[sql] Import reference version of SQLite 3.17..

third_party/sqlite/sqlite-src-3170000/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 sqlite3_uint64 u64;
+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 nDim2;                   /* Twice the number of dimensions */
+  u8 eCoordType;              /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */
+  u8 nBytesPerCell;           /* Bytes consumed per cell */
+  u8 inWrTrans;               /* True if inside write transaction */
+  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 */ 
+  u32 nBusy;                  /* Current number of users of this structure */
+  i64 nRowEst;                /* Estimated number of rows in this table */
+  u32 nCursor;                /* Number of open cursors */
+
+  /* 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 */
+
+  /* Blob I/O on xxx_node */
+  sqlite3_blob *pNodeBlob;
+
+  /* Statements to read/write/delete a record from xxx_node */
+  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
+
+/* What version of GCC is being used.  0 means GCC is not being used */
+#ifndef GCC_VERSION
+#if defined(__GNUC__) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define GCC_VERSION (__GNUC__*1000000+__GNUC_MINOR__*1000+__GNUC_PATCHLEVEL__)
+#else
+# define GCC_VERSION 0
+#endif
+#endif
+
+/* What version of CLANG is being used.  0 means CLANG is not being used */
+#ifndef CLANG_VERSION
+#if defined(__clang__) && !defined(_WIN32) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define CLANG_VERSION \
+            (__clang_major__*1000000+__clang_minor__*1000+__clang_patchlevel__)
+#else
+# define CLANG_VERSION 0
+#endif
+#endif
+
+/* The testcase() macro should already be defined in the amalgamation.  If
+** it is not, make it a no-op.
+*/
+#ifndef SQLITE_AMALGAMATION
+# define testcase(X)
+#endif
+
+/*
+** Macros to determine whether the machine is big or little endian,
+** and whether or not that determination is run-time or compile-time.
+**
+** For best performance, an attempt is made to guess at the byte-order
+** using C-preprocessor macros.  If that is unsuccessful, or if
+** -DSQLITE_RUNTIME_BYTEORDER=1 is set, then byte-order is determined
+** at run-time.
+*/
+#ifndef SQLITE_BYTEORDER
+#if defined(i386)     || defined(__i386__)   || defined(_M_IX86) ||    \
+    defined(__x86_64) || defined(__x86_64__) || defined(_M_X64)  ||    \
+    defined(_M_AMD64) || defined(_M_ARM)     || defined(__x86)   ||    \
+    defined(__arm__)
+# define SQLITE_BYTEORDER    1234
+#elif defined(sparc)    || defined(__ppc__)
+# define SQLITE_BYTEORDER    4321
+#else
+# define SQLITE_BYTEORDER    0     /* 0 means "unknown at compile-time" */
+#endif
+#endif
+
+
+/* What version of MSVC is being used.  0 means MSVC is not being used */
+#ifndef MSVC_VERSION
+#if defined(_MSC_VER) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define MSVC_VERSION _MSC_VER
+#else
+# define MSVC_VERSION 0
+#endif
+#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){
+  assert( ((((char*)p) - (char*)0)&3)==0 );  /* p is always 4-byte aligned */
+#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  pCoord->u = _byteswap_ulong(*(u32*)p);
+#elif SQLITE_BYTEORDER==1234 && (GCC_VERSION>=4003000 || CLANG_VERSION>=3000000)
+  pCoord->u = __builtin_bswap32(*(u32*)p);
+#elif SQLITE_BYTEORDER==4321
+  pCoord->u = *(u32*)p;
+#else
+  pCoord->u = (
+    (((u32)p[0]) << 24) + 
+    (((u32)p[1]) << 16) + 
+    (((u32)p[2]) <<  8) + 
+    (((u32)p[3]) <<  0)
+  );
+#endif
+}
+static i64 readInt64(u8 *p){
+#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  u64 x;
+  memcpy(&x, p, 8);
+  return (i64)_byteswap_uint64(x);
+#elif SQLITE_BYTEORDER==1234 && (GCC_VERSION>=4003000 || CLANG_VERSION>=3000000)
+  u64 x;
+  memcpy(&x, p, 8);
+  return (i64)__builtin_bswap64(x);
+#elif SQLITE_BYTEORDER==4321
+  i64 x;
+  memcpy(&x, p, 8);
+  return x;
+#else
+  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)
+  );
+#endif
+}
+
+/*
+** 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 void writeInt16(u8 *p, int i){
+  p[0] = (i>> 8)&0xFF;
+  p[1] = (i>> 0)&0xFF;
+}
+static int writeCoord(u8 *p, RtreeCoord *pCoord){
+  u32 i;
+  assert( ((((char*)p) - (char*)0)&3)==0 );  /* p is always 4-byte aligned */
+  assert( sizeof(RtreeCoord)==4 );
+  assert( sizeof(u32)==4 );
+#if SQLITE_BYTEORDER==1234 && (GCC_VERSION>=4003000 || CLANG_VERSION>=3000000)
+  i = __builtin_bswap32(pCoord->u);
+  memcpy(p, &i, 4);
+#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  i = _byteswap_ulong(pCoord->u);
+  memcpy(p, &i, 4);
+#elif SQLITE_BYTEORDER==4321
+  i = pCoord->u;
+  memcpy(p, &i, 4);
+#else
+  i = pCoord->u;
+  p[0] = (i>>24)&0xFF;
+  p[1] = (i>>16)&0xFF;
+  p[2] = (i>> 8)&0xFF;
+  p[3] = (i>> 0)&0xFF;
+#endif
+  return 4;
+}
+static int writeInt64(u8 *p, i64 i){
+#if SQLITE_BYTEORDER==1234 && (GCC_VERSION>=4003000 || CLANG_VERSION>=3000000)
+  i = (i64)__builtin_bswap64((u64)i);
+  memcpy(p, &i, 8);
+#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  i = (i64)_byteswap_uint64((u64)i);
+  memcpy(p, &i, 8);
+#elif SQLITE_BYTEORDER==4321
+  memcpy(p, &i, 8);
+#else
+  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;
+#endif
+  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;
+}
+
+/*
+** Clear the Rtree.pNodeBlob object
+*/
+static void nodeBlobReset(Rtree *pRtree){
+  if( pRtree->pNodeBlob && pRtree->inWrTrans==0 && pRtree->nCursor==0 ){
+    sqlite3_blob *pBlob = pRtree->pNodeBlob;
+    pRtree->pNodeBlob = 0;
+    sqlite3_blob_close(pBlob);
+  }
+}
+
+/*
+** 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 = SQLITE_OK;
+  RtreeNode *pNode = 0;
+
+  /* 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;
+  }
+
+  if( pRtree->pNodeBlob ){
+    sqlite3_blob *pBlob = pRtree->pNodeBlob;
+    pRtree->pNodeBlob = 0;
+    rc = sqlite3_blob_reopen(pBlob, iNode);
+    pRtree->pNodeBlob = pBlob;
+    if( rc ){
+      nodeBlobReset(pRtree);
+      if( rc==SQLITE_NOMEM ) return SQLITE_NOMEM;
+    }
+  }
+  if( pRtree->pNodeBlob==0 ){
+    char *zTab = sqlite3_mprintf("%s_node", pRtree->zName);
+    if( zTab==0 ) return SQLITE_NOMEM;
+    rc = sqlite3_blob_open(pRtree->db, pRtree->zDb, zTab, "data", iNode, 0,
+                           &pRtree->pNodeBlob);
+    sqlite3_free(zTab);
+  }
+  if( rc ){
+    nodeBlobReset(pRtree);
+    *ppNode = 0;
+    /* If unable to open an sqlite3_blob on the desired row, that can only
+    ** be because the shadow tables hold erroneous data. */
+    if( rc==SQLITE_ERROR ) rc = SQLITE_CORRUPT_VTAB;
+  }else if( pRtree->iNodeSize==sqlite3_blob_bytes(pRtree->pNodeBlob) ){
+    pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode)+pRtree->iNodeSize);
+    if( !pNode ){
+      rc = SQLITE_NOMEM;
+    }else{
+      pNode->pParent = pParent;
+      pNode->zData = (u8 *)&pNode[1];
+      pNode->nRef = 1;
+      pNode->iNode = iNode;
+      pNode->isDirty = 0;
+      pNode->pNext = 0;
+      rc = sqlite3_blob_read(pRtree->pNodeBlob, pNode->zData,
+                             pRtree->iNodeSize, 0);
+      nodeReference(pParent);
+    }
+  }
+
+  /* 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->nDim2; 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 = 0;
+  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
+  pData = pNode->zData + (12 + pRtree->nBytesPerCell*iCell);
+  pCoord = pCell->aCoord;
+  do{
+    readCoord(pData, &pCoord[ii]);
+    readCoord(pData+4, &pCoord[ii+1]);
+    pData += 8;
+    ii += 2;
+  }while( ii<pRtree->nDim2 );
+}
+
+
+/* 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 ){
+    pRtree->inWrTrans = 0;
+    pRtree->nCursor = 0;
+    nodeBlobReset(pRtree);
+    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{
+    nodeBlobReset(pRtree);
+    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;
+  Rtree *pRtree = (Rtree *)pVTab;
+  RtreeCursor *pCsr;
+
+  pCsr = (RtreeCursor *)sqlite3_malloc(sizeof(RtreeCursor));
+  if( pCsr ){
+    memset(pCsr, 0, sizeof(RtreeCursor));
+    pCsr->base.pVtab = pVTab;
+    rc = SQLITE_OK;
+    pRtree->nCursor++;
+  }
+  *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;
+  assert( pRtree->nCursor>0 );
+  freeCursorConstraints(pCsr);
+  sqlite3_free(pCsr->aPoint);
+  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
+  sqlite3_free(pCsr);
+  pRtree->nCursor--;
+  nodeBlobReset(pRtree);
+  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 five versions of this macro.  The last one is generic.  The
+** other four are various architectures-specific optimizations.
+*/
+#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+#define RTREE_DECODE_COORD(eInt, a, r) {                        \
+    RtreeCoord c;    /* Coordinate decoded */                   \
+    c.u = _byteswap_ulong(*(u32*)a);                            \
+    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
+}
+#elif SQLITE_BYTEORDER==1234 && (GCC_VERSION>=4003000 || CLANG_VERSION>=3000000)
+#define RTREE_DECODE_COORD(eInt, a, r) {                        \
+    RtreeCoord c;    /* Coordinate decoded */                   \
+    c.u = __builtin_bswap32(*(u32*)a);                          \
+    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
+}
+#elif 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 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 */
+){
+  sqlite3_rtree_query_info *pInfo = pConstraint->pInfo; /* Callback info */
+  int nCoord = pInfo->nCoord;                           /* No. of coordinates */
+  int rc;                                             /* Callback return code */
+  RtreeCoord c;                                       /* Translator union */
+  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;
+#ifndef SQLITE_RTREE_INT_ONLY
+  if( eInt==0 ){
+    switch( nCoord ){
+      case 10:  readCoord(pCellData+36, &c); aCoord[9] = c.f;
+                readCoord(pCellData+32, &c); aCoord[8] = c.f;
+      case 8:   readCoord(pCellData+28, &c); aCoord[7] = c.f;
+                readCoord(pCellData+24, &c); aCoord[6] = c.f;
+      case 6:   readCoord(pCellData+20, &c); aCoord[5] = c.f;
+                readCoord(pCellData+16, &c); aCoord[4] = c.f;
+      case 4:   readCoord(pCellData+12, &c); aCoord[3] = c.f;
+                readCoord(pCellData+8,  &c); aCoord[2] = c.f;
+      default:  readCoord(pCellData+4,  &c); aCoord[1] = c.f;
+                readCoord(pCellData,    &c); aCoord[0] = c.f;
+    }
+  }else
+#endif
+  {
+    switch( nCoord ){
+      case 10:  readCoord(pCellData+36, &c); aCoord[9] = c.i;
+                readCoord(pCellData+32, &c); aCoord[8] = c.i;
+      case 8:   readCoord(pCellData+28, &c); aCoord[7] = c.i;
+                readCoord(pCellData+24, &c); aCoord[6] = c.i;
+      case 6:   readCoord(pCellData+20, &c); aCoord[5] = c.i;
+                readCoord(pCellData+16, &c); aCoord[4] = c.i;
+      case 4:   readCoord(pCellData+12, &c); aCoord[3] = c.i;
+                readCoord(pCellData+8,  &c); aCoord[2] = c.i;
+      default:  readCoord(pCellData+4,  &c); aCoord[1] = c.i;
+                readCoord(pCellData,    &c); aCoord[0] = c.i;
+    }
+  }
+  if( pConstraint->op==RTREE_MATCH ){
+    int eWithin = 0;
+    rc = pConstraint->u.xGeom((sqlite3_rtree_geometry*)pInfo,
+                              nCoord, aCoord, &eWithin);
+    if( eWithin==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 );
+  assert( ((((char*)pCellData) - (char*)0)&3)==0 );  /* 4-byte aligned */
+  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;
+  assert( ((((char*)pCellData) - (char*)0)&3)==0 );  /* 4-byte aligned */
+  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 two 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 = (u8)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{
+    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 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 = (u8)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->nDim2;
+            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, (u8)(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;
+}
+
+/*
+** 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;
+      pIdxInfo->estimatedRows = 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++] = (char)(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/2);
+  pIdxInfo->estimatedCost = (double)6.0 * (double)nRow;
+  pIdxInfo->estimatedRows = 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;
+  assert( pRtree->nDim>=1 && pRtree->nDim<=5 );
+#ifndef SQLITE_RTREE_INT_ONLY
+  if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
+    switch( pRtree->nDim ){
+      case 5:  area  = p->aCoord[9].f - p->aCoord[8].f;
+      case 4:  area *= p->aCoord[7].f - p->aCoord[6].f;
+      case 3:  area *= p->aCoord[5].f - p->aCoord[4].f;
+      case 2:  area *= p->aCoord[3].f - p->aCoord[2].f;
+      default: area *= p->aCoord[1].f - p->aCoord[0].f;
+    }
+  }else
+#endif
+  {
+    switch( pRtree->nDim ){
+      case 5:  area  = p->aCoord[9].i - p->aCoord[8].i;
+      case 4:  area *= p->aCoord[7].i - p->aCoord[6].i;
+      case 3:  area *= p->aCoord[5].i - p->aCoord[4].i;
+      case 2:  area *= p->aCoord[3].i - p->aCoord[2].i;
+      default: area *= p->aCoord[1].i - p->aCoord[0].i;
+    }
+  }
+  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 = 0;
+  int ii = pRtree->nDim2 - 2;
+  do{
+    margin += (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));
+    ii -= 2;
+  }while( ii>=0 );
+  return margin;
+}
+
+/*
+** Store the union of cells p1 and p2 in p1.
+*/
+static void cellUnion(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){
+  int ii = 0;
+  if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
+    do{
+      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);
+      ii += 2;
+    }while( ii<pRtree->nDim2 );
+  }else{
+    do{
+      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);
+      ii += 2;
+    }while( ii<pRtree->nDim2 );
+  }
+}
+
+/*
+** 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->nDim2; 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->nDim2; 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) */
+
+/*
+** A constraint has failed while inserting a row into an rtree table. 
+** Assuming no OOM error occurs, this function sets the error message 
+** (at pRtree->base.zErrMsg) to an appropriate value and returns
+** SQLITE_CONSTRAINT.
+**
+** Parameter iCol is the index of the leftmost column involved in the
+** constraint failure. If it is 0, then the constraint that failed is
+** the unique constraint on the id column. Otherwise, it is the rtree
+** (c1<=c2) constraint on columns iCol and iCol+1 that has failed.
+**
+** If an OOM occurs, SQLITE_NOMEM is returned instead of SQLITE_CONSTRAINT.
+*/
+static int rtreeConstraintError(Rtree *pRtree, int iCol){
+  sqlite3_stmt *pStmt = 0;
+  char *zSql; 
+  int rc;
+
+  assert( iCol==0 || iCol%2 );
+  zSql = sqlite3_mprintf("SELECT * FROM %Q.%Q", pRtree->zDb, pRtree->zName);
+  if( zSql ){
+    rc = sqlite3_prepare_v2(pRtree->db, zSql, -1, &pStmt, 0);
+  }else{
+    rc = SQLITE_NOMEM;
+  }
+  sqlite3_free(zSql);
+
+  if( rc==SQLITE_OK ){
+    if( iCol==0 ){
+      const char *zCol = sqlite3_column_name(pStmt, 0);
+      pRtree->base.zErrMsg = sqlite3_mprintf(
+          "UNIQUE constraint failed: %s.%s", pRtree->zName, zCol
+      );
+    }else{
+      const char *zCol1 = sqlite3_column_name(pStmt, iCol);
+      const char *zCol2 = sqlite3_column_name(pStmt, iCol+1);
+      pRtree->base.zErrMsg = sqlite3_mprintf(
+          "rtree constraint failed: %s.(%s<=%s)", pRtree->zName, zCol1, zCol2
+      );
+    }
+  }
+
+  sqlite3_finalize(pStmt);
+  return (rc==SQLITE_OK ? SQLITE_CONSTRAINT : rc);
+}
+
+
+
+/*
+** 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->nDim2 + 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 = rtreeConstraintError(pRtree, ii+1);
+          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 = rtreeConstraintError(pRtree, ii+1);
+          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 = rtreeConstraintError(pRtree, 0);
+            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;
+}
+
+/*
+** Called when a transaction starts.
+*/
+static int rtreeBeginTransaction(sqlite3_vtab *pVtab){
+  Rtree *pRtree = (Rtree *)pVtab;
+  assert( pRtree->inWrTrans==0 );
+  pRtree->inWrTrans++;
+  return SQLITE_OK;
+}
+
+/*
+** Called when a transaction completes (either by COMMIT or ROLLBACK).
+** The sqlite3_blob object should be released at this point.
+*/
+static int rtreeEndTransaction(sqlite3_vtab *pVtab){
+  Rtree *pRtree = (Rtree *)pVtab;
+  pRtree->inWrTrans = 0;
+  nodeBlobReset(pRtree);
+  return SQLITE_OK;
+}
+
+/*
+** 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;
+
+  rc = sqlite3_table_column_metadata(
+      db, pRtree->zDb, "sqlite_stat1",0,0,0,0,0,0
+  );
+  if( rc!=SQLITE_OK ){
+    pRtree->nRowEst = RTREE_DEFAULT_ROWEST;
+    return rc==SQLITE_ERROR ? SQLITE_OK : rc;
+  }
+  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 */
+  rtreeBeginTransaction,      /* xBegin - begin transaction */
+  rtreeEndTransaction,        /* xSync - sync transaction */
+  rtreeEndTransaction,        /* xCommit - commit transaction */
+  rtreeEndTransaction,        /* 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 8
+  static const char *azSql[N_STATEMENT] = {
+    /* Write the xxx_node table */
+    "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->pWriteNode;
+  appStmt[1] = &pRtree->pDeleteNode;
+  appStmt[2] = &pRtree->pReadRowid;
+  appStmt[3] = &pRtree->pWriteRowid;
+  appStmt[4] = &pRtree->pDeleteRowid;
+  appStmt[5] = &pRtree->pReadParent;
+  appStmt[6] = &pRtree->pWriteParent;
+  appStmt[7] = &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 = (u8)((argc-4)/2);
+  pRtree->nDim2 = pRtree->nDim*2;
+  pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;
+  pRtree->eCoordType = (u8)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 = (u8)sqlite3_value_int(apArg[0]);
+  tree.nDim2 = tree.nDim*2;
+  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.nDim2; 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