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Overview
Comment:Add the sqlite3_rtree_query_callback() API to the RTree virtual table.
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SHA1: 3dca2809352c6c6d56db74447a814f77011c6220
User & Date: drh 2014-04-28 17:51:12
Context
2014-04-28
18:02
Merge all recent trunk enhancements and fixes into the sessions branch. check-in: e158812c user: drh tags: sessions
17:56
Add the sqlite3_rtree_query_callback() API to the RTree virtual table. (Cherrypick from the sessions branch.) check-in: af2cbe64 user: drh tags: trunk
17:51
Add the sqlite3_rtree_query_callback() API to the RTree virtual table. check-in: 3dca2809 user: drh tags: sessions
2014-04-25
16:29
Enhance the sqlite3_rtree_query_info object to report on the number of elements in the priority queue at each level. Closed-Leaf check-in: f7dad408 user: drh tags: rtree-enhancements
2014-04-18
01:10
Merge recent trunk changes into sessions. check-in: 95e77efe user: drh tags: sessions
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**      of 4-byte coordinates. For leaf nodes the integer is the rowid
**      of a record. For internal nodes it is the node number of a
**      child page.
*/

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

/*
** 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

#if !defined(NDEBUG) && !defined(SQLITE_DEBUG) 
# define NDEBUG 1
#endif

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

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


#ifndef SQLITE_AMALGAMATION
#include "sqlite3rtree.h"
typedef sqlite3_int64 i64;
typedef unsigned char u8;

typedef unsigned int u32;
#endif

/*  The following macro is used to suppress compiler warnings.
*/
#ifndef UNUSED_PARAMETER
# define UNUSED_PARAMETER(x) (void)(x)
................................................................................
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;
typedef struct RtreeMatchArg RtreeMatchArg;
typedef struct RtreeGeomCallback RtreeGeomCallback;
typedef union RtreeCoord RtreeCoord;


/* 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

/* The xBestIndex method of this virtual table requires an estimate of
** the number of rows in the virtual table to calculate the costs of
** various strategies. If possible, this estimate is loaded from the
** sqlite_stat1 table (with RTREE_MIN_ROWEST as a hard-coded minimum).
** Otherwise, if no sqlite_stat1 entry is available, use 
** RTREE_DEFAULT_ROWEST.
................................................................................
#define RTREE_DEFAULT_ROWEST 1048576
#define RTREE_MIN_ROWEST         100

/* 
** An rtree virtual-table object.
*/
struct Rtree {
  sqlite3_vtab base;
  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 */
  i64 nRowEst;                /* Estimated number of rows in this table */

  /* List of nodes removed during a CondenseTree operation. List is
  ** linked together via the pointer normally used for hash chains -
  ** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree 
  ** headed by the node (leaf nodes have RtreeNode.iNode==0).
................................................................................
  sqlite3_stmt *pDeleteRowid;

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

  int eCoordType;
};

/* Possible values for eCoordType: */
#define RTREE_COORD_REAL32 0
#define RTREE_COORD_INT32  1

/*
** If SQLITE_RTREE_INT_ONLY is defined, then this virtual table will
** only deal with integer coordinates.  No floating point operations
** will be done.
*/
#ifdef SQLITE_RTREE_INT_ONLY
  typedef sqlite3_int64 RtreeDValue;       /* High accuracy coordinate */
  typedef int RtreeValue;                  /* Low accuracy coordinate */

#else
  typedef double RtreeDValue;              /* High accuracy coordinate */
  typedef float RtreeValue;                /* Low accuracy coordinate */

#endif


















/*
** The minimum number of cells allowed for a node is a third of the 
** maximum. In Gutman's notation:
**
**     m = M/3
**
................................................................................
** supported cell size is 48 bytes (8 byte rowid + ten 4 byte coordinates).
** Therefore all non-root nodes must contain at least 3 entries. Since 
** 2^40 is greater than 2^64, an r-tree structure always has a depth of
** 40 or less.
*/
#define RTREE_MAX_DEPTH 40









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







};








union RtreeCoord {
  RtreeValue f;
  int i;


};

/*
** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
** formatted as a RtreeDValue (double or int64). This macro assumes that local
** variable pRtree points to the Rtree structure associated with the
** RtreeCoord.
................................................................................

/*
** A search constraint.
*/
struct RtreeConstraint {
  int iCoord;                     /* Index of constrained coordinate */
  int op;                         /* Constraining operation */

  RtreeDValue rValue;             /* Constraint value. */
  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
  sqlite3_rtree_geometry *pGeom;  /* Constraint callback argument for a MATCH */



};

/* 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
#define RTREE_MATCH 0x46



/* 
** An rtree structure node.
*/
struct RtreeNode {
  RtreeNode *pParent;               /* Parent node */
  i64 iNode;
  int nRef;
  int isDirty;
  u8 *zData;
  RtreeNode *pNext;                 /* Next node in this hash chain */
};


#define NCELL(pNode) readInt16(&(pNode)->zData[2])

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






















};


/*
** Value for the first field of every RtreeMatchArg object. The MATCH
** operator tests that the first field of a blob operand matches this
** value to avoid operating on invalid blobs (which could cause a segfault).
*/
#define RTREE_GEOMETRY_MAGIC 0x891245AB

/*
** An instance of this structure must be supplied as a blob argument to
** the right-hand-side of an SQL MATCH operator used to constrain an
** r-tree query.

*/
struct RtreeMatchArg {
  u32 magic;                      /* Always RTREE_GEOMETRY_MAGIC */
  int (*xGeom)(sqlite3_rtree_geometry *, int, RtreeDValue*, int *);
  void *pContext;
  int nParam;
  RtreeDValue aParam[1];
};

/*
** When a geometry callback is created (see sqlite3_rtree_geometry_callback),
** a single instance of the following structure is allocated. It is used
** as the context for the user-function created by by s_r_g_c(). The object
** is eventually deleted by the destructor mechanism provided by
** sqlite3_create_function_v2() (which is called by s_r_g_c() to create
** the geometry callback function).
*/
struct RtreeGeomCallback {
  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
  void *pContext;
};

#ifndef MAX
# define MAX(x,y) ((x) < (y) ? (y) : (x))
#endif
#ifndef MIN
# define MIN(x,y) ((x) > (y) ? (y) : (x))
................................................................................
}

/*
** 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){
................................................................................
  }
  return pNode;
}

/*
** Obtain a reference to an r-tree node.
*/
static int
nodeAcquire(
  Rtree *pRtree,             /* R-tree structure */
  i64 iNode,                 /* Node number to load */
  RtreeNode *pParent,        /* Either the parent node or NULL */
  RtreeNode **ppNode         /* OUT: Acquired node */
){
  int rc;
  int rc2 = SQLITE_OK;
................................................................................
  return rc;
}

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

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

/*
** 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);

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

  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);
................................................................................
  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;
................................................................................

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

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

/*
** Deserialize cell iCell of node pNode. Populate the structure pointed
** to by pCell with the results.
*/
static void nodeGetCell(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  int iCell,
  RtreeCell *pCell
){
  int ii;


  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);

  for(ii=0; ii<pRtree->nDim*2; ii++){
    nodeGetCoord(pRtree, pNode, iCell, ii, &pCell->aCoord[ii]);



  }
}


/* Forward declaration for the function that does the work of
** the virtual table module xCreate() and xConnect() methods.
*/
................................................................................
/*
** Free the RtreeCursor.aConstraint[] array and its contents.
*/
static void freeCursorConstraints(RtreeCursor *pCsr){
  if( pCsr->aConstraint ){
    int i;                        /* Used to iterate through constraint array */
    for(i=0; i<pCsr->nConstraint; i++){
      sqlite3_rtree_geometry *pGeom = pCsr->aConstraint[i].pGeom;
      if( pGeom ){
        if( pGeom->xDelUser ) pGeom->xDelUser(pGeom->pUser);
        sqlite3_free(pGeom);
      }
    }
    sqlite3_free(pCsr->aConstraint);
    pCsr->aConstraint = 0;
  }
}

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

  rc = nodeRelease(pRtree, pCsr->pNode);
  sqlite3_free(pCsr);
  return rc;
}

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

}

/*
** The r-tree constraint passed as the second argument to this function is
** guaranteed to be a MATCH constraint.













*/
static int testRtreeGeom(
  Rtree *pRtree,                  /* R-Tree object */
  RtreeConstraint *pConstraint,   /* MATCH constraint to test */
  RtreeCell *pCell,               /* Cell to test */



  int *pbRes                      /* OUT: Test result */
){
  int i;
  RtreeDValue aCoord[RTREE_MAX_DIMENSIONS*2];
  int nCoord = pRtree->nDim*2;




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






  for(i=0; i<nCoord; i++){
    aCoord[i] = DCOORD(pCell->aCoord[i]);






  }
  return pConstraint->xGeom(pConstraint->pGeom, nCoord, aCoord, pbRes);

}

/* 
** Cursor pCursor currently points to a cell in a non-leaf page.
** Set *pbEof to true if the sub-tree headed by the cell is filtered
** (excluded) by the constraints in the pCursor->aConstraint[] 
** array, or false otherwise.
**
** Return SQLITE_OK if successful or an SQLite error code if an error
** occurs within a geometry callback.


*/
static int testRtreeCell(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
  RtreeCell cell;
  int ii;
  int bRes = 0;
  int rc = SQLITE_OK;

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

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





    );






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



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



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




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













      }
    }
  }

  *pbEof = bRes;
  return rc;
}

/* 
** Test if the cell that cursor pCursor currently points to
** would be filtered (excluded) by the constraints in the 
** pCursor->aConstraint[] array. If so, set *pbEof to true before
** returning. If the cell is not filtered (excluded) by the constraints,
** set pbEof to zero.



**
** Return SQLITE_OK if successful or an SQLite error code if an error
** occurs within a geometry callback.
**
** This function assumes that the cell is part of a leaf node.










*/
static int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
  RtreeCell cell;
  int ii;
  *pbEof = 0;


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

        break;



      }
    }

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



    }

  }

  return SQLITE_OK;
}

/*
** Cursor pCursor currently points at a node that heads a sub-tree of
** height iHeight (if iHeight==0, then the node is a leaf). Descend
** to point to the left-most cell of the sub-tree that matches the 
** configured constraints.





*/
static int descendToCell(
  Rtree *pRtree, 
  RtreeCursor *pCursor, 
  int iHeight,
  int *pEof                 /* OUT: Set to true if cannot descend */





){
  int isEof;
  int rc;
  int ii;
  RtreeNode *pChild;
  sqlite3_int64 iRowid;


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


  assert( iHeight>=0 );


  if( iHeight==0 ){
    rc = testRtreeEntry(pRtree, pCursor, &isEof);
  }else{
    rc = testRtreeCell(pRtree, pCursor, &isEof);
  }

  if( rc!=SQLITE_OK || isEof || iHeight==0 ){
    goto descend_to_cell_out;
  }

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

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

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

descend_to_cell_out:
  *pEof = isEof;
  return rc;

}

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

  for(ii=0; ii<nCell; ii++){
    if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){
      *piIndex = ii;
      return SQLITE_OK;
    }
  }
  return SQLITE_CORRUPT_VTAB;
................................................................................
  RtreeNode *pParent = pNode->pParent;
  if( pParent ){
    return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);
  }
  *piIndex = -1;
  return SQLITE_OK;
}

/* 





























































































































































































































































































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

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

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




  return rc;
}

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



  assert(pCsr->pNode);

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

  return SQLITE_OK;
}

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







  if( i==0 ){
    i64 iRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
    sqlite3_result_int64(ctx, iRowid);
  }else{
    RtreeCoord c;

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

  return SQLITE_OK;
}

/* 
** Use nodeAcquire() to obtain the leaf node containing the record with 
** rowid iRowid. If successful, set *ppLeaf to point to the node and
** return SQLITE_OK. If there is no such record in the table, set
** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf
** to zero and return an SQLite error code.
*/
static int findLeafNode(Rtree *pRtree, i64 iRowid, RtreeNode **ppLeaf){





  int rc;
  *ppLeaf = 0;
  sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);
  if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){
    i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);

    rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);
    sqlite3_reset(pRtree->pReadRowid);
  }else{
    rc = sqlite3_reset(pRtree->pReadRowid);
  }
  return rc;
}
................................................................................
/*
** This function is called to configure the RtreeConstraint object passed
** as the second argument for a MATCH constraint. The value passed as the
** first argument to this function is the right-hand operand to the MATCH
** operator.
*/
static int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){
  RtreeMatchArg *p;
  sqlite3_rtree_geometry *pGeom;
  int nBlob;


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

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

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

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

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

  pCons->xGeom = p->xGeom;
  pCons->pGeom = pGeom;


  return SQLITE_OK;
}

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

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


  rtreeReference(pRtree);

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

  if( idxNum==1 ){
    /* Special case - lookup by rowid. */
    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */

    i64 iRowid = sqlite3_value_int64(argv[0]);

    rc = findLeafNode(pRtree, iRowid, &pLeaf);
    pCsr->pNode = pLeaf; 
    if( pLeaf ){
      assert( rc==SQLITE_OK );





      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &pCsr->iCell);




    }
  }else{
    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
    ** with the configured constraints. 
    */

    if( argc>0 ){
      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
      pCsr->nConstraint = argc;
      if( !pCsr->aConstraint ){
        rc = SQLITE_NOMEM;
      }else{
        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);

        assert( (idxStr==0 && argc==0)
                || (idxStr && (int)strlen(idxStr)==argc*2) );
        for(ii=0; ii<argc; ii++){
          RtreeConstraint *p = &pCsr->aConstraint[ii];
          p->op = idxStr[ii*2];
          p->iCoord = idxStr[ii*2+1]-'a';
          if( p->op==RTREE_MATCH ){
            /* A MATCH operator. The right-hand-side must be a blob that
            ** can be cast into an RtreeMatchArg object. One created using
            ** an sqlite3_rtree_geometry_callback() SQL user function.
            */
            rc = deserializeGeometry(argv[ii], p);
            if( rc!=SQLITE_OK ){
              break;
            }



          }else{
#ifdef SQLITE_RTREE_INT_ONLY
            p->rValue = sqlite3_value_int64(argv[ii]);
#else
            p->rValue = sqlite3_value_double(argv[ii]);
#endif
          }
        }
      }
    }
  
    if( rc==SQLITE_OK ){
      pCsr->pNode = 0;
      rc = nodeAcquire(pRtree, 1, 0, &pRoot);
    }

    if( rc==SQLITE_OK ){

      int isEof = 1;
      int nCell = NCELL(pRoot);
      pCsr->pNode = pRoot;
      for(pCsr->iCell=0; rc==SQLITE_OK && pCsr->iCell<nCell; pCsr->iCell++){
        assert( pCsr->pNode==pRoot );
        rc = descendToCell(pRtree, pCsr, pRtree->iDepth, &isEof);
        if( !isEof ){
          break;
        }
      }
      if( rc==SQLITE_OK && isEof ){
        assert( pCsr->pNode==pRoot );
        nodeRelease(pRtree, pRoot);
        pCsr->pNode = 0;


      }
      assert( rc!=SQLITE_OK || !pCsr->pNode || pCsr->iCell<NCELL(pCsr->pNode) );
    }
  }


  rtreeRelease(pRtree);
  return rc;
}

/*
** Set the pIdxInfo->estimatedRows variable to nRow. Unless this
** extension is currently being used by a version of SQLite too old to
................................................................................
        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;
        default:
          assert( p->op==SQLITE_INDEX_CONSTRAINT_MATCH );
          op = RTREE_MATCH; 
          break;
      }
      zIdxStr[iIdx++] = op;
      zIdxStr[iIdx++] = p->iColumn - 1 + 'a';
      pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
      pIdxInfo->aConstraintUsage[ii].omit = 1;
    }
  }

  pIdxInfo->idxNum = 2;
  pIdxInfo->needToFreeIdxStr = 1;
................................................................................
  RtreeCell cell;
  memcpy(&cell, p, sizeof(RtreeCell));
  area = cellArea(pRtree, &cell);
  cellUnion(pRtree, &cell, pCell);
  return (cellArea(pRtree, &cell)-area);
}

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

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

        if( x2<x1 ){
          o = 0.0;

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

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


/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
................................................................................
  RtreeNode *pNode;
  rc = nodeAcquire(pRtree, 1, 0, &pNode);

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

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

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

    RtreeCell *aCell = 0;

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

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

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

................................................................................
  sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
  sqlite3_step(pRtree->pWriteParent);
  return sqlite3_reset(pRtree->pWriteParent);
}

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

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

/*
** Implementation of the linear variant of the PickSeeds() function from
** Guttman[84].
*/
static void LinearPickSeeds(
  Rtree *pRtree,
  RtreeCell *aCell, 
  int nCell, 
  int *piLeftSeed, 
  int *piRightSeed
){
  int i;
  int iLeftSeed = 0;
  int iRightSeed = 1;
  RtreeDValue maxNormalInnerWidth = (RtreeDValue)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++){
    RtreeDValue x1 = DCOORD(aCell[0].aCoord[i*2]);
    RtreeDValue x2 = DCOORD(aCell[0].aCoord[i*2+1]);
    RtreeDValue x3 = x1;
    RtreeDValue x4 = x2;
    int jj;

    int iCellLeft = 0;
    int iCellRight = 0;

    for(jj=1; jj<nCell; jj++){
      RtreeDValue left = DCOORD(aCell[jj].aCoord[i*2]);
      RtreeDValue right = DCOORD(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 ){
      RtreeDValue 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;
  RtreeDValue fDiff;
  int ii;
  for(ii=0; ii<nCell; ii++){
    if( aiUsed[ii]==0 ){
      RtreeDValue left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
      RtreeDValue right = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
      RtreeDValue 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;
  RtreeDValue fWaste = 0.0;

  for(ii=0; ii<nCell; ii++){
    for(jj=ii+1; jj<nCell; jj++){
      RtreeDValue right = cellArea(pRtree, &aCell[jj]);
      RtreeDValue growth = cellGrowth(pRtree, &aCell[ii], &aCell[jj]);
      RtreeDValue 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:
................................................................................
        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,
................................................................................
){
  int **aaSorted;
  int *aSpare;
  int ii;

  int iBestDim = 0;
  int iBestSplit = 0;
  RtreeDValue fBestMargin = 0.0;

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

  aaSorted = (int **)sqlite3_malloc(nByte);
  if( !aaSorted ){
    return SQLITE_NOMEM;
  }
................................................................................
    for(jj=0; jj<nCell; jj++){
      aaSorted[ii][jj] = jj;
    }
    SortByDimension(pRtree, aaSorted[ii], nCell, ii, aCell, aSpare);
  }

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

    for(
      nLeft=RTREE_MINCELLS(pRtree); 
      nLeft<=(nCell-RTREE_MINCELLS(pRtree)); 
      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;
................................................................................
    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);
  if( !aiUsed ){
    return SQLITE_NOMEM;
  }
  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);
    RtreeDValue 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
){
................................................................................
    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 by calling
  ** nodeWrite(). Node pRight always needs a node number, as it was created
  ** by nodeNew() above. But node pLeft sometimes already has a node number.
................................................................................
    }
  }
  for(iDim=0; iDim<pRtree->nDim; iDim++){
    aCenterCoord[iDim] = (aCenterCoord[iDim]/(nCell*(RtreeDValue)2));
  }

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

................................................................................
    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{
    rc = AdjustTree(pRtree, pNode, pCell);
    if( rc==SQLITE_OK ){
      if( iHeight==0 ){
        rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
      }else{
        rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
................................................................................
  /* Obtain a reference to the root node to initialize Rtree.iDepth */
  rc = nodeAcquire(pRtree, 1, 0, &pRoot);

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

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

  pRtree->db = db;

  if( isCreate ){
    char *zCreate = sqlite3_mprintf(
"CREATE TABLE \"%w\".\"%w_node\"(nodeno INTEGER PRIMARY KEY, data BLOB);"
"CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY, nodeno INTEGER);"
"CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY, parentnode INTEGER);"

"INSERT INTO '%q'.'%q_node' VALUES(1, zeroblob(%d))",
      zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, pRtree->iNodeSize
    );
    if( !zCreate ){
      return SQLITE_NOMEM;
    }
    rc = sqlite3_exec(db, zCreate, 0, 0, 0);
................................................................................
}


/*
** 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.
................................................................................
    int jj;

    nodeGetCell(&tree, &node, ii, &cell);
    sqlite3_snprintf(512-nCell,&zCell[nCell],"%lld", cell.iRowid);
    nCell = (int)strlen(zCell);
    for(jj=0; jj<tree.nDim*2; jj++){
#ifndef SQLITE_RTREE_INT_ONLY
      sqlite3_snprintf(512-nCell,&zCell[nCell], " %f",
                       (double)cell.aCoord[jj].f);
#else
      sqlite3_snprintf(512-nCell,&zCell[nCell], " %d",
                       cell.aCoord[jj].i);
#endif
      nCell = (int)strlen(zCell);
    }
................................................................................
      zText = sqlite3_mprintf("{%s}", zCell);
    }
  }
  
  sqlite3_result_text(ctx, zText, -1, sqlite3_free);
}










static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
  UNUSED_PARAMETER(nArg);
  if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB 
   || sqlite3_value_bytes(apArg[0])<2
  ){
    sqlite3_result_error(ctx, "Invalid argument to rtreedepth()", -1); 
  }else{
................................................................................
    rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
  }

  return rc;
}

/*
** A version of sqlite3_free() that can be used as a callback. This is used
** in two places - as the destructor for the blob value returned by the
** invocation of a geometry function, and as the destructor for the geometry
** functions themselves.

*/
static void doSqlite3Free(void *p){



  sqlite3_free(p);
}

/*
** Each call to sqlite3_rtree_geometry_callback() creates an ordinary SQLite
** scalar user function. This C function is the callback used for all such
** registered SQL functions.
**
** The scalar user functions return a blob that is interpreted by r-tree
** table MATCH operators.






*/
static void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){
  RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);
  RtreeMatchArg *pBlob;
  int nBlob;

  nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(RtreeDValue);
  pBlob = (RtreeMatchArg *)sqlite3_malloc(nBlob);
  if( !pBlob ){
    sqlite3_result_error_nomem(ctx);
  }else{
    int i;
    pBlob->magic = RTREE_GEOMETRY_MAGIC;
    pBlob->xGeom = pGeomCtx->xGeom;
    pBlob->pContext = pGeomCtx->pContext;
    pBlob->nParam = nArg;
    for(i=0; i<nArg; i++){
#ifdef SQLITE_RTREE_INT_ONLY
      pBlob->aParam[i] = sqlite3_value_int64(aArg[i]);
#else
      pBlob->aParam[i] = sqlite3_value_double(aArg[i]);
#endif
    }
    sqlite3_result_blob(ctx, pBlob, nBlob, doSqlite3Free);
  }
}

/*
** Register a new geometry function for use with the r-tree MATCH operator.
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,
  const char *zGeom,
  int (*xGeom)(sqlite3_rtree_geometry *, int, RtreeDValue *, int *),
  void *pContext
){
  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */

  /* Allocate and populate the context object. */
  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
  if( !pGeomCtx ) return SQLITE_NOMEM;
  pGeomCtx->xGeom = xGeom;


  pGeomCtx->pContext = pContext;




  /* Create the new user-function. Register a destructor function to delete
  ** the context object when it is no longer required.  */





















  return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY, 
      (void *)pGeomCtx, geomCallback, 0, 0, doSqlite3Free
  );
}

#if !SQLITE_CORE
#ifdef _WIN32
__declspec(dllexport)
#endif







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50
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57
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59
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63
64
65
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71
72
73
74
75
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77
78
79
..
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
...
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123

124
125
126
127
128
129
130
...
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
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175
176
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181
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194
...
204
205
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222
223
224
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226
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235
236
237
238
239
240
241
242
243
244
245
246

247
248
249
250
251
252
253
254
255
...
266
267
268
269
270
271
272
273
274
275

276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
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296
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312
313
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315
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317
318
319
320
321
322
323
324
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326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
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343
344
345
346
347
348
349
350
351

352
353
354













355
356
357
358
359
360
361
...
441
442
443
444
445
446
447



448
449
450
451
452
453
454
455
...
501
502
503
504
505
506
507

508
509
510
511
512
513
514
515
...
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
...
622
623
624
625
626
627
628

629
630
631
632
633
634
635
636
637
638
639
...
646
647
648
649
650
651
652

653
654
655
656
657
658
659
660
...
671
672
673
674
675
676
677

678
679
680
681
682
683
684
685
...
699
700
701
702
703
704
705
706
707
708
709
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711
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714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742

743
744
745
746
747
748
749
750
751
752
...
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
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886
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888
889
890
891
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893
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895
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899
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901
902
903

904
905
906
907

908
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910
911
912
913
914
915
916
917
918
919
920
921
922




923
924
925
926




927
928
929
930


931
932
933
934
935
936


937
938
939
940
941
942
943

944
945

946







947
948
949












950
951
952
953
954
955
956
957
958
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960
961
962
963




964
965
966



967
968
969



970
971
972
973

974



975
976
977
978
979
980
981
982
983
984
985
986
987
988
989



990
991
992
993





994
995
996
997




998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008




1009
1010





1011
1012

1013
1014
1015


1016







1017
1018
1019
1020
1021
1022



1023
1024
1025
1026
1027
1028
1029
1030
1031



1032

1033
1034
1035
1036
1037
1038
1039
1040
1041





1042
1043
1044
1045
1046
1047





1048
1049

1050

1051
1052

1053
1054
1055
1056
1057

1058
1059

1060





























1061
1062
1063
1064
1065
1066
1067
1068
....
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
....
1091
1092
1093
1094
1095
1096
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1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
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1166
1167
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1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
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1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
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1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
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1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
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1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387

1388
1389
1390











1391






















1392
1393
1394
1395
1396
1397
1398
1399
1400
1401

1402

1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425

1426
1427

1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439

1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
....
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
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1491
1492
1493
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1497
1498
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1500
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1513
1514
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1516
1517
1518
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1520
1521
1522
1523
1524
1525
1526
1527
1528

1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545


1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
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1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598

1599



1600
1601
1602
1603

1604
1605
1606
1607







1608
1609
1610
1611

1612
1613

1614
1615
1616
1617
1618
1619
1620
1621
....
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
....
1802
1803
1804
1805
1806
1807
1808

1809
1810
1811
1812
1813

1814
1815
1816
1817







1818
1819
1820
1821

1822
1823

1824

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1835
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1849
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1858
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1865
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1876
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1949
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2082
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2089
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2188























































2189
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3453
**      of 4-byte coordinates. For leaf nodes the integer is the rowid
**      of a record. For internal nodes it is the node number of a
**      child page.
*/

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











































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

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

#ifndef SQLITE_AMALGAMATION
#include "sqlite3rtree.h"
typedef sqlite3_int64 i64;
typedef unsigned char u8;
typedef unsigned short u16;
typedef unsigned int u32;
#endif

/*  The following macro is used to suppress compiler warnings.
*/
#ifndef UNUSED_PARAMETER
# define UNUSED_PARAMETER(x) (void)(x)
................................................................................
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;
typedef struct RtreeMatchArg RtreeMatchArg;
typedef struct RtreeGeomCallback RtreeGeomCallback;
typedef union RtreeCoord RtreeCoord;
typedef struct RtreeSearchPoint RtreeSearchPoint;

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

/* Size of hash table Rtree.aHash. This hash table is not expected to
** ever contain very many entries, so a fixed number of buckets is 
** used.
*/
#define HASHSIZE 97

/* The xBestIndex method of this virtual table requires an estimate of
** the number of rows in the virtual table to calculate the costs of
** various strategies. If possible, this estimate is loaded from the
** sqlite_stat1 table (with RTREE_MIN_ROWEST as a hard-coded minimum).
** Otherwise, if no sqlite_stat1 entry is available, use 
** RTREE_DEFAULT_ROWEST.
................................................................................
#define RTREE_DEFAULT_ROWEST 1048576
#define RTREE_MIN_ROWEST         100

/* 
** An rtree virtual-table object.
*/
struct Rtree {
  sqlite3_vtab base;          /* Base class.  Must be first */
  sqlite3 *db;                /* Host database connection */
  int iNodeSize;              /* Size in bytes of each node in the node table */
  u8 nDim;                    /* Number of dimensions */
  u8 eCoordType;              /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */
  u8 nBytesPerCell;           /* Bytes consumed per cell */
  int iDepth;                 /* Current depth of the r-tree structure */
  char *zDb;                  /* Name of database containing r-tree table */
  char *zName;                /* Name of r-tree table */ 

  int nBusy;                  /* Current number of users of this structure */
  i64 nRowEst;                /* Estimated number of rows in this table */

  /* List of nodes removed during a CondenseTree operation. List is
  ** linked together via the pointer normally used for hash chains -
  ** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree 
  ** headed by the node (leaf nodes have RtreeNode.iNode==0).
................................................................................
  sqlite3_stmt *pDeleteRowid;

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

  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ 
};

/* Possible values for Rtree.eCoordType: */
#define RTREE_COORD_REAL32 0
#define RTREE_COORD_INT32  1

/*
** If SQLITE_RTREE_INT_ONLY is defined, then this virtual table will
** only deal with integer coordinates.  No floating point operations
** will be done.
*/
#ifdef SQLITE_RTREE_INT_ONLY
  typedef sqlite3_int64 RtreeDValue;       /* High accuracy coordinate */
  typedef int RtreeValue;                  /* Low accuracy coordinate */
# define RTREE_ZERO 0
#else
  typedef double RtreeDValue;              /* High accuracy coordinate */
  typedef float RtreeValue;                /* Low accuracy coordinate */
# define RTREE_ZERO 0.0
#endif

/*
** When doing a search of an r-tree, instances of the following structure
** record intermediate results from the tree walk.
**
** The id is always a node-id.  For iLevel>=1 the id is the node-id of
** the node that the RtreeSearchPoint represents.  When iLevel==0, however,
** the id is of the parent node and the cell that RtreeSearchPoint
** represents is the iCell-th entry in the parent node.
*/
struct RtreeSearchPoint {
  RtreeDValue rScore;    /* The score for this node.  Smallest goes first. */
  sqlite3_int64 id;      /* Node ID */
  u8 iLevel;             /* 0=entries.  1=leaf node.  2+ for higher */
  u8 eWithin;            /* PARTLY_WITHIN or FULLY_WITHIN */
  u8 iCell;              /* Cell index within the node */
};

/*
** The minimum number of cells allowed for a node is a third of the 
** maximum. In Gutman's notation:
**
**     m = M/3
**
................................................................................
** supported cell size is 48 bytes (8 byte rowid + ten 4 byte coordinates).
** Therefore all non-root nodes must contain at least 3 entries. Since 
** 2^40 is greater than 2^64, an r-tree structure always has a depth of
** 40 or less.
*/
#define RTREE_MAX_DEPTH 40


/*
** Number of entries in the cursor RtreeNode cache.  The first entry is
** used to cache the RtreeNode for RtreeCursor.sPoint.  The remaining
** entries cache the RtreeNode for the first elements of the priority queue.
*/
#define RTREE_CACHE_SZ  5

/* 
** An rtree cursor object.
*/
struct RtreeCursor {
  sqlite3_vtab_cursor base;         /* Base class.  Must be first */
  u8 atEOF;                         /* True if at end of search */
  u8 bPoint;                        /* True if sPoint is valid */
  int iStrategy;                    /* Copy of idxNum search parameter */
  int nConstraint;                  /* Number of entries in aConstraint */
  RtreeConstraint *aConstraint;     /* Search constraints. */
  int nPointAlloc;                  /* Number of slots allocated for aPoint[] */
  int nPoint;                       /* Number of slots used in aPoint[] */
  int mxLevel;                      /* iLevel value for root of the tree */
  RtreeSearchPoint *aPoint;         /* Priority queue for search points */
  RtreeSearchPoint sPoint;          /* Cached next search point */
  RtreeNode *aNode[RTREE_CACHE_SZ]; /* Rtree node cache */
  u32 anQueue[RTREE_MAX_DEPTH+1];   /* Number of queued entries by iLevel */
};

/* Return the Rtree of a RtreeCursor */
#define RTREE_OF_CURSOR(X)   ((Rtree*)((X)->base.pVtab))

/*
** A coordinate can be either a floating point number or a integer.  All
** coordinates within a single R-Tree are always of the same time.
*/
union RtreeCoord {
  RtreeValue f;      /* Floating point value */

  int i;             /* Integer value */
  u32 u;             /* Unsigned for byte-order conversions */
};

/*
** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
** formatted as a RtreeDValue (double or int64). This macro assumes that local
** variable pRtree points to the Rtree structure associated with the
** RtreeCoord.
................................................................................

/*
** A search constraint.
*/
struct RtreeConstraint {
  int iCoord;                     /* Index of constrained coordinate */
  int op;                         /* Constraining operation */
  union {
    RtreeDValue rValue;             /* Constraint value. */
    int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*);

    int (*xQueryFunc)(sqlite3_rtree_query_info*);
  } u;
  sqlite3_rtree_query_info *pInfo;  /* xGeom and xQueryFunc argument */
};

/* Possible values for RtreeConstraint.op */
#define RTREE_EQ    0x41  /* A */
#define RTREE_LE    0x42  /* B */
#define RTREE_LT    0x43  /* C */
#define RTREE_GE    0x44  /* D */
#define RTREE_GT    0x45  /* E */
#define RTREE_MATCH 0x46  /* F: Old-style sqlite3_rtree_geometry_callback() */
#define RTREE_QUERY 0x47  /* G: New-style sqlite3_rtree_query_callback() */


/* 
** An rtree structure node.
*/
struct RtreeNode {
  RtreeNode *pParent;         /* Parent node */
  i64 iNode;                  /* The node number */
  int nRef;                   /* Number of references to this node */
  int isDirty;                /* True if the node needs to be written to disk */
  u8 *zData;                  /* Content of the node, as should be on disk */
  RtreeNode *pNext;           /* Next node in this hash collision chain */
};

/* Return the number of cells in a node  */
#define NCELL(pNode) readInt16(&(pNode)->zData[2])

/* 
** A single cell from a node, deserialized
*/
struct RtreeCell {
  i64 iRowid;                                 /* Node or entry ID */
  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];  /* Bounding box coordinates */
};


/*
** This object becomes the sqlite3_user_data() for the SQL functions
** that are created by sqlite3_rtree_geometry_callback() and
** sqlite3_rtree_query_callback() and which appear on the right of MATCH
** operators in order to constrain a search.
**
** xGeom and xQueryFunc are the callback functions.  Exactly one of 
** xGeom and xQueryFunc fields is non-NULL, depending on whether the
** SQL function was created using sqlite3_rtree_geometry_callback() or
** sqlite3_rtree_query_callback().
** 
** This object is deleted automatically by the destructor mechanism in
** sqlite3_create_function_v2().
*/
struct RtreeGeomCallback {
  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
  int (*xQueryFunc)(sqlite3_rtree_query_info*);
  void (*xDestructor)(void*);
  void *pContext;
};


/*
** Value for the first field of every RtreeMatchArg object. The MATCH
** operator tests that the first field of a blob operand matches this
** value to avoid operating on invalid blobs (which could cause a segfault).
*/
#define RTREE_GEOMETRY_MAGIC 0x891245AB

/*
** An instance of this structure (in the form of a BLOB) is returned by
** the SQL functions that sqlite3_rtree_geometry_callback() and
** sqlite3_rtree_query_callback() create, and is read as the right-hand
** operand to the MATCH operator of an R-Tree.
*/
struct RtreeMatchArg {
  u32 magic;                  /* Always RTREE_GEOMETRY_MAGIC */

  RtreeGeomCallback cb;       /* Info about the callback functions */
  int nParam;                 /* Number of parameters to the SQL function */
  RtreeDValue aParam[1];      /* Values for parameters to the SQL function */













};

#ifndef MAX
# define MAX(x,y) ((x) < (y) ? (y) : (x))
#endif
#ifndef MIN
# define MIN(x,y) ((x) > (y) ? (y) : (x))
................................................................................
}

/*
** Given a node number iNode, return the corresponding key to use
** in the Rtree.aHash table.
*/
static int nodeHash(i64 iNode){



  return iNode % HASHSIZE;
}

/*
** Search the node hash table for node iNode. If found, return a pointer
** to it. Otherwise, return 0.
*/
static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
................................................................................
  }
  return pNode;
}

/*
** Obtain a reference to an r-tree node.
*/

static int nodeAcquire(
  Rtree *pRtree,             /* R-tree structure */
  i64 iNode,                 /* Node number to load */
  RtreeNode *pParent,        /* Either the parent node or NULL */
  RtreeNode **ppNode         /* OUT: Acquired node */
){
  int rc;
  int rc2 = SQLITE_OK;
................................................................................
  return rc;
}

/*
** Overwrite cell iCell of node pNode with the contents of pCell.
*/
static void nodeOverwriteCell(
  Rtree *pRtree,             /* The overall R-Tree */
  RtreeNode *pNode,          /* The node into which the cell is to be written */
  RtreeCell *pCell,          /* The cell to write */
  int iCell                  /* Index into pNode into which pCell is written */
){
  int ii;
  u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
  p += writeInt64(p, pCell->iRowid);
  for(ii=0; ii<(pRtree->nDim*2); ii++){
    p += writeCoord(p, &pCell->aCoord[ii]);
  }
  pNode->isDirty = 1;
}

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

/*
** Insert the contents of cell pCell into node pNode. If the insert
** is successful, return SQLITE_OK.
**
** If there is not enough free space in pNode, return SQLITE_FULL.
*/

static int nodeInsertCell(
  Rtree *pRtree,                /* The overall R-Tree */
  RtreeNode *pNode,             /* Write new cell into this node */
  RtreeCell *pCell              /* The cell to be inserted */
){
  int nCell;                    /* Current number of cells in pNode */
  int nMaxCell;                 /* Maximum number of cells for pNode */

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

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

  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);
................................................................................
  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;
................................................................................

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

/*
** Return coordinate iCoord from cell iCell in node pNode.
*/
static void nodeGetCoord(
  Rtree *pRtree,               /* The overall R-Tree */
  RtreeNode *pNode,            /* The node from which to extract a coordinate */
  int iCell,                   /* The index of the cell within the node */
  int iCoord,                  /* Which coordinate to extract */
  RtreeCoord *pCoord           /* OUT: Space to write result to */
){
  readCoord(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord], pCoord);
}

/*
** Deserialize cell iCell of node pNode. Populate the structure pointed
** to by pCell with the results.
*/
static void nodeGetCell(
  Rtree *pRtree,               /* The overall R-Tree */
  RtreeNode *pNode,            /* The node containing the cell to be read */
  int iCell,                   /* Index of the cell within the node */
  RtreeCell *pCell             /* OUT: Write the cell contents here */
){
  u8 *pData;
  u8 *pEnd;
  RtreeCoord *pCoord;
  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
  pData = pNode->zData + (12 + pRtree->nBytesPerCell*iCell);
  pEnd = pData + pRtree->nDim*8;

  pCoord = pCell->aCoord;
  for(; pData<pEnd; pData+=4, pCoord++){
    readCoord(pData, pCoord);
  }
}


/* Forward declaration for the function that does the work of
** the virtual table module xCreate() and xConnect() methods.
*/
................................................................................
/*
** Free the RtreeCursor.aConstraint[] array and its contents.
*/
static void freeCursorConstraints(RtreeCursor *pCsr){
  if( pCsr->aConstraint ){
    int i;                        /* Used to iterate through constraint array */
    for(i=0; i<pCsr->nConstraint; i++){
      sqlite3_rtree_query_info *pInfo = pCsr->aConstraint[i].pInfo;
      if( pInfo ){
        if( pInfo->xDelUser ) pInfo->xDelUser(pInfo->pUser);
        sqlite3_free(pInfo);
      }
    }
    sqlite3_free(pCsr->aConstraint);
    pCsr->aConstraint = 0;
  }
}

/* 
** Rtree virtual table module xClose method.
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
  Rtree *pRtree = (Rtree *)(cur->pVtab);
  int ii;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  freeCursorConstraints(pCsr);
  sqlite3_free(pCsr->aPoint);
  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
  sqlite3_free(pCsr);
  return SQLITE_OK;
}

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

  return pCsr->atEOF;
}

/*

** Convert raw bits from the on-disk RTree record into a coordinate value.
** The on-disk format is big-endian and needs to be converted for little-
** endian platforms.  The on-disk record stores integer coordinates if
** eInt is true and it stores 32-bit floating point records if eInt is
** false.  a[] is the four bytes of the on-disk record to be decoded.
** Store the results in "r".
**
** There are three versions of this macro, one each for little-endian and
** big-endian processors and a third generic implementation.  The endian-
** specific implementations are much faster and are preferred if the
** processor endianness is known at compile-time.  The SQLITE_BYTEORDER
** macro is part of sqliteInt.h and hence the endian-specific
** implementation will only be used if this module is compiled as part
** of the amalgamation.
*/




#if defined(SQLITE_BYTEORDER) && SQLITE_BYTEORDER==1234
#define RTREE_DECODE_COORD(eInt, a, r) {                        \
    RtreeCoord c;    /* Coordinate decoded */                   \
    memcpy(&c.u,a,4);                                           \




    c.u = ((c.u>>24)&0xff)|((c.u>>8)&0xff00)|                   \
          ((c.u&0xff)<<24)|((c.u&0xff00)<<8);                   \
    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}


#elif defined(SQLITE_BYTEORDER) && SQLITE_BYTEORDER==4321
#define RTREE_DECODE_COORD(eInt, a, r) {                        \
    RtreeCoord c;    /* Coordinate decoded */                   \
    memcpy(&c.u,a,4);                                           \
    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}


#else
#define RTREE_DECODE_COORD(eInt, a, r) {                        \
    RtreeCoord c;    /* Coordinate decoded */                   \
    c.u = ((u32)a[0]<<24) + ((u32)a[1]<<16)                     \
           +((u32)a[2]<<8) + a[3];                              \
    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}

#endif


/*







** Check the RTree node or entry given by pCellData and p against the MATCH
** constraint pConstraint.  
*/












static int rtreeCallbackConstraint(
  RtreeConstraint *pConstraint,  /* The constraint to test */
  int eInt,                      /* True if RTree holding integer coordinates */
  u8 *pCellData,                 /* Raw cell content */
  RtreeSearchPoint *pSearch,     /* Container of this cell */
  sqlite3_rtree_dbl *prScore,    /* OUT: score for the cell */
  int *peWithin                  /* OUT: visibility of the cell */
){
  int i;                                                /* Loop counter */
  sqlite3_rtree_query_info *pInfo = pConstraint->pInfo; /* Callback info */
  int nCoord = pInfo->nCoord;                           /* No. of coordinates */
  int rc;                                             /* Callback return code */
  sqlite3_rtree_dbl aCoord[RTREE_MAX_DIMENSIONS*2];   /* Decoded coordinates */





  assert( pConstraint->op==RTREE_MATCH || pConstraint->op==RTREE_QUERY );
  assert( nCoord==2 || nCoord==4 || nCoord==6 || nCoord==8 || nCoord==10 );




  if( pConstraint->op==RTREE_QUERY && pSearch->iLevel==1 ){
    pInfo->iRowid = readInt64(pCellData);
  }



  pCellData += 8;
  for(i=0; i<nCoord; i++, pCellData += 4){
    RTREE_DECODE_COORD(eInt, pCellData, aCoord[i]);
  }

  if( pConstraint->op==RTREE_MATCH ){



    rc = pConstraint->u.xGeom((sqlite3_rtree_geometry*)pInfo,
                              nCoord, aCoord, &i);
    if( i==0 ) *peWithin = NOT_WITHIN;
    *prScore = RTREE_ZERO;
  }else{
    pInfo->aCoord = aCoord;
    pInfo->iLevel = pSearch->iLevel - 1;
    pInfo->rScore = pInfo->rParentScore = pSearch->rScore;
    pInfo->eWithin = pInfo->eParentWithin = pSearch->eWithin;
    rc = pConstraint->u.xQueryFunc(pInfo);
    if( pInfo->eWithin<*peWithin ) *peWithin = pInfo->eWithin;
    if( pInfo->rScore<*prScore || *prScore<RTREE_ZERO ){
      *prScore = pInfo->rScore;
    }
  }



  return rc;
}

/* 





** Check the internal RTree node given by pCellData against constraint p.
** If this constraint cannot be satisfied by any child within the node,
** set *peWithin to NOT_WITHIN.
*/




static void rtreeNonleafConstraint(
  RtreeConstraint *p,        /* The constraint to test */
  int eInt,                  /* True if RTree holds integer coordinates */
  u8 *pCellData,             /* Raw cell content as appears on disk */
  int *peWithin              /* Adjust downward, as appropriate */
){
  sqlite3_rtree_dbl val;     /* Coordinate value convert to a double */

  /* p->iCoord might point to either a lower or upper bound coordinate
  ** in a coordinate pair.  But make pCellData point to the lower bound.
  */




  pCellData += 8 + 4*(p->iCoord&0xfe);






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

  switch( p->op ){
    case RTREE_LE:
    case RTREE_LT:


    case RTREE_EQ:







      RTREE_DECODE_COORD(eInt, pCellData, val);
      /* val now holds the lower bound of the coordinate pair */
      if( p->u.rValue>=val ) return;
      if( p->op!=RTREE_EQ ) break;  /* RTREE_LE and RTREE_LT end here */
      /* Fall through for the RTREE_EQ case */




    default: /* RTREE_GT or RTREE_GE,  or fallthrough of RTREE_EQ */
      pCellData += 4;
      RTREE_DECODE_COORD(eInt, pCellData, val);
      /* val now holds the upper bound of the coordinate pair */
      if( p->u.rValue<=val ) return;
  }
  *peWithin = NOT_WITHIN;
}




/*

** Check the leaf RTree cell given by pCellData against constraint p.
** If this constraint is not satisfied, set *peWithin to NOT_WITHIN.
** If the constraint is satisfied, leave *peWithin unchanged.
**
** The constraint is of the form:  xN op $val
**
** The op is given by p->op.  The xN is p->iCoord-th coordinate in
** pCellData.  $val is given by p->u.rValue.
*/





static void rtreeLeafConstraint(
  RtreeConstraint *p,        /* The constraint to test */
  int eInt,                  /* True if RTree holds integer coordinates */
  u8 *pCellData,             /* Raw cell content as appears on disk */
  int *peWithin              /* Adjust downward, as appropriate */
){





  RtreeDValue xN;      /* Coordinate value converted to a double */


  assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 

      || p->op==RTREE_GT || p->op==RTREE_EQ );
  pCellData += 8 + p->iCoord*4;

  RTREE_DECODE_COORD(eInt, pCellData, xN);
  switch( p->op ){
    case RTREE_LE: if( xN <= p->u.rValue ) return;  break;
    case RTREE_LT: if( xN <  p->u.rValue ) return;  break;
    case RTREE_GE: if( xN >= p->u.rValue ) return;  break;

    case RTREE_GT: if( xN >  p->u.rValue ) return;  break;
    default:       if( xN == p->u.rValue ) return;  break;

  }





























  *peWithin = NOT_WITHIN;
}

/*
** One of the cells in node pNode is guaranteed to have a 64-bit 
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(
................................................................................
  Rtree *pRtree, 
  RtreeNode *pNode, 
  i64 iRowid,
  int *piIndex
){
  int ii;
  int nCell = NCELL(pNode);
  assert( nCell<200 );
  for(ii=0; ii<nCell; ii++){
    if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){
      *piIndex = ii;
      return SQLITE_OK;
    }
  }
  return SQLITE_CORRUPT_VTAB;
................................................................................
  RtreeNode *pParent = pNode->pParent;
  if( pParent ){
    return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);
  }
  *piIndex = -1;
  return SQLITE_OK;
}

/*
** Compare two search points.  Return negative, zero, or positive if the first
** is less than, equal to, or greater than the second.
**
** The rScore is the primary key.  Smaller rScore values come first.
** If the rScore is a tie, then use iLevel as the tie breaker with smaller
** iLevel values coming first.  In this way, if rScore is the same for all
** SearchPoints, then iLevel becomes the deciding factor and the result
** is a depth-first search, which is the desired default behavior.
*/
static int rtreeSearchPointCompare(
  const RtreeSearchPoint *pA,
  const RtreeSearchPoint *pB
){
  if( pA->rScore<pB->rScore ) return -1;
  if( pA->rScore>pB->rScore ) return +1;
  if( pA->iLevel<pB->iLevel ) return -1;
  if( pA->iLevel>pB->iLevel ) return +1;
  return 0;
}

/*
** Interchange to search points in a cursor.
*/
static void rtreeSearchPointSwap(RtreeCursor *p, int i, int j){
  RtreeSearchPoint t = p->aPoint[i];
  assert( i<j );
  p->aPoint[i] = p->aPoint[j];
  p->aPoint[j] = t;
  i++; j++;
  if( i<RTREE_CACHE_SZ ){
    if( j>=RTREE_CACHE_SZ ){
      nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);
      p->aNode[i] = 0;
    }else{
      RtreeNode *pTemp = p->aNode[i];
      p->aNode[i] = p->aNode[j];
      p->aNode[j] = pTemp;
    }
  }
}

/*
** Return the search point with the lowest current score.
*/
static RtreeSearchPoint *rtreeSearchPointFirst(RtreeCursor *pCur){
  return pCur->bPoint ? &pCur->sPoint : pCur->nPoint ? pCur->aPoint : 0;
}

/*
** Get the RtreeNode for the search point with the lowest score.
*/
static RtreeNode *rtreeNodeOfFirstSearchPoint(RtreeCursor *pCur, int *pRC){
  sqlite3_int64 id;
  int ii = 1 - pCur->bPoint;
  assert( ii==0 || ii==1 );
  assert( pCur->bPoint || pCur->nPoint );
  if( pCur->aNode[ii]==0 ){
    assert( pRC!=0 );
    id = ii ? pCur->aPoint[0].id : pCur->sPoint.id;
    *pRC = nodeAcquire(RTREE_OF_CURSOR(pCur), id, 0, &pCur->aNode[ii]);
  }
  return pCur->aNode[ii];
}

/*
** Push a new element onto the priority queue
*/
static RtreeSearchPoint *rtreeEnqueue(
  RtreeCursor *pCur,    /* The cursor */
  RtreeDValue rScore,   /* Score for the new search point */
  u8 iLevel             /* Level for the new search point */
){
  int i, j;
  RtreeSearchPoint *pNew;
  if( pCur->nPoint>=pCur->nPointAlloc ){
    int nNew = pCur->nPointAlloc*2 + 8;
    pNew = sqlite3_realloc(pCur->aPoint, nNew*sizeof(pCur->aPoint[0]));
    if( pNew==0 ) return 0;
    pCur->aPoint = pNew;
    pCur->nPointAlloc = nNew;
  }
  i = pCur->nPoint++;
  pNew = pCur->aPoint + i;
  pNew->rScore = rScore;
  pNew->iLevel = iLevel;
  assert( iLevel>=0 && iLevel<=RTREE_MAX_DEPTH );
  while( i>0 ){
    RtreeSearchPoint *pParent;
    j = (i-1)/2;
    pParent = pCur->aPoint + j;
    if( rtreeSearchPointCompare(pNew, pParent)>=0 ) break;
    rtreeSearchPointSwap(pCur, j, i);
    i = j;
    pNew = pParent;
  }
  return pNew;
}

/*
** Allocate a new RtreeSearchPoint and return a pointer to it.  Return
** NULL if malloc fails.
*/
static RtreeSearchPoint *rtreeSearchPointNew(
  RtreeCursor *pCur,    /* The cursor */
  RtreeDValue rScore,   /* Score for the new search point */
  u8 iLevel             /* Level for the new search point */
){
  RtreeSearchPoint *pNew, *pFirst;
  pFirst = rtreeSearchPointFirst(pCur);
  pCur->anQueue[iLevel]++;
  if( pFirst==0
   || pFirst->rScore>rScore 
   || (pFirst->rScore==rScore && pFirst->iLevel>iLevel)
  ){
    if( pCur->bPoint ){
      int ii;
      pNew = rtreeEnqueue(pCur, rScore, iLevel);
      if( pNew==0 ) return 0;
      ii = (int)(pNew - pCur->aPoint) + 1;
      if( ii<RTREE_CACHE_SZ ){
        assert( pCur->aNode[ii]==0 );
        pCur->aNode[ii] = pCur->aNode[0];
       }else{
        nodeRelease(RTREE_OF_CURSOR(pCur), pCur->aNode[0]);
      }
      pCur->aNode[0] = 0;
      *pNew = pCur->sPoint;
    }
    pCur->sPoint.rScore = rScore;
    pCur->sPoint.iLevel = iLevel;
    pCur->bPoint = 1;
    return &pCur->sPoint;
  }else{
    return rtreeEnqueue(pCur, rScore, iLevel);
  }
}

#if 0
/* Tracing routines for the RtreeSearchPoint queue */
static void tracePoint(RtreeSearchPoint *p, int idx, RtreeCursor *pCur){
  if( idx<0 ){ printf(" s"); }else{ printf("%2d", idx); }
  printf(" %d.%05lld.%02d %g %d",
    p->iLevel, p->id, p->iCell, p->rScore, p->eWithin
  );
  idx++;
  if( idx<RTREE_CACHE_SZ ){
    printf(" %p\n", pCur->aNode[idx]);
  }else{
    printf("\n");
  }
}
static void traceQueue(RtreeCursor *pCur, const char *zPrefix){
  int ii;
  printf("=== %9s ", zPrefix);
  if( pCur->bPoint ){
    tracePoint(&pCur->sPoint, -1, pCur);
  }
  for(ii=0; ii<pCur->nPoint; ii++){
    if( ii>0 || pCur->bPoint ) printf("              ");
    tracePoint(&pCur->aPoint[ii], ii, pCur);
  }
}
# define RTREE_QUEUE_TRACE(A,B) traceQueue(A,B)
#else
# define RTREE_QUEUE_TRACE(A,B)   /* no-op */
#endif

/* Remove the search point with the lowest current score.
*/
static void rtreeSearchPointPop(RtreeCursor *p){
  int i, j, k, n;
  i = 1 - p->bPoint;
  assert( i==0 || i==1 );
  if( p->aNode[i] ){
    nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);
    p->aNode[i] = 0;
  }
  if( p->bPoint ){
    p->anQueue[p->sPoint.iLevel]--;
    p->bPoint = 0;
  }else if( p->nPoint ){
    p->anQueue[p->aPoint[0].iLevel]--;
    n = --p->nPoint;
    p->aPoint[0] = p->aPoint[n];
    if( n<RTREE_CACHE_SZ-1 ){
      p->aNode[1] = p->aNode[n+1];
      p->aNode[n+1] = 0;
    }
    i = 0;
    while( (j = i*2+1)<n ){
      k = j+1;
      if( k<n && rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[j])<0 ){
        if( rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[i])<0 ){
          rtreeSearchPointSwap(p, i, k);
          i = k;
        }else{
          break;
        }
      }else{
        if( rtreeSearchPointCompare(&p->aPoint[j], &p->aPoint[i])<0 ){
          rtreeSearchPointSwap(p, i, j);
          i = j;
        }else{
          break;
        }
      }
    }
  }
}


/*
** Continue the search on cursor pCur until the front of the queue
** contains an entry suitable for returning as a result-set row,
** or until the RtreeSearchPoint queue is empty, indicating that the
** query has completed.
*/
static int rtreeStepToLeaf(RtreeCursor *pCur){
  RtreeSearchPoint *p;
  Rtree *pRtree = RTREE_OF_CURSOR(pCur);
  RtreeNode *pNode;
  int eWithin;
  int rc = SQLITE_OK;
  int nCell;
  int nConstraint = pCur->nConstraint;
  int ii;
  int eInt;
  RtreeSearchPoint x;

  eInt = pRtree->eCoordType==RTREE_COORD_INT32;
  while( (p = rtreeSearchPointFirst(pCur))!=0 && p->iLevel>0 ){
    pNode = rtreeNodeOfFirstSearchPoint(pCur, &rc);
    if( rc ) return rc;
    nCell = NCELL(pNode);
    assert( nCell<200 );
    while( p->iCell<nCell ){
      sqlite3_rtree_dbl rScore = (sqlite3_rtree_dbl)-1;
      u8 *pCellData = pNode->zData + (4+pRtree->nBytesPerCell*p->iCell);
      eWithin = FULLY_WITHIN;
      for(ii=0; ii<nConstraint; ii++){
        RtreeConstraint *pConstraint = pCur->aConstraint + ii;
        if( pConstraint->op>=RTREE_MATCH ){
          rc = rtreeCallbackConstraint(pConstraint, eInt, pCellData, p,
                                       &rScore, &eWithin);
          if( rc ) return rc;
        }else if( p->iLevel==1 ){
          rtreeLeafConstraint(pConstraint, eInt, pCellData, &eWithin);
        }else{
          rtreeNonleafConstraint(pConstraint, eInt, pCellData, &eWithin);
        }
        if( eWithin==NOT_WITHIN ) break;
      }
      p->iCell++;
      if( eWithin==NOT_WITHIN ) continue;
      x.iLevel = p->iLevel - 1;
      if( x.iLevel ){
        x.id = readInt64(pCellData);
        x.iCell = 0;
      }else{
        x.id = p->id;
        x.iCell = p->iCell - 1;
      }
      if( p->iCell>=nCell ){
        RTREE_QUEUE_TRACE(pCur, "POP-S:");
        rtreeSearchPointPop(pCur);
      }
      if( rScore<RTREE_ZERO ) rScore = RTREE_ZERO;
      p = rtreeSearchPointNew(pCur, rScore, x.iLevel);
      if( p==0 ) return SQLITE_NOMEM;
      p->eWithin = eWithin;
      p->id = x.id;
      p->iCell = x.iCell;
      RTREE_QUEUE_TRACE(pCur, "PUSH-S:");
      break;
    }
    if( p->iCell>=nCell ){
      RTREE_QUEUE_TRACE(pCur, "POP-Se:");
      rtreeSearchPointPop(pCur);
    }
  }
  pCur->atEOF = p==0;
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xNext method.
*/
static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){

  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
  int rc = SQLITE_OK;












  /* Move to the next entry that matches the configured constraints. */






















  RTREE_QUEUE_TRACE(pCsr, "POP-Nx:");
  rtreeSearchPointPop(pCsr);
  rc = rtreeStepToLeaf(pCsr);
  return rc;
}

/* 
** Rtree virtual table module xRowid method.
*/
static int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){

  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;

  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
  int rc = SQLITE_OK;
  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
  if( rc==SQLITE_OK && p ){
    *pRowid = nodeGetRowid(RTREE_OF_CURSOR(pCsr), pNode, p->iCell);
  }
  return rc;
}

/* 
** Rtree virtual table module xColumn method.
*/
static int rtreeColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){
  Rtree *pRtree = (Rtree *)cur->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
  RtreeCoord c;
  int rc = SQLITE_OK;
  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);

  if( rc ) return rc;
  if( p==0 ) return SQLITE_OK;
  if( i==0 ){

    sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));
  }else{

    if( rc ) return rc;
    nodeGetCoord(pRtree, pNode, p->iCell, i-1, &c);
#ifndef SQLITE_RTREE_INT_ONLY
    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
      sqlite3_result_double(ctx, c.f);
    }else
#endif
    {
      assert( pRtree->eCoordType==RTREE_COORD_INT32 );
      sqlite3_result_int(ctx, c.i);
    }
  }

  return SQLITE_OK;
}

/* 
** Use nodeAcquire() to obtain the leaf node containing the record with 
** rowid iRowid. If successful, set *ppLeaf to point to the node and
** return SQLITE_OK. If there is no such record in the table, set
** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf
** to zero and return an SQLite error code.
*/
static int findLeafNode(
  Rtree *pRtree,              /* RTree to search */
  i64 iRowid,                 /* The rowid searching for */
  RtreeNode **ppLeaf,         /* Write the node here */
  sqlite3_int64 *piNode       /* Write the node-id here */
){
  int rc;
  *ppLeaf = 0;
  sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);
  if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){
    i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);
    if( piNode ) *piNode = iNode;
    rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);
    sqlite3_reset(pRtree->pReadRowid);
  }else{
    rc = sqlite3_reset(pRtree->pReadRowid);
  }
  return rc;
}
................................................................................
/*
** This function is called to configure the RtreeConstraint object passed
** as the second argument for a MATCH constraint. The value passed as the
** first argument to this function is the right-hand operand to the MATCH
** operator.
*/
static int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){
  RtreeMatchArg *pBlob;              /* BLOB returned by geometry function */
  sqlite3_rtree_query_info *pInfo;   /* Callback information */
  int nBlob;                         /* Size of the geometry function blob */
  int nExpected;                     /* Expected size of the BLOB */

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

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

  pInfo = (sqlite3_rtree_query_info*)sqlite3_malloc( sizeof(*pInfo)+nBlob );
  if( !pInfo ) return SQLITE_NOMEM;
  memset(pInfo, 0, sizeof(*pInfo));
  pBlob = (RtreeMatchArg*)&pInfo[1];

  memcpy(pBlob, sqlite3_value_blob(pValue), nBlob);
  nExpected = (int)(sizeof(RtreeMatchArg) +
                    (pBlob->nParam-1)*sizeof(RtreeDValue));
  if( pBlob->magic!=RTREE_GEOMETRY_MAGIC || nBlob!=nExpected ){
    sqlite3_free(pInfo);
    return SQLITE_ERROR;
  }
  pInfo->pContext = pBlob->cb.pContext;
  pInfo->nParam = pBlob->nParam;
  pInfo->aParam = pBlob->aParam;

  if( pBlob->cb.xGeom ){
    pCons->u.xGeom = pBlob->cb.xGeom;
  }else{
    pCons->op = RTREE_QUERY;
    pCons->u.xQueryFunc = pBlob->cb.xQueryFunc;
  }
  pCons->pInfo = pInfo;
  return SQLITE_OK;
}

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

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

  rtreeReference(pRtree);

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

  if( idxNum==1 ){
    /* Special case - lookup by rowid. */
    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
    RtreeSearchPoint *p;     /* Search point for the the leaf */
    i64 iRowid = sqlite3_value_int64(argv[0]);
    i64 iNode = 0;
    rc = findLeafNode(pRtree, iRowid, &pLeaf, &iNode);


    if( rc==SQLITE_OK && pLeaf!=0 ){
      p = rtreeSearchPointNew(pCsr, RTREE_ZERO, 0);
      assert( p!=0 );  /* Always returns pCsr->sPoint */
      pCsr->aNode[0] = pLeaf;
      p->id = iNode;
      p->eWithin = PARTLY_WITHIN;
      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &iCell);
      p->iCell = iCell;
      RTREE_QUEUE_TRACE(pCsr, "PUSH-F1:");
    }else{
      pCsr->atEOF = 1;
    }
  }else{
    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
    ** with the configured constraints. 
    */
    rc = nodeAcquire(pRtree, 1, 0, &pRoot);
    if( rc==SQLITE_OK && argc>0 ){
      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
      pCsr->nConstraint = argc;
      if( !pCsr->aConstraint ){
        rc = SQLITE_NOMEM;
      }else{
        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);
        memset(pCsr->anQueue, 0, sizeof(u32)*(pRtree->iDepth + 1));
        assert( (idxStr==0 && argc==0)
                || (idxStr && (int)strlen(idxStr)==argc*2) );
        for(ii=0; ii<argc; ii++){
          RtreeConstraint *p = &pCsr->aConstraint[ii];
          p->op = idxStr[ii*2];
          p->iCoord = idxStr[ii*2+1]-'0';
          if( p->op>=RTREE_MATCH ){
            /* A MATCH operator. The right-hand-side must be a blob that
            ** can be cast into an RtreeMatchArg object. One created using
            ** an sqlite3_rtree_geometry_callback() SQL user function.
            */
            rc = deserializeGeometry(argv[ii], p);
            if( rc!=SQLITE_OK ){
              break;
            }
            p->pInfo->nCoord = pRtree->nDim*2;
            p->pInfo->anQueue = pCsr->anQueue;
            p->pInfo->mxLevel = pRtree->iDepth + 1;
          }else{
#ifdef SQLITE_RTREE_INT_ONLY
            p->u.rValue = sqlite3_value_int64(argv[ii]);
#else
            p->u.rValue = sqlite3_value_double(argv[ii]);
#endif
          }
        }
      }
    }

    if( rc==SQLITE_OK ){



      RtreeSearchPoint *pNew;
      pNew = rtreeSearchPointNew(pCsr, RTREE_ZERO, pRtree->iDepth+1);
      if( pNew==0 ) return SQLITE_NOMEM;
      pNew->id = 1;

      pNew->iCell = 0;
      pNew->eWithin = PARTLY_WITHIN;
      assert( pCsr->bPoint==1 );
      pCsr->aNode[0] = pRoot;







      pRoot = 0;
      RTREE_QUEUE_TRACE(pCsr, "PUSH-Fm:");
      rc = rtreeStepToLeaf(pCsr);
    }

  }


  nodeRelease(pRtree, pRoot);
  rtreeRelease(pRtree);
  return rc;
}

/*
** Set the pIdxInfo->estimatedRows variable to nRow. Unless this
** extension is currently being used by a version of SQLite too old to
................................................................................
        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;
        default:
          assert( p->op==SQLITE_INDEX_CONSTRAINT_MATCH );
          op = RTREE_MATCH; 
          break;
      }
      zIdxStr[iIdx++] = op;
      zIdxStr[iIdx++] = p->iColumn - 1 + '0';
      pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
      pIdxInfo->aConstraintUsage[ii].omit = 1;
    }
  }

  pIdxInfo->idxNum = 2;
  pIdxInfo->needToFreeIdxStr = 1;
................................................................................
  RtreeCell cell;
  memcpy(&cell, p, sizeof(RtreeCell));
  area = cellArea(pRtree, &cell);
  cellUnion(pRtree, &cell, pCell);
  return (cellArea(pRtree, &cell)-area);
}


static RtreeDValue cellOverlap(
  Rtree *pRtree, 
  RtreeCell *p, 
  RtreeCell *aCell, 
  int nCell

){
  int ii;
  RtreeDValue overlap = RTREE_ZERO;
  for(ii=0; ii<nCell; ii++){







    int jj;
    RtreeDValue o = (RtreeDValue)1;
    for(jj=0; jj<(pRtree->nDim*2); jj+=2){
      RtreeDValue x1, x2;

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

      if( x2<x1 ){

        o = (RtreeDValue)0;
        break;
      }else{
        o = o * (x2-x1);
      }
    }
    overlap += o;
  }

  return overlap;
}




















/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
................................................................................
  RtreeNode *pNode;
  rc = nodeAcquire(pRtree, 1, 0, &pNode);

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

    RtreeDValue fMinGrowth = RTREE_ZERO;
    RtreeDValue fMinArea = RTREE_ZERO;





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

    RtreeCell *aCell = 0;

















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
















      if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
        bBest = 1;
      }

      if( bBest ){
        fMinGrowth = growth;
        fMinArea = area;
        iBest = cell.iRowid;
      }
    }

................................................................................
  sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
  sqlite3_step(pRtree->pWriteParent);
  return sqlite3_reset(pRtree->pWriteParent);
}

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























































































































































/*
** Arguments aIdx, aDistance and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to 
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to the indexed values in aDistance. For
** example, assuming the inputs:
................................................................................
        assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
      }
    }
#endif
  }
}


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

  int iBestDim = 0;
  int iBestSplit = 0;
  RtreeDValue fBestMargin = RTREE_ZERO;

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

  aaSorted = (int **)sqlite3_malloc(nByte);
  if( !aaSorted ){
    return SQLITE_NOMEM;
  }
................................................................................
    for(jj=0; jj<nCell; jj++){
      aaSorted[ii][jj] = jj;
    }
    SortByDimension(pRtree, aaSorted[ii], nCell, ii, aCell, aSpare);
  }

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

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

  sqlite3_free(aaSorted);
  return SQLITE_OK;
}


























































static int updateMapping(
  Rtree *pRtree, 
  i64 iRowid, 
  RtreeNode *pNode, 
  int iHeight
){
................................................................................
    rc = SQLITE_NOMEM;
    goto splitnode_out;
  }

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

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

  /* Ensure both child nodes have node numbers assigned to them by calling
  ** nodeWrite(). Node pRight always needs a node number, as it was created
  ** by nodeNew() above. But node pLeft sometimes already has a node number.
................................................................................
    }
  }
  for(iDim=0; iDim<pRtree->nDim; iDim++){
    aCenterCoord[iDim] = (aCenterCoord[iDim]/(nCell*(RtreeDValue)2));
  }

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

................................................................................
    if( pChild ){
      nodeRelease(pRtree, pChild->pParent);
      nodeReference(pNode);
      pChild->pParent = pNode;
    }
  }
  if( nodeInsertCell(pRtree, pNode, pCell) ){

    if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
      rc = SplitNode(pRtree, pNode, pCell, iHeight);
    }else{
      pRtree->iReinsertHeight = iHeight;
      rc = Reinsert(pRtree, pNode, pCell, iHeight);
    }



  }else{
    rc = AdjustTree(pRtree, pNode, pCell);
    if( rc==SQLITE_OK ){
      if( iHeight==0 ){
        rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
      }else{
        rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
................................................................................
  /* Obtain a reference to the root node to initialize Rtree.iDepth */
  rc = nodeAcquire(pRtree, 1, 0, &pRoot);

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

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

  pRtree->db = db;

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


/*
** Implementation of a scalar function that decodes r-tree nodes to
** human readable strings. This can be used for debugging and analysis.
**
** The scalar function takes two arguments: (1) the number of dimensions
** to the rtree (between 1 and 5, inclusive) and (2) a blob of data containing
** an r-tree node.  For a two-dimensional r-tree structure called "rt", to
** deserialize all nodes, a statement like:
**
**   SELECT rtreenode(2, data) FROM rt_node;
**
** The human readable string takes the form of a Tcl list with one
** entry for each cell in the r-tree node. Each entry is itself a
** list, containing the 8-byte rowid/pageno followed by the 
** <num-dimension>*2 coordinates.
................................................................................
    int jj;

    nodeGetCell(&tree, &node, ii, &cell);
    sqlite3_snprintf(512-nCell,&zCell[nCell],"%lld", cell.iRowid);
    nCell = (int)strlen(zCell);
    for(jj=0; jj<tree.nDim*2; jj++){
#ifndef SQLITE_RTREE_INT_ONLY
      sqlite3_snprintf(512-nCell,&zCell[nCell], " %g",
                       (double)cell.aCoord[jj].f);
#else
      sqlite3_snprintf(512-nCell,&zCell[nCell], " %d",
                       cell.aCoord[jj].i);
#endif
      nCell = (int)strlen(zCell);
    }
................................................................................
      zText = sqlite3_mprintf("{%s}", zCell);
    }
  }
  
  sqlite3_result_text(ctx, zText, -1, sqlite3_free);
}

/* This routine implements an SQL function that returns the "depth" parameter
** from the front of a blob that is an r-tree node.  For example:
**
**     SELECT rtreedepth(data) FROM rt_node WHERE nodeno=1;
**
** The depth value is 0 for all nodes other than the root node, and the root
** node always has nodeno=1, so the example above is the primary use for this
** routine.  This routine is intended for testing and analysis only.
*/
static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
  UNUSED_PARAMETER(nArg);
  if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB 
   || sqlite3_value_bytes(apArg[0])<2
  ){
    sqlite3_result_error(ctx, "Invalid argument to rtreedepth()", -1); 
  }else{
................................................................................
    rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
  }

  return rc;
}

/*
** This routine deletes the RtreeGeomCallback object that was attached
** one of the SQL functions create by sqlite3_rtree_geometry_callback()
** or sqlite3_rtree_query_callback().  In other words, this routine is the
** destructor for an RtreeGeomCallback objecct.  This routine is called when
** the corresponding SQL function is deleted.
*/

static void rtreeFreeCallback(void *p){
  RtreeGeomCallback *pInfo = (RtreeGeomCallback*)p;
  if( pInfo->xDestructor ) pInfo->xDestructor(pInfo->pContext);
  sqlite3_free(p);
}

/*
** Each call to sqlite3_rtree_geometry_callback() or
** sqlite3_rtree_query_callback() creates an ordinary SQLite
** scalar function that is implemented by this routine.
**
** All this function does is construct an RtreeMatchArg object that
** contains the geometry-checking callback routines and a list of
** parameters to this function, then return that RtreeMatchArg object
** as a BLOB.
**
** The R-Tree MATCH operator will read the returned BLOB, deserialize
** the RtreeMatchArg object, and use the RtreeMatchArg object to figure
** out which elements of the R-Tree should be returned by the query.
*/
static void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){
  RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);
  RtreeMatchArg *pBlob;
  int nBlob;

  nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(RtreeDValue);
  pBlob = (RtreeMatchArg *)sqlite3_malloc(nBlob);
  if( !pBlob ){
    sqlite3_result_error_nomem(ctx);
  }else{
    int i;
    pBlob->magic = RTREE_GEOMETRY_MAGIC;
    pBlob->cb = pGeomCtx[0];

    pBlob->nParam = nArg;
    for(i=0; i<nArg; i++){
#ifdef SQLITE_RTREE_INT_ONLY
      pBlob->aParam[i] = sqlite3_value_int64(aArg[i]);
#else
      pBlob->aParam[i] = sqlite3_value_double(aArg[i]);
#endif
    }
    sqlite3_result_blob(ctx, pBlob, nBlob, sqlite3_free);
  }
}

/*
** Register a new geometry function for use with the r-tree MATCH operator.
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,                  /* Register SQL function on this connection */
  const char *zGeom,            /* Name of the new SQL function */
  int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*), /* Callback */
  void *pContext                /* Extra data associated with the callback */
){
  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */

  /* Allocate and populate the context object. */
  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
  if( !pGeomCtx ) return SQLITE_NOMEM;
  pGeomCtx->xGeom = xGeom;
  pGeomCtx->xQueryFunc = 0;
  pGeomCtx->xDestructor = 0;
  pGeomCtx->pContext = pContext;
  return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY, 
      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
  );
}



/*
** Register a new 2nd-generation geometry function for use with the
** r-tree MATCH operator.
*/
int sqlite3_rtree_query_callback(
  sqlite3 *db,                 /* Register SQL function on this connection */
  const char *zQueryFunc,      /* Name of new SQL function */
  int (*xQueryFunc)(sqlite3_rtree_query_info*), /* Callback */
  void *pContext,              /* Extra data passed into the callback */
  void (*xDestructor)(void*)   /* Destructor for the extra data */
){
  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */

  /* Allocate and populate the context object. */
  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
  if( !pGeomCtx ) return SQLITE_NOMEM;
  pGeomCtx->xGeom = 0;
  pGeomCtx->xQueryFunc = xQueryFunc;
  pGeomCtx->xDestructor = xDestructor;
  pGeomCtx->pContext = pContext;
  return sqlite3_create_function_v2(db, zQueryFunc, -1, SQLITE_ANY, 
      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
  );
}

#if !SQLITE_CORE
#ifdef _WIN32
__declspec(dllexport)
#endif

Changes to ext/rtree/rtree1.test.

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  }
  return $out
}

# 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_intout { SELECT * FROM t1 ORDER BY ii }
} {1 5 10 2 15 20}
do_test rtree-1.4.3 {
................................................................................
  }
} {2}

#-------------------------------------------------------------------------
# Test on-conflict clause handling.
#
db_delete_and_reopen
do_execsql_test 12.0 {
  CREATE VIRTUAL TABLE t1 USING rtree_i32(idx, x1, x2, y1, y2);
  INSERT INTO t1 VALUES(1,   1, 2, 3, 4);



  INSERT INTO t1 VALUES(2,   2, 3, 4, 5);
  INSERT INTO t1 VALUES(3,   3, 4, 5, 6);

  CREATE TABLE source(idx, x1, x2, y1, y2);
  INSERT INTO source VALUES(5, 8, 8, 8, 8);
  INSERT INTO source VALUES(2, 7, 7, 7, 7);
  
}
db_save_and_close
foreach {tn sql_template testdata} {
  1    "INSERT %CONF% INTO t1 VALUES(2, 7, 7, 7, 7)" {
    ROLLBACK 0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
    ABORT    0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
    IGNORE   0 0 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}







|
<
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>
>
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<







 







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>
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>






<







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130
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451
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457
  }
  return $out
}

# Test that it is possible to open an existing database that contains
# r-tree tables.
#
do_execsql_test rtree-1.4.1a {

  CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2);
  INSERT INTO t1 VALUES(1, 5.0, 10.0);
  SELECT substr(hex(data),1,40) FROM t1_node;
} {00000001000000000000000140A0000041200000}
do_execsql_test rtree-1.4.1b {
  INSERT INTO t1 VALUES(2, 15.0, 20.0);

} {}
do_test rtree-1.4.2 {
  db close
  sqlite3 db test.db
  execsql_intout { SELECT * FROM t1 ORDER BY ii }
} {1 5 10 2 15 20}
do_test rtree-1.4.3 {
................................................................................
  }
} {2}

#-------------------------------------------------------------------------
# Test on-conflict clause handling.
#
db_delete_and_reopen
do_execsql_test 12.0.1 {
  CREATE VIRTUAL TABLE t1 USING rtree_i32(idx, x1, x2, y1, y2);
  INSERT INTO t1 VALUES(1,   1, 2, 3, 4);
  SELECT substr(hex(data),1,56) FROM t1_node;
} {00000001000000000000000100000001000000020000000300000004}
do_execsql_test 12.0.2 {
  INSERT INTO t1 VALUES(2,   2, 3, 4, 5);
  INSERT INTO t1 VALUES(3,   3, 4, 5, 6);

  CREATE TABLE source(idx, x1, x2, y1, y2);
  INSERT INTO source VALUES(5, 8, 8, 8, 8);
  INSERT INTO source VALUES(2, 7, 7, 7, 7);

}
db_save_and_close
foreach {tn sql_template testdata} {
  1    "INSERT %CONF% INTO t1 VALUES(2, 7, 7, 7, 7)" {
    ROLLBACK 0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6}
    ABORT    0 1 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}
    IGNORE   0 0 {1 1 2 3 4   2 2 3 4 5   3 3 4 5 6   4 4 5 6 7}

Changes to ext/rtree/rtree6.test.

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    CREATE TABLE t2(k INTEGER PRIMARY KEY, v);
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
  }
} {}

do_test rtree6-1.2 {
  rtree_strategy {SELECT * FROM t1 WHERE x1>10}
} {Ea}

do_test rtree6-1.3 {
  rtree_strategy {SELECT * FROM t1 WHERE x1<10}
} {Ca}

do_test rtree6-1.4 {
  rtree_strategy {SELECT * FROM t1,t2 WHERE k=ii AND x1<10}
} {Ca}

do_test rtree6-1.5 {
  rtree_strategy {SELECT * FROM t1,t2 WHERE k=+ii AND x1<10}
} {Ca}

do_eqp_test rtree6.2.1 {
  SELECT * FROM t1,t2 WHERE k=+ii AND x1<10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:Ca} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.2 {
  SELECT * FROM t1,t2 WHERE k=ii AND x1<10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:Ca} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.3 {
  SELECT * FROM t1,t2 WHERE k=ii
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.4 {
  SELECT * FROM t1,t2 WHERE v=10 and x1<10 and x2>10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:CaEb} 
  0 1 1 {SEARCH TABLE t2 USING AUTOMATIC COVERING INDEX (v=?)}
}

do_eqp_test rtree6.2.5 {
  SELECT * FROM t1,t2 WHERE k=ii AND x1<v
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:} 
................................................................................
  rtree_strategy {
    SELECT * FROM t3 WHERE 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 
  }
} {EaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEa}
do_test rtree6.3.3 {
  rtree_strategy {
    SELECT * FROM t3 WHERE 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5
  }
} {EaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEaEa}

do_execsql_test rtree6-3.4 {
  SELECT * FROM t3 WHERE x1>0.5 AND x1>0.8 AND x1>1.1
} {}
do_execsql_test rtree6-3.5 {
  SELECT * FROM t3 WHERE 
    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 







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    CREATE TABLE t2(k INTEGER PRIMARY KEY, v);
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
  }
} {}

do_test rtree6-1.2 {
  rtree_strategy {SELECT * FROM t1 WHERE x1>10}
} {E0}

do_test rtree6-1.3 {
  rtree_strategy {SELECT * FROM t1 WHERE x1<10}
} {C0}

do_test rtree6-1.4 {
  rtree_strategy {SELECT * FROM t1,t2 WHERE k=ii AND x1<10}
} {C0}

do_test rtree6-1.5 {
  rtree_strategy {SELECT * FROM t1,t2 WHERE k=+ii AND x1<10}
} {C0}

do_eqp_test rtree6.2.1 {
  SELECT * FROM t1,t2 WHERE k=+ii AND x1<10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:C0} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.2 {
  SELECT * FROM t1,t2 WHERE k=ii AND x1<10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:C0} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.3 {
  SELECT * FROM t1,t2 WHERE k=ii
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:} 
  0 1 1 {SEARCH TABLE t2 USING INTEGER PRIMARY KEY (rowid=?)}
}

do_eqp_test rtree6.2.4 {
  SELECT * FROM t1,t2 WHERE v=10 and x1<10 and x2>10
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:C0E1} 
  0 1 1 {SEARCH TABLE t2 USING AUTOMATIC COVERING INDEX (v=?)}
}

do_eqp_test rtree6.2.5 {
  SELECT * FROM t1,t2 WHERE k=ii AND x1<v
} {
  0 0 0 {SCAN TABLE t1 VIRTUAL TABLE INDEX 2:} 
................................................................................
  rtree_strategy {
    SELECT * FROM t3 WHERE 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 
  }
} {E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0}
do_test rtree6.3.3 {
  rtree_strategy {
    SELECT * FROM t3 WHERE 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 
      x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5
  }
} {E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0}

do_execsql_test rtree6-3.4 {
  SELECT * FROM t3 WHERE x1>0.5 AND x1>0.8 AND x1>1.1
} {}
do_execsql_test rtree6-3.5 {
  SELECT * FROM t3 WHERE 
    x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND x1>0.5 AND 

Changes to ext/rtree/rtreeB.test.

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      INSERT INTO t1 VALUES(1073741824, 0.0, 0.0, 100.0, 100.0);
      INSERT INTO t1 VALUES(2147483646, 0.0, 0.0, 200.0, 200.0);
      INSERT INTO t1 VALUES(4294967296, 0.0, 0.0, 300.0, 300.0);
      INSERT INTO t1 VALUES(8589934592, 20.0, 20.0, 150.0, 150.0);
      INSERT INTO t1 VALUES(9223372036854775807, 150, 150, 400, 400);
      SELECT rtreenode(2, data) FROM t1_node;
    }
  } {{{1073741824 0.000000 0.000000 100.000000 100.000000} {2147483646 0.000000 0.000000 200.000000 200.000000} {4294967296 0.000000 0.000000 300.000000 300.000000} {8589934592 20.000000 20.000000 150.000000 150.000000} {9223372036854775807 150.000000 150.000000 400.000000 400.000000}}}
}

finish_test







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      INSERT INTO t1 VALUES(1073741824, 0.0, 0.0, 100.0, 100.0);
      INSERT INTO t1 VALUES(2147483646, 0.0, 0.0, 200.0, 200.0);
      INSERT INTO t1 VALUES(4294967296, 0.0, 0.0, 300.0, 300.0);
      INSERT INTO t1 VALUES(8589934592, 20.0, 20.0, 150.0, 150.0);
      INSERT INTO t1 VALUES(9223372036854775807, 150, 150, 400, 400);
      SELECT rtreenode(2, data) FROM t1_node;
    }
  } {{{1073741824 0 0 100 100} {2147483646 0 0 200 200} {4294967296 0 0 300 300} {8589934592 20 20 150 150} {9223372036854775807 150 150 400 400}}}
}

finish_test

Changes to ext/rtree/rtreeC.test.

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}

do_eqp_test 1.1 {
  SELECT * FROM r_tree, t 
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 1 {SCAN TABLE t}
  0 1 0 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 1.2 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 1.3 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 1.5 {
  SELECT * FROM t, r_tree
} {
  0 0 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:}
  0 1 0 {SCAN TABLE t} 
................................................................................
sqlite3 db test.db

do_eqp_test 2.1 {
  SELECT * FROM r_tree, t 
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 1 {SCAN TABLE t}
  0 1 0 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 2.2 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 2.3 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:DdBcDbBa}
}

do_eqp_test 2.5 {
  SELECT * FROM t, r_tree
} {
  0 0 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:}
  0 1 0 {SCAN TABLE t} 
................................................................................
    execsql { SELECT * FROM rt }
  } {1 2.0 3.0}
  db close
}


finish_test








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}

do_eqp_test 1.1 {
  SELECT * FROM r_tree, t 
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 1 {SCAN TABLE t}
  0 1 0 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 1.2 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 1.3 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 1.5 {
  SELECT * FROM t, r_tree
} {
  0 0 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:}
  0 1 0 {SCAN TABLE t} 
................................................................................
sqlite3 db test.db

do_eqp_test 2.1 {
  SELECT * FROM r_tree, t 
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 1 {SCAN TABLE t}
  0 1 0 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 2.2 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND t.x<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 2.3 {
  SELECT * FROM t, r_tree
  WHERE t.x>=min_x AND t.x<=max_x AND t.y>=min_y AND ?<=max_y
} {
  0 0 0 {SCAN TABLE t}
  0 1 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:D3B2D1B0}
}

do_eqp_test 2.5 {
  SELECT * FROM t, r_tree
} {
  0 0 1 {SCAN TABLE r_tree VIRTUAL TABLE INDEX 2:}
  0 1 0 {SCAN TABLE t} 
................................................................................
    execsql { SELECT * FROM rt }
  } {1 2.0 3.0}
  db close
}


finish_test

Added ext/rtree/rtreeE.test.



































































































































































































































































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# 2010 August 28
#
# 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 tests for the r-tree module. Specifically, it tests
# that new-style custom r-tree queries (geometry callbacks) work.
# 

if {![info exists testdir]} {
  set testdir [file join [file dirname [info script]] .. .. test]
} 
source $testdir/tester.tcl
ifcapable !rtree { finish_test ; return }
ifcapable rtree_int_only { finish_test; return }


#-------------------------------------------------------------------------
# Test the example 2d "circle" geometry callback.
#
register_circle_geom db

do_execsql_test rtreeE-1.1 {
  PRAGMA page_size=512;
  CREATE VIRTUAL TABLE rt1 USING rtree(id,x0,x1,y0,y1);
  
  /* A tight pattern of small boxes near 0,0 */
  WITH RECURSIVE
    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
  INSERT INTO rt1 SELECT x+5*y, x, x+2, y, y+2 FROM x, y;

  /* A looser pattern of small boxes near 100, 0 */
  WITH RECURSIVE
    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
  INSERT INTO rt1 SELECT 100+x+5*y, x*3+100, x*3+102, y*3, y*3+2 FROM x, y;

  /* A looser pattern of larger boxes near 0, 200 */
  WITH RECURSIVE
    x(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM x WHERE x<4),
    y(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM y WHERE y<4)
  INSERT INTO rt1 SELECT 200+x+5*y, x*7, x*7+15, y*7+200, y*7+215 FROM x, y;
} {}

# Queries against each of the three clusters */
do_execsql_test rtreeE-1.1 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0.0, 0.0, 50.0, 3) ORDER BY id;
} {0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24}
do_execsql_test rtreeE-1.2 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(100.0, 0.0, 50.0, 3) ORDER BY id;
} {100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124}
do_execsql_test rtreeE-1.3 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0.0, 200.0, 50.0, 3) ORDER BY id;
} {200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224}

# The Qcircle geometry function gives a lower score to larger leaf-nodes.
# This causes the 200s to sort before the 100s and the 0s to sort before
# last.
#
do_execsql_test rtreeE-1.4 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0,0,1000,3) AND id%100==0
} {200 100 0}

# Exclude odd rowids on a depth-first search
do_execsql_test rtreeE-1.5 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0,0,1000,4) ORDER BY +id
} {0 2 4 6 8 10 12 14 16 18 20 22 24 100 102 104 106 108 110 112 114 116 118 120 122 124 200 202 204 206 208 210 212 214 216 218 220 222 224}

# Exclude odd rowids on a breadth-first search.
do_execsql_test rtreeE-1.6 {
  SELECT id FROM rt1 WHERE id MATCH Qcircle(0,0,1000,5) ORDER BY +id
} {0 2 4 6 8 10 12 14 16 18 20 22 24 100 102 104 106 108 110 112 114 116 118 120 122 124 200 202 204 206 208 210 212 214 216 218 220 222 224}

# Construct a large 2-D RTree with thousands of random entries.
#
do_test rtreeE-2.1 {
  db eval {
    CREATE TABLE t2(id,x0,x1,y0,y1);
    CREATE VIRTUAL TABLE rt2 USING rtree(id,x0,x1,y0,y1);
    BEGIN;
  }
  expr srand(0)
  for {set i 1} {$i<=10000} {incr i} {
    set dx [expr {int(rand()*40)+1}]
    set dy [expr {int(rand()*40)+1}]
    set x0 [expr {int(rand()*(10000 - $dx))}]
    set x1 [expr {$x0+$dx}]
    set y0 [expr {int(rand()*(10000 - $dy))}]
    set y1 [expr {$y0+$dy}]
    set id [expr {$i+10000}]
    db eval {INSERT INTO t2 VALUES($id,$x0,$x1,$y0,$y1)}
  }
  db eval {
    INSERT INTO rt2 SELECT * FROM t2;
    COMMIT;
  }
} {}

for {set i 1} {$i<=200} {incr i} {
  set dx [expr {int(rand()*100)}]
  set dy [expr {int(rand()*100)}]
  set x0 [expr {int(rand()*(10000 - $dx))}]
  set x1 [expr {$x0+$dx}]
  set y0 [expr {int(rand()*(10000 - $dy))}]
  set y1 [expr {$y0+$dy}]
  set ans [db eval {SELECT id FROM t2 WHERE x1>=$x0 AND x0<=$x1 AND y1>=$y0 AND y0<=$y1 ORDER BY id}]
  do_execsql_test rtreeE-2.2.$i {
    SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch($x0,$x1,$y0,$y1) ORDER BY id
  } $ans
}

# Run query that have very deep priority queues
#
set ans [db eval {SELECT id FROM t2 WHERE x1>=0 AND x0<=5000 AND y1>=0 AND y0<=5000 ORDER BY id}]
do_execsql_test rtreeE-2.3 {
  SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch(0,5000,0,5000) ORDER BY id
} $ans
set ans [db eval {SELECT id FROM t2 WHERE x1>=0 AND x0<=10000 AND y1>=0 AND y0<=10000 ORDER BY id}]
do_execsql_test rtreeE-2.4 {
  SELECT id FROM rt2 WHERE id MATCH breadthfirstsearch(0,10000,0,10000) ORDER BY id
} $ans

finish_test

Changes to ext/rtree/sqlite3rtree.h.

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#include <sqlite3.h>

#ifdef __cplusplus
extern "C" {
#endif

typedef struct sqlite3_rtree_geometry sqlite3_rtree_geometry;











/*
** Register a geometry callback named zGeom that can be used as part of an
** R-Tree geometry query as follows:
**
**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zGeom(... params ...)
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,
  const char *zGeom,
#ifdef SQLITE_RTREE_INT_ONLY
  int (*xGeom)(sqlite3_rtree_geometry*, int n, sqlite3_int64 *a, int *pRes),
#else
  int (*xGeom)(sqlite3_rtree_geometry*, int n, double *a, int *pRes),
#endif
  void *pContext
);


/*
** A pointer to a structure of the following type is passed as the first
** argument to callbacks registered using rtree_geometry_callback().
*/
struct sqlite3_rtree_geometry {
  void *pContext;                 /* Copy of pContext passed to s_r_g_c() */
  int nParam;                     /* Size of array aParam[] */
  double *aParam;                 /* Parameters passed to SQL geom function */
  void *pUser;                    /* Callback implementation user data */
  void (*xDelUser)(void *);       /* Called by SQLite to clean up pUser */
};



















































#ifdef __cplusplus
}  /* end of the 'extern "C"' block */
#endif

#endif  /* ifndef _SQLITE3RTREE_H_ */







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#include <sqlite3.h>

#ifdef __cplusplus
extern "C" {
#endif

typedef struct sqlite3_rtree_geometry sqlite3_rtree_geometry;
typedef struct sqlite3_rtree_query_info sqlite3_rtree_query_info;

/* The double-precision datatype used by RTree depends on the
** SQLITE_RTREE_INT_ONLY compile-time option.
*/
#ifdef SQLITE_RTREE_INT_ONLY
  typedef sqlite3_int64 sqlite3_rtree_dbl;
#else
  typedef double sqlite3_rtree_dbl;
#endif

/*
** Register a geometry callback named zGeom that can be used as part of an
** R-Tree geometry query as follows:
**
**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zGeom(... params ...)
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,
  const char *zGeom,



  int (*xGeom)(sqlite3_rtree_geometry*, int, sqlite3_rtree_dbl*,int*),

  void *pContext
);


/*
** A pointer to a structure of the following type is passed as the first
** argument to callbacks registered using rtree_geometry_callback().
*/
struct sqlite3_rtree_geometry {
  void *pContext;                 /* Copy of pContext passed to s_r_g_c() */
  int nParam;                     /* Size of array aParam[] */
  sqlite3_rtree_dbl *aParam;      /* Parameters passed to SQL geom function */
  void *pUser;                    /* Callback implementation user data */
  void (*xDelUser)(void *);       /* Called by SQLite to clean up pUser */
};

/*
** Register a 2nd-generation geometry callback named zScore that can be 
** used as part of an R-Tree geometry query as follows:
**
**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zQueryFunc(... params ...)
*/
int sqlite3_rtree_query_callback(
  sqlite3 *db,
  const char *zQueryFunc,
  int (*xQueryFunc)(sqlite3_rtree_query_info*),
  void *pContext,
  void (*xDestructor)(void*)
);


/*
** A pointer to a structure of the following type is passed as the 
** argument to scored geometry callback registered using
** sqlite3_rtree_query_callback().
**
** Note that the first 5 fields of this structure are identical to
** sqlite3_rtree_geometry.  This structure is a subclass of
** sqlite3_rtree_geometry.
*/
struct sqlite3_rtree_query_info {
  void *pContext;                   /* pContext from when function registered */
  int nParam;                       /* Number of function parameters */
  sqlite3_rtree_dbl *aParam;        /* value of function parameters */
  void *pUser;                      /* callback can use this, if desired */
  void (*xDelUser)(void*);          /* function to free pUser */
  sqlite3_rtree_dbl *aCoord;        /* Coordinates of node or entry to check */
  unsigned int *anQueue;            /* Number of pending entries in the queue */
  int nCoord;                       /* Number of coordinates */
  int iLevel;                       /* Level of current node or entry */
  int mxLevel;                      /* The largest iLevel value in the tree */
  sqlite3_int64 iRowid;             /* Rowid for current entry */
  sqlite3_rtree_dbl rParentScore;   /* Score of parent node */
  int eParentWithin;                /* Visibility of parent node */
  int eWithin;                      /* OUT: Visiblity */
  sqlite3_rtree_dbl rScore;         /* OUT: Write the score here */
};

/*
** Allowed values for sqlite3_rtree_query.eWithin and .eParentWithin.
*/
#define NOT_WITHIN       0   /* Object completely outside of query region */
#define PARTLY_WITHIN    1   /* Object partially overlaps query region */
#define FULLY_WITHIN     2   /* Object fully contained within query region */


#ifdef __cplusplus
}  /* end of the 'extern "C"' block */
#endif

#endif  /* ifndef _SQLITE3RTREE_H_ */

Changes to main.mk.

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parse.c:	$(TOP)/src/parse.y lemon $(TOP)/addopcodes.awk
	cp $(TOP)/src/parse.y .
	rm -f parse.h
	./lemon $(OPTS) parse.y
	mv parse.h parse.h.temp
	$(NAWK) -f $(TOP)/addopcodes.awk parse.h.temp >parse.h

sqlite3.h:	$(TOP)/src/sqlite.h.in $(TOP)/manifest.uuid $(TOP)/VERSION
	tclsh $(TOP)/tool/mksqlite3h.tcl $(TOP) >sqlite3.h

keywordhash.h:	$(TOP)/tool/mkkeywordhash.c
	$(BCC) -o mkkeywordhash $(OPTS) $(TOP)/tool/mkkeywordhash.c
	./mkkeywordhash >keywordhash.h









|







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parse.c:	$(TOP)/src/parse.y lemon $(TOP)/addopcodes.awk
	cp $(TOP)/src/parse.y .
	rm -f parse.h
	./lemon $(OPTS) parse.y
	mv parse.h parse.h.temp
	$(NAWK) -f $(TOP)/addopcodes.awk parse.h.temp >parse.h

sqlite3.h:	$(TOP)/src/sqlite.h.in $(TOP)/manifest.uuid $(TOP)/VERSION $(TOP)/ext/rtree/sqlite3rtree.h
	tclsh $(TOP)/tool/mksqlite3h.tcl $(TOP) >sqlite3.h

keywordhash.h:	$(TOP)/tool/mkkeywordhash.c
	$(BCC) -o mkkeywordhash $(OPTS) $(TOP)/tool/mkkeywordhash.c
	./mkkeywordhash >keywordhash.h


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    double xmax;
    double ymin;
    double ymax;
  } aBox[2];
  double centerx;
  double centery;
  double radius;


};

/*
** Destructor function for Circle objects allocated by circle_geom().
*/
static void circle_del(void *p){
  sqlite3_free(p);
................................................................................

/*
** Implementation of "circle" r-tree geometry callback.
*/
static int circle_geom(
  sqlite3_rtree_geometry *p,
  int nCoord, 
#ifdef SQLITE_RTREE_INT_ONLY
  sqlite3_int64 *aCoord,
#else
  double *aCoord, 
#endif
  int *pRes
){
  int i;                          /* Iterator variable */
  Circle *pCircle;                /* Structure defining circular region */
  double xmin, xmax;              /* X dimensions of box being tested */
  double ymin, ymax;              /* X dimensions of box being tested */

  if( p->pUser==0 ){





    /* If pUser is still 0, then the parameter values have not been tested
    ** for correctness or stored into a Circle structure yet. Do this now. */

    /* This geometry callback is for use with a 2-dimensional r-tree table.
    ** Return an error if the table does not have exactly 2 dimensions. */
    if( nCoord!=4 ) return SQLITE_ERROR;

................................................................................
    pCircle->aBox[0].xmax = pCircle->centerx;
    pCircle->aBox[0].ymin = pCircle->centery + pCircle->radius;
    pCircle->aBox[0].ymax = pCircle->centery - pCircle->radius;
    pCircle->aBox[1].xmin = pCircle->centerx + pCircle->radius;
    pCircle->aBox[1].xmax = pCircle->centerx - pCircle->radius;
    pCircle->aBox[1].ymin = pCircle->centery;
    pCircle->aBox[1].ymax = pCircle->centery;

  }

  pCircle = (Circle *)p->pUser;
  xmin = aCoord[0];
  xmax = aCoord[1];
  ymin = aCoord[2];
  ymax = aCoord[3];

  /* Check if any of the 4 corners of the bounding-box being tested lie 
  ** inside the circular region. If they do, then the bounding-box does
  ** intersect the region of interest. Set the output variable to true and
  ** return SQLITE_OK in this case. */
  for(i=0; i<4; i++){
    double x = (i&0x01) ? xmax : xmin;
    double y = (i&0x02) ? ymax : ymin;
................................................................................
  }

  /* The specified bounding box does not intersect the circular region. Set
  ** the output variable to zero and return SQLITE_OK. */
  *pRes = 0;
  return SQLITE_OK;
}





































































































































































/* END of implementation of "circle" geometry callback.
**************************************************************************
*************************************************************************/

#include <assert.h>
#include "tcl.h"
................................................................................
**   cube(x, y, z, width, height, depth)
**
** The width, height and depth parameters must all be greater than zero.
*/
static int cube_geom(
  sqlite3_rtree_geometry *p,
  int nCoord,
#ifdef SQLITE_RTREE_INT_ONLY
  sqlite3_int64 *aCoord, 
#else
  double *aCoord, 
#endif
  int *piRes
){
  Cube *pCube = (Cube *)p->pUser;

  assert( p->pContext==(void *)&gHere );

  if( pCube==0 ){
................................................................................

  if( objc!=2 ){
    Tcl_WrongNumArgs(interp, 1, objv, "DB");
    return TCL_ERROR;
  }
  if( getDbPointer(interp, Tcl_GetString(objv[1]), &db) ) return TCL_ERROR;
  rc = sqlite3_rtree_geometry_callback(db, "circle", circle_geom, 0);








  Tcl_SetResult(interp, (char *)sqlite3ErrName(rc), TCL_STATIC);
#endif
  return TCL_OK;
}

int Sqlitetestrtree_Init(Tcl_Interp *interp){
  Tcl_CreateObjCommand(interp, "register_cube_geom", register_cube_geom, 0, 0);
  Tcl_CreateObjCommand(interp, "register_circle_geom",register_circle_geom,0,0);
  return TCL_OK;
}







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    double xmax;
    double ymin;
    double ymax;
  } aBox[2];
  double centerx;
  double centery;
  double radius;
  double mxArea;
  int eScoreType;
};

/*
** Destructor function for Circle objects allocated by circle_geom().
*/
static void circle_del(void *p){
  sqlite3_free(p);
................................................................................

/*
** Implementation of "circle" r-tree geometry callback.
*/
static int circle_geom(
  sqlite3_rtree_geometry *p,
  int nCoord, 



  sqlite3_rtree_dbl *aCoord,

  int *pRes
){
  int i;                          /* Iterator variable */
  Circle *pCircle;                /* Structure defining circular region */
  double xmin, xmax;              /* X dimensions of box being tested */
  double ymin, ymax;              /* X dimensions of box being tested */

  xmin = aCoord[0];
  xmax = aCoord[1];
  ymin = aCoord[2];
  ymax = aCoord[3];
  pCircle = (Circle *)p->pUser;
  if( pCircle==0 ){
    /* If pUser is still 0, then the parameter values have not been tested
    ** for correctness or stored into a Circle structure yet. Do this now. */

    /* This geometry callback is for use with a 2-dimensional r-tree table.
    ** Return an error if the table does not have exactly 2 dimensions. */
    if( nCoord!=4 ) return SQLITE_ERROR;

................................................................................
    pCircle->aBox[0].xmax = pCircle->centerx;
    pCircle->aBox[0].ymin = pCircle->centery + pCircle->radius;
    pCircle->aBox[0].ymax = pCircle->centery - pCircle->radius;
    pCircle->aBox[1].xmin = pCircle->centerx + pCircle->radius;
    pCircle->aBox[1].xmax = pCircle->centerx - pCircle->radius;
    pCircle->aBox[1].ymin = pCircle->centery;
    pCircle->aBox[1].ymax = pCircle->centery;
    pCircle->mxArea = (xmax - xmin)*(ymax - ymin) + 1.0;
  }







  /* Check if any of the 4 corners of the bounding-box being tested lie 
  ** inside the circular region. If they do, then the bounding-box does
  ** intersect the region of interest. Set the output variable to true and
  ** return SQLITE_OK in this case. */
  for(i=0; i<4; i++){
    double x = (i&0x01) ? xmax : xmin;
    double y = (i&0x02) ? ymax : ymin;
................................................................................
  }

  /* The specified bounding box does not intersect the circular region. Set
  ** the output variable to zero and return SQLITE_OK. */
  *pRes = 0;
  return SQLITE_OK;
}

/*
** Implementation of "circle" r-tree geometry callback using the 
** 2nd-generation interface that allows scoring.
*/
static int circle_query_func(sqlite3_rtree_query_info *p){
  int i;                          /* Iterator variable */
  Circle *pCircle;                /* Structure defining circular region */
  double xmin, xmax;              /* X dimensions of box being tested */
  double ymin, ymax;              /* X dimensions of box being tested */
  int nWithin = 0;                /* Number of corners inside the circle */

  xmin = p->aCoord[0];
  xmax = p->aCoord[1];
  ymin = p->aCoord[2];
  ymax = p->aCoord[3];
  pCircle = (Circle *)p->pUser;
  if( pCircle==0 ){
    /* If pUser is still 0, then the parameter values have not been tested
    ** for correctness or stored into a Circle structure yet. Do this now. */

    /* This geometry callback is for use with a 2-dimensional r-tree table.
    ** Return an error if the table does not have exactly 2 dimensions. */
    if( p->nCoord!=4 ) return SQLITE_ERROR;

    /* Test that the correct number of parameters (4) have been supplied,
    ** and that the parameters are in range (that the radius of the circle 
    ** radius is greater than zero). */
    if( p->nParam!=4 || p->aParam[2]<0.0 ) return SQLITE_ERROR;

    /* Allocate a structure to cache parameter data in. Return SQLITE_NOMEM
    ** if the allocation fails. */
    pCircle = (Circle *)(p->pUser = sqlite3_malloc(sizeof(Circle)));
    if( !pCircle ) return SQLITE_NOMEM;
    p->xDelUser = circle_del;

    /* Record the center and radius of the circular region. One way that
    ** tested bounding boxes that intersect the circular region are detected
    ** is by testing if each corner of the bounding box lies within radius
    ** units of the center of the circle. */
    pCircle->centerx = p->aParam[0];
    pCircle->centery = p->aParam[1];
    pCircle->radius = p->aParam[2];
    pCircle->eScoreType = (int)p->aParam[3];

    /* Define two bounding box regions. The first, aBox[0], extends to
    ** infinity in the X dimension. It covers the same range of the Y dimension
    ** as the circular region. The second, aBox[1], extends to infinity in
    ** the Y dimension and is constrained to the range of the circle in the
    ** X dimension.
    **
    ** Then imagine each box is split in half along its short axis by a line
    ** that intersects the center of the circular region. A bounding box
    ** being tested can be said to intersect the circular region if it contains
    ** points from each half of either of the two infinite bounding boxes.
    */
    pCircle->aBox[0].xmin = pCircle->centerx;
    pCircle->aBox[0].xmax = pCircle->centerx;
    pCircle->aBox[0].ymin = pCircle->centery + pCircle->radius;
    pCircle->aBox[0].ymax = pCircle->centery - pCircle->radius;
    pCircle->aBox[1].xmin = pCircle->centerx + pCircle->radius;
    pCircle->aBox[1].xmax = pCircle->centerx - pCircle->radius;
    pCircle->aBox[1].ymin = pCircle->centery;
    pCircle->aBox[1].ymax = pCircle->centery;
    pCircle->mxArea = 200.0*200.0;
  }

  /* Check if any of the 4 corners of the bounding-box being tested lie 
  ** inside the circular region. If they do, then the bounding-box does
  ** intersect the region of interest. Set the output variable to true and
  ** return SQLITE_OK in this case. */
  for(i=0; i<4; i++){
    double x = (i&0x01) ? xmax : xmin;
    double y = (i&0x02) ? ymax : ymin;
    double d2;
    
    d2  = (x-pCircle->centerx)*(x-pCircle->centerx);
    d2 += (y-pCircle->centery)*(y-pCircle->centery);
    if( d2<(pCircle->radius*pCircle->radius) ) nWithin++;
  }

  /* Check if the bounding box covers any other part of the circular region.
  ** See comments above for a description of how this test works. If it does
  ** cover part of the circular region, set the output variable to true
  ** and return SQLITE_OK. */
  if( nWithin==0 ){
    for(i=0; i<2; i++){
      if( xmin<=pCircle->aBox[i].xmin 
       && xmax>=pCircle->aBox[i].xmax 
       && ymin<=pCircle->aBox[i].ymin 
       && ymax>=pCircle->aBox[i].ymax 
      ){
        nWithin = 1;
        break;
      }
    }
  }

  if( pCircle->eScoreType==1 ){
    /* Depth first search */
    p->rScore = p->iLevel;
  }else if( pCircle->eScoreType==2 ){
    /* Breadth first search */
    p->rScore = 100 - p->iLevel;
  }else if( pCircle->eScoreType==3 ){
    /* Depth-first search, except sort the leaf nodes by area with
    ** the largest area first */
    if( p->iLevel==1 ){
      p->rScore = 1.0 - (xmax-xmin)*(ymax-ymin)/pCircle->mxArea;
      if( p->rScore<0.01 ) p->rScore = 0.01;
    }else{
      p->rScore = 0.0;
    }
  }else if( pCircle->eScoreType==4 ){
    /* Depth-first search, except exclude odd rowids */
    p->rScore = p->iLevel;
    if( p->iRowid&1 ) nWithin = 0;
  }else{
    /* Breadth-first search, except exclude odd rowids */
    p->rScore = 100 - p->iLevel;
    if( p->iRowid&1 ) nWithin = 0;
  }
  if( nWithin==0 ){
    p->eWithin = NOT_WITHIN;
  }else if( nWithin>=4 ){
    p->eWithin = FULLY_WITHIN;
  }else{
    p->eWithin = PARTLY_WITHIN;
  }
  return SQLITE_OK;
}
/*
** Implementation of "breadthfirstsearch" r-tree geometry callback using the 
** 2nd-generation interface that allows scoring.
**
**     ... WHERE id MATCH breadthfirstsearch($x0,$x1,$y0,$y1) ...
**
** It returns all entries whose bounding boxes overlap with $x0,$x1,$y0,$y1.
*/
static int bfs_query_func(sqlite3_rtree_query_info *p){
  double x0,x1,y0,y1;        /* Dimensions of box being tested */
  double bx0,bx1,by0,by1;    /* Boundary of the query function */

  if( p->nParam!=4 ) return SQLITE_ERROR;
  x0 = p->aCoord[0];
  x1 = p->aCoord[1];
  y0 = p->aCoord[2];
  y1 = p->aCoord[3];
  bx0 = p->aParam[0];
  bx1 = p->aParam[1];
  by0 = p->aParam[2];
  by1 = p->aParam[3];
  p->rScore = 100 - p->iLevel;
  if( p->eParentWithin==FULLY_WITHIN ){
    p->eWithin = FULLY_WITHIN;
  }else if( x0>=bx0 && x1<=bx1 && y0>=by0 && y1<=by1 ){
    p->eWithin = FULLY_WITHIN;
  }else if( x1>=bx0 && x0<=bx1 && y1>=by0 && y0<=by1 ){
    p->eWithin = PARTLY_WITHIN;
  }else{
    p->eWithin = NOT_WITHIN;
  }
  return SQLITE_OK;
}

/* END of implementation of "circle" geometry callback.
**************************************************************************
*************************************************************************/

#include <assert.h>
#include "tcl.h"
................................................................................
**   cube(x, y, z, width, height, depth)
**
** The width, height and depth parameters must all be greater than zero.
*/
static int cube_geom(
  sqlite3_rtree_geometry *p,
  int nCoord,



  sqlite3_rtree_dbl *aCoord,

  int *piRes
){
  Cube *pCube = (Cube *)p->pUser;

  assert( p->pContext==(void *)&gHere );

  if( pCube==0 ){
................................................................................

  if( objc!=2 ){
    Tcl_WrongNumArgs(interp, 1, objv, "DB");
    return TCL_ERROR;
  }
  if( getDbPointer(interp, Tcl_GetString(objv[1]), &db) ) return TCL_ERROR;
  rc = sqlite3_rtree_geometry_callback(db, "circle", circle_geom, 0);
  if( rc==SQLITE_OK ){
    rc = sqlite3_rtree_query_callback(db, "Qcircle",
                                      circle_query_func, 0, 0);
  }
  if( rc==SQLITE_OK ){
    rc = sqlite3_rtree_query_callback(db, "breadthfirstsearch",
                                      bfs_query_func, 0, 0);
  }
  Tcl_SetResult(interp, (char *)sqlite3ErrName(rc), TCL_STATIC);
#endif
  return TCL_OK;
}

int Sqlitetestrtree_Init(Tcl_Interp *interp){
  Tcl_CreateObjCommand(interp, "register_cube_geom", register_cube_geom, 0, 0);
  Tcl_CreateObjCommand(interp, "register_circle_geom",register_circle_geom,0,0);
  return TCL_OK;
}

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  const char *zPath, 
  int flags, 
  int *pResOut
){
  vfstrace_info *pInfo = (vfstrace_info*)pVfs->pAppData;
  sqlite3_vfs *pRoot = pInfo->pRootVfs;
  int rc;
  vfstrace_printf(pInfo, "%s.xDelete(\"%s\",%d)",
                  pInfo->zVfsName, zPath, flags);
  rc = pRoot->xAccess(pRoot, zPath, flags, pResOut);
  vfstrace_print_errcode(pInfo, " -> %s", rc);
  vfstrace_printf(pInfo, ", out=%d\n", *pResOut);
  return rc;
}








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  const char *zPath, 
  int flags, 
  int *pResOut
){
  vfstrace_info *pInfo = (vfstrace_info*)pVfs->pAppData;
  sqlite3_vfs *pRoot = pInfo->pRootVfs;
  int rc;
  vfstrace_printf(pInfo, "%s.xAccess(\"%s\",%d)",
                  pInfo->zVfsName, zPath, flags);
  rc = pRoot->xAccess(pRoot, zPath, flags, pResOut);
  vfstrace_print_errcode(pInfo, " -> %s", rc);
  vfstrace_printf(pInfo, ", out=%d\n", *pResOut);
  return rc;
}

Added test/show_speedtest1_rtree.tcl.



















































































































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#!/usr/bin/tclsh
#
# This script displays the field of rectangles used by --testset rtree
# of speedtest1.  Run this script as follows:
#
#      rm test.db
#      ./speedtest1 --testset rtree --size 25 test.db
#      sqlite3 --separator ' ' test.db 'SELECT * FROM rt1' >data.txt
#      wish show_speedtest1_rtree.tcl
#
# The filename "data.txt" is hard coded into this script and so that name
# must be used on lines 3 and 4 above.  Elsewhere, different filenames can
# be used.  The --size N parameter can be adjusted as desired.
#
package require Tk
set f [open data.txt rb]
set data [read $f]
close $f
canvas .c
frame .b
button .b.b1 -text X-Y -command refill-xy
button .b.b2 -text X-Z -command refill-xz
button .b.b3 -text Y-Z -command refill-yz
pack .b.b1 .b.b2 .b.b3 -side left
pack .c -side top -fill both -expand 1
pack .b -side top
proc resize_canvas_to_fit {} {
  foreach {x0 y0 x1 y1} [.c bbox all] break
  set w [expr {$x1-$x0}]
  set h [expr {$y1-$y0}]
  .c config -width $w -height $h
}
proc refill-xy {} {
  .c delete all
  foreach {id x0 x1 y0 y1 z0 z1} $::data {
    .c create rectangle $x0 $y0 $x1 $y1
  }
  .c scale all 0 0 0.05 0.05
  resize_canvas_to_fit
}
proc refill-xz {} {
  .c delete all
  foreach {id x0 x1 y0 y1 z0 z1} $::data {
    .c create rectangle $x0 $z0 $x1 $z1
  }
  .c scale all 0 0 0.05 0.05
  resize_canvas_to_fit
}
proc refill-yz {} {
  .c delete all
  foreach {id x0 x1 y0 y1 z0 z1} $::data {
    .c create rectangle $y0 $z0 $y1 $z1
  }
  .c scale all 0 0 0.05 0.05
  resize_canvas_to_fit
}
refill-xy

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  "  --sqlonly           No-op.  Only show the SQL that would have been run.\n"
  "  --size N            Relative test size.  Default=100\n"
  "  --stats             Show statistics at the end\n"
  "  --testset T         Run test-set T\n"
  "  --trace             Turn on SQL tracing\n"
  "  --utf16be           Set text encoding to UTF-16BE\n"
  "  --utf16le           Set text encoding to UTF-16LE\n"

  "  --without-rowid     Use WITHOUT ROWID where appropriate\n"
;


#include "sqlite3.h"
#include <assert.h>
#include <stdio.h>
................................................................................
  sqlite3_stmt *pStmt;       /* Current SQL statement */
  sqlite3_int64 iStart;      /* Start-time for the current test */
  sqlite3_int64 iTotal;      /* Total time */
  int bWithoutRowid;         /* True for --without-rowid */
  int bReprepare;            /* True to reprepare the SQL on each rerun */
  int bSqlOnly;              /* True to print the SQL once only */
  int bExplain;              /* Print SQL with EXPLAIN prefix */

  int szTest;                /* Scale factor for test iterations */
  const char *zWR;           /* Might be WITHOUT ROWID */
  const char *zNN;           /* Might be NOT NULL */
  const char *zPK;           /* Might be UNIQUE or PRIMARY KEY */
  unsigned int x, y;         /* Pseudo-random number generator state */
  int nResult;               /* Size of the current result */
  char zResult[3000];        /* Text of the current result */
................................................................................
    ");",
    nElem, nElem
  );
  speedtest1_run();
  speedtest1_end_test();

}


















































































































































































/*
** A testset used for debugging speedtest1 itself.
*/
void testset_debug1(void){
  unsigned i, n;
  unsigned x1, x2;
................................................................................
        zTSet = argv[++i];
      }else if( strcmp(z,"trace")==0 ){
        doTrace = 1;
      }else if( strcmp(z,"utf16le")==0 ){
        zEncoding = "utf16le";
      }else if( strcmp(z,"utf16be")==0 ){
        zEncoding = "utf16be";


      }else if( strcmp(z,"without-rowid")==0 ){
        g.zWR = "WITHOUT ROWID";
        g.zPK = "PRIMARY KEY";
      }else if( strcmp(z, "help")==0 || strcmp(z,"?")==0 ){
        printf(zHelp, argv[0]);
        exit(0);
      }else{
................................................................................
  if( g.bExplain ) printf(".explain\n.echo on\n");
  if( strcmp(zTSet,"main")==0 ){
    testset_main();
  }else if( strcmp(zTSet,"debug1")==0 ){
    testset_debug1();
  }else if( strcmp(zTSet,"cte")==0 ){
    testset_cte();


  }else{
    fatal_error("unknown testset: \"%s\"\n", zTSet);

  }
  speedtest1_final();

  /* Database connection statistics printed after both prepared statements
  ** have been finalized */
#if SQLITE_VERSION_NUMBER>=3007009
  if( showStats ){







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  "  --sqlonly           No-op.  Only show the SQL that would have been run.\n"
  "  --size N            Relative test size.  Default=100\n"
  "  --stats             Show statistics at the end\n"
  "  --testset T         Run test-set T\n"
  "  --trace             Turn on SQL tracing\n"
  "  --utf16be           Set text encoding to UTF-16BE\n"
  "  --utf16le           Set text encoding to UTF-16LE\n"
  "  --verify            Run additional verification steps.\n"
  "  --without-rowid     Use WITHOUT ROWID where appropriate\n"
;


#include "sqlite3.h"
#include <assert.h>
#include <stdio.h>
................................................................................
  sqlite3_stmt *pStmt;       /* Current SQL statement */
  sqlite3_int64 iStart;      /* Start-time for the current test */
  sqlite3_int64 iTotal;      /* Total time */
  int bWithoutRowid;         /* True for --without-rowid */
  int bReprepare;            /* True to reprepare the SQL on each rerun */
  int bSqlOnly;              /* True to print the SQL once only */
  int bExplain;              /* Print SQL with EXPLAIN prefix */
  int bVerify;               /* Try to verify that results are correct */
  int szTest;                /* Scale factor for test iterations */
  const char *zWR;           /* Might be WITHOUT ROWID */
  const char *zNN;           /* Might be NOT NULL */
  const char *zPK;           /* Might be UNIQUE or PRIMARY KEY */
  unsigned int x, y;         /* Pseudo-random number generator state */
  int nResult;               /* Size of the current result */
  char zResult[3000];        /* Text of the current result */
................................................................................
    ");",
    nElem, nElem
  );
  speedtest1_run();
  speedtest1_end_test();

}

/* Generate two numbers between 1 and mx.  The first number is less than
** the second.  Usually the numbers are near each other but can sometimes
** be far apart.
*/
static void twoCoords(
  int p1, int p2,                   /* Parameters adjusting sizes */
  unsigned mx,                      /* Range of 1..mx */
  unsigned *pX0, unsigned *pX1      /* OUT: write results here */
){
  unsigned d, x0, x1, span;

  span = mx/100 + 1;
  if( speedtest1_random()%3==0 ) span *= p1;
  if( speedtest1_random()%p2==0 ) span = mx/2;
  d = speedtest1_random()%span + 1;
  x0 = speedtest1_random()%(mx-d) + 1;
  x1 = x0 + d;
  *pX0 = x0;
  *pX1 = x1;
}

/* The following routine is an R-Tree geometry callback.  It returns
** true if the object overlaps a slice on the Y coordinate between the
** two values given as arguments.  In other words
**
**     SELECT count(*) FROM rt1 WHERE id MATCH xslice(10,20);
**
** Is the same as saying:
**
**     SELECT count(*) FROM rt1 WHERE y1>=10 AND y0<=20;
*/
static int xsliceGeometryCallback(
  sqlite3_rtree_geometry *p,
  int nCoord,
  double *aCoord,
  int *pRes
){
  *pRes = aCoord[3]>=p->aParam[0] && aCoord[2]<=p->aParam[1];
  return SQLITE_OK;
}

/*
** A testset for the R-Tree virtual table
*/
void testset_rtree(int p1, int p2){
  unsigned i, n;
  unsigned mxCoord;
  unsigned x0, x1, y0, y1, z0, z1;
  unsigned iStep;
  int *aCheck = sqlite3_malloc( sizeof(int)*g.szTest*100 );

  mxCoord = 15000;
  n = g.szTest*100;
  speedtest1_begin_test(100, "%d INSERTs into an r-tree", n);
  speedtest1_exec("BEGIN");
  speedtest1_exec("CREATE VIRTUAL TABLE rt1 USING rtree(id,x0,x1,y0,y1,z0,z1)");
  speedtest1_prepare("INSERT INTO rt1(id,x0,x1,y0,y1,z0,z1)"
                     "VALUES(?1,?2,?3,?4,?5,?6,?7)");
  for(i=1; i<=n; i++){
    twoCoords(p1, p2, mxCoord, &x0, &x1);
    twoCoords(p1, p2, mxCoord, &y0, &y1);
    twoCoords(p1, p2, mxCoord, &z0, &z1);
    sqlite3_bind_int(g.pStmt, 1, i);
    sqlite3_bind_int(g.pStmt, 2, x0);
    sqlite3_bind_int(g.pStmt, 3, x1);
    sqlite3_bind_int(g.pStmt, 4, y0);
    sqlite3_bind_int(g.pStmt, 5, y1);
    sqlite3_bind_int(g.pStmt, 6, z0);
    sqlite3_bind_int(g.pStmt, 7, z1);
    speedtest1_run();
  }
  speedtest1_exec("COMMIT");
  speedtest1_end_test();

  speedtest1_begin_test(101, "Copy from rtree to a regular table");
  speedtest1_exec("CREATE TABLE t1(id INTEGER PRIMARY KEY,x0,x1,y0,y1,z0,z1)");
  speedtest1_exec("INSERT INTO t1 SELECT * FROM rt1");
  speedtest1_end_test();

  n = g.szTest*20;
  speedtest1_begin_test(110, "%d one-dimensional intersect slice queries", n);
  speedtest1_prepare("SELECT count(*) FROM rt1 WHERE x0>=?1 AND x1<=?2");
  iStep = mxCoord/n;
  for(i=0; i<n; i++){
    sqlite3_bind_int(g.pStmt, 1, i*iStep);
    sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
    speedtest1_run();
    aCheck[i] = atoi(g.zResult);
  }
  speedtest1_end_test();

  if( g.bVerify ){
    n = g.szTest*20;
    speedtest1_begin_test(111, "Verify result from 1-D intersect slice queries");
    speedtest1_prepare("SELECT count(*) FROM t1 WHERE x0>=?1 AND x1<=?2");
    iStep = mxCoord/n;
    for(i=0; i<n; i++){
      sqlite3_bind_int(g.pStmt, 1, i*iStep);
      sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
      speedtest1_run();
      if( aCheck[i]!=atoi(g.zResult) ){
        fatal_error("Count disagree step %d: %d..%d.  %d vs %d",
                    i, i*iStep, (i+1)*iStep, aCheck[i], atoi(g.zResult));
      }
    }
    speedtest1_end_test();
  }
  
  n = g.szTest*20;
  speedtest1_begin_test(120, "%d one-dimensional overlap slice queries", n);
  speedtest1_prepare("SELECT count(*) FROM rt1 WHERE y1>=?1 AND y0<=?2");
  iStep = mxCoord/n;
  for(i=0; i<n; i++){
    sqlite3_bind_int(g.pStmt, 1, i*iStep);
    sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
    speedtest1_run();
    aCheck[i] = atoi(g.zResult);
  }
  speedtest1_end_test();

  if( g.bVerify ){
    n = g.szTest*20;
    speedtest1_begin_test(121, "Verify result from 1-D overlap slice queries");
    speedtest1_prepare("SELECT count(*) FROM t1 WHERE y1>=?1 AND y0<=?2");
    iStep = mxCoord/n;
    for(i=0; i<n; i++){
      sqlite3_bind_int(g.pStmt, 1, i*iStep);
      sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
      speedtest1_run();
      if( aCheck[i]!=atoi(g.zResult) ){
        fatal_error("Count disagree step %d: %d..%d.  %d vs %d",
                    i, i*iStep, (i+1)*iStep, aCheck[i], atoi(g.zResult));
      }
    }
    speedtest1_end_test();
  }
  

  n = g.szTest*20;
  speedtest1_begin_test(125, "%d custom geometry callback queries", n);
  sqlite3_rtree_geometry_callback(g.db, "xslice", xsliceGeometryCallback, 0);
  speedtest1_prepare("SELECT count(*) FROM rt1 WHERE id MATCH xslice(?1,?2)");
  iStep = mxCoord/n;
  for(i=0; i<n; i++){
    sqlite3_bind_int(g.pStmt, 1, i*iStep);
    sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
    speedtest1_run();
    if( aCheck[i]!=atoi(g.zResult) ){
      fatal_error("Count disagree step %d: %d..%d.  %d vs %d",
                  i, i*iStep, (i+1)*iStep, aCheck[i], atoi(g.zResult));
    }
  }
  speedtest1_end_test();

  n = g.szTest*80;
  speedtest1_begin_test(130, "%d three-dimensional intersect box queries", n);
  speedtest1_prepare("SELECT count(*) FROM rt1 WHERE x1>=?1 AND x0<=?2"
                     " AND y1>=?1 AND y0<=?2 AND z1>=?1 AND z0<=?2");
  iStep = mxCoord/n;
  for(i=0; i<n; i++){
    sqlite3_bind_int(g.pStmt, 1, i*iStep);
    sqlite3_bind_int(g.pStmt, 2, (i+1)*iStep);
    speedtest1_run();
    aCheck[i] = atoi(g.zResult);
  }
  speedtest1_end_test();

  n = g.szTest*100;
  speedtest1_begin_test(140, "%d rowid queries", n);
  speedtest1_prepare("SELECT * FROM rt1 WHERE id=?1");
  for(i=1; i<=n; i++){
    sqlite3_bind_int(g.pStmt, 1, i);
    speedtest1_run();
  }
  speedtest1_end_test();
}

/*
** A testset used for debugging speedtest1 itself.
*/
void testset_debug1(void){
  unsigned i, n;
  unsigned x1, x2;
................................................................................
        zTSet = argv[++i];
      }else if( strcmp(z,"trace")==0 ){
        doTrace = 1;
      }else if( strcmp(z,"utf16le")==0 ){
        zEncoding = "utf16le";
      }else if( strcmp(z,"utf16be")==0 ){
        zEncoding = "utf16be";
      }else if( strcmp(z,"verify")==0 ){
        g.bVerify = 1;
      }else if( strcmp(z,"without-rowid")==0 ){
        g.zWR = "WITHOUT ROWID";
        g.zPK = "PRIMARY KEY";
      }else if( strcmp(z, "help")==0 || strcmp(z,"?")==0 ){
        printf(zHelp, argv[0]);
        exit(0);
      }else{
................................................................................
  if( g.bExplain ) printf(".explain\n.echo on\n");
  if( strcmp(zTSet,"main")==0 ){
    testset_main();
  }else if( strcmp(zTSet,"debug1")==0 ){
    testset_debug1();
  }else if( strcmp(zTSet,"cte")==0 ){
    testset_cte();
  }else if( strcmp(zTSet,"rtree")==0 ){
    testset_rtree(6, 147);
  }else{
    fatal_error("unknown testset: \"%s\"\nChoices: main debug1 cte rtree\n",
                 zTSet);
  }
  speedtest1_final();

  /* Database connection statistics printed after both prepared statements
  ** have been finalized */
#if SQLITE_VERSION_NUMBER>=3007009
  if( showStats ){