
-
-/*
-** 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 = RTREE_ZERO;
-    RtreeDValue fMinArea = RTREE_ZERO;
-
-    int nCell = NCELL(pNode);
-    RtreeCell cell;
-    RtreeNode *pChild;
-
-    RtreeCell *aCell = 0;
-
-    /* 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( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
-        bBest = 1;
-      }
-      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
-** all ancestor elements.
-*/
-static int 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 ){
-    RtreeNode *pParent = p->pParent;
-    RtreeCell cell;
-    int iCell;
-
-    if( nodeParentIndex(pRtree, p, &iCell) ){
-      return SQLITE_CORRUPT_VTAB;
-    }
-
-    nodeGetCell(pRtree, pParent, iCell, &cell);
-    if( !cellContains(pRtree, &cell, pCell) ){
-      cellUnion(pRtree, &cell, pCell);
-      nodeOverwriteCell(pRtree, pParent, &cell, iCell);
-    }
- 
-    p = pParent;
-  }
-  return SQLITE_OK;
-}
-
-/*
-** 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);
-
-
-/*
-** 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, 
-  RtreeDValue *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{
-        RtreeDValue fLeft = aDistance[aLeft[iLeft]];
-        RtreeDValue 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++){
-        RtreeDValue left = aDistance[aIdx[jj-1]];
-        RtreeDValue 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 ){
-      RtreeDValue xleft1 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2]);
-      RtreeDValue xleft2 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2+1]);
-      RtreeDValue xright1 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2]);
-      RtreeDValue 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++){
-        RtreeDValue xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
-        RtreeDValue xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
-        RtreeDValue xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
-        RtreeDValue xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
-        assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
-      }
-    }
-#endif
-  }
-}
-
-/*
-** 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 = 0;
-  int iBestSplit = 0;
-  RtreeDValue fBestMargin = RTREE_ZERO;
-
-  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++){
-    RtreeDValue margin = RTREE_ZERO;
-    RtreeDValue fBestOverlap = RTREE_ZERO;
-    RtreeDValue fBestArea = RTREE_ZERO;
-    int iBestLeft = 0;
-    int nLeft;
-
-    for(
-      nLeft=RTREE_MINCELLS(pRtree); 
-      nLeft<=(nCell-RTREE_MINCELLS(pRtree)); 
-      nLeft++
-    ){
-      RtreeCell left;
-      RtreeCell right;
-      int kk;
-      RtreeDValue overlap;
-      RtreeDValue 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);
-      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;
-}
-
-
-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);
-    pLeft = nodeNew(pRtree, pNode);
-    pRtree->iDepth++;
-    pNode->isDirty = 1;
-    writeInt16(pNode->zData, pRtree->iDepth);
-  }else{
-    pLeft = pNode;
-    pRight = nodeNew(pRtree, pLeft->pParent);
-    nodeReference(pLeft);
-  }
-
-  if( !pLeft || !pRight ){
-    rc = SQLITE_NOMEM;
-    goto splitnode_out;
-  }
-
-  memset(pLeft->zData, 0, pRtree->iNodeSize);
-  memset(pRight->zData, 0, pRtree->iNodeSize);
-
-  rc = splitNodeStartree(pRtree, aCell, nCell, pLeft, pRight,
-                         &leftbbox, &rightbbox);
-  if( rc!=SQLITE_OK ){
-    goto splitnode_out;
-  }
-
-  /* Ensure both child nodes have node numbers assigned to them by calling
-  ** nodeWrite(). Node pRight always needs a node number, as it was created
-  ** by nodeNew() above. But node pLeft sometimes already has a node number.
-  ** In this case avoid the all to nodeWrite().
-  */
-  if( 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;
-    rc = nodeParentIndex(pRtree, pLeft, &iCell);
-    if( rc==SQLITE_OK ){
-      nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);
-      rc = AdjustTree(pRtree, pParent, &leftbbox);
-    }
-    if( rc!=SQLITE_OK ){
-      goto splitnode_out;
-    }
-  }
-  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;
-}
-
-/*
-** If node pLeaf is not the root of the r-tree and its pParent pointer is 
-** still NULL, load all ancestor nodes of pLeaf into memory and populate
-** the pLeaf->pParent chain all the way up to the root node.
-**
-** This operation is required when a row is deleted (or updated - an update
-** is implemented as a delete followed by an insert). SQLite provides the
-** rowid of the row to delete, which can be used to find the leaf on which
-** the entry resides (argument pLeaf). Once the leaf is located, this 
-** function is called to determine its ancestry.
-*/
-static int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){
-  int rc = SQLITE_OK;
-  RtreeNode *pChild = pLeaf;
-  while( rc==SQLITE_OK && pChild->iNode!=1 && pChild->pParent==0 ){
-    int rc2 = SQLITE_OK;          /* sqlite3_reset() return code */
-    sqlite3_bind_int64(pRtree->pReadParent, 1, pChild->iNode);
-    rc = sqlite3_step(pRtree->pReadParent);
-    if( rc==SQLITE_ROW ){
-      RtreeNode *pTest;           /* Used to test for reference loops */
-      i64 iNode;                  /* Node number of parent node */
-
-      /* Before setting pChild->pParent, test that we are not creating a
-      ** loop of references (as we would if, say, pChild==pParent). We don't
-      ** want to do this as it leads to a memory leak when trying to delete
-      ** the referenced counted node structures.
-      */
-      iNode = sqlite3_column_int64(pRtree->pReadParent, 0);
-      for(pTest=pLeaf; pTest && pTest->iNode!=iNode; pTest=pTest->pParent);
-      if( !pTest ){
-        rc2 = nodeAcquire(pRtree, iNode, 0, &pChild->pParent);
-      }
-    }
-    rc = sqlite3_reset(pRtree->pReadParent);
-    if( rc==SQLITE_OK ) rc = rc2;
-    if( rc==SQLITE_OK && !pChild->pParent ) rc = SQLITE_CORRUPT_VTAB;
-    pChild = pChild->pParent;
-  }
-  return rc;
-}
-
-static int deleteCell(Rtree *, RtreeNode *, int, int);
-
-static int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){
-  int rc;
-  int rc2;
-  RtreeNode *pParent = 0;
-  int iCell;
-
-  assert( pNode->nRef==1 );
-
-  /* Remove the entry in the parent cell. */
-  rc = nodeParentIndex(pRtree, pNode, &iCell);
-  if( rc==SQLITE_OK ){
-    pParent = pNode->pParent;
-    pNode->pParent = 0;
-    rc = deleteCell(pRtree, pParent, iCell, iHeight+1);
-  }
-  rc2 = nodeRelease(pRtree, pParent);
-  if( rc==SQLITE_OK ){
-    rc = rc2;
-  }
-  if( rc!=SQLITE_OK ){
-    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 int fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){
-  RtreeNode *pParent = pNode->pParent;
-  int rc = SQLITE_OK; 
-  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;
-    rc = nodeParentIndex(pRtree, pNode, &ii);
-    if( rc==SQLITE_OK ){
-      nodeOverwriteCell(pRtree, pParent, &box, ii);
-      rc = fixBoundingBox(pRtree, pParent);
-    }
-  }
-  return rc;
-}
-
-/*
-** 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){
-  RtreeNode *pParent;
-  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.
-  */
-  pParent = pNode->pParent;
-  assert( pParent || pNode->iNode==1 );
-  if( pParent ){
-    if( NCELL(pNode)<RTREE_MINCELLS(pRtree) ){
-      rc = removeNode(pRtree, pNode, iHeight);
-    }else{
-      rc = fixBoundingBox(pRtree, pNode);
-    }
-  }
-
-  return rc;
-}
-
-static int Reinsert(
-  Rtree *pRtree, 
-  RtreeNode *pNode, 
-  RtreeCell *pCell, 
-  int iHeight
-){
-  int *aOrder;
-  int *aSpare;
-  RtreeCell *aCell;
-  RtreeDValue *aDistance;
-  int nCell;
-  RtreeDValue aCenterCoord[RTREE_MAX_DIMENSIONS];
-  int iDim;
-  int ii;
-  int rc = SQLITE_OK;
-  int n;
-
-  memset(aCenterCoord, 0, sizeof(RtreeDValue)*RTREE_MAX_DIMENSIONS);
-
-  nCell = NCELL(pNode)+1;
-  n = (nCell+1)&(~1);
-
-  /* Allocate the buffers used by this operation. The allocation is
-  ** relinquished before this function returns.
-  */
-  aCell = (RtreeCell *)sqlite3_malloc(n * (
-    sizeof(RtreeCell)     +         /* aCell array */
-    sizeof(int)           +         /* aOrder array */
-    sizeof(int)           +         /* aSpare array */
-    sizeof(RtreeDValue)             /* aDistance array */
-  ));
-  if( !aCell ){
-    return SQLITE_NOMEM;
-  }
-  aOrder    = (int *)&aCell[n];
-  aSpare    = (int *)&aOrder[n];
-  aDistance = (RtreeDValue *)&aSpare[n];
-
-  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]/(nCell*(RtreeDValue)2));
-  }
-
-  for(ii=0; ii<nCell; ii++){
-    aDistance[ii] = RTREE_ZERO;
-    for(iDim=0; iDim<pRtree->nDim; iDim++){
-      RtreeDValue 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 ){
-    rc = 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( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
-      rc = SplitNode(pRtree, pNode, pCell, iHeight);
-    }else{
-      pRtree->iReinsertHeight = iHeight;
-      rc = Reinsert(pRtree, pNode, pCell, iHeight);
-    }
-  }else{
-    rc = AdjustTree(pRtree, pNode, pCell);
-    if( rc==SQLITE_OK ){
-      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, (int)pNode->iNode, &pInsert);
-    if( rc==SQLITE_OK ){
-      int rc2;
-      rc = rtreeInsertCell(pRtree, pInsert, &cell, (int)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;
-}
-
-/*
-** Remove the entry with rowid=iDelete from the r-tree structure.
-*/
-static int rtreeDeleteRowid(Rtree *pRtree, sqlite3_int64 iDelete){
-  int rc;                         /* Return code */
-  RtreeNode *pLeaf = 0;           /* Leaf node containing record iDelete */
-  int iCell;                      /* Index of iDelete cell in pLeaf */
-  RtreeNode *pRoot;               /* Root node of rtree structure */
-
-
-  /* Obtain a reference to the root node to initialize 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 ){
-    rc = findLeafNode(pRtree, iDelete, &pLeaf, 0);
-  }
-
-  /* Delete the cell in question from the leaf node. */
-  if( rc==SQLITE_OK ){
-    int rc2;
-    rc = nodeRowidIndex(pRtree, pLeaf, iDelete, &iCell);
-    if( rc==SQLITE_OK ){
-      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 && NCELL(pRoot)==1 ){
-    int rc2;
-    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);
-    }
-    rc2 = nodeRelease(pRtree, pChild);
-    if( rc==SQLITE_OK ) rc = rc2;
-    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);
-  }
-
-  return rc;
-}
-
-/*
-** Rounding constants for float->double conversion.
-*/
-#define RNDTOWARDS  (1.0 - 1.0/8388608.0)  /* Round towards zero */
-#define RNDAWAY     (1.0 + 1.0/8388608.0)  /* Round away from zero */
-
-#if !defined(SQLITE_RTREE_INT_ONLY)
-/*
-** Convert an sqlite3_value into an RtreeValue (presumably a float)
-** while taking care to round toward negative or positive, respectively.
-*/
-static RtreeValue rtreeValueDown(sqlite3_value *v){
-  double d = sqlite3_value_double(v);
-  float f = (float)d;
-  if( f>d ){
-    f = (float)(d*(d<0 ? RNDAWAY : RNDTOWARDS));
-  }
-  return f;
-}
-static RtreeValue rtreeValueUp(sqlite3_value *v){
-  double d = sqlite3_value_double(v);
-  float f = (float)d;
-  if( f<d ){
-    f = (float)(d*(d<0 ? RNDTOWARDS : RNDAWAY));
-  }
-  return f;
-}
-#endif /* !defined(SQLITE_RTREE_INT_ONLY) */
-
-
-/*
-** 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;
-  RtreeCell cell;                 /* New cell to insert if nData>1 */
-  int bHaveRowid = 0;             /* Set to 1 after new rowid is determined */
-
-  rtreeReference(pRtree);
-  assert(nData>=1);
-
-  cell.iRowid = 0;  /* Used only to suppress a compiler warning */
-
-  /* Constraint handling. A write operation on an r-tree table may return
-  ** SQLITE_CONSTRAINT for two reasons:
-  **
-  **   1. A duplicate rowid value, or
-  **   2. The supplied data violates the "x2>=x1" constraint.
-  **
-  ** In the first case, if the conflict-handling mode is REPLACE, then
-  ** the conflicting row can be removed before proceeding. In the second
-  ** case, SQLITE_CONSTRAINT must be returned regardless of the
-  ** conflict-handling mode specified by the user.
-  */
-  if( nData>1 ){
-    int ii;
-
-    /* Populate the cell.aCoord[] array. The first coordinate is azData[3].
-    **
-    ** NB: nData can only be less than nDim*2+3 if the rtree is mis-declared
-    ** with "column" that are interpreted as table constraints.
-    ** Example:  CREATE VIRTUAL TABLE bad USING rtree(x,y,CHECK(y>5));
-    ** This problem was discovered after years of use, so we silently ignore
-    ** these kinds of misdeclared tables to avoid breaking any legacy.
-    */
-    assert( nData<=(pRtree->nDim*2 + 3) );
-
-#ifndef SQLITE_RTREE_INT_ONLY
-    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
-      for(ii=0; ii<nData-4; ii+=2){
-        cell.aCoord[ii].f = rtreeValueDown(azData[ii+3]);
-        cell.aCoord[ii+1].f = rtreeValueUp(azData[ii+4]);
-        if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
-          rc = SQLITE_CONSTRAINT;
-          goto constraint;
-        }
-      }
-    }else
-#endif
-    {
-      for(ii=0; ii<nData-4; 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;
-        }
-      }
-    }
-
-    /* If a rowid value was supplied, check if it is already present in 
-    ** the table. If so, the constraint has failed. */
-    if( sqlite3_value_type(azData[2])!=SQLITE_NULL ){
-      cell.iRowid = sqlite3_value_int64(azData[2]);
-      if( sqlite3_value_type(azData[0])==SQLITE_NULL
-       || sqlite3_value_int64(azData[0])!=cell.iRowid
-      ){
-        int steprc;
-        sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
-        steprc = sqlite3_step(pRtree->pReadRowid);
-        rc = sqlite3_reset(pRtree->pReadRowid);
-        if( SQLITE_ROW==steprc ){
-          if( sqlite3_vtab_on_conflict(pRtree->db)==SQLITE_REPLACE ){
-            rc = rtreeDeleteRowid(pRtree, cell.iRowid);
-          }else{
-            rc = SQLITE_CONSTRAINT;
-            goto constraint;
-          }
-        }
-      }
-      bHaveRowid = 1;
-    }
-  }
-
-  /* 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 ){
-    rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(azData[0]));
-  }
-
-  /* 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 the new record into the r-tree */
-    RtreeNode *pLeaf = 0;
-
-    /* Figure out the rowid of the new row. */
-    if( bHaveRowid==0 ){
-      rc = newRowid(pRtree, &cell.iRowid);
-    }
-    *pRowid = cell.iRowid;
-
-    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;
-}
-
-/*
-** This function populates the pRtree->nRowEst variable with an estimate
-** of the number of rows in the virtual table. If possible, this is based
-** on sqlite_stat1 data. Otherwise, use RTREE_DEFAULT_ROWEST.
-*/
-static int rtreeQueryStat1(sqlite3 *db, Rtree *pRtree){
-  const char *zFmt = "SELECT stat FROM %Q.sqlite_stat1 WHERE tbl = '%q_rowid'";
-  char *zSql;
-  sqlite3_stmt *p;
-  int rc;
-  i64 nRow = 0;
-
-  zSql = sqlite3_mprintf(zFmt, pRtree->zDb, pRtree->zName);
-  if( zSql==0 ){
-    rc = SQLITE_NOMEM;
-  }else{
-    rc = sqlite3_prepare_v2(db, zSql, -1, &p, 0);
-    if( rc==SQLITE_OK ){
-      if( sqlite3_step(p)==SQLITE_ROW ) nRow = sqlite3_column_int64(p, 0);
-      rc = sqlite3_finalize(p);
-    }else if( rc!=SQLITE_NOMEM ){
-      rc = SQLITE_OK;
-    }
-
-    if( rc==SQLITE_OK ){
-      if( nRow==0 ){
-        pRtree->nRowEst = RTREE_DEFAULT_ROWEST;
-      }else{
-        pRtree->nRowEst = MAX(nRow, RTREE_MIN_ROWEST);
-      }
-    }
-    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 */
-  0,                          /* xSavepoint */
-  0,                          /* xRelease */
-  0                           /* xRollbackTo */
-};
-
-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;
-
-  rc = rtreeQueryStat1(db, pRtree);
-  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;
-}
-
-/*
-** The second argument to this function contains the text of an SQL statement
-** that returns a single integer value. The statement is compiled and executed
-** using database connection db. If successful, the integer value returned
-** is written to *piVal and SQLITE_OK returned. Otherwise, an SQLite error
-** code is returned and the value of *piVal after returning is not defined.
-*/
-static int getIntFromStmt(sqlite3 *db, const char *zSql, int *piVal){
-  int rc = SQLITE_NOMEM;
-  if( zSql ){
-    sqlite3_stmt *pStmt = 0;
-    rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);
-    if( rc==SQLITE_OK ){
-      if( SQLITE_ROW==sqlite3_step(pStmt) ){
-        *piVal = sqlite3_column_int(pStmt, 0);
-      }
-      rc = sqlite3_finalize(pStmt);
-    }
-  }
-  return rc;
-}
-
-/*
-** This function is called from within the xConnect() or xCreate() method to
-** determine the node-size used by the rtree table being created or connected
-** to. If successful, pRtree->iNodeSize is populated and SQLITE_OK returned.
-** Otherwise, an SQLite error code is returned.
-**
-** If this function is being called as part of an xConnect(), then the rtree
-** table already exists. In this case the node-size is determined by inspecting
-** the root node of the tree.
-**
-** Otherwise, for an xCreate(), use 64 bytes less than the database page-size. 
-** This ensures that each node is stored on a single database page. If the 
-** database page-size is so large that more than RTREE_MAXCELLS entries 
-** would fit in a single node, use a smaller node-size.
-*/
-static int getNodeSize(
-  sqlite3 *db,                    /* Database handle */
-  Rtree *pRtree,                  /* Rtree handle */
-  int isCreate,                   /* True for xCreate, false for xConnect */
-  char **pzErr                    /* OUT: Error message, if any */
-){
-  int rc;
-  char *zSql;
-  if( isCreate ){
-    int iPageSize = 0;
-    zSql = sqlite3_mprintf("PRAGMA %Q.page_size", pRtree->zDb);
-    rc = getIntFromStmt(db, zSql, &iPageSize);
-    if( rc==SQLITE_OK ){
-      pRtree->iNodeSize = iPageSize-64;
-      if( (4+pRtree->nBytesPerCell*RTREE_MAXCELLS)<pRtree->iNodeSize ){
-        pRtree->iNodeSize = 4+pRtree->nBytesPerCell*RTREE_MAXCELLS;
-      }
-    }else{
-      *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
-    }
-  }else{
-    zSql = sqlite3_mprintf(
-        "SELECT length(data) FROM '%q'.'%q_node' WHERE nodeno = 1",
-        pRtree->zDb, pRtree->zName
-    );
-    rc = getIntFromStmt(db, zSql, &pRtree->iNodeSize);
-    if( rc!=SQLITE_OK ){
-      *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
-    }
-  }
-
-  sqlite3_free(zSql);
-  return rc;
-}
-
-/* 
-** 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;
-  Rtree *pRtree;
-  int nDb;              /* Length of string argv[1] */
-  int nName;            /* Length of string argv[2] */
-  int eCoordType = (pAux ? RTREE_COORD_INT32 : RTREE_COORD_REAL32);
-
-  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;
-  }
-
-  sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);
-
-  /* Allocate the sqlite3_vtab structure */
-  nDb = (int)strlen(argv[1]);
-  nName = (int)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. */
-  rc = getNodeSize(db, pRtree, isCreate, pzErr);
-
-  /* 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==SQLITE_OK ){
-    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{
-    assert( *ppVtab==0 );
-    assert( pRtree->nBusy==1 );
-    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: (1) the number of dimensions
-** to the rtree (between 1 and 5, inclusive) and (2) a blob of data containing
-** an r-tree node.  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;
-
-  UNUSED_PARAMETER(nArg);
-  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],"%lld", cell.iRowid);
-    nCell = (int)strlen(zCell);
-    for(jj=0; jj<tree.nDim*2; jj++){
-#ifndef SQLITE_RTREE_INT_ONLY
-      sqlite3_snprintf(512-nCell,&zCell[nCell], " %g",
-                       (double)cell.aCoord[jj].f);
-#else
-      sqlite3_snprintf(512-nCell,&zCell[nCell], " %d",
-                       cell.aCoord[jj].i);
-#endif
-      nCell = (int)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);
-}
-
-/* This routine implements an SQL function that returns the "depth" parameter
-** from the front of a blob that is an r-tree node.  For example:
-**
-**     SELECT rtreedepth(data) FROM rt_node WHERE nodeno=1;
-**
-** The depth value is 0 for all nodes other than the root node, and the root
-** node always has nodeno=1, so the example above is the primary use for this
-** routine.  This routine is intended for testing and analysis only.
-*/
-static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
-  UNUSED_PARAMETER(nArg);
-  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){
-  const int utf8 = SQLITE_UTF8;
-  int rc;
-
-  rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);
-  if( rc==SQLITE_OK ){
-    rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
-  }
-  if( rc==SQLITE_OK ){
-#ifdef SQLITE_RTREE_INT_ONLY
-    void *c = (void *)RTREE_COORD_INT32;
-#else
-    void *c = (void *)RTREE_COORD_REAL32;
-#endif
-    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;
-}
-
-/*
-** This routine deletes the RtreeGeomCallback object that was attached
-** one of the SQL functions create by sqlite3_rtree_geometry_callback()
-** or sqlite3_rtree_query_callback().  In other words, this routine is the
-** destructor for an RtreeGeomCallback objecct.  This routine is called when
-** the corresponding SQL function is deleted.
-*/
-static void rtreeFreeCallback(void *p){
-  RtreeGeomCallback *pInfo = (RtreeGeomCallback*)p;
-  if( pInfo->xDestructor ) pInfo->xDestructor(pInfo->pContext);
-  sqlite3_free(p);
-}
-
-/*
-** This routine frees the BLOB that is returned by geomCallback().
-*/
-static void rtreeMatchArgFree(void *pArg){
-  int i;
-  RtreeMatchArg *p = (RtreeMatchArg*)pArg;
-  for(i=0; i<p->nParam; i++){
-    sqlite3_value_free(p->apSqlParam[i]);
-  }
-  sqlite3_free(p);
-}
-
-/*
-** Each call to sqlite3_rtree_geometry_callback() or
-** sqlite3_rtree_query_callback() creates an ordinary SQLite
-** scalar function that is implemented by this routine.
-**
-** All this function does is construct an RtreeMatchArg object that
-** contains the geometry-checking callback routines and a list of
-** parameters to this function, then return that RtreeMatchArg object
-** as a BLOB.
-**
-** The R-Tree MATCH operator will read the returned BLOB, deserialize
-** the RtreeMatchArg object, and use the RtreeMatchArg object to figure
-** out which elements of the R-Tree should be returned by the query.
-*/
-static void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){
-  RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);
-  RtreeMatchArg *pBlob;
-  int nBlob;
-  int memErr = 0;
-
-  nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(RtreeDValue)
-           + nArg*sizeof(sqlite3_value*);
-  pBlob = (RtreeMatchArg *)sqlite3_malloc(nBlob);
-  if( !pBlob ){
-    sqlite3_result_error_nomem(ctx);
-  }else{
-    int i;
-    pBlob->magic = RTREE_GEOMETRY_MAGIC;
-    pBlob->cb = pGeomCtx[0];
-    pBlob->apSqlParam = (sqlite3_value**)&pBlob->aParam[nArg];
-    pBlob->nParam = nArg;
-    for(i=0; i<nArg; i++){
-      pBlob->apSqlParam[i] = sqlite3_value_dup(aArg[i]);
-      if( pBlob->apSqlParam[i]==0 ) memErr = 1;
-#ifdef SQLITE_RTREE_INT_ONLY
-      pBlob->aParam[i] = sqlite3_value_int64(aArg[i]);
-#else
-      pBlob->aParam[i] = sqlite3_value_double(aArg[i]);
-#endif
-    }
-    if( memErr ){
-      sqlite3_result_error_nomem(ctx);
-      rtreeMatchArgFree(pBlob);
-    }else{
-      sqlite3_result_blob(ctx, pBlob, nBlob, rtreeMatchArgFree);
-    }
-  }
-}
-
-/*
-** Register a new geometry function for use with the r-tree MATCH operator.
-*/
-int sqlite3_rtree_geometry_callback(
-  sqlite3 *db,                  /* Register SQL function on this connection */
-  const char *zGeom,            /* Name of the new SQL function */
-  int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*), /* Callback */
-  void *pContext                /* Extra data associated with the callback */
-){
-  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */
-
-  /* Allocate and populate the context object. */
-  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
-  if( !pGeomCtx ) return SQLITE_NOMEM;
-  pGeomCtx->xGeom = xGeom;
-  pGeomCtx->xQueryFunc = 0;
-  pGeomCtx->xDestructor = 0;
-  pGeomCtx->pContext = pContext;
-  return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY, 
-      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
-  );
-}
-
-/*
-** Register a new 2nd-generation geometry function for use with the
-** r-tree MATCH operator.
-*/
-int sqlite3_rtree_query_callback(
-  sqlite3 *db,                 /* Register SQL function on this connection */
-  const char *zQueryFunc,      /* Name of new SQL function */
-  int (*xQueryFunc)(sqlite3_rtree_query_info*), /* Callback */
-  void *pContext,              /* Extra data passed into the callback */
-  void (*xDestructor)(void*)   /* Destructor for the extra data */
-){
-  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */
-
-  /* Allocate and populate the context object. */
-  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
-  if( !pGeomCtx ) return SQLITE_NOMEM;
-  pGeomCtx->xGeom = 0;
-  pGeomCtx->xQueryFunc = xQueryFunc;
-  pGeomCtx->xDestructor = xDestructor;
-  pGeomCtx->pContext = pContext;
-  return sqlite3_create_function_v2(db, zQueryFunc, -1, SQLITE_ANY, 
-      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
-  );
-}
-
-#if !SQLITE_CORE
-#ifdef _WIN32
-__declspec(dllexport)
-#endif
-int sqlite3_rtree_init(
-  sqlite3 *db,
-  char **pzErrMsg,
-  const sqlite3_api_routines *pApi
-){
-  SQLITE_EXTENSION_INIT2(pApi)
-  return sqlite3RtreeInit(db);
-}
-#endif
-
-#endif