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Overview
Comment:Import 'rtree' extension. (CVS 5159)
Downloads: Tarball | ZIP archive | SQL archive
Timelines: family | ancestors | descendants | both | trunk
Files: files | file ages | folders
SHA1: b104dcd6adadbd3fe15a348fe9d4d290119e139e
User & Date: danielk1977 2008-05-26 18:41:54
Context
2008-05-26
20:19
Update the amalgamation builder to incorporate the RTREE extension. (CVS 5160) check-in: aa8eba33 user: drh tags: trunk
18:41
Import 'rtree' extension. (CVS 5159) check-in: b104dcd6 user: danielk1977 tags: trunk
18:33
Fix the LIKE query optimizer so that it works with LIKE patterns ending in '@%' on NOCASE columns. Ticket #3139. (CVS 5158) check-in: 33548744 user: drh tags: trunk
Changes
Hide Diffs Unified Diffs Ignore Whitespace Patch

Added ext/rtree/README.























































































































































































































































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This directory contains an SQLite extension that implements a virtual 
table type that allows users to create, query and manipulate r-tree[1] 
data structures inside of SQLite databases. Users create, populate 
and query r-tree structures using ordinary SQL statements.

    1.  SQL Interface

        1.1  Table Creation
        1.2  Data Manipulation
        1.3  Data Querying
        1.4  Introspection and Analysis

    2.  Compilation and Deployment

    3.  References


1. SQL INTERFACE

  1.1 Table Creation.

    All r-tree virtual tables have an odd number of columns between
    3 and 11. Unlike regular SQLite tables, r-tree tables are strongly 
    typed. 

    The leftmost column is always the pimary key and contains 64-bit 
    integer values. Each subsequent column contains a 32-bit real
    value. For each pair of real values, the first (leftmost) must be 
    less than or greater than the second. R-tree tables may be 
    constructed using the following syntax:

      CREATE VIRTUAL TABLE <name> USING rtree(<column-names>)

    For example:

      CREATE VIRTUAL TABLE boxes USING rtree(boxno, xmin, xmax, ymin, ymax);
      CREATE VIRTUAL TABLE boxes USING rtree(1, 1.0, 3.0, 2.0, 4.0);

    Constructing a virtual r-tree table <name> creates the following three
    real tables in the database to store the data structure:

      <name>_node
      <name>_rowid
      <name>_parent

    Dropping or modifying the contents of these tables directly will
    corrupt the r-tree structure. To delete an r-tree from a database,
    use a regular DROP TABLE statement:

      DROP TABLE <name>;

    Dropping the main r-tree table automatically drops the automatically
    created tables. 

  1.2 Data Manipulation (INSERT, UPDATE, DELETE).

    The usual INSERT, UPDATE or DELETE syntax is used to manipulate data
    stored in an r-tree table. Please note the following:

      * Inserting a NULL value into the primary key column has the
        same effect as inserting a NULL into an INTEGER PRIMARY KEY
        column of a regular table. The system automatically assigns
        an unused integer key value to the new record. Usually, this
        is one greater than the largest primary key value currently
        present in the table.

      * Attempting to insert a duplicate primary key value fails with
        an SQLITE_CONSTRAINT error.

      * Attempting to insert or modify a record such that the value
        stored in the (N*2)th column is greater than that stored in
        the (N*2+1)th column fails with an SQLITE_CONSTRAINT error.

      * When a record is inserted, values are always converted to 
        the required type (64-bit integer or 32-bit real) as if they
        were part of an SQL CAST expression. Non-numeric strings are
        converted to zero.

  1.3 Queries.

    R-tree tables may be queried using all of the same SQL syntax supported
    by regular tables. However, some query patterns are more efficient faster
    than others.

    R-trees support fast lookup by primary key value (O(logN), like 
    regular tables).

    Any combination of equality and range (<, <=, >, >=) constraints
    on spatial data columns may be used to optimize other queries. This
    is the key advantage to using r-tree tables instead of creating 
    indices on regular tables.

  1.4 Introspection and Analysis.

    TODO: Describe rtreenode() and rtreedepth() functions.


2. COMPILATION AND USAGE

  The easiest way to compile and use the ICU extension is to build
  and use it as a dynamically loadable SQLite extension. To do this
  using gcc on *nix:

    gcc -shared rtree.c -o libSqliteRtree.so

  You may need to add "-I" flags so that gcc can find sqlite3ext.h
  and sqlite3.h. The resulting shared lib, libSqliteIcu.so, may be
  loaded into sqlite in the same way as any other dynamicly loadable
  extension.


3. REFERENCES

  [1]  Atonin Guttman, "R-trees - A Dynamic Index Structure For Spatial 
       Searching", University of California Berkeley, 1984.

  [2]  Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, Bernhard Seeger,
       "The R*-tree: An Efficient and Robust Access Method for Points and
       Rectangles", Universitaet Bremen, 1990.



Added ext/rtree/rtree.c.





















































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































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/*
** 2001 September 15
**
** The author disclaims copyright to this source code.  In place of
** a legal notice, here is a blessing:
**
**    May you do good and not evil.
**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** This file contains code for implementations of the r-tree and r*-tree
** algorithms packaged as an SQLite virtual table module.
**
** $Id: rtree.c,v 1.1 2008/05/26 18:41:54 danielk1977 Exp $
*/

#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RTREE)

/*
** This file contains an implementation of a couple of different variants
** of the r-tree algorithm. See the README file for further details. The 
** same data-structure is used for all, but the algorithms for insert and
** delete operations vary. The variants used are selected at compile time 
** by defining the following symbols:
*/

/* Either, both or none of the following may be set to activate 
** r*tree variant algorithms.
*/
#define VARIANT_RSTARTREE_CHOOSESUBTREE 0
#define VARIANT_RSTARTREE_REINSERT      1

/* 
** Exactly one of the following must be set to 1.
*/
#define VARIANT_GUTTMAN_QUADRATIC_SPLIT 0
#define VARIANT_GUTTMAN_LINEAR_SPLIT    0
#define VARIANT_RSTARTREE_SPLIT         1

#define VARIANT_GUTTMAN_SPLIT \
        (VARIANT_GUTTMAN_LINEAR_SPLIT||VARIANT_GUTTMAN_QUADRATIC_SPLIT)

#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
  #define PickNext QuadraticPickNext
  #define PickSeeds QuadraticPickSeeds
  #define AssignCells splitNodeGuttman
#endif
#if VARIANT_GUTTMAN_LINEAR_SPLIT
  #define PickNext LinearPickNext
  #define PickSeeds LinearPickSeeds
  #define AssignCells splitNodeGuttman
#endif
#if VARIANT_RSTARTREE_SPLIT
  #define AssignCells splitNodeStartree
#endif


#ifndef SQLITE_CORE
  #include "sqlite3ext.h"
  SQLITE_EXTENSION_INIT1
#else
  #include "sqlite3.h"
#endif

#include <string.h>
#include <assert.h>

typedef sqlite3_int64 i64;
typedef unsigned char u8;
typedef unsigned int u32;

typedef struct Rtree Rtree;
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;

/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */
#define RTREE_MAX_DIMENSIONS 5

/* Size of hash table Rtree.aHash. This hash table is not expected to
** ever contain very many entries, so a fixed number of buckets is 
** used.
*/
#define HASHSIZE 128

/* 
** An rtree virtual-table object.
*/
struct Rtree {
  sqlite3_vtab base;
  sqlite3 *db;                /* Host database connection */
  int iNodeSize;              /* Size in bytes of each node in the node table */
  int nDim;                   /* Number of dimensions */
  int nBytesPerCell;          /* Bytes consumed per cell */
  int iDepth;                 /* Current depth of the r-tree structure */
  char *zDb;                  /* Name of database containing r-tree table */
  char *zName;                /* Name of r-tree table */ 
  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ 
  int nBusy;                  /* Current number of users of this structure */

  /* List of nodes removed during a CondenseTree operation. List is
  ** linked together via the pointer normally used for hash chains -
  ** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree 
  ** headed by the node (leaf nodes have RtreeNode.iNode==0).
  */
  RtreeNode *pDeleted;
  int iReinsertHeight;        /* Height of sub-trees Reinsert() has run on */

  /* Statements to read/write/delete a record from xxx_node */
  sqlite3_stmt *pReadNode;
  sqlite3_stmt *pWriteNode;
  sqlite3_stmt *pDeleteNode;

  /* Statements to read/write/delete a record from xxx_rowid */
  sqlite3_stmt *pReadRowid;
  sqlite3_stmt *pWriteRowid;
  sqlite3_stmt *pDeleteRowid;

  /* Statements to read/write/delete a record from xxx_parent */
  sqlite3_stmt *pReadParent;
  sqlite3_stmt *pWriteParent;
  sqlite3_stmt *pDeleteParent;
};

/*
** The minimum number of cells allowed for a node is a third of the 
** maximum. In Gutman's notation:
**
**     m = M/3
**
** If an R*-tree "Reinsert" operation is required, the same number of
** cells are removed from the overfull node and reinserted into the tree.
*/
#define RTREE_MINCELLS(p) ((((p)->iNodeSize-4)/(p)->nBytesPerCell)/3)
#define RTREE_REINSERT(p) RTREE_MINCELLS(p)
#define RTREE_MAXCELLS 51

/* 
** An rtree cursor object.
*/
struct RtreeCursor {
  sqlite3_vtab_cursor base;
  RtreeNode *pNode;                 /* Node cursor is currently pointing at */
  int iCell;                        /* Index of current cell in pNode */
  int iStrategy;                    /* Copy of idxNum search parameter */
  int nConstraint;                  /* Number of entries in aConstraint */
  RtreeConstraint *aConstraint;     /* Search constraints. */
};

/*
** A search constraint.
*/
struct RtreeConstraint {
  int iCoord;                       /* Index of constrained coordinate */
  int op;                           /* Constraining operation */
  float rValue;                     /* Constraint value. */
};

/* Possible values for RtreeConstraint.op */
#define RTREE_EQ 0x41
#define RTREE_LE 0x42
#define RTREE_LT 0x43
#define RTREE_GE 0x44
#define RTREE_GT 0x45

/* 
** An rtree structure node.
**
** Data format (RtreeNode.zData):
**
**   1. If the node is the root node (node 1), then the first 2 bytes
**      of the node contain the tree depth as a big-endian integer.
**      For non-root nodes, the first 2 bytes are left unused.
**
**   2. The next 2 bytes contain the number of entries currently 
**      stored in the node.
**
**   3. The remainder of the node contains the node entries. Each entry
**      consists of a single 8-byte integer followed by an even number
**      of 4-byte coordinates. For leaf nodes the integer is the rowid
**      of a record. For internal nodes it is the node number of a
**      child page.
*/
struct RtreeNode {
  RtreeNode *pParent;               /* Parent node */
  i64 iNode;
  int nRef;
  int isDirty;
  u8 *zData;
  RtreeNode *pNext;                 /* Next node in this hash chain */
};
#define NCELL(pNode) readInt16(&(pNode)->zData[2])

/* 
** Structure to store a deserialized rtree record.
*/
struct RtreeCell {
  i64 iRowid;
  float aCoord[RTREE_MAX_DIMENSIONS*2];
};

#define MAX(x,y) ((x) < (y) ? (y) : (x))
#define MIN(x,y) ((x) > (y) ? (y) : (x))

/*
** 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 float readReal32(u8 *p){
  u32 i = (
    (((u32)p[0]) << 24) + 
    (((u32)p[1]) << 16) + 
    (((u32)p[2]) <<  8) + 
    (((u32)p[3]) <<  0)
  );
  return *(float *)&i;
}
static i64 readInt64(u8 *p){
  return (
    (((i64)p[0]) << 56) + 
    (((i64)p[1]) << 48) + 
    (((i64)p[2]) << 40) + 
    (((i64)p[3]) << 32) + 
    (((i64)p[4]) << 24) + 
    (((i64)p[5]) << 16) + 
    (((i64)p[6]) <<  8) + 
    (((i64)p[7]) <<  0)
  );
}

/*
** Functions to serialize a 16 bit integer, 32 bit real number and
** 64 bit integer. The value returned is the number of bytes written
** to the argument buffer (always 2, 4 and 8 respectively).
*/
static int writeInt16(u8 *p, int i){
  p[0] = (i>> 8)&0xFF;
  p[1] = (i>> 0)&0xFF;
  return 2;
}
static int writeReal32(u8 *p, float f){
  u32 i;
  assert( sizeof(float)==4 );
  assert( sizeof(u32)==4 );
  i = *(u32 *)&f;
  p[0] = (i>>24)&0xFF;
  p[1] = (i>>16)&0xFF;
  p[2] = (i>> 8)&0xFF;
  p[3] = (i>> 0)&0xFF;
  return 4;
}
static int writeInt64(u8 *p, i64 i){
  p[0] = (i>>56)&0xFF;
  p[1] = (i>>48)&0xFF;
  p[2] = (i>>40)&0xFF;
  p[3] = (i>>32)&0xFF;
  p[4] = (i>>24)&0xFF;
  p[5] = (i>>16)&0xFF;
  p[6] = (i>> 8)&0xFF;
  p[7] = (i>> 0)&0xFF;
  return 8;
}

/*
** Increment the reference count of node p.
*/
static void nodeReference(RtreeNode *p){
  if( p ){
    p->nRef++;
  }
}

/*
** Clear the content of node p (set all bytes to 0x00).
*/
static void nodeZero(Rtree *pRtree, RtreeNode *p){
  if( p ){
    memset(&p->zData[2], 0, pRtree->iNodeSize-2);
    p->isDirty = 1;
  }
}

/*
** Given a node number iNode, return the corresponding key to use
** in the Rtree.aHash table.
*/
static int nodeHash(i64 iNode){
  return (
    (iNode>>56) ^ (iNode>>48) ^ (iNode>>40) ^ (iNode>>32) ^ 
    (iNode>>24) ^ (iNode>>16) ^ (iNode>> 8) ^ (iNode>> 0)
  ) % HASHSIZE;
}

/*
** Search the node hash table for node iNode. If found, return a pointer
** to it. Otherwise, return 0.
*/
static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
  RtreeNode *p;
  assert( iNode!=0 );
  for(p=pRtree->aHash[nodeHash(iNode)]; p && p->iNode!=iNode; p=p->pNext);
  return p;
}

/*
** Add node pNode to the node hash table.
*/
static void nodeHashInsert(Rtree *pRtree, RtreeNode *pNode){
  if( pNode ){
    int iHash;
    assert( pNode->pNext==0 );
    iHash = nodeHash(pNode->iNode);
    pNode->pNext = pRtree->aHash[iHash];
    pRtree->aHash[iHash] = pNode;
  }
}

/*
** Remove node pNode from the node hash table.
*/
static void nodeHashDelete(Rtree *pRtree, RtreeNode *pNode){
  RtreeNode **pp;
  if( pNode->iNode!=0 ){
    pp = &pRtree->aHash[nodeHash(pNode->iNode)];
    for( ; (*pp)!=pNode; pp = &(*pp)->pNext){ assert(*pp); }
    *pp = pNode->pNext;
    pNode->pNext = 0;
  }
}

/*
** Allocate and return new r-tree node. Initially, (RtreeNode.iNode==0),
** indicating that node has not yet been assigned a node number. It is
** assigned a node number when nodeWrite() is called to write the
** node contents out to the database.
*/
static RtreeNode *nodeNew(Rtree *pRtree, RtreeNode *pParent, int zero){
  RtreeNode *pNode;
  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
  if( pNode ){
    memset(pNode, 0, sizeof(RtreeNode) + (zero?pRtree->iNodeSize:0));
    pNode->zData = (u8 *)&pNode[1];
    pNode->nRef = 1;
    pNode->pParent = pParent;
    pNode->isDirty = 1;
    nodeReference(pParent);
  }
  return pNode;
}

/*
** Obtain a reference to an r-tree node.
*/
static int
nodeAcquire(
  Rtree *pRtree,             /* R-tree structure */
  i64 iNode,                 /* Node number to load */
  RtreeNode *pParent,        /* Either the parent node or NULL */
  RtreeNode **ppNode         /* OUT: Acquired node */
){
  int rc;
  RtreeNode *pNode;

  /* Check if the requested node is already in the hash table. If so,
  ** increase its reference count and return it.
  */
  if( (pNode = nodeHashLookup(pRtree, iNode)) ){
    assert( !pParent || !pNode->pParent || pNode->pParent==pParent );
    if( pParent ){
      pNode->pParent = pParent;
    }
    pNode->nRef++;
    *ppNode = pNode;
    return SQLITE_OK;
  }

  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
  if( !pNode ){
    *ppNode = 0;
    return SQLITE_NOMEM;
  }
  pNode->pParent = pParent;
  pNode->zData = (u8 *)&pNode[1];
  pNode->nRef = 1;
  pNode->iNode = iNode;
  pNode->isDirty = 0;
  pNode->pNext = 0;

  sqlite3_bind_int64(pRtree->pReadNode, 1, iNode);
  rc = sqlite3_step(pRtree->pReadNode);
  if( rc==SQLITE_ROW ){
    const u8 *zBlob = sqlite3_column_blob(pRtree->pReadNode, 0);
    memcpy(pNode->zData, zBlob, pRtree->iNodeSize);
    nodeReference(pParent);
  }else{
    sqlite3_free(pNode);
    pNode = 0;
  }

  *ppNode = pNode;
  rc = sqlite3_reset(pRtree->pReadNode);

  if( rc==SQLITE_OK && iNode==1 ){
    pRtree->iDepth = readInt16(pNode->zData);
  }

  assert( (rc==SQLITE_OK && pNode) || (pNode==0 && rc!=SQLITE_OK) );
  nodeHashInsert(pRtree, pNode);

  return rc;
}

/*
** Overwrite cell iCell of node pNode with the contents of pCell.
*/
static void nodeOverwriteCell(
  Rtree *pRtree, 
  RtreeNode *pNode,  
  RtreeCell *pCell, 
  int iCell
){
  int ii;
  u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
  p += writeInt64(p, pCell->iRowid);
  for(ii=0; ii<(pRtree->nDim*2); ii++){
    p += writeReal32(p, pCell->aCoord[ii]);
  }
  pNode->isDirty = 1;
}

/*
** Remove cell the cell with index iCell from node pNode.
*/
static void nodeDeleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell){
  u8 *pDst = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
  u8 *pSrc = &pDst[pRtree->nBytesPerCell];
  int nByte = (NCELL(pNode) - iCell - 1) * pRtree->nBytesPerCell;
  memmove(pDst, pSrc, nByte);
  writeInt16(&pNode->zData[2], NCELL(pNode)-1);
  pNode->isDirty = 1;
}

/*
** Insert the contents of cell pCell into node pNode. If the insert
** is successful, return SQLITE_OK.
**
** If there is not enough free space in pNode, return SQLITE_FULL.
*/
static int
nodeInsertCell(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  RtreeCell *pCell 
){
  int nCell;                    /* Current number of cells in pNode */
  int nMaxCell;                 /* Maximum number of cells for pNode */

  nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;
  nCell = NCELL(pNode);

  assert(nCell<=nMaxCell);

  if( nCell<nMaxCell ){
    nodeOverwriteCell(pRtree, pNode, pCell, nCell);
    writeInt16(&pNode->zData[2], nCell+1);
    pNode->isDirty = 1;
  }

  return (nCell==nMaxCell);
}

/*
** If the node is dirty, write it out to the database.
*/
static int
nodeWrite(Rtree *pRtree, RtreeNode *pNode){
  int rc = SQLITE_OK;
  if( pNode->isDirty ){
    sqlite3_stmt *p = pRtree->pWriteNode;
    if( pNode->iNode ){
      sqlite3_bind_int64(p, 1, pNode->iNode);
    }else{
      sqlite3_bind_null(p, 1);
    }
    sqlite3_bind_blob(p, 2, pNode->zData, pRtree->iNodeSize, SQLITE_STATIC);
    sqlite3_step(p);
    pNode->isDirty = 0;
    rc = sqlite3_reset(p);
    if( pNode->iNode==0 && rc==SQLITE_OK ){
      pNode->iNode = sqlite3_last_insert_rowid(pRtree->db);
      nodeHashInsert(pRtree, pNode);
    }
  }
  return rc;
}

/*
** Release a reference to a node. If the node is dirty and the reference
** count drops to zero, the node data is written to the database.
*/
static int
nodeRelease(Rtree *pRtree, RtreeNode *pNode){
  int rc = SQLITE_OK;
  if( pNode ){
    assert( pNode->nRef>0 );
    pNode->nRef--;
    if( pNode->nRef==0 ){
      if( pNode->iNode==1 ){
        pRtree->iDepth = -1;
      }
      if( pNode->pParent ){
        rc = nodeRelease(pRtree, pNode->pParent);
      }
      if( rc==SQLITE_OK ){
        rc = nodeWrite(pRtree, pNode);
      }
      nodeHashDelete(pRtree, pNode);
      sqlite3_free(pNode);
    }
  }
  return rc;
}

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

/*
** Return coordinate iCoord from cell iCell in node pNode.
*/
static float nodeGetCoord(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  int iCell,
  int iCoord
){
  return readReal32(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord]);
}

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


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

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

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

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

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

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

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

  return rc;
}

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

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

  return rc;
}

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

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

/* 
** Cursor pCursor currently points to a cell in a non-leaf page.
** Return true if the sub-tree headed by the cell is filtered
** (excluded) by the constraints in the pCursor->aConstraint[] 
** array, or false otherwise.
*/
static int testRtreeCell(Rtree *pRtree, RtreeCursor *pCursor){
  RtreeCell cell;
  int ii;

  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];

    float cell_min = cell.aCoord[(p->iCoord>>1)*2];
    float cell_max = cell.aCoord[(p->iCoord>>1)*2+1];
    assert( cell_min<=cell_max );

    switch( p->op ){
      case RTREE_LE: case RTREE_LT: {
        if( p->rValue<cell_min ){
          return 1;
        }
        break;
      }

      case RTREE_GE: case RTREE_GT: {
        if( p->rValue>cell_max ){
          return 1;
        }
        break;
      }

      case RTREE_EQ: {
        if( p->rValue>cell_max || p->rValue<cell_min ){
          return 1;
        }
        break;
      }
#ifndef NDEBUG
      default: assert(!"Internal error");
#endif
    }
  }

  return 0;
}

/* 
** Return true if the cell that cursor pCursor currently points to
** would be filtered (excluded) by the constraints in the 
** pCursor->aConstraint[] array, or false otherwise.
**
** This function assumes that the cell is part of a leaf node.
*/
static int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor){
  RtreeCell cell;
  int ii;

  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    float cell_val = cell.aCoord[p->iCoord];
    int res;
    switch( p->op ){
      case RTREE_LE: res = (cell_val<=p->rValue); break;
      case RTREE_LT: res = (cell_val<p->rValue);  break;
      case RTREE_GE: res = (cell_val>=p->rValue); break;
      case RTREE_GT: res = (cell_val>p->rValue);  break;
      case RTREE_EQ: res = (cell_val==p->rValue); break;
#ifndef NDEBUG
      default: assert(!"Internal error");
#endif
    }
    if( !res ) return 1;
  }

  return 0;
}

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

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

  assert( iHeight>=0 );

  if( iHeight==0 ){
    isEof = testRtreeEntry(pRtree, pCursor);
  }else{
    isEof = testRtreeCell(pRtree, pCursor);
  }
  if( isEof || iHeight==0 ){
    *pEof = isEof;
    return SQLITE_OK;
  }

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

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

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

  *pEof = isEof;
  return SQLITE_OK;
}

/*
** One of the cells in node pNode is guaranteed to have a 64-bit 
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(Rtree *pRtree, RtreeNode *pNode, i64 iRowid){
  int ii;
  for(ii=0; nodeGetRowid(pRtree, pNode, ii)!=iRowid; ii++){
    assert( ii<(NCELL(pNode)-1) );
  }
  return ii;
}

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

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

  if( pCsr->iStrategy==1 ){
    /* This "scan" is a direct lookup by rowid. There is no next entry. */
    nodeRelease(pRtree, pCsr->pNode);
    pCsr->pNode = 0;
  }

  else if( pCsr->pNode ){
    /* Move to the next entry that matches the configured constraints. */
    int iHeight = 0;
    while( pCsr->pNode ){
      RtreeNode *pNode = pCsr->pNode;
      int nCell = NCELL(pNode);
      for(pCsr->iCell++; pCsr->iCell<nCell; pCsr->iCell++){
        int isEof;
        rc = descendToCell(pRtree, pCsr, iHeight, &isEof);
        if( rc!=SQLITE_OK || !isEof ){
          return rc;
        }
      }
      pCsr->pNode = pNode->pParent;
      pCsr->iCell = nodeParentIndex(pRtree, pNode);
      nodeReference(pCsr->pNode);
      nodeRelease(pRtree, pNode);
      iHeight++;
    }
  }

  return rc;
}

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

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

  return SQLITE_OK;
}

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

  if( i==0 ){
    i64 iRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
    sqlite3_result_int64(ctx, iRowid);
  }else{
    float fCoord = nodeGetCoord(pRtree, pCsr->pNode, pCsr->iCell, i-1);
    sqlite3_result_double(ctx, fCoord);
  }

  return SQLITE_OK;
}

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


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

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

  rtreeReference(pRtree);

  sqlite3_free(pCsr->aConstraint);
  pCsr->aConstraint = 0;
  pCsr->iStrategy = idxNum;

  if( idxNum==1 ){
    /* Special case - lookup by rowid. */
    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
    i64 iRowid = sqlite3_value_int64(argv[0]);
    rc = findLeafNode(pRtree, iRowid, &pLeaf);
    pCsr->pNode = pLeaf; 
    if( pLeaf && rc==SQLITE_OK ){
      pCsr->iCell = nodeRowidIndex(pRtree, pLeaf, iRowid);
    }
  }else{
    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
    ** with the configured constraints. 
    */
    if( argc>0 ){
      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
      pCsr->nConstraint = argc;
      if( !pCsr->aConstraint ){
        rc = SQLITE_NOMEM;
      }else{
        assert( (idxStr==0 && argc==0) || strlen(idxStr)==argc*2 );
        for(ii=0; ii<argc; ii++){
          RtreeConstraint *p = &pCsr->aConstraint[ii];
          p->op = idxStr[ii*2];
          p->iCoord = idxStr[ii*2+1]-'a';
          p->rValue = sqlite3_value_double(argv[ii]);
        }
      }
    }
  
    if( rc==SQLITE_OK ){
      pCsr->pNode = 0;
      rc = nodeAcquire(pRtree, 1, 0, &pRoot);
    }
    if( rc==SQLITE_OK ){
      int isEof = 1;
      int nCell = NCELL(pRoot);
      pCsr->pNode = pRoot;
      for(pCsr->iCell=0; rc==SQLITE_OK && pCsr->iCell<nCell; pCsr->iCell++){
        assert( pCsr->pNode==pRoot );
        rc = descendToCell(pRtree, pCsr, pRtree->iDepth, &isEof);
        if( !isEof ){
          break;
        }
      }
      if( rc==SQLITE_OK && isEof ){
        assert( pCsr->pNode==pRoot );
        nodeRelease(pRtree, pRoot);
        pCsr->pNode = 0;
      }
      assert( rc!=SQLITE_OK || !pCsr->pNode || pCsr->iCell<NCELL(pCsr->pNode) );
    }
  }

  rtreeRelease(pRtree);
  return rc;
}

/*
** Rtree virtual table module xBestIndex method. There are three
** table scan strategies to choose from (in order from most to 
** least desirable):
**
**   idxNum     idxStr        Strategy
**   ------------------------------------------------
**     1        Unused        Direct lookup by rowid.
**     2        See below     R-tree query.
**     3        Unused        Full table scan.
**   ------------------------------------------------
**
** If strategy 1 or 3 is used, then idxStr is not meaningful. If strategy
** 2 is used, idxStr is formatted to contain 2 bytes for each 
** constraint used. The first two bytes of idxStr correspond to 
** the constraint in sqlite3_index_info.aConstraintUsage[] with
** (argvIndex==1) etc.
**
** The first of each pair of bytes in idxStr identifies the constraint
** operator as follows:
**
**   Operator    Byte Value
**   ----------------------
**      =        0x41 ('A')
**     <=        0x42 ('B')
**      <        0x43 ('C')
**     >=        0x44 ('D')
**      >        0x45 ('E')
**   ----------------------
**
** The second of each pair of bytes identifies the coordinate column
** to which the constraint applies. The leftmost coordinate column
** is 'a', the second from the left 'b' etc.
*/
static int rtreeBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
  int rc = SQLITE_OK;
  int ii;

  int iIdx = 0;
  char zIdxStr[RTREE_MAX_DIMENSIONS*2+1];
  memset(zIdxStr, 0, RTREE_MAX_DIMENSIONS*2+1);

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

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

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

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

/*
** Return the N-dimensional volumn of the cell stored in *p.
*/
static float cellArea(Rtree *pRtree, RtreeCell *p){
  float area = 1.0;
  int ii;
  for(ii=0; ii<(pRtree->nDim*2); ii+=2){
    area = area * (p->aCoord[ii+1] - p->aCoord[ii]);
  }
  return area;
}

/*
** Return the margin length of cell p. The margin length is the sum
** of the objects size in each dimension.
*/
static float cellMargin(Rtree *pRtree, RtreeCell *p){
  float margin = 0.0;
  int ii;
  for(ii=0; ii<(pRtree->nDim*2); ii+=2){
    margin += (p->aCoord[ii+1] - p->aCoord[ii]);
  }
  return margin;
}

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

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

#if VARIANT_RSTARTREE_CHOOSESUBTREE || VARIANT_RSTARTREE_SPLIT
static float cellOverlap(
  Rtree *pRtree, 
  RtreeCell *p, 
  RtreeCell *aCell, 
  int nCell, 
  int iExclude
){
  int ii;
  float overlap = 0.0;
  for(ii=0; ii<nCell; ii++){
    if( ii!=iExclude ){
      int jj;
      float o = 1.0;
      for(jj=0; jj<(pRtree->nDim*2); jj+=2){

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

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

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


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

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

    float fMinGrowth;
    float fMinArea;
    float fMinOverlap;

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

    RtreeCell *aCell = 0;

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

    /* Select the child node which will be enlarged the least if pCell
    ** is inserted into it. Resolve ties by choosing the entry with
    ** the smallest area.
    */
    for(iCell=0; iCell<nCell; iCell++){
      float growth;
      float area;
      float overlap = 0.0;
      nodeGetCell(pRtree, pNode, iCell, &cell);
      growth = cellGrowth(pRtree, &cell, pCell);
      area = cellArea(pRtree, &cell);
#if VARIANT_RSTARTREE_CHOOSESUBTREE
      if( ii==(pRtree->iDepth-1) ){
        overlap = cellOverlapEnlargement(pRtree,&cell,pCell,aCell,nCell,iCell);
      }
#endif
      if( (iCell==0) 
       || (overlap<fMinOverlap) 
       || (overlap==fMinOverlap && growth<fMinGrowth)
       || (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
      ){
        fMinOverlap = overlap;
        fMinGrowth = growth;
        fMinArea = area;
        iBest = cell.iRowid;
      }
    }

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

  *ppLeaf = pNode;
  return rc;
}

/*
** A cell with the same content as pCell has just been inserted into
** the node pNode. This function updates the bounding box cells in
** all ancestor elements.
*/
static void AdjustTree(
  Rtree *pRtree,                    /* Rtree table */
  RtreeNode *pNode,                 /* Adjust ancestry of this node. */
  RtreeCell *pCell                  /* This cell was just inserted */
){
  RtreeNode *p = pNode;
  while( p->pParent ){
    RtreeCell cell;
    RtreeNode *pParent = p->pParent;
    int iCell = nodeParentIndex(pRtree, p);

    nodeGetCell(pRtree, pParent, iCell, &cell);
    if( cellGrowth(pRtree, &cell, pCell)>0.0 ){
      cellUnion(pRtree, &cell, pCell);
      nodeOverwriteCell(pRtree, pParent, &cell, iCell);
    }
 
    p = pParent;
  }
}

/*
** Write mapping (iRowid->iNode) to the <rtree>_rowid table.
*/
static int rowidWrite(Rtree *pRtree, sqlite3_int64 iRowid, sqlite3_int64 iNode){
  sqlite3_bind_int64(pRtree->pWriteRowid, 1, iRowid);
  sqlite3_bind_int64(pRtree->pWriteRowid, 2, iNode);
  sqlite3_step(pRtree->pWriteRowid);
  return sqlite3_reset(pRtree->pWriteRowid);
}

/*
** Write mapping (iNode->iPar) to the <rtree>_parent table.
*/
static int parentWrite(Rtree *pRtree, sqlite3_int64 iNode, sqlite3_int64 iPar){
  sqlite3_bind_int64(pRtree->pWriteParent, 1, iNode);
  sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
  sqlite3_step(pRtree->pWriteParent);
  return sqlite3_reset(pRtree->pWriteParent);
}

static int insertCell(Rtree *, RtreeNode *, RtreeCell *, int);

#if VARIANT_GUTTMAN_LINEAR_SPLIT
/*
** Implementation of the linear variant of the PickNext() function from
** Guttman[84].
*/
static RtreeCell *LinearPickNext(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  RtreeCell *pLeftBox, 
  RtreeCell *pRightBox,
  int *aiUsed
){
  int ii;
  for(ii=0; aiUsed[ii]; ii++);
  aiUsed[ii] = 1;
  return &aCell[ii];
}

/*
** Implementation of the linear variant of the PickSeeds() function from
** Guttman[84].
*/
static void LinearPickSeeds(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  int *piLeftSeed, 
  int *piRightSeed
){
  int i;
  int iLeftSeed = 0;
  int iRightSeed = 1;
  float maxNormalInnerWidth = 0.0;

  /* Pick two "seed" cells from the array of cells. The algorithm used
  ** here is the LinearPickSeeds algorithm from Gutman[1984]. The 
  ** indices of the two seed cells in the array are stored in local
  ** variables iLeftSeek and iRightSeed.
  */
  for(i=0; i<pRtree->nDim; i++){
    float x1 = aCell[0].aCoord[i*2];
    float x2 = aCell[0].aCoord[i*2+1];
    float x3 = x1;
    float x4 = x2;
    int jj;

    int iCellLeft = 0;
    int iCellRight = 0;

    for(jj=1; jj<nCell; jj++){
      float left = aCell[jj].aCoord[i*2];
      float right = aCell[jj].aCoord[i*2+1];

      if( left<x1 ) x1 = left;
      if( right>x4 ) x4 = right;
      if( left>x3 ){
        x3 = left;
        iCellRight = jj;
      }
      if( right<x2 ){
        x2 = right;
        iCellLeft = jj;
      }
    }

    if( x4!=x1 ){
      float normalwidth = (x3 - x2) / (x4 - x1);
      if( normalwidth>maxNormalInnerWidth ){
        iLeftSeed = iCellLeft;
        iRightSeed = iCellRight;
      }
    }
  }

  *piLeftSeed = iLeftSeed;
  *piRightSeed = iRightSeed;
}
#endif /* VARIANT_GUTTMAN_LINEAR_SPLIT */

#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
/*
** Implementation of the quadratic variant of the PickNext() function from
** Guttman[84].
*/
static RtreeCell *QuadraticPickNext(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  RtreeCell *pLeftBox, 
  RtreeCell *pRightBox,
  int *aiUsed
){
  #define FABS(a) ((a)<0.0?-1.0*(a):(a))

  int iSelect = -1;
  float fDiff;
  int ii;
  for(ii=0; ii<nCell; ii++){
    if( aiUsed[ii]==0 ){
      float left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
      float right = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
      float diff = FABS(right-left);
      if( iSelect<0 || diff>fDiff ){
        fDiff = diff;
        iSelect = ii;
      }
    }
  }
  aiUsed[iSelect] = 1;
  return &aCell[iSelect];
}

/*
** Implementation of the quadratic variant of the PickSeeds() function from
** Guttman[84].
*/
static void QuadraticPickSeeds(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  int *piLeftSeed, 
  int *piRightSeed
){
  int ii;
  int jj;

  int iLeftSeed = 0;
  int iRightSeed = 1;
  float fWaste = 0.0;

  for(ii=0; ii<nCell; ii++){
    for(jj=ii+1; jj<nCell; jj++){
      float right = cellArea(pRtree, &aCell[jj]);
      float growth = cellGrowth(pRtree, &aCell[ii], &aCell[jj]);
      float waste = growth - right;

      if( waste>fWaste ){
        iLeftSeed = ii;
        iRightSeed = jj;
        fWaste = waste;
      }
    }
  }

  *piLeftSeed = iLeftSeed;
  *piRightSeed = iRightSeed;
}
#endif /* VARIANT_GUTTMAN_QUADRATIC_SPLIT */

/*
** Arguments aIdx, aDistance and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to 
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to the indexed values in aDistance. For
** example, assuming the inputs:
**
**   aIdx      = { 0,   1,   2,   3 }
**   aDistance = { 5.0, 2.0, 7.0, 6.0 }
**
** this function sets the aIdx array to contain:
**
**   aIdx      = { 0,   1,   2,   3 }
**
** The aSpare array is used as temporary working space by the
** sorting algorithm.
*/
static void SortByDistance(
  int *aIdx, 
  int nIdx, 
  float *aDistance, 
  int *aSpare
){
  if( nIdx>1 ){
    int iLeft = 0;
    int iRight = 0;

    int nLeft = nIdx/2;
    int nRight = nIdx-nLeft;
    int *aLeft = aIdx;
    int *aRight = &aIdx[nLeft];

    SortByDistance(aLeft, nLeft, aDistance, aSpare);
    SortByDistance(aRight, nRight, aDistance, aSpare);

    memcpy(aSpare, aLeft, sizeof(int)*nLeft);
    aLeft = aSpare;

    while( iLeft<nLeft || iRight<nRight ){
      if( iLeft==nLeft ){
        aIdx[iLeft+iRight] = aRight[iRight];
        iRight++;
      }else if( iRight==nRight ){
        aIdx[iLeft+iRight] = aLeft[iLeft];
        iLeft++;
      }else{
        float fLeft = aDistance[aLeft[iLeft]];
        float fRight = aDistance[aRight[iRight]];
        if( fLeft<fRight ){
          aIdx[iLeft+iRight] = aLeft[iLeft];
          iLeft++;
        }else{
          aIdx[iLeft+iRight] = aRight[iRight];
          iRight++;
        }
      }
    }

#if 0
    /* Check that the sort worked */
    {
      int jj;
      for(jj=1; jj<nIdx; jj++){
        float left = aDistance[aIdx[jj-1]];
        float right = aDistance[aIdx[jj]];
        assert( left<=right );
      }
    }
#endif
  }
}

/*
** Arguments aIdx, aCell and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to 
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to dimension iDim of the cells in aCell. The
** minimum value of dimension iDim is considered first, the
** maximum used to break ties.
**
** The aSpare array is used as temporary working space by the
** sorting algorithm.
*/
static void SortByDimension(
  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(aLeft, nLeft, iDim, aCell, aSpare);
    SortByDimension(aRight, nRight, iDim, aCell, aSpare);

    memcpy(aSpare, aLeft, sizeof(int)*nLeft);
    aLeft = aSpare;
    while( iLeft<nLeft || iRight<nRight ){
      float xleft1 = aCell[aLeft[iLeft]].aCoord[iDim*2];
      float xleft2 = aCell[aLeft[iLeft]].aCoord[iDim*2+1];
      float xright1 = aCell[aRight[iRight]].aCoord[iDim*2];
      float xright2 = aCell[aRight[iRight]].aCoord[iDim*2+1];

      if( (iLeft!=nLeft) && ((iRight==nRight)
       || (xleft1<xright1)
       || (xleft1==xright1 && xleft2<xright2)
      )){
        aIdx[iLeft+iRight] = aLeft[iLeft];
        iLeft++;
      }else{
        aIdx[iLeft+iRight] = aRight[iRight];
        iRight++;
      }
    }

#if 0
    /* Check that the sort worked */
    {
      int jj;
      for(jj=1; jj<nIdx; jj++){
        float xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
        float xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
        float xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
        float xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
        assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
      }
    }
#endif
  }
}

#if VARIANT_RSTARTREE_SPLIT
/*
** Implementation of the R*-tree variant of SplitNode from Beckman[1990].
*/
static int splitNodeStartree(
  Rtree *pRtree,
  RtreeCell *aCell,
  int nCell,
  RtreeNode *pLeft,
  RtreeNode *pRight,
  RtreeCell *pBboxLeft,
  RtreeCell *pBboxRight
){
  int **aaSorted;
  int *aSpare;
  int ii;

  int iBestDim;
  int iBestSplit;
  float fBestMargin;

  int nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));

  aaSorted = (int **)sqlite3_malloc(nByte);
  if( !aaSorted ){
    return SQLITE_NOMEM;
  }

  aSpare = &((int *)&aaSorted[pRtree->nDim])[pRtree->nDim*nCell];
  memset(aaSorted, 0, nByte);
  for(ii=0; ii<pRtree->nDim; ii++){
    int jj;
    aaSorted[ii] = &((int *)&aaSorted[pRtree->nDim])[ii*nCell];
    for(jj=0; jj<nCell; jj++){
      aaSorted[ii][jj] = jj;
    }
    SortByDimension(aaSorted[ii], nCell, ii, aCell, aSpare);
  }

  for(ii=0; ii<pRtree->nDim; ii++){
    float margin = 0.0;
    float fBestOverlap;
    float fBestArea;
    int iBestLeft;
    int nLeft;

    for(
      nLeft=RTREE_MINCELLS(pRtree); 
      nLeft<=(nCell-RTREE_MINCELLS(pRtree)); 
      nLeft++
    ){
      RtreeCell left;
      RtreeCell right;
      int kk;
      float overlap;
      float area;

      memcpy(&left, &aCell[aaSorted[ii][0]], sizeof(RtreeCell));
      memcpy(&right, &aCell[aaSorted[ii][nCell-1]], sizeof(RtreeCell));
      for(kk=1; kk<(nCell-1); kk++){
        if( kk<nLeft ){
          cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
        }else{
          cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);
        }
      }
      margin += cellMargin(pRtree, &left);
      margin += cellMargin(pRtree, &right);
      overlap = cellOverlap(pRtree, &left, &right, 1, -1);
      area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
      if( (nLeft==RTREE_MINCELLS(pRtree))
       || (overlap<fBestOverlap)
       || (overlap==fBestOverlap && area<fBestArea)
      ){
        iBestLeft = nLeft;
        fBestOverlap = overlap;
        fBestArea = area;
      }
    }

    if( ii==0 || margin<fBestMargin ){
      iBestDim = ii;
      fBestMargin = margin;
      iBestSplit = iBestLeft;
    }
  }

  memcpy(pBboxLeft, &aCell[aaSorted[iBestDim][0]], sizeof(RtreeCell));
  memcpy(pBboxRight, &aCell[aaSorted[iBestDim][iBestSplit]], sizeof(RtreeCell));
  for(ii=0; ii<nCell; ii++){
    RtreeNode *pTarget = (ii<iBestSplit)?pLeft:pRight;
    RtreeCell *pBbox = (ii<iBestSplit)?pBboxLeft:pBboxRight;
    RtreeCell *pCell = &aCell[aaSorted[iBestDim][ii]];
    nodeInsertCell(pRtree, pTarget, pCell);
    cellUnion(pRtree, pBbox, pCell);
  }

  sqlite3_free(aaSorted);
  return SQLITE_OK;
}
#endif

#if VARIANT_GUTTMAN_SPLIT
/*
** Implementation of the regular R-tree SplitNode from Guttman[1984].
*/
static int splitNodeGuttman(
  Rtree *pRtree,
  RtreeCell *aCell,
  int nCell,
  RtreeNode *pLeft,
  RtreeNode *pRight,
  RtreeCell *pBboxLeft,
  RtreeCell *pBboxRight
){
  int iLeftSeed = 0;
  int iRightSeed = 1;
  int *aiUsed;
  int i;

  aiUsed = sqlite3_malloc(sizeof(int)*nCell);
  memset(aiUsed, 0, sizeof(int)*nCell);

  PickSeeds(pRtree, aCell, nCell, &iLeftSeed, &iRightSeed);

  memcpy(pBboxLeft, &aCell[iLeftSeed], sizeof(RtreeCell));
  memcpy(pBboxRight, &aCell[iRightSeed], sizeof(RtreeCell));
  nodeInsertCell(pRtree, pLeft, &aCell[iLeftSeed]);
  nodeInsertCell(pRtree, pRight, &aCell[iRightSeed]);
  aiUsed[iLeftSeed] = 1;
  aiUsed[iRightSeed] = 1;

  for(i=nCell-2; i>0; i--){
    RtreeCell *pNext;
    pNext = PickNext(pRtree, aCell, nCell, pBboxLeft, pBboxRight, aiUsed);
    float diff =  
      cellGrowth(pRtree, pBboxLeft, pNext) - 
      cellGrowth(pRtree, pBboxRight, pNext)
    ;
    if( (RTREE_MINCELLS(pRtree)-NCELL(pRight)==i)
     || (diff>0.0 && (RTREE_MINCELLS(pRtree)-NCELL(pLeft)!=i))
    ){
      nodeInsertCell(pRtree, pRight, pNext);
      cellUnion(pRtree, pBboxRight, pNext);
    }else{
      nodeInsertCell(pRtree, pLeft, pNext);
      cellUnion(pRtree, pBboxLeft, pNext);
    }
  }

  sqlite3_free(aiUsed);
  return SQLITE_OK;
}
#endif

static int updateMapping(
  Rtree *pRtree, 
  i64 iRowid, 
  RtreeNode *pNode, 
  int iHeight
){
  int (*xSetMapping)(Rtree *, sqlite3_int64, sqlite3_int64);
  xSetMapping = ((iHeight==0)?rowidWrite:parentWrite);
  if( iHeight>0 ){
    RtreeNode *pChild = nodeHashLookup(pRtree, iRowid);
    if( pChild ){
      nodeRelease(pRtree, pChild->pParent);
      nodeReference(pNode);
      pChild->pParent = pNode;
    }
  }
  return xSetMapping(pRtree, iRowid, pNode->iNode);
}

static int SplitNode(
  Rtree *pRtree,
  RtreeNode *pNode,
  RtreeCell *pCell,
  int iHeight
){
  int i;
  int newCellIsRight = 0;

  int rc = SQLITE_OK;
  int nCell = NCELL(pNode);
  RtreeCell *aCell;
  int *aiUsed;

  RtreeNode *pLeft = 0;
  RtreeNode *pRight = 0;

  RtreeCell leftbbox;
  RtreeCell rightbbox;

  /* Allocate an array and populate it with a copy of pCell and 
  ** all cells from node pLeft. Then zero the original node.
  */
  aCell = sqlite3_malloc((sizeof(RtreeCell)+sizeof(int))*(nCell+1));
  if( !aCell ){
    rc = SQLITE_NOMEM;
    goto splitnode_out;
  }
  aiUsed = (int *)&aCell[nCell+1];
  memset(aiUsed, 0, sizeof(int)*(nCell+1));
  for(i=0; i<nCell; i++){
    nodeGetCell(pRtree, pNode, i, &aCell[i]);
  }
  nodeZero(pRtree, pNode);
  memcpy(&aCell[nCell], pCell, sizeof(RtreeCell));
  nCell++;

  if( pNode->iNode==1 ){
    pRight = nodeNew(pRtree, pNode, 1);
    pLeft = nodeNew(pRtree, pNode, 1);
    pRtree->iDepth++;
    pNode->isDirty = 1;
    writeInt16(pNode->zData, pRtree->iDepth);
  }else{
    pLeft = pNode;
    pRight = nodeNew(pRtree, pLeft->pParent, 1);
    nodeReference(pLeft);
  }

  if( !pLeft || !pRight ){
    rc = SQLITE_NOMEM;
    goto splitnode_out;
  }

  memset(pLeft->zData, 0, pRtree->iNodeSize);
  memset(pRight->zData, 0, pRtree->iNodeSize);

  rc = AssignCells(pRtree, aCell, nCell, pLeft, pRight, &leftbbox, &rightbbox);
  if( rc!=SQLITE_OK ){
    goto splitnode_out;
  }

  /* Ensure both child nodes have node numbers assigned to them. */
  if( (0==pRight->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pRight)))
   || (0==pLeft->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pLeft)))
  ){
    goto splitnode_out;
  }

  rightbbox.iRowid = pRight->iNode;
  leftbbox.iRowid = pLeft->iNode;

  if( pNode->iNode==1 ){
    rc = insertCell(pRtree, pLeft->pParent, &leftbbox, iHeight+1);
    if( rc!=SQLITE_OK ){
      goto splitnode_out;
    }
  }else{
    RtreeNode *pParent = pLeft->pParent;
    int iCell = nodeParentIndex(pRtree, pLeft);
    nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);
    AdjustTree(pRtree, pParent, &leftbbox);
  }
  if( (rc = insertCell(pRtree, pRight->pParent, &rightbbox, iHeight+1)) ){
    goto splitnode_out;
  }

  for(i=0; i<NCELL(pRight); i++){
    i64 iRowid = nodeGetRowid(pRtree, pRight, i);
    rc = updateMapping(pRtree, iRowid, pRight, iHeight);
    if( iRowid==pCell->iRowid ){
      newCellIsRight = 1;
    }
    if( rc!=SQLITE_OK ){
      goto splitnode_out;
    }
  }
  if( pNode->iNode==1 ){
    for(i=0; i<NCELL(pLeft); i++){
      i64 iRowid = nodeGetRowid(pRtree, pLeft, i);
      rc = updateMapping(pRtree, iRowid, pLeft, iHeight);
      if( rc!=SQLITE_OK ){
        goto splitnode_out;
      }
    }
  }else if( newCellIsRight==0 ){
    rc = updateMapping(pRtree, pCell->iRowid, pLeft, iHeight);
  }

  if( rc==SQLITE_OK ){
    rc = nodeRelease(pRtree, pRight);
    pRight = 0;
  }
  if( rc==SQLITE_OK ){
    rc = nodeRelease(pRtree, pLeft);
    pLeft = 0;
  }

splitnode_out:
  nodeRelease(pRtree, pRight);
  nodeRelease(pRtree, pLeft);
  sqlite3_free(aCell);
  return rc;
}

static int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){
  int rc = SQLITE_OK;
  if( pLeaf->iNode!=1 && pLeaf->pParent==0 ){
    sqlite3_bind_int64(pRtree->pReadParent, 1, pLeaf->iNode);
    if( sqlite3_step(pRtree->pReadParent)==SQLITE_ROW ){
      i64 iNode = sqlite3_column_int64(pRtree->pReadParent, 0);
      rc = nodeAcquire(pRtree, iNode, 0, &pLeaf->pParent);
    }else{
      rc = SQLITE_ERROR;
    }
    sqlite3_reset(pRtree->pReadParent);
    if( rc==SQLITE_OK ){
      rc = fixLeafParent(pRtree, pLeaf->pParent);
    }
  }
  return rc;
}

static int deleteCell(Rtree *, RtreeNode *, int, int);

static int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){
  int rc;
  RtreeNode *pParent;
  int iCell;

  assert( pNode->nRef==1 );

  /* Remove the entry in the parent cell. */
  iCell = nodeParentIndex(pRtree, pNode);
  pParent = pNode->pParent;
  pNode->pParent = 0;
  if( SQLITE_OK!=(rc = deleteCell(pRtree, pParent, iCell, iHeight+1)) 
   || SQLITE_OK!=(rc = nodeRelease(pRtree, pParent))
  ){
    return rc;
  }

  /* Remove the xxx_node entry. */
  sqlite3_bind_int64(pRtree->pDeleteNode, 1, pNode->iNode);
  sqlite3_step(pRtree->pDeleteNode);
  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteNode)) ){
    return rc;
  }

  /* Remove the xxx_parent entry. */
  sqlite3_bind_int64(pRtree->pDeleteParent, 1, pNode->iNode);
  sqlite3_step(pRtree->pDeleteParent);
  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteParent)) ){
    return rc;
  }
  
  /* Remove the node from the in-memory hash table and link it into
  ** the Rtree.pDeleted list. Its contents will be re-inserted later on.
  */
  nodeHashDelete(pRtree, pNode);
  pNode->iNode = iHeight;
  pNode->pNext = pRtree->pDeleted;
  pNode->nRef++;
  pRtree->pDeleted = pNode;

  return SQLITE_OK;
}

static void fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){
  RtreeNode *pParent = pNode->pParent;
  if( pParent ){
    int ii; 
    int nCell = NCELL(pNode);
    RtreeCell box;                            /* Bounding box for pNode */
    nodeGetCell(pRtree, pNode, 0, &box);
    for(ii=1; ii<nCell; ii++){
      RtreeCell cell;
      nodeGetCell(pRtree, pNode, ii, &cell);
      cellUnion(pRtree, &box, &cell);
    }
    box.iRowid = pNode->iNode;
    ii = nodeParentIndex(pRtree, pNode);
    nodeOverwriteCell(pRtree, pParent, &box, ii);
    fixBoundingBox(pRtree, pParent);
  }
}

/*
** Delete the cell at index iCell of node pNode. After removing the
** cell, adjust the r-tree data structure if required.
*/
static int deleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell, int iHeight){
  int rc;

  if( SQLITE_OK!=(rc = fixLeafParent(pRtree, pNode)) ){
    return rc;
  }

  /* Remove the cell from the node. This call just moves bytes around
  ** the in-memory node image, so it cannot fail.
  */
  nodeDeleteCell(pRtree, pNode, iCell);

  /* If the node is not the tree root and now has less than the minimum
  ** number of cells, remove it from the tree. Otherwise, update the
  ** cell in the parent node so that it tightly contains the updated
  ** node.
  */
  if( pNode->iNode!=1 ){
    RtreeNode *pParent = pNode->pParent;
    if( (pParent->iNode!=1 || NCELL(pParent)!=1) 
     && (NCELL(pNode)<RTREE_MINCELLS(pRtree))
    ){
      rc = removeNode(pRtree, pNode, iHeight);
    }else{
      fixBoundingBox(pRtree, pNode);
    }
  }

  return rc;
}

static int Reinsert(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  RtreeCell *pCell, 
  int iHeight
){
  int *aOrder;
  int *aSpare;
  RtreeCell *aCell;
  float *aDistance;
  int nCell;
  float aCenterCoord[RTREE_MAX_DIMENSIONS];
  int iDim;
  int ii;
  int rc = SQLITE_OK;

  memset(aCenterCoord, 0, sizeof(float)*RTREE_MAX_DIMENSIONS);

  nCell = NCELL(pNode)+1;

  /* Allocate the buffers used by this operation. The allocation is
  ** relinquished before this function returns.
  */
  aCell = (RtreeCell *)sqlite3_malloc(nCell * (
    sizeof(RtreeCell) +         /* aCell array */
    sizeof(int)       +         /* aOrder array */
    sizeof(int)       +         /* aSpare array */
    sizeof(float)               /* aDistance array */
  ));
  if( !aCell ){
    return SQLITE_NOMEM;
  }
  aOrder    = (int *)&aCell[nCell];
  aSpare    = (int *)&aOrder[nCell];
  aDistance = (float *)&aSpare[nCell];

  for(ii=0; ii<nCell; ii++){
    if( ii==(nCell-1) ){
      memcpy(&aCell[ii], pCell, sizeof(RtreeCell));
    }else{
      nodeGetCell(pRtree, pNode, ii, &aCell[ii]);
    }
    aOrder[ii] = ii;
    for(iDim=0; iDim<pRtree->nDim; iDim++){
      aCenterCoord[iDim] += aCell[ii].aCoord[iDim*2];
      aCenterCoord[iDim] += aCell[ii].aCoord[iDim*2+1];
    }
  }
  for(iDim=0; iDim<pRtree->nDim; iDim++){
    aCenterCoord[iDim] = aCenterCoord[iDim]/((float)nCell*2.0);
  }

  for(ii=0; ii<nCell; ii++){
    aDistance[ii] = 0.0;
    for(iDim=0; iDim<pRtree->nDim; iDim++){
      float coord = aCell[ii].aCoord[iDim*2+1] - aCell[ii].aCoord[iDim*2];
      aDistance[ii] += (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);
    }
  }

  SortByDistance(aOrder, nCell, aDistance, aSpare);
  nodeZero(pRtree, pNode);

  for(ii=0; rc==SQLITE_OK && ii<(nCell-(RTREE_MINCELLS(pRtree)+1)); ii++){
    RtreeCell *p = &aCell[aOrder[ii]];
    nodeInsertCell(pRtree, pNode, p);
    if( p->iRowid==pCell->iRowid ){
      if( iHeight==0 ){
        rc = rowidWrite(pRtree, p->iRowid, pNode->iNode);
      }else{
        rc = parentWrite(pRtree, p->iRowid, pNode->iNode);
      }
    }
  }
  if( rc==SQLITE_OK ){
    fixBoundingBox(pRtree, pNode);
  }
  for(; rc==SQLITE_OK && ii<nCell; ii++){
    /* Find a node to store this cell in. pNode->iNode currently contains
    ** the height of the sub-tree headed by the cell.
    */
    RtreeNode *pInsert;
    RtreeCell *p = &aCell[aOrder[ii]];
    rc = ChooseLeaf(pRtree, p, iHeight, &pInsert);
    if( rc==SQLITE_OK ){
      int rc2;
      rc = insertCell(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 insertCell(
  Rtree *pRtree,
  RtreeNode *pNode,
  RtreeCell *pCell,
  int iHeight
){
  int rc = SQLITE_OK;
  if( iHeight>0 ){
    RtreeNode *pChild = nodeHashLookup(pRtree, pCell->iRowid);
    if( pChild ){
      nodeRelease(pRtree, pChild->pParent);
      nodeReference(pNode);
      pChild->pParent = pNode;
    }
  }
  if( nodeInsertCell(pRtree, pNode, pCell) ){
#if VARIANT_RSTARTREE_REINSERT
    if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
      rc = SplitNode(pRtree, pNode, pCell, iHeight);
    }else{
      pRtree->iReinsertHeight = iHeight;
      rc = Reinsert(pRtree, pNode, pCell, iHeight);
    }
#else
    rc = SplitNode(pRtree, pNode, pCell, iHeight);
#endif
  }else{
    AdjustTree(pRtree, pNode, pCell);
    if( iHeight==0 ){
      rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
    }else{
      rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
    }
  }
  return rc;
}

static int reinsertNodeContent(Rtree *pRtree, RtreeNode *pNode){
  int ii;
  int rc = SQLITE_OK;
  int nCell = NCELL(pNode);

  for(ii=0; rc==SQLITE_OK && ii<nCell; ii++){
    RtreeNode *pInsert;
    RtreeCell cell;
    nodeGetCell(pRtree, pNode, ii, &cell);

    /* Find a node to store this cell in. pNode->iNode currently contains
    ** the height of the sub-tree headed by the cell.
    */
    rc = ChooseLeaf(pRtree, &cell, pNode->iNode, &pInsert);
    if( rc==SQLITE_OK ){
      int rc2;
      rc = insertCell(pRtree, pInsert, &cell, pNode->iNode);
      rc2 = nodeRelease(pRtree, pInsert);
      if( rc==SQLITE_OK ){
        rc = rc2;
      }
    }
  }
  return rc;
}

/*
** Select a currently unused rowid for a new r-tree record.
*/
static int newRowid(Rtree *pRtree, i64 *piRowid){
  int rc;
  sqlite3_bind_null(pRtree->pWriteRowid, 1);
  sqlite3_bind_null(pRtree->pWriteRowid, 2);
  sqlite3_step(pRtree->pWriteRowid);
  rc = sqlite3_reset(pRtree->pWriteRowid);
  *piRowid = sqlite3_last_insert_rowid(pRtree->db);
  return rc;
}

#ifndef NDEBUG
static int hashIsEmpty(Rtree *pRtree){
  int ii;
  for(ii=0; ii<HASHSIZE; ii++){
    assert( !pRtree->aHash[ii] );
  }
  return 1;
}
#endif

/*
** The xUpdate method for rtree module virtual tables.
*/
int rtreeUpdate(
  sqlite3_vtab *pVtab, 
  int nData, 
  sqlite3_value **azData, 
  sqlite_int64 *pRowid
){
  Rtree *pRtree = (Rtree *)pVtab;
  int rc = SQLITE_OK;

  rtreeReference(pRtree);

  assert(nData>=1);
  assert(hashIsEmpty(pRtree));

  /* If azData[0] is not an SQL NULL value, it is the rowid of a
  ** record to delete from the r-tree table. The following block does
  ** just that.
  */
  if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){
    i64 iDelete;                /* The rowid to delete */
    RtreeNode *pLeaf;           /* Leaf node containing record iDelete */
    int iCell;                  /* Index of iDelete cell in pLeaf */
    RtreeNode *pRoot;

    /* Obtain a reference to the root node to initialise Rtree.iDepth */
    rc = nodeAcquire(pRtree, 1, 0, &pRoot);

    /* Obtain a reference to the leaf node that contains the entry 
    ** about to be deleted. 
    */
    if( rc==SQLITE_OK ){
      iDelete = sqlite3_value_int64(azData[0]);
      rc = findLeafNode(pRtree, iDelete, &pLeaf);
    }

    /* Delete the cell in question from the leaf node. */
    if( rc==SQLITE_OK ){
      int rc2;
      iCell = nodeRowidIndex(pRtree, pLeaf, iDelete);
      rc = deleteCell(pRtree, pLeaf, iCell, 0);
      rc2 = nodeRelease(pRtree, pLeaf);
      if( rc==SQLITE_OK ){
        rc = rc2;
      }
    }

    /* Delete the corresponding entry in the <rtree>_rowid table. */
    if( rc==SQLITE_OK ){
      sqlite3_bind_int64(pRtree->pDeleteRowid, 1, iDelete);
      sqlite3_step(pRtree->pDeleteRowid);
      rc = sqlite3_reset(pRtree->pDeleteRowid);
    }

    /* Check if the root node now has exactly one child. If so, remove
    ** it, schedule the contents of the child for reinsertion and 
    ** reduce the tree height by one.
    **
    ** This is equivalent to copying the contents of the child into
    ** the root node (the operation that Gutman's paper says to perform 
    ** in this scenario).
    */
    if( rc==SQLITE_OK && pRtree->iDepth>0 ){
      if( rc==SQLITE_OK && NCELL(pRoot)==1 ){
        RtreeNode *pChild;
        i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
        rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);
        if( rc==SQLITE_OK ){
          rc = removeNode(pRtree, pChild, pRtree->iDepth-1);
        }
        if( rc==SQLITE_OK ){
          pRtree->iDepth--;
          writeInt16(pRoot->zData, pRtree->iDepth);
          pRoot->isDirty = 1;
        }
      }
    }

    /* Re-insert the contents of any underfull nodes removed from the tree. */
    for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){
      if( rc==SQLITE_OK ){
        rc = reinsertNodeContent(pRtree, pLeaf);
      }
      pRtree->pDeleted = pLeaf->pNext;
      sqlite3_free(pLeaf);
    }

    /* Release the reference to the root node. */
    if( rc==SQLITE_OK ){
      rc = nodeRelease(pRtree, pRoot);
    }else{
      nodeRelease(pRtree, pRoot);
    }
  }

  /* If the azData[] array contains more than one element, elements
  ** (azData[2]..azData[argc-1]) contain a new record to insert into
  ** the r-tree structure.
  */
  if( rc==SQLITE_OK && nData>1 ){
    /* Insert a new record into the r-tree */
    RtreeCell cell;
    int ii;
    RtreeNode *pLeaf;

    /* Populate the cell.aCoord[] array. The first coordinate is azData[3]. */
    assert( nData==(pRtree->nDim*2 + 3) );
    for(ii=0; ii<(pRtree->nDim*2); ii+=2){
      cell.aCoord[ii] = (float)sqlite3_value_double(azData[ii+3]);
      cell.aCoord[ii+1] = (float)sqlite3_value_double(azData[ii+4]);
      if( cell.aCoord[ii]>cell.aCoord[ii+1] ){
        rc = SQLITE_CONSTRAINT;
        goto constraint;
      }
    }

    /* Figure out the rowid of the new row. */
    if( sqlite3_value_type(azData[2])==SQLITE_NULL ){
      rc = newRowid(pRtree, &cell.iRowid);
    }else{
      cell.iRowid = sqlite3_value_int64(azData[2]);
      sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
      if( SQLITE_ROW==sqlite3_step(pRtree->pReadRowid) ){
        sqlite3_reset(pRtree->pReadRowid);
        rc = SQLITE_CONSTRAINT;
        goto constraint;
      }
      rc = sqlite3_reset(pRtree->pReadRowid);
    }

    if( rc==SQLITE_OK ){
      rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);
    }
    if( rc==SQLITE_OK ){
      int rc2;
      pRtree->iReinsertHeight = -1;
      rc = insertCell(pRtree, pLeaf, &cell, 0);
      rc2 = nodeRelease(pRtree, pLeaf);
      if( rc==SQLITE_OK ){
        rc = rc2;
      }
    }
  }

constraint:
  rtreeRelease(pRtree);
  return rc;
}

/*
** The xRename method for rtree module virtual tables.
*/
static int rtreeRename(sqlite3_vtab *pVtab, const char *zNewName){
  Rtree *pRtree = (Rtree *)pVtab;
  int rc = SQLITE_NOMEM;
  char *zSql = sqlite3_mprintf(
    "ALTER TABLE %Q.'%q_node'   RENAME TO '%q_node';"
    "ALTER TABLE %Q.'%q_parent' RENAME TO '%q_parent';"
    "ALTER TABLE %Q.'%q_rowid'  RENAME TO '%q_rowid';"
    , pRtree->zDb, pRtree->zName, zNewName 
    , pRtree->zDb, pRtree->zName, zNewName 
    , pRtree->zDb, pRtree->zName, zNewName
  );
  if( zSql ){
    rc = sqlite3_exec(pRtree->db, zSql, 0, 0, 0);
    sqlite3_free(zSql);
  }
  return rc;
}

static sqlite3_module rtreeModule = {
  0,                         /* iVersion */
  rtreeCreate,                /* xCreate - create a table */
  rtreeConnect,               /* xConnect - connect to an existing table */
  rtreeBestIndex,             /* xBestIndex - Determine search strategy */
  rtreeDisconnect,            /* xDisconnect - Disconnect from a table */
  rtreeDestroy,               /* xDestroy - Drop a table */
  rtreeOpen,                  /* xOpen - open a cursor */
  rtreeClose,                 /* xClose - close a cursor */
  rtreeFilter,                /* xFilter - configure scan constraints */
  rtreeNext,                  /* xNext - advance a cursor */
  rtreeEof,                   /* xEof */
  rtreeColumn,                /* xColumn - read data */
  rtreeRowid,                 /* xRowid - read data */
  rtreeUpdate,                /* xUpdate - write data */
  0,                          /* xBegin - begin transaction */
  0,                          /* xSync - sync transaction */
  0,                          /* xCommit - commit transaction */
  0,                          /* xRollback - rollback transaction */
  0,                          /* xFindFunction - function overloading */
  rtreeRename                 /* xRename - rename the table */
};

static int rtreeSqlInit(
  Rtree *pRtree, 
  sqlite3 *db, 
  const char *zDb, 
  const char *zPrefix, 
  int isCreate
){
  int rc = SQLITE_OK;

  #define N_STATEMENT 9
  static const char *azSql[N_STATEMENT] = {
    /* Read and write the xxx_node table */
    "SELECT data FROM '%q'.'%q_node' WHERE nodeno = :1",
    "INSERT OR REPLACE INTO '%q'.'%q_node' VALUES(:1, :2)",
    "DELETE FROM '%q'.'%q_node' WHERE nodeno = :1",

    /* Read and write the xxx_rowid table */
    "SELECT nodeno FROM '%q'.'%q_rowid' WHERE rowid = :1",
    "INSERT OR REPLACE INTO '%q'.'%q_rowid' VALUES(:1, :2)",
    "DELETE FROM '%q'.'%q_rowid' WHERE rowid = :1",

    /* Read and write the xxx_parent table */
    "SELECT parentnode FROM '%q'.'%q_parent' WHERE nodeno = :1",
    "INSERT OR REPLACE INTO '%q'.'%q_parent' VALUES(:1, :2)",
    "DELETE FROM '%q'.'%q_parent' WHERE nodeno = :1"
  };
  sqlite3_stmt **appStmt[N_STATEMENT];
  int i;

  pRtree->db = db;

  if( isCreate ){
    char *zCreate = sqlite3_mprintf(
"CREATE TABLE '%q'.'%q_node'(nodeno INTEGER PRIMARY KEY, data BLOB);"
"CREATE TABLE '%q'.'%q_rowid'(rowid INTEGER PRIMARY KEY, nodeno INTEGER);"
"CREATE TABLE '%q'.'%q_parent'(nodeno INTEGER PRIMARY KEY, parentnode INTEGER);"
"INSERT INTO '%q'.'%q_node' VALUES(1, zeroblob(%d))",
      zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, pRtree->iNodeSize
    );
    if( !zCreate ){
      return SQLITE_NOMEM;
    }
    rc = sqlite3_exec(db, zCreate, 0, 0, 0);
    sqlite3_free(zCreate);
    if( rc!=SQLITE_OK ){
      return rc;
    }
  }

  appStmt[0] = &pRtree->pReadNode;
  appStmt[1] = &pRtree->pWriteNode;
  appStmt[2] = &pRtree->pDeleteNode;
  appStmt[3] = &pRtree->pReadRowid;
  appStmt[4] = &pRtree->pWriteRowid;
  appStmt[5] = &pRtree->pDeleteRowid;
  appStmt[6] = &pRtree->pReadParent;
  appStmt[7] = &pRtree->pWriteParent;
  appStmt[8] = &pRtree->pDeleteParent;

  for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){
    char *zSql = sqlite3_mprintf(azSql[i], zDb, zPrefix);
    if( zSql ){
      rc = sqlite3_prepare_v2(db, zSql, -1, appStmt[i], 0); 
    }else{
      rc = SQLITE_NOMEM;
    }
    sqlite3_free(zSql);
  }

  return rc;
}

/*
** This routine queries database handle db for the page-size used by
** database zDb. If successful, the page-size in bytes is written to
** *piPageSize and SQLITE_OK returned. Otherwise, and an SQLite error 
** code is returned.
*/
static int getPageSize(sqlite3 *db, const char *zDb, int *piPageSize){
  int rc = SQLITE_NOMEM;
  char *zSql;
  sqlite3_stmt *pStmt = 0;

  zSql = sqlite3_mprintf("PRAGMA %Q.page_size", zDb);
  if( !zSql ){
    return SQLITE_NOMEM;
  }

  rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);
  sqlite3_free(zSql);
  if( rc!=SQLITE_OK ){
    return rc;
  }

  if( SQLITE_ROW==sqlite3_step(pStmt) ){
    *piPageSize = sqlite3_column_int(pStmt, 0);
  }
  return sqlite3_finalize(pStmt);
}

/* 
** This function is the implementation of both the xConnect and xCreate
** methods of the r-tree virtual table.
**
**   argv[0]   -> module name
**   argv[1]   -> database name
**   argv[2]   -> table name
**   argv[...] -> column names...
*/
static int rtreeInit(
  sqlite3 *db,                        /* Database connection */
  void *pAux,                         /* Pointer to head of rtree list */
  int argc, const char *const*argv,   /* Parameters to CREATE TABLE statement */
  sqlite3_vtab **ppVtab,              /* OUT: New virtual table */
  char **pzErr,                       /* OUT: Error message, if any */
  int isCreate                        /* True for xCreate, false for xConnect */
){
  int rc = SQLITE_OK;
  int iPageSize = 0;
  Rtree *pRtree;
  int nDb;              /* Length of string argv[1] */
  int nName;            /* Length of string argv[2] */

  const char *aErrMsg[] = {
    0,                                                    /* 0 */
    "Wrong number of columns for an rtree table",         /* 1 */
    "Too few columns for an rtree table",                 /* 2 */
    "Too many columns for an rtree table"                 /* 3 */
  };

  int iErr = (argc<6) ? 2 : argc>(RTREE_MAX_DIMENSIONS*2+4) ? 3 : argc%2;
  if( aErrMsg[iErr] ){
    *pzErr = sqlite3_mprintf("%s", aErrMsg[iErr]);
    return SQLITE_ERROR;
  }

  rc = getPageSize(db, argv[1], &iPageSize);
  if( rc!=SQLITE_OK ){
    return rc;
  }

  /* Allocate the sqlite3_vtab structure */
  nDb = strlen(argv[1]);
  nName = strlen(argv[2]);
  pRtree = (Rtree *)sqlite3_malloc(sizeof(Rtree)+nDb+nName+2);
  if( !pRtree ){
    return SQLITE_NOMEM;
  }
  memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);
  pRtree->nBusy = 1;
  pRtree->base.pModule = &rtreeModule;
  pRtree->zDb = (char *)&pRtree[1];
  pRtree->zName = &pRtree->zDb[nDb+1];
  pRtree->nDim = (argc-4)/2;
  pRtree->nBytesPerCell = 8 + pRtree->nDim*4*2;
  memcpy(pRtree->zDb, argv[1], nDb);
  memcpy(pRtree->zName, argv[2], nName);

  /* Figure out the node size to use. By default, use 64 bytes less than
  ** the database page-size. This ensures that each node is stored on
  ** a single database page.
  **
  ** If the databasd page-size is so large that more than RTREE_MAXCELLS
  ** entries would fit in a single node, use a smaller node-size.
  */
  pRtree->iNodeSize = iPageSize-64;
  if( (4+pRtree->nBytesPerCell*RTREE_MAXCELLS)<pRtree->iNodeSize ){
    pRtree->iNodeSize = 4+pRtree->nBytesPerCell*RTREE_MAXCELLS;
  }

  /* Create/Connect to the underlying relational database schema. If
  ** that is successful, call sqlite3_declare_vtab() to configure
  ** the r-tree table schema.
  */
  if( (rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate)) ){
    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
  }else{
    char *zSql = sqlite3_mprintf("CREATE TABLE x(%s", argv[3]);
    char *zTmp;
    int ii;
    for(ii=4; zSql && ii<argc; ii++){
      zTmp = zSql;
      zSql = sqlite3_mprintf("%s, %s", zTmp, argv[ii]);
      sqlite3_free(zTmp);
    }
    if( zSql ){
      zTmp = zSql;
      zSql = sqlite3_mprintf("%s);", zTmp);
      sqlite3_free(zTmp);
    }
    if( !zSql || sqlite3_declare_vtab(db, zSql) ){
      rc = SQLITE_NOMEM;
    }
    sqlite3_free(zSql);
  }

  if( rc==SQLITE_OK ){
    *ppVtab = (sqlite3_vtab *)pRtree;
  }else{
    rtreeRelease(pRtree);
  }
  return rc;
}


/*
** Implementation of a scalar function that decodes r-tree nodes to
** human readable strings. This can be used for debugging and analysis.
**
** The scalar function takes two arguments, a blob of data containing
** an r-tree node, and the number of dimensions the r-tree indexes.
** For a two-dimensional r-tree structure called "rt", to deserialize
** all nodes, a statement like:
**
**   SELECT rtreenode(2, data) FROM rt_node;
**
** The human readable string takes the form of a Tcl list with one
** entry for each cell in the r-tree node. Each entry is itself a
** list, containing the 8-byte rowid/pageno followed by the 
** <num-dimension>*2 coordinates.
*/
static void rtreenode(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
  char *zText = 0;
  RtreeNode node;
  Rtree tree;
  int ii;

  memset(&node, 0, sizeof(RtreeNode));
  memset(&tree, 0, sizeof(Rtree));
  tree.nDim = sqlite3_value_int(apArg[0]);
  tree.nBytesPerCell = 8 + 8 * tree.nDim;
  node.zData = (u8 *)sqlite3_value_blob(apArg[1]);

  for(ii=0; ii<NCELL(&node); ii++){
    char zCell[512];
    int nCell = 0;
    RtreeCell cell;
    int jj;

    nodeGetCell(&tree, &node, ii, &cell);
    sqlite3_snprintf(512-nCell,&zCell[nCell],"%d", cell.iRowid);
    nCell = strlen(zCell);
    for(jj=0; jj<tree.nDim*2; jj++){
      sqlite3_snprintf(512-nCell,&zCell[nCell]," %f",(double)cell.aCoord[jj]);
      nCell = strlen(zCell);
    }

    if( zText ){
      char *zTextNew = sqlite3_mprintf("%s {%s}", zText, zCell);
      sqlite3_free(zText);
      zText = zTextNew;
    }else{
      zText = sqlite3_mprintf("{%s}", zCell);
    }
  }
  
  sqlite3_result_text(ctx, zText, -1, sqlite3_free);
}

static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
  if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB 
   || sqlite3_value_bytes(apArg[0])<2
  ){
    sqlite3_result_error(ctx, "Invalid argument to rtreedepth()", -1); 
  }else{
    u8 *zBlob = (u8 *)sqlite3_value_blob(apArg[0]);
    sqlite3_result_int(ctx, readInt16(zBlob));
  }
}

/*
** Register the r-tree module with database handle db. This creates the
** virtual table module "rtree" and the debugging/analysis scalar 
** function "rtreenode".
*/
int sqlite3RtreeInit(sqlite3 *db){
  int rc = SQLITE_OK;

  if( rc==SQLITE_OK ){
    int utf8 = SQLITE_UTF8;
    rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);
  }
  if( rc==SQLITE_OK ){
    int utf8 = SQLITE_UTF8;
    rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
  }
  if( rc==SQLITE_OK ){
    rc = sqlite3_create_module_v2(db, "rtree", &rtreeModule, 0, 0);
  }

  return rc;
}

#if !SQLITE_CORE
int sqlite3_extension_init(
  sqlite3 *db,
  char **pzErrMsg,
  const sqlite3_api_routines *pApi
){
  SQLITE_EXTENSION_INIT2(pApi)
  return sqlite3RtreeInit(db);
}
#endif

#endif

Added ext/rtree/rtree.test.























































































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#
#    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 runs all rtree related tests.
#
# $Id: rtree.test,v 1.1 2008/05/26 18:41:54 danielk1977 Exp $

set testdir [file join [file dirname $argv0] .. .. test]
source $testdir/tester.tcl
rename finish_test really_finish_test
proc finish_test {} {}
set ISQUICK 1

set EXCLUDE {
  rtree.test
}

# Files to include in the test.  If this list is empty then everything
# that is not in the EXCLUDE list is run.
#
set INCLUDE {
}

foreach testfile [lsort -dictionary [glob [file dirname $argv0]/*.test]] {
  set tail [file tail $testfile]
  if {[lsearch -exact $EXCLUDE $tail]>=0} continue
  if {[llength $INCLUDE]>0 && [lsearch -exact $INCLUDE $tail]<0} continue
  source $testfile
  catch {db close}
  if {$sqlite_open_file_count>0} {
    puts "$tail did not close all files: $sqlite_open_file_count"
    incr nErr
    lappend ::failList $tail
    set sqlite_open_file_count 0
  }
}

set sqlite_open_file_count 0
really_finish_test

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# 2008 Feb 19
#
# 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.
#
#***********************************************************************
#
# The focus of this file is testing the r-tree extension.
#
# $Id: rtree1.test,v 1.1 2008/05/26 18:41:54 danielk1977 Exp $
#

set testdir [file join [file dirname $argv0] .. .. test]
source $testdir/tester.tcl

# Test plan:
#
#   rtree-1.*: Creating/destroying r-tree tables.
#   rtree-2.*: Test the implicit constraints - unique rowid and
#              (coord[N]<=coord[N+1]) for even values of N. Also
#              automatic assigning of rowid values.
#   rtree-3.*: Linear scans of r-tree data.
#   rtree-4.*: Test INSERT
#   rtree-5.*: Test DELETE
#   rtree-6.*: Test UPDATE
#   rtree-7.*: Test renaming an r-tree table.
#   rtree-8.*: Test constrained scans of r-tree data.
#

ifcapable !rtree {
  finish_test
  return
}

#----------------------------------------------------------------------------
# Test cases rtree-1.* test CREATE and DROP table statements.
#

# Test creating and dropping an rtree table.
#
do_test rtree-1.1.1 {
  execsql { CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2) }
} {}
do_test rtree-1.1.2 {
  execsql { SELECT name FROM sqlite_master ORDER BY name }
} {t1 t1_node t1_parent t1_rowid}
do_test rtree-1.1.3 {
  execsql { 
    DROP TABLE t1; 
    SELECT name FROM sqlite_master ORDER BY name;
  }
} {}

# Test creating and dropping an rtree table with an odd name in
# an attached database.
#
do_test rtree-1.2.1 {
  execsql {
    ATTACH 'test2.db' AS aux;
    CREATE VIRTUAL TABLE aux.'a" "b' USING rtree(ii, x1, x2, y1, y2);
  }
} {}
do_test rtree-1.2.2 {
  execsql { SELECT name FROM sqlite_master ORDER BY name }
} {}
do_test rtree-1.2.3 {
  execsql { SELECT name FROM aux.sqlite_master ORDER BY name }
} {{a" "b} {a" "b_node} {a" "b_parent} {a" "b_rowid}}
do_test rtree-1.2.4 {
  execsql { 
    DROP TABLE aux.'a" "b'; 
    SELECT name FROM aux.sqlite_master ORDER BY name;
  }
} {}

# Test that the logic for checking the number of columns specified
# for an rtree table. Acceptable values are odd numbers between 3 and
# 11, inclusive.
#
set cols [list i1 i2 i3 i4 i5 i6 i7 i8 i9 iA iB iC iD iE iF iG iH iI iJ iK]
for {set nCol 1} {$nCol<[llength $cols]} {incr nCol} {

  set columns [join [lrange $cols 0 [expr {$nCol-1}]] ,]

  set X {0 {}}
  if {$nCol%2 == 0}  { set X {1 {Wrong number of columns for an rtree table}} }
  if {$nCol < 3}     { set X {1 {Too few columns for an rtree table}} }
  if {$nCol > 11}    { set X {1 {Too many columns for an rtree table}} }

  do_test rtree-1.3.$nCol {
    catchsql " 
      CREATE VIRTUAL TABLE t1 USING rtree($columns);
    "
  } $X

  catchsql { DROP TABLE t1 }
}

# Test that it is possible to open an existing database that contains
# r-tree tables.
#
do_test rtree-1.4.1 {
  execsql {
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2);
    INSERT INTO t1 VALUES(1, 5.0, 10.0);
    INSERT INTO t1 VALUES(2, 15.0, 20.0);
  }
} {}
do_test rtree-1.4.2 {
  db close
  sqlite3 db test.db
  execsql { SELECT * FROM t1 ORDER BY ii }
} {1 5.0 10.0 2 15.0 20.0}
do_test rtree-1.4.3 {
  execsql { DROP TABLE t1 }
} {}

# Test that it is possible to create an r-tree table with ridiculous
# column names.
#
do_test rtree-1.5.1 {
  execsql {
    CREATE VIRTUAL TABLE t1 USING rtree("the key", "x dim.", "x2'dim");
    INSERT INTO t1 VALUES(1, 2, 3);
    SELECT "the key", "x dim.", "x2'dim" FROM t1;
  }
} {1 2.0 3.0}
do_test rtree-1.5.1 {
  execsql { DROP TABLE t1 }
} {}

# Force the r-tree constructor to fail.
#
do_test rtree-1.6.1 {
  execsql { CREATE TABLE t1_rowid(a); }
  catchsql {
    CREATE VIRTUAL TABLE t1 USING rtree("the key", "x dim.", "x2'dim");
  }
} {1 {table 't1_rowid' already exists}}
do_test rtree-1.6.1 {
  execsql { DROP TABLE t1_rowid }
} {}

#----------------------------------------------------------------------------
# Test cases rtree-2.* 
#
do_test rtree-2.1.1 {
  execsql { 
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
    SELECT * FROM t1;
  }
} {}

do_test rtree-2.1.2 {
  execsql { INSERT INTO t1 VALUES(NULL, 1, 3, 2, 4) }
  execsql { SELECT * FROM t1 }
} {1 1.0 3.0 2.0 4.0}
do_test rtree-2.1.3 {
  execsql { INSERT INTO t1 VALUES(NULL, 1, 3, 2, 4) }
  execsql { SELECT rowid FROM t1 ORDER BY rowid }
} {1 2}
do_test rtree-2.1.3 {
  execsql { INSERT INTO t1 VALUES(NULL, 1, 3, 2, 4) }
  execsql { SELECT ii FROM t1 ORDER BY ii }
} {1 2 3}

do_test rtree-2.2.1 {
  catchsql { INSERT INTO t1 VALUES(2, 1, 3, 2, 4) }
} {1 {constraint failed}}
do_test rtree-2.2.2 {
  catchsql { INSERT INTO t1 VALUES(4, 1, 3, 4, 2) }
} {1 {constraint failed}}
do_test rtree-2.2.3 {
  catchsql { INSERT INTO t1 VALUES(4, 3, 1, 2, 4) }
} {1 {constraint failed}}
do_test rtree-2.2.4 {
  execsql { SELECT ii FROM t1 ORDER BY ii }
} {1 2 3}

do_test rtree-2.X {
  execsql { DROP TABLE t1 }
} {}

#----------------------------------------------------------------------------
# Test cases rtree-3.* test linear scans of r-tree table data. To test
# this we have to insert some data into an r-tree, but that is not the
# focus of these tests.
#
do_test rtree-3.1.1 {
  execsql { 
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
    SELECT * FROM t1;
  }
} {}
do_test rtree-3.1.2 {
  execsql { 
    INSERT INTO t1 VALUES(5, 1, 3, 2, 4);
    SELECT * FROM t1;
  }
} {5 1.0 3.0 2.0 4.0}
do_test rtree-3.1.3 {
  execsql {
    INSERT INTO t1 VALUES(6, 2, 6, 4, 8);
    SELECT * FROM t1;
  }
} {5 1.0 3.0 2.0 4.0 6 2.0 6.0 4.0 8.0}

# Test the constraint on the coordinates (c[i]<=c[i+1] where (i%2==0)):
do_test rtree-3.2.1 {
  catchsql { INSERT INTO t1 VALUES(7, 2, 6, 4, 3) }
} {1 {constraint failed}}
do_test rtree-3.2.2 {
  catchsql { INSERT INTO t1 VALUES(8, 2, 6, 3, 3) }
} {0 {}}

#----------------------------------------------------------------------------
# Test cases rtree-5.* test DELETE operations.
#
do_test rtree-5.1.1 {
  execsql { CREATE VIRTUAL TABLE t2 USING rtree(ii, x1, x2) }
} {}
do_test rtree-5.1.2 {
  execsql { 
    INSERT INTO t2 VALUES(1, 10, 20);
    INSERT INTO t2 VALUES(2, 30, 40);
    INSERT INTO t2 VALUES(3, 50, 60);
    SELECT * FROM t2 ORDER BY ii;
  }
} {1 10.0 20.0 2 30.0 40.0 3 50.0 60.0}
do_test rtree-5.1.3 {
  execsql { 
    DELETE FROM t2 WHERE ii=2;
    SELECT * FROM t2 ORDER BY ii;
  }
} {1 10.0 20.0 3 50.0 60.0}
do_test rtree-5.1.4 {
  execsql { 
    DELETE FROM t2 WHERE ii=1;
    SELECT * FROM t2 ORDER BY ii;
  }
} {3 50.0 60.0}
do_test rtree-5.1.5 {
  execsql { 
    DELETE FROM t2 WHERE ii=3;
    SELECT * FROM t2 ORDER BY ii;
  }
} {}
do_test rtree-5.1.6 {
  execsql { SELECT * FROM t2_rowid }
} {}

#----------------------------------------------------------------------------
# Test cases rtree-5.* test UPDATE operations.
#
do_test rtree-6.1.1 {
  execsql { CREATE VIRTUAL TABLE t3 USING rtree(ii, x1, x2, y1, y2) }
} {}
do_test rtree-6.1.2 {
  execsql {
    INSERT INTO t3 VALUES(1, 2, 3, 4, 5);
    UPDATE t3 SET x2=5;
    SELECT * FROM t3;
  }
} {1 2.0 5.0 4.0 5.0}
do_test rtree-6.1.3 {
  execsql { UPDATE t3 SET ii = 2 }
  execsql { SELECT * FROM t3 }
} {2 2.0 5.0 4.0 5.0}

#----------------------------------------------------------------------------
# Test cases rtree-7.* test rename operations.
#
do_test rtree-7.1.1 {
  execsql {
    CREATE VIRTUAL TABLE t4 USING rtree(ii, x1, x2, y1, y2, z1, z2);
    INSERT INTO t4 VALUES(1, 2, 3, 4, 5, 6, 7);
  }
} {}
do_test rtree-7.1.2 {
  execsql { ALTER TABLE t4 RENAME TO t5 }
  execsql { SELECT * FROM t5 }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}
do_test rtree-7.1.3 {
  db close
  sqlite3 db test.db
  execsql { SELECT * FROM t5 }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}
do_test rtree-7.1.4 {
  execsql { ALTER TABLE t5 RENAME TO 'raisara "one"'''}
  execsql { SELECT * FROM "raisara ""one""'" }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}
do_test rtree-7.1.5 {
  execsql { SELECT * FROM 'raisara "one"''' }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}
do_test rtree-7.1.6 {
  execsql { ALTER TABLE "raisara ""one""'" RENAME TO "abc 123" }
  execsql { SELECT * FROM "abc 123" }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}
do_test rtree-7.1.7 {
  db close
  sqlite3 db test.db
  execsql { SELECT * FROM "abc 123" }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}

# An error midway through a rename operation.
do_test rtree-7.2.1 {
  execsql { 
    CREATE TABLE t4_node(a);
  }
  catchsql { ALTER TABLE "abc 123" RENAME TO t4 }
} {1 {SQL logic error or missing database}}
do_test rtree-7.2.2 {
  execsql { SELECT * FROM "abc 123" }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}
do_test rtree-7.2.3 {
  execsql { 
    DROP TABLE t4_node;
    CREATE TABLE t4_rowid(a);
  }
  catchsql { ALTER TABLE "abc 123" RENAME TO t4 }
} {1 {SQL logic error or missing database}}
do_test rtree-7.2.4 {
  db close
  sqlite3 db test.db
  execsql { SELECT * FROM "abc 123" }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}
do_test rtree-7.2.5 {
  execsql { DROP TABLE t4_rowid }
  execsql { ALTER TABLE "abc 123" RENAME TO t4 }
  execsql { SELECT * FROM t4 }
} {1 2.0 3.0 4.0 5.0 6.0 7.0}


#----------------------------------------------------------------------------
# Test cases rtree-8.*
#

# Test that the function to determine if a leaf cell is part of the
# result set works.
do_test rtree-8.1.1 {
  execsql {
    CREATE VIRTUAL TABLE t6 USING rtree(ii, x1, x2);
    INSERT INTO t6 VALUES(1, 3, 7);
    INSERT INTO t6 VALUES(2, 4, 6);
  }
} {}
do_test rtree-8.1.2 { execsql { SELECT ii FROM t6 WHERE x1>2 } } {1 2}
do_test rtree-8.1.3 { execsql { SELECT ii FROM t6 WHERE x1>3 } } {2}
do_test rtree-8.1.4 { execsql { SELECT ii FROM t6 WHERE x1>4 } } {}
do_test rtree-8.1.5 { execsql { SELECT ii FROM t6 WHERE x1>5 } } {}
do_test rtree-8.1.6 { execsql { SELECT ii FROM t6 WHERE x1<3 } } {}
do_test rtree-8.1.7 { execsql { SELECT ii FROM t6 WHERE x1<4 } } {1}
do_test rtree-8.1.8 { execsql { SELECT ii FROM t6 WHERE x1<5 } } {1 2}


finish_test

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# 2008 Feb 19
#
# 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.
#
#***********************************************************************
#
# The focus of this file is testing the r-tree extension.
#
# $Id: rtree2.test,v 1.1 2008/05/26 18:41:54 danielk1977 Exp $
#

set testdir [file join [file dirname $argv0] .. .. test]
source $testdir/tester.tcl
source [file join [file dirname $argv0] rtree_util.tcl]

ifcapable !rtree {
  finish_test
  return
}

set ::NROW   1000
set ::NDEL     10
set ::NSELECT 100

for {set nDim 1} {$nDim <= 5} {incr nDim} {

  do_test rtree2-$nDim.1 {
    set cols [list]
    foreach c [list c0 c1 c2 c3 c4 c5 c6 c7 c8 c9] {
      lappend cols "$c REAL"
    }
    set cols [join [lrange $cols 0 [expr {$nDim*2-1}]] ", "]
    execsql " 
      CREATE VIRTUAL TABLE t1 USING rtree(ii, $cols);
      CREATE TABLE t2 (ii, $cols);
    "
  } {}

  do_test rtree2-$nDim.2 {
    db transaction {
      for {set ii 0} {$ii < $::NROW} {incr ii} {
#puts "Row $ii"
        set values [list]
        for {set jj 0} {$jj<$nDim*2} {incr jj} {
          lappend values [expr int(rand()*1000)]
        }
        set values [join $values ,]
#puts [rtree_treedump db t1]
#puts "INSERT INTO t2 VALUES($ii, $values)"
        set rc [catch {db eval "INSERT INTO t1 VALUES($ii, $values)"}]
        if {$rc} {
          incr ii -1
        } else {
          db eval "INSERT INTO t2 VALUES($ii, $values)"
        }
#if {[rtree_check db t1]} {
#puts [rtree_treedump db t1]
#exit
#}
      }
    }

    set t1 [execsql {SELECT * FROM t1 ORDER BY ii}]
    set t2 [execsql {SELECT * FROM t2 ORDER BY ii}]
    set rc [expr {$t1 eq $t2}]
    if {$rc != 1} {
      puts $t1
      puts $t2
    }
    set rc
  } {1}

  do_test rtree2-$nDim.3 {
    rtree_check db t1
  } 0

  set OPS [list < > <= >= =]
  for {set ii 0} {$ii < $::NSELECT} {incr ii} {
    do_test rtree2-$nDim.4.$ii.1 {
      set where [list]
      foreach look_three_dots! {. . .} {
        set colidx [expr int(rand()*($nDim*2+1))-1]
        if {$colidx<0} {
          set col ii
        } else {
          set col "c$colidx"
        }
        set op  [lindex $OPS [expr int(rand()*[llength $OPS])]]
        set val [expr int(rand()*1000)]
        lappend where "$col $op $val"
      }
      set where [join $where " AND "]

      set t1 [execsql "SELECT * FROM t1 WHERE $where ORDER BY ii"]
      set t2 [execsql "SELECT * FROM t2 WHERE $where ORDER BY ii"]
      set rc [expr {$t1 eq $t2}]
      if {$rc != 1} {
puts $where
        puts $t1
        puts $t2
puts [rtree_treedump db t1]
breakpoint
set t1 [execsql "SELECT * FROM t1 WHERE $where ORDER BY ii"]
exit
      }
      set rc
    } {1}
  }

  for {set ii 0} {$ii < $::NROW} {incr ii $::NDEL} {
    #puts [rtree_treedump db t1]
    do_test rtree2-$nDim.5.$ii.1 {
      execsql "DELETE FROM t2 WHERE ii <= $::ii"
      execsql "DELETE FROM t1 WHERE ii <= $::ii"

      set t1 [execsql {SELECT * FROM t1 ORDER BY ii}]
      set t2 [execsql {SELECT * FROM t2 ORDER BY ii}]
      set rc [expr {$t1 eq $t2}]
      if {$rc != 1} {
        puts $t1
        puts $t2
      }
      set rc
    } {1}
    do_test rtree2-$nDim.5.$ii.2 {
      rtree_check db t1
    } {0}
  }

  do_test rtree2-$nDim.6 {
    execsql {
      DROP TABLE t1;
      DROP TABLE t2;
    }
  } {}
}

finish_test

Added ext/rtree/rtree3.test.

















































































































































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# 2008 Feb 19
#
# 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.
#
#***********************************************************************
#
# The focus of this file is testing that the r-tree correctly handles
# out-of-memory conditions.
#
# $Id: rtree3.test,v 1.1 2008/05/26 18:41:54 danielk1977 Exp $
#

set testdir [file join [file dirname $argv0] .. .. test]
source $testdir/tester.tcl

ifcapable !rtree {
  finish_test
  return
}

# Only run these tests if memory debugging is turned on.
#
source $testdir/malloc_common.tcl
if {!$MEMDEBUG} {
   puts "Skipping malloc tests: not compiled with -DSQLITE_MEMDEBUG..."
   finish_test
   return
}

do_malloc_test rtree3-1 -sqlbody {
  BEGIN TRANSACTION;
  CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
  INSERT INTO rt VALUES(NULL, 3, 5, 7, 9);
  INSERT INTO rt VALUES(NULL, 13, 15, 17, 19);
  DELETE FROM rt WHERE ii = 1;
  SELECT * FROM rt;
  SELECT ii FROM rt WHERE ii = 2;
  COMMIT;
} 
do_malloc_test rtree3-2 -sqlprep {
  CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
  INSERT INTO rt VALUES(NULL, 3, 5, 7, 9);
} -sqlbody {
  DROP TABLE rt;
} 


do_malloc_test rtree3-3 -sqlprep {
  CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
  INSERT INTO rt VALUES(NULL, 3, 5, 7, 9);
} -tclbody {
  db eval BEGIN
  for {set ii 0} {$ii < 100} {incr ii} {
    set f [expr rand()]
    db eval {INSERT INTO rt VALUES(NULL, $f*10.0, $f*10.0, $f*15.0, $f*15.0)}
  }
  db eval COMMIT
  db eval BEGIN
  for {set ii 0} {$ii < 100} {incr ii} {
    set f [expr rand()]
    db eval { DELETE FROM rt WHERE x1<($f*10.0) AND x1>($f*10.5) }
  }
  db eval COMMIT
} 

finish_test

Added ext/rtree/rtree_perf.tcl.

























































































































































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set testdir [file join [file dirname $argv0] .. .. test]
source $testdir/tester.tcl

ifcapable !rtree {
  finish_test
  return
}

set NROW   10000
set NQUERY   500

puts "Generating $NROW rows of data..."
set data [list]
for {set ii 0} {$ii < $NROW} {incr ii} {
  set x1 [expr {rand()*1000}]
  set x2 [expr {$x1+rand()*50}]
  set y1 [expr {rand()*1000}]
  set y2 [expr {$y1+rand()*50}]
  lappend data $x1 $x2 $y1 $y2
}
puts "Finished generating data"


set sql1 {CREATE TABLE btree(ii INTEGER PRIMARY KEY, x1, x2, y1, y2)}
set sql2 {CREATE VIRTUAL TABLE rtree USING rtree(ii, x1, x2, y1, y2)}
puts "Creating tables:"
puts "  $sql1"
puts "  $sql2"
db eval $sql1
db eval $sql2

db eval "pragma cache_size=100"

puts -nonewline "Inserting into btree... "
flush stdout
set btree_time [time {db transaction {
  set ii 1
  foreach {x1 x2 y1 y2} $data {
    db eval {INSERT INTO btree VALUES($ii, $x1, $x2, $y1, $y2)}
    incr ii
  }
}}]
puts "$btree_time"

puts -nonewline "Inserting into rtree... "
flush stdout
set rtree_time [time {db transaction {
  set ii 1
  foreach {x1 x2 y1 y2} $data {
    incr ii
    db eval {INSERT INTO rtree VALUES($ii, $x1, $x2, $y1, $y2)}
  }
}}]
puts "$rtree_time"


puts -nonewline "Selecting from btree... "
flush stdout
set btree_select_time [time {
  foreach {x1 x2 y1 y2} [lrange $data 0 [expr $NQUERY*4-1]] {
    db eval {SELECT * FROM btree WHERE x1<$x1 AND x2>$x2 AND y1<$y1 AND y2>$y2}
 }
}]
puts "$btree_select_time"

puts -nonewline "Selecting from rtree... "
flush stdout
set rtree_select_time [time {
  foreach {x1 x2 y1 y2} [lrange $data 0 [expr $NQUERY*4-1]] {
    db eval {SELECT * FROM rtree WHERE x1<$x1 AND x2>$x2 AND y1<$y1 AND y2>$y2}
  }
}]
puts "$rtree_select_time"


Added ext/rtree/rtree_util.tcl.







































































































































































































































































































































































































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# 2008 Feb 19
#
# 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 Tcl code that may be useful for testing or
# analyzing r-tree structures created with this module. It is
# used by both test procedures and the r-tree viewer application.
#
# $Id: rtree_util.tcl,v 1.1 2008/05/26 18:41:54 danielk1977 Exp $
#


#--------------------------------------------------------------------------
# PUBLIC API:
#
#   rtree_depth
#   rtree_ndim
#   rtree_node
#   rtree_mincells
#   rtree_check
#   rtree_dump
#   rtree_treedump
#

proc rtree_depth {db zTab} {
  $db one "SELECT rtreedepth(data) FROM ${zTab}_node WHERE nodeno=1"
}

proc rtree_nodedepth {db zTab iNode} {
  set iDepth [rtree_depth $db $zTab]
  
  set ii $iNode
  while {$ii != 1} {
    set sql "SELECT parentnode FROM ${zTab}_parent WHERE nodeno = $ii"
    set ii [db one $sql]
    incr iDepth -1
  }
  
  return $iDepth
}

# Return the number of dimensions of the rtree.
#
proc rtree_ndim {db zTab} {
  set nDim [expr {(([llength [$db eval "pragma table_info($zTab)"]]/6)-1)/2}]
}

# Return the contents of rtree node $iNode.
#
proc rtree_node {db zTab iNode {iPrec 6}} {
  set nDim [rtree_ndim $db $zTab]
  set sql "
    SELECT rtreenode($nDim, data) FROM ${zTab}_node WHERE nodeno = $iNode
  "
  set node [db one $sql]

  set nCell [llength $node]
  set nCoord [expr $nDim*2]
  for {set ii 0} {$ii < $nCell} {incr ii} {
    for {set jj 1} {$jj <= $nCoord} {incr jj} {
      set newval [format "%.${iPrec}f" [lindex $node $ii $jj]]
      lset node $ii $jj $newval
    }
  }
  set node
}

proc rtree_mincells {db zTab} {
  set n [$db one "select length(data) FROM ${zTab}_node LIMIT 1"]
  set nMax [expr {int(($n-4)/(8+[rtree_ndim $db $zTab]*2*4))}]
  return [expr {int($nMax/3)}]
}

# An integrity check for the rtree $zTab accessible via database 
# connection $db.
#
proc rtree_check {db zTab} {
  array unset ::checked
 
  # Check each r-tree node.
  set rc [catch {
    rtree_node_check $db $zTab 1 [rtree_depth $db $zTab]
  } msg]
  if {$rc && $msg ne ""} { error $msg }

  # Check that the _rowid and _parent tables have the right 
  # number of entries.
  set nNode   [$db one "SELECT count(*) FROM ${zTab}_node"]
  set nRow    [$db one "SELECT count(*) FROM ${zTab}"]
  set nRowid  [$db one "SELECT count(*) FROM ${zTab}_rowid"]
  set nParent [$db one "SELECT count(*) FROM ${zTab}_parent"]

  if {$nNode != ($nParent+1)} { 
    error "Wrong number of entries in ${zTab}_parent"
  }
  if {$nRow != $nRowid} { 
    error "Wrong number of entries in ${zTab}_rowid"
  }
  
  return $rc
}

proc rtree_node_check {db zTab iNode iDepth} {
  if {[info exists ::checked($iNode)]} { error "Second ref to $iNode" }
  set ::checked($iNode) 1

  set node [rtree_node $db $zTab $iNode]
  if {$iNode!=1 && [llength $node]==0} { error "No such node: $iNode" }

  if {$iNode != 1 && [llength $node]<[rtree_mincells $db $zTab]} {
    puts "Node $iNode: Has only [llength $node] cells"
    error ""
  }
  if {$iNode == 1 && [llength $node]==1 && [rtree_depth $db $zTab]>0} {
    set depth [rtree_depth $db $zTab]
    puts "Node $iNode: Has only 1 child (tree depth is $depth)"
    error ""
  }

  set nDim [expr {([llength [lindex $node 0]]-1)/2}]

  if {$iDepth > 0} {
    set d [expr $iDepth-1]
    foreach cell $node {
      set shouldbe [rtree_node_check $db $zTab [lindex $cell 0] $d]
      if {$cell ne $shouldbe} {
        puts "Node $iNode: Cell is: {$cell}, should be {$shouldbe}"
        error ""
      }
    }
  }

  set mapping_table "${zTab}_parent" 
  set mapping_sql "SELECT parentnode FROM $mapping_table WHERE rowid = \$rowid"
  if {$iDepth==0} { 
    set mapping_table "${zTab}_rowid"
    set mapping_sql "SELECT nodeno FROM $mapping_table WHERE rowid = \$rowid"
  }
  foreach cell $node {
    set rowid [lindex $cell 0]
    set mapping [db one $mapping_sql]
    if {$mapping != $iNode} {
      puts "Node $iNode: $mapping_table entry for cell $rowid is $mapping"
      error ""
    }
  }

  set ret [list $iNode]
  for {set ii 1} {$ii <= $nDim*2} {incr ii} {
    set f [lindex $node 0 $ii]
    foreach cell $node {
      set f2 [lindex $cell $ii]
      if {($ii%2)==1 && $f2<$f} {set f $f2}
      if {($ii%2)==0 && $f2>$f} {set f $f2}
    }
    lappend ret $f
  }
  return $ret
}

proc rtree_dump {db zTab} {
  set zRet ""
  set nDim [expr {(([llength [$db eval "pragma table_info($zTab)"]]/6)-1)/2}]
  set sql "SELECT nodeno, rtreenode($nDim, data) AS node FROM ${zTab}_node"
  $db eval $sql {
    append zRet [format "% -10s %s\n" $nodeno $node]
  }
  set zRet
}

proc rtree_nodetreedump {db zTab zIndent iDepth iNode} {
  set ret ""
  set node [rtree_node $db $zTab $iNode 1]
  append ret [format "%-3d %s%s\n" $iNode $zIndent $node]
  if {$iDepth>0} {
    foreach cell $node {
      set i [lindex $cell 0]
      append ret [rtree_nodetreedump $db $zTab "$zIndent  " [expr $iDepth-1] $i]
    }
  }
  set ret
}

proc rtree_treedump {db zTab} {
  set d [rtree_depth $db $zTab]
  rtree_nodetreedump $db $zTab "" $d 1
}

Added ext/rtree/viewrtree.tcl.



























































































































































































































































































































































































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load ./libsqlite3.dylib
#package require sqlite3
source [file join [file dirname $argv0] rtree_util.tcl]

wm title . "SQLite r-tree viewer"

if {[llength $argv]!=1} {
  puts stderr "Usage: $argv0 <database-file>"
  puts stderr ""
  exit
}
sqlite3 db [lindex $argv 0]

canvas .c -background white -width 400 -height 300 -highlightthickness 0

button .b -text "Parent Node" -command {
  set sql "SELECT parentnode FROM $::O(zTab)_parent WHERE nodeno = $::O(iNode)"
  set ::O(iNode) [db one $sql]
  if {$::O(iNode) eq ""} {set ::O(iNode) 1}
  view_node
}

set O(iNode) 1
set O(zTab) ""
set O(listbox_captions)  [list]
set O(listbox_itemmap)   [list]
set O(listbox_highlight) -1

listbox   .l -listvariable ::O(listbox_captions) -yscrollcommand {.ls set}
scrollbar .ls -command {.l yview}
label     .status -font courier -anchor w
label     .title -anchor w -text "Node 1:" -background white -borderwidth 0


set rtree_tables [list]
db eval {
  SELECT name 
  FROM sqlite_master 
  WHERE type='table' AND sql LIKE '%virtual%table%using%rtree%'
} {
  set nCol [expr [llength [db eval "pragma table_info($name)"]]/6]
  if {$nCol != 5} {
    puts stderr "Not viewing $name - is not 2-dimensional"
  } else {
    lappend rtree_tables [list Table $name]
  }
}
if {$rtree_tables eq ""} {
  puts stderr "Cannot find an r-tree table in database [lindex $argv 0]"
  puts stderr ""
  exit
}
eval tk_optionMenu .select option_var $rtree_tables
trace add variable option_var write set_option_var
proc set_option_var {args} {
  set ::O(zTab) [lindex $::option_var 1]
  set ::O(iNode) 1
  view_node
}
set ::O(zTab) [lindex $::rtree_tables 0 1]

bind .l <1> {listbox_click [.l nearest %y]}
bind .l <Motion> {listbox_mouseover [.l nearest %y]}
bind .l <Leave>  {listbox_mouseover -1}

proc listbox_click {sel} {
  if {$sel ne ""} {
    set ::O(iNode) [lindex $::O(listbox_captions) $sel 1]
    view_node
  }
}
proc listbox_mouseover {i} {
  set oldid [lindex $::O(listbox_itemmap) $::O(listbox_highlight)]
  .c itemconfigure $oldid -fill ""

  .l selection clear 0 end
  .status configure -text ""
  if {$i>=0} {
    set id [lindex $::O(listbox_itemmap) $i]
    .c itemconfigure $id -fill grey
    .c lower $id
    set ::O(listbox_highlight) $i
    .l selection set $i
    .status configure -text [cell_report db $::O(zTab) $::O(iNode) $i]
  }
}

grid configure .select  -row 0 -column 0 -columnspan 2 -sticky nsew
grid configure .b       -row 1 -column 0 -columnspan 2 -sticky nsew
grid configure .l       -row 2 -column 0               -sticky nsew
grid configure .status  -row 3 -column 0 -columnspan 3 -sticky nsew

grid configure .title   -row 0 -column 2               -sticky nsew
grid configure .c       -row 1 -column 2 -rowspan 2    -sticky nsew
grid configure .ls      -row 2 -column 1               -sticky nsew

grid columnconfigure . 2 -weight 1
grid rowconfigure    . 2 -weight 1

proc node_bbox {data} {
  set xmin 0
  set xmax 0
  set ymin 0
  set ymax 0
  foreach {rowid xmin xmax ymin ymax} [lindex $data 0] break
  foreach cell [lrange $data 1 end] {
    foreach {rowid x1 x2 y1 y2} $cell break
    if {$x1 < $xmin} {set xmin $x1}
    if {$x2 > $xmax} {set xmax $x2}
    if {$y1 < $ymin} {set ymin $y1}
    if {$y2 > $ymax} {set ymax $y2}
  }
  list $xmin $xmax $ymin $ymax
}

proc view_node {} {
  set iNode $::O(iNode)
  set zTab $::O(zTab)

  set data [rtree_node db $zTab $iNode 12]
  set depth [rtree_nodedepth db $zTab $iNode]

  .c delete all
  set ::O(listbox_captions) [list]
  set ::O(listbox_itemmap) [list]
  set $::O(listbox_highlight) -1

  .b configure -state normal
  if {$iNode == 1} {.b configure -state disabled}
  .title configure -text "Node $iNode: [cell_report db $zTab $iNode -1]"

  foreach {xmin xmax ymin ymax} [node_bbox $data] break
  set total_area 0.0

  set xscale [expr {double([winfo width .c]-20)/($xmax-$xmin)}]
  set yscale [expr {double([winfo height .c]-20)/($ymax-$ymin)}]

  set xoff [expr {10.0 - $xmin*$xscale}]
  set yoff [expr {10.0 - $ymin*$yscale}]

  foreach cell $data {
    foreach {rowid x1 x2 y1 y2} $cell break
    set total_area [expr {$total_area + ($x2-$x1)*($y2-$y1)}]
    set x1 [expr {$x1*$xscale + $xoff}]
    set x2 [expr {$x2*$xscale + $xoff}]
    set y1 [expr {$y1*$yscale + $yoff}]
    set y2 [expr {$y2*$yscale + $yoff}]

    set id [.c create rectangle $x1 $y1 $x2 $y2]
    if {$depth>0} {
      lappend ::O(listbox_captions) "Node $rowid"
      lappend ::O(listbox_itemmap) $id
    }
  }
}

proc cell_report {db zTab iParent iCell} {
  set data [rtree_node db $zTab $iParent 12]
  set cell [lindex $data $iCell]

  foreach {xmin xmax ymin ymax} [node_bbox $data] break
  set total_area [expr ($xmax-$xmin)*($ymax-$ymin)]

  if {$cell eq ""} {
    set cell_area 0.0
    foreach cell $data {
      foreach {rowid x1 x2 y1 y2} $cell break
      set cell_area [expr $cell_area+($x2-$x1)*($y2-$y1)]
    }
    set cell_area [expr $cell_area/[llength $data]]
    set zReport [format "Size = %.1f x %.1f    Average child area = %.1f%%" \
      [expr $xmax-$xmin] [expr $ymax-$ymin] [expr 100.0*$cell_area/$total_area]\
    ]
    append zReport "   Sub-tree height: [rtree_nodedepth db $zTab $iParent]"
  } else {
    foreach {rowid x1 x2 y1 y2} $cell break
    set cell_area  [expr ($x2-$x1)*($y2-$y1)]
    set zReport [format "Size = %.1f x %.1f    Area = %.1f%%" \
      [expr $x2-$x1] [expr $y2-$y1] [expr 100.0*$cell_area/$total_area]
    ]
  }

  return $zReport
}

view_node
bind .c <Configure> view_node

Changes to main.mk.

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         main.o malloc.o mem1.o mem2.o mem3.o mem4.o mem5.o \
         mutex.o mutex_os2.o mutex_unix.o mutex_w32.o \
         opcodes.o os.o os_os2.o os_unix.o os_win.o \
         pager.o parse.o pragma.o prepare.o printf.o random.o \
         select.o table.o $(TCLOBJ) tokenize.o trigger.o \
         update.o util.o vacuum.o \
         vdbe.o vdbeapi.o vdbeaux.o vdbeblob.o vdbefifo.o vdbemem.o \
         where.o utf.o legacy.o vtab.o

EXTOBJ = icu.o
EXTOBJ += fts1.o \
	  fts1_hash.o \
	  fts1_tokenizer1.o \
	  fts1_porter.o
EXTOBJ += fts2.o \
................................................................................
	$(TCCX) -DSQLITE_CORE -c $(TOP)/ext/fts3/fts3_porter.c

fts3_tokenizer.o:	$(TOP)/ext/fts3/fts3_tokenizer.c $(HDR) $(EXTHDR)
	$(TCCX) -DSQLITE_CORE -c $(TOP)/ext/fts3/fts3_tokenizer.c

fts3_tokenizer1.o:	$(TOP)/ext/fts3/fts3_tokenizer1.c $(HDR) $(EXTHDR)
	$(TCCX) -DSQLITE_CORE -c $(TOP)/ext/fts3/fts3_tokenizer1.c





# Rules for building test programs and for running tests
#
tclsqlite3:	$(TOP)/src/tclsqlite.c libsqlite3.a
	$(TCCX) $(TCL_FLAGS) -DTCLSH=1 -o tclsqlite3 \
		$(TOP)/src/tclsqlite.c libsqlite3.a $(LIBTCL) $(THREADLIB)







|







 







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         main.o malloc.o mem1.o mem2.o mem3.o mem4.o mem5.o \
         mutex.o mutex_os2.o mutex_unix.o mutex_w32.o \
         opcodes.o os.o os_os2.o os_unix.o os_win.o \
         pager.o parse.o pragma.o prepare.o printf.o random.o \
         select.o table.o $(TCLOBJ) tokenize.o trigger.o \
         update.o util.o vacuum.o \
         vdbe.o vdbeapi.o vdbeaux.o vdbeblob.o vdbefifo.o vdbemem.o \
         where.o utf.o legacy.o vtab.o rtree.o

EXTOBJ = icu.o
EXTOBJ += fts1.o \
	  fts1_hash.o \
	  fts1_tokenizer1.o \
	  fts1_porter.o
EXTOBJ += fts2.o \
................................................................................
	$(TCCX) -DSQLITE_CORE -c $(TOP)/ext/fts3/fts3_porter.c

fts3_tokenizer.o:	$(TOP)/ext/fts3/fts3_tokenizer.c $(HDR) $(EXTHDR)
	$(TCCX) -DSQLITE_CORE -c $(TOP)/ext/fts3/fts3_tokenizer.c

fts3_tokenizer1.o:	$(TOP)/ext/fts3/fts3_tokenizer1.c $(HDR) $(EXTHDR)
	$(TCCX) -DSQLITE_CORE -c $(TOP)/ext/fts3/fts3_tokenizer1.c

rtree.o:	$(TOP)/ext/rtree/rtree.c $(HDR) $(EXTHDR)
	$(TCCX) -DSQLITE_CORE -c $(TOP)/ext/rtree/rtree.c


# Rules for building test programs and for running tests
#
tclsqlite3:	$(TOP)/src/tclsqlite.c libsqlite3.a
	$(TCCX) $(TCL_FLAGS) -DTCLSH=1 -o tclsqlite3 \
		$(TOP)/src/tclsqlite.c libsqlite3.a $(LIBTCL) $(THREADLIB)

Changes to src/main.c.

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**
*************************************************************************
** Main file for the SQLite library.  The routines in this file
** implement the programmer interface to the library.  Routines in
** other files are for internal use by SQLite and should not be
** accessed by users of the library.
**
** $Id: main.c,v 1.440 2008/05/22 13:56:17 danielk1977 Exp $
*/
#include "sqliteInt.h"
#include <ctype.h>
#ifdef SQLITE_ENABLE_FTS3
# include "fts3.h"
#endif

................................................................................

#ifdef SQLITE_ENABLE_ICU
  if( !db->mallocFailed && rc==SQLITE_OK ){
    extern int sqlite3IcuInit(sqlite3*);
    rc = sqlite3IcuInit(db);
  }
#endif








  sqlite3Error(db, rc, 0);

  /* -DSQLITE_DEFAULT_LOCKING_MODE=1 makes EXCLUSIVE the default locking
  ** mode.  -DSQLITE_DEFAULT_LOCKING_MODE=0 make NORMAL the default locking
  ** mode.  Doing nothing at all also makes NORMAL the default.
  */
#ifdef SQLITE_DEFAULT_LOCKING_MODE







|







 







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**
*************************************************************************
** Main file for the SQLite library.  The routines in this file
** implement the programmer interface to the library.  Routines in
** other files are for internal use by SQLite and should not be
** accessed by users of the library.
**
** $Id: main.c,v 1.441 2008/05/26 18:41:54 danielk1977 Exp $
*/
#include "sqliteInt.h"
#include <ctype.h>
#ifdef SQLITE_ENABLE_FTS3
# include "fts3.h"
#endif

................................................................................

#ifdef SQLITE_ENABLE_ICU
  if( !db->mallocFailed && rc==SQLITE_OK ){
    extern int sqlite3IcuInit(sqlite3*);
    rc = sqlite3IcuInit(db);
  }
#endif

#ifdef SQLITE_ENABLE_RTREE
  if( !db->mallocFailed && rc==SQLITE_OK){
    extern int sqlite3RtreeInit(sqlite3*);
    rc = sqlite3RtreeInit(db);
  }
#endif

  sqlite3Error(db, rc, 0);

  /* -DSQLITE_DEFAULT_LOCKING_MODE=1 makes EXCLUSIVE the default locking
  ** mode.  -DSQLITE_DEFAULT_LOCKING_MODE=0 make NORMAL the default locking
  ** mode.  Doing nothing at all also makes NORMAL the default.
  */
#ifdef SQLITE_DEFAULT_LOCKING_MODE

Changes to src/test_config.c.

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** 
** This file contains code used for testing the SQLite system.
** None of the code in this file goes into a deliverable build.
** 
** The focus of this file is providing the TCL testing layer
** access to compile-time constants.
**
** $Id: test_config.c,v 1.25 2008/04/14 01:00:58 drh Exp $
*/

#include "sqliteLimit.h"

#include "sqliteInt.h"
#include "tcl.h"
#include <stdlib.h>
................................................................................
#endif

#ifdef SQLITE_OMIT_REINDEX
  Tcl_SetVar2(interp, "sqlite_options", "reindex", "0", TCL_GLOBAL_ONLY);
#else
  Tcl_SetVar2(interp, "sqlite_options", "reindex", "1", TCL_GLOBAL_ONLY);
#endif







#ifdef SQLITE_OMIT_SCHEMA_PRAGMAS
  Tcl_SetVar2(interp, "sqlite_options", "schema_pragmas", "0", TCL_GLOBAL_ONLY);
#else
  Tcl_SetVar2(interp, "sqlite_options", "schema_pragmas", "1", TCL_GLOBAL_ONLY);
#endif








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** 
** This file contains code used for testing the SQLite system.
** None of the code in this file goes into a deliverable build.
** 
** The focus of this file is providing the TCL testing layer
** access to compile-time constants.
**
** $Id: test_config.c,v 1.26 2008/05/26 18:41:54 danielk1977 Exp $
*/

#include "sqliteLimit.h"

#include "sqliteInt.h"
#include "tcl.h"
#include <stdlib.h>
................................................................................
#endif

#ifdef SQLITE_OMIT_REINDEX
  Tcl_SetVar2(interp, "sqlite_options", "reindex", "0", TCL_GLOBAL_ONLY);
#else
  Tcl_SetVar2(interp, "sqlite_options", "reindex", "1", TCL_GLOBAL_ONLY);
#endif

#ifdef SQLITE_ENABLE_RTREE
  Tcl_SetVar2(interp, "sqlite_options", "rtree", "1", TCL_GLOBAL_ONLY);
#else
  Tcl_SetVar2(interp, "sqlite_options", "rtree", "0", TCL_GLOBAL_ONLY);
#endif

#ifdef SQLITE_OMIT_SCHEMA_PRAGMAS
  Tcl_SetVar2(interp, "sqlite_options", "schema_pragmas", "0", TCL_GLOBAL_ONLY);
#else
  Tcl_SetVar2(interp, "sqlite_options", "schema_pragmas", "1", TCL_GLOBAL_ONLY);
#endif