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Overview
Comment:Initial implementation of the ability to have auxiliary columns in an rtree virtual table that store arbitrary content. It mostly works, but there are some minor issues in OOM corner cases.
Downloads: Tarball | ZIP archive | SQL archive
Timelines: family | ancestors | descendants | both | aux-data-in-rtree
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SHA3-256:0c87fec970221f954e0a92f3ef0437b382255479fac5b403ee37b1bb5ab29719
User & Date: drh 2018-05-16 17:57:30
Context
2018-05-16
18:18
Fix the OOM issue mentioned in the previous check-in. check-in: c489d8e4 user: drh tags: aux-data-in-rtree
17:57
Initial implementation of the ability to have auxiliary columns in an rtree virtual table that store arbitrary content. It mostly works, but there are some minor issues in OOM corner cases. check-in: 0c87fec9 user: drh tags: aux-data-in-rtree
15:35
Enhance the sqlite3_str_new() interface so that it always returns a valid and non-NULL pointer even in an OOM condition. check-in: ed5b0968 user: drh tags: trunk
Changes
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Changes to ext/rtree/rtree.c.

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  sqlite3 *db;                /* Host database connection */
  int iNodeSize;              /* Size in bytes of each node in the node table */
  u8 nDim;                    /* Number of dimensions */
  u8 nDim2;                   /* Twice the number of dimensions */
  u8 eCoordType;              /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */
  u8 nBytesPerCell;           /* Bytes consumed per cell */
  u8 inWrTrans;               /* True if inside write transaction */

  int iDepth;                 /* Current depth of the r-tree structure */
  char *zDb;                  /* Name of database containing r-tree table */
  char *zName;                /* Name of r-tree table */ 
  u32 nBusy;                  /* Current number of users of this structure */
  i64 nRowEst;                /* Estimated number of rows in this table */
  u32 nCursor;                /* Number of open cursors */


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

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




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

/* Possible values for Rtree.eCoordType: */
#define RTREE_COORD_REAL32 0
#define RTREE_COORD_INT32  1
................................................................................
/* 
** 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))
................................................................................
    sqlite3_finalize(pRtree->pDeleteNode);
    sqlite3_finalize(pRtree->pReadRowid);
    sqlite3_finalize(pRtree->pWriteRowid);
    sqlite3_finalize(pRtree->pDeleteRowid);
    sqlite3_finalize(pRtree->pReadParent);
    sqlite3_finalize(pRtree->pWriteParent);
    sqlite3_finalize(pRtree->pDeleteParent);


    sqlite3_free(pRtree);
  }
}

/* 
** Rtree virtual table module xDisconnect method.
*/
................................................................................
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
  Rtree *pRtree = (Rtree *)(cur->pVtab);
  int ii;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  assert( pRtree->nCursor>0 );
  freeCursorConstraints(pCsr);

  sqlite3_free(pCsr->aPoint);
  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
  sqlite3_free(pCsr);
  pRtree->nCursor--;
  nodeBlobReset(pRtree);
  return SQLITE_OK;
}
................................................................................
*/
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.
................................................................................
  Rtree *pRtree = (Rtree *)cur->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
  RtreeCoord c;
  int rc = SQLITE_OK;
  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);

  if( rc ) return rc;
  if( p==0 ) return SQLITE_OK;
  if( i==0 ){
    sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));
  }else{

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






  }














  return SQLITE_OK;
}

/* 
** Use nodeAcquire() to obtain the leaf node containing the record with 
** rowid iRowid. If successful, set *ppLeaf to point to the node and
** return SQLITE_OK. If there is no such record in the table, set
................................................................................

/*
** The xUpdate method for rtree module virtual tables.
*/
static int rtreeUpdate(
  sqlite3_vtab *pVtab, 
  int nData, 
  sqlite3_value **azData, 
  sqlite_int64 *pRowid
){
  Rtree *pRtree = (Rtree *)pVtab;
  int rc = SQLITE_OK;
  RtreeCell cell;                 /* New cell to insert if nData>1 */
  int bHaveRowid = 0;             /* Set to 1 after new rowid is determined */

................................................................................
  ** In the first case, if the conflict-handling mode is REPLACE, then
  ** the conflicting row can be removed before proceeding. In the second
  ** case, SQLITE_CONSTRAINT must be returned regardless of the
  ** conflict-handling mode specified by the user.
  */
  if( nData>1 ){
    int ii;



    /* Populate the cell.aCoord[] array. The first coordinate is azData[3].
    **
    ** NB: nData can only be less than nDim*2+3 if the rtree is mis-declared
    ** with "column" that are interpreted as table constraints.
    ** Example:  CREATE VIRTUAL TABLE bad USING rtree(x,y,CHECK(y>5));
    ** This problem was discovered after years of use, so we silently ignore
    ** these kinds of misdeclared tables to avoid breaking any legacy.
    */
    assert( nData<=(pRtree->nDim2 + 3) );

#ifndef SQLITE_RTREE_INT_ONLY
    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
      for(ii=0; ii<nData-4; ii+=2){
        cell.aCoord[ii].f = rtreeValueDown(azData[ii+3]);
        cell.aCoord[ii+1].f = rtreeValueUp(azData[ii+4]);
        if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
          rc = rtreeConstraintError(pRtree, ii+1);
          goto constraint;
        }
      }
    }else
#endif
    {
      for(ii=0; ii<nData-4; ii+=2){
        cell.aCoord[ii].i = sqlite3_value_int(azData[ii+3]);
        cell.aCoord[ii+1].i = sqlite3_value_int(azData[ii+4]);
        if( cell.aCoord[ii].i>cell.aCoord[ii+1].i ){
          rc = rtreeConstraintError(pRtree, ii+1);
          goto constraint;
        }
      }
    }

    /* If a rowid value was supplied, check if it is already present in 
    ** the table. If so, the constraint has failed. */
    if( sqlite3_value_type(azData[2])!=SQLITE_NULL ){
      cell.iRowid = sqlite3_value_int64(azData[2]);
      if( sqlite3_value_type(azData[0])==SQLITE_NULL
       || sqlite3_value_int64(azData[0])!=cell.iRowid
      ){
        int steprc;
        sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
        steprc = sqlite3_step(pRtree->pReadRowid);
        rc = sqlite3_reset(pRtree->pReadRowid);
        if( SQLITE_ROW==steprc ){
          if( sqlite3_vtab_on_conflict(pRtree->db)==SQLITE_REPLACE ){
................................................................................
          }
        }
      }
      bHaveRowid = 1;
    }
  }

  /* If azData[0] is not an SQL NULL value, it is the rowid of a
  ** record to delete from the r-tree table. The following block does
  ** just that.
  */
  if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){
    rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(azData[0]));
  }

  /* If the azData[] array contains more than one element, elements
  ** (azData[2]..azData[argc-1]) contain a new record to insert into
  ** the r-tree structure.
  */
  if( rc==SQLITE_OK && nData>1 ){
    /* Insert the new record into the r-tree */
    RtreeNode *pLeaf = 0;

    /* Figure out the rowid of the new row. */
................................................................................
      pRtree->iReinsertHeight = -1;
      rc = rtreeInsertCell(pRtree, pLeaf, &cell, 0);
      rc2 = nodeRelease(pRtree, pLeaf);
      if( rc==SQLITE_OK ){
        rc = rc2;
      }
    }










  }

constraint:
  rtreeRelease(pRtree);
  return rc;
}

................................................................................
  int isCreate
){
  int rc = SQLITE_OK;

  #define N_STATEMENT 8
  static const char *azSql[N_STATEMENT] = {
    /* Write the xxx_node table */
    "INSERT OR REPLACE INTO '%q'.'%q_node' VALUES(:1, :2)",
    "DELETE FROM '%q'.'%q_node' WHERE nodeno = :1",

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

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

  pRtree->db = db;

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


"CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY, nodeno INTEGER);"








"CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY,"
                                  " parentnode INTEGER);"
"INSERT INTO '%q'.'%q_node' VALUES(1, zeroblob(%d))",



      zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, pRtree->iNodeSize
    );

    if( !zCreate ){
      return SQLITE_NOMEM;
    }
    rc = sqlite3_exec(db, zCreate, 0, 0, 0);
    sqlite3_free(zCreate);
    if( rc!=SQLITE_OK ){
      return rc;
................................................................................
  appStmt[4] = &pRtree->pDeleteRowid;
  appStmt[5] = &pRtree->pReadParent;
  appStmt[6] = &pRtree->pWriteParent;
  appStmt[7] = &pRtree->pDeleteParent;

  rc = rtreeQueryStat1(db, pRtree);
  for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){










    char *zSql = sqlite3_mprintf(azSql[i], zDb, zPrefix);
    if( zSql ){
      rc = sqlite3_prepare_v3(db, zSql, -1, SQLITE_PREPARE_PERSISTENT,
                              appStmt[i], 0); 
    }else{
      rc = SQLITE_NOMEM;
    }
    sqlite3_free(zSql);


























  }

  return rc;
}

/*
** The second argument to this function contains the text of an SQL statement
................................................................................
  int isCreate                        /* True for xCreate, false for xConnect */
){
  int rc = SQLITE_OK;
  Rtree *pRtree;
  int nDb;              /* Length of string argv[1] */
  int nName;            /* Length of string argv[2] */
  int eCoordType = (pAux ? RTREE_COORD_INT32 : RTREE_COORD_REAL32);





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

  };

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

  sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);

  /* Allocate the sqlite3_vtab structure */
  nDb = (int)strlen(argv[1]);
................................................................................
    return SQLITE_NOMEM;
  }
  memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);
  pRtree->nBusy = 1;
  pRtree->base.pModule = &rtreeModule;
  pRtree->zDb = (char *)&pRtree[1];
  pRtree->zName = &pRtree->zDb[nDb+1];
  pRtree->nDim = (u8)((argc-4)/2);
  pRtree->nDim2 = pRtree->nDim*2;
  pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;
  pRtree->eCoordType = (u8)eCoordType;
  memcpy(pRtree->zDb, argv[1], nDb);
  memcpy(pRtree->zName, argv[2], nName);

  /* Figure out the node size to use. */
  rc = getNodeSize(db, pRtree, isCreate, pzErr);

  /* Create/Connect to the underlying relational database schema. If
  ** that is successful, call sqlite3_declare_vtab() to configure
  ** the r-tree table schema.
  */
  if( rc==SQLITE_OK ){
    if( (rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate)) ){
      *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
    }else{
      sqlite3_str *pSql = sqlite3_str_new(db);
      char *zSql;
      int ii;
      if( pSql==0 ){
        zSql = 0;
      }else{
        sqlite3_str_appendf(pSql, "CREATE TABLE x(%s", argv[3]);
        for(ii=4; ii<argc; ii++){







          sqlite3_str_appendf(pSql, ", %s", argv[ii]);
        }

        sqlite3_str_appendf(pSql, ");");
        zSql = sqlite3_str_finish(pSql);
      }
      if( !zSql ){
        rc = SQLITE_NOMEM;



      }else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){
        *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
      }
      sqlite3_free(zSql);










    }



  }






  if( rc==SQLITE_OK ){




    *ppVtab = (sqlite3_vtab *)pRtree;
  }else{




    assert( *ppVtab==0 );
    assert( pRtree->nBusy==1 );
    rtreeRelease(pRtree);
  }
  return rc;
}


/*
** Implementation of a scalar function that decodes r-tree nodes to
** human readable strings. This can be used for debugging and analysis.







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....
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....
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3641
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3647
  sqlite3 *db;                /* Host database connection */
  int iNodeSize;              /* Size in bytes of each node in the node table */
  u8 nDim;                    /* Number of dimensions */
  u8 nDim2;                   /* Twice the number of dimensions */
  u8 eCoordType;              /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */
  u8 nBytesPerCell;           /* Bytes consumed per cell */
  u8 inWrTrans;               /* True if inside write transaction */
  u8 nAux;                    /* # of auxiliary columns in %_rowid */
  int iDepth;                 /* Current depth of the r-tree structure */
  char *zDb;                  /* Name of database containing r-tree table */
  char *zName;                /* Name of r-tree table */ 
  u32 nBusy;                  /* Current number of users of this structure */
  i64 nRowEst;                /* Estimated number of rows in this table */
  u32 nCursor;                /* Number of open cursors */
  char *zReadAuxSql;          /* SQL for statement to read aux data */

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

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

  /* Statement for writing to the "aux:" fields, if there are any */
  sqlite3_stmt *pWriteAux;

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

/* Possible values for Rtree.eCoordType: */
#define RTREE_COORD_REAL32 0
#define RTREE_COORD_INT32  1
................................................................................
/* 
** 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 */
  u8 bAuxValid;                     /* True if pReadAux 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 */
  sqlite3_stmt *pReadAux;           /* Statement to read aux-data */
  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))
................................................................................
    sqlite3_finalize(pRtree->pDeleteNode);
    sqlite3_finalize(pRtree->pReadRowid);
    sqlite3_finalize(pRtree->pWriteRowid);
    sqlite3_finalize(pRtree->pDeleteRowid);
    sqlite3_finalize(pRtree->pReadParent);
    sqlite3_finalize(pRtree->pWriteParent);
    sqlite3_finalize(pRtree->pDeleteParent);
    sqlite3_finalize(pRtree->pWriteAux);
    sqlite3_free(pRtree->zReadAuxSql);
    sqlite3_free(pRtree);
  }
}

/* 
** Rtree virtual table module xDisconnect method.
*/
................................................................................
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
  Rtree *pRtree = (Rtree *)(cur->pVtab);
  int ii;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  assert( pRtree->nCursor>0 );
  freeCursorConstraints(pCsr);
  sqlite3_finalize(pCsr->pReadAux);
  sqlite3_free(pCsr->aPoint);
  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
  sqlite3_free(pCsr);
  pRtree->nCursor--;
  nodeBlobReset(pRtree);
  return SQLITE_OK;
}
................................................................................
*/
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:");
  if( pCsr->bAuxValid ){
    pCsr->bAuxValid = 0;
    sqlite3_reset(pCsr->pReadAux);
  }
  rtreeSearchPointPop(pCsr);
  rc = rtreeStepToLeaf(pCsr);
  return rc;
}

/* 
** Rtree virtual table module xRowid method.
................................................................................
  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( p==0 || pNode==0 ) return SQLITE_OK;
  if( i==0 ){
    sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));

  }else if( i<=pRtree->nDim2 ){
    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);
    }
  }else{
    if( !pCsr->bAuxValid ){
      if( pCsr->pReadAux==0 ){
        rc = sqlite3_prepare_v3(pRtree->db, pRtree->zReadAuxSql, -1, 0,
                                &pCsr->pReadAux, 0);
        if( rc ) return rc;
      }
      sqlite3_bind_int64(pCsr->pReadAux, 1, 
          nodeGetRowid(pRtree, pNode, p->iCell));
      rc = sqlite3_step(pCsr->pReadAux);
      if( rc==SQLITE_ROW ){
        pCsr->bAuxValid = 1;
      }else{
        sqlite3_reset(pCsr->pReadAux);
        if( rc==SQLITE_DONE ) rc = SQLITE_OK;
        return rc;
      }
    }
    sqlite3_result_value(ctx,
         sqlite3_column_value(pCsr->pReadAux, i - pRtree->nDim2 + 1));
  }  
  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
................................................................................

/*
** The xUpdate method for rtree module virtual tables.
*/
static int rtreeUpdate(
  sqlite3_vtab *pVtab, 
  int nData, 
  sqlite3_value **aData, 
  sqlite_int64 *pRowid
){
  Rtree *pRtree = (Rtree *)pVtab;
  int rc = SQLITE_OK;
  RtreeCell cell;                 /* New cell to insert if nData>1 */
  int bHaveRowid = 0;             /* Set to 1 after new rowid is determined */

................................................................................
  ** In the first case, if the conflict-handling mode is REPLACE, then
  ** the conflicting row can be removed before proceeding. In the second
  ** case, SQLITE_CONSTRAINT must be returned regardless of the
  ** conflict-handling mode specified by the user.
  */
  if( nData>1 ){
    int ii;
    int nn = nData - 4;

    if( nn > pRtree->nDim2 ) nn = pRtree->nDim2;
    /* Populate the cell.aCoord[] array. The first coordinate is aData[3].
    **
    ** NB: nData can only be less than nDim*2+3 if the rtree is mis-declared
    ** with "column" that are interpreted as table constraints.
    ** Example:  CREATE VIRTUAL TABLE bad USING rtree(x,y,CHECK(y>5));
    ** This problem was discovered after years of use, so we silently ignore
    ** these kinds of misdeclared tables to avoid breaking any legacy.
    */


#ifndef SQLITE_RTREE_INT_ONLY
    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
      for(ii=0; ii<nn; ii+=2){
        cell.aCoord[ii].f = rtreeValueDown(aData[ii+3]);
        cell.aCoord[ii+1].f = rtreeValueUp(aData[ii+4]);
        if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
          rc = rtreeConstraintError(pRtree, ii+1);
          goto constraint;
        }
      }
    }else
#endif
    {
      for(ii=0; ii<nn; ii+=2){
        cell.aCoord[ii].i = sqlite3_value_int(aData[ii+3]);
        cell.aCoord[ii+1].i = sqlite3_value_int(aData[ii+4]);
        if( cell.aCoord[ii].i>cell.aCoord[ii+1].i ){
          rc = rtreeConstraintError(pRtree, ii+1);
          goto constraint;
        }
      }
    }

    /* If a rowid value was supplied, check if it is already present in 
    ** the table. If so, the constraint has failed. */
    if( sqlite3_value_type(aData[2])!=SQLITE_NULL ){
      cell.iRowid = sqlite3_value_int64(aData[2]);
      if( sqlite3_value_type(aData[0])==SQLITE_NULL
       || sqlite3_value_int64(aData[0])!=cell.iRowid
      ){
        int steprc;
        sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
        steprc = sqlite3_step(pRtree->pReadRowid);
        rc = sqlite3_reset(pRtree->pReadRowid);
        if( SQLITE_ROW==steprc ){
          if( sqlite3_vtab_on_conflict(pRtree->db)==SQLITE_REPLACE ){
................................................................................
          }
        }
      }
      bHaveRowid = 1;
    }
  }

  /* If aData[0] is not an SQL NULL value, it is the rowid of a
  ** record to delete from the r-tree table. The following block does
  ** just that.
  */
  if( sqlite3_value_type(aData[0])!=SQLITE_NULL ){
    rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(aData[0]));
  }

  /* If the aData[] array contains more than one element, elements
  ** (aData[2]..aData[argc-1]) contain a new record to insert into
  ** the r-tree structure.
  */
  if( rc==SQLITE_OK && nData>1 ){
    /* Insert the new record into the r-tree */
    RtreeNode *pLeaf = 0;

    /* Figure out the rowid of the new row. */
................................................................................
      pRtree->iReinsertHeight = -1;
      rc = rtreeInsertCell(pRtree, pLeaf, &cell, 0);
      rc2 = nodeRelease(pRtree, pLeaf);
      if( rc==SQLITE_OK ){
        rc = rc2;
      }
    }
    if( pRtree->nAux ){
      sqlite3_stmt *pUp = pRtree->pWriteAux;
      int jj;
      sqlite3_bind_int64(pUp, 1, *pRowid);
      for(jj=0; jj<pRtree->nAux; jj++){
        sqlite3_bind_value(pUp, jj+2, aData[pRtree->nDim2+3+jj]);
      }
      sqlite3_step(pUp);
      rc = sqlite3_reset(pUp);
    }
  }

constraint:
  rtreeRelease(pRtree);
  return rc;
}

................................................................................
  int isCreate
){
  int rc = SQLITE_OK;

  #define N_STATEMENT 8
  static const char *azSql[N_STATEMENT] = {
    /* Write the xxx_node table */
    "INSERT OR REPLACE INTO '%q'.'%q_node' VALUES(?1, ?2)",
    "DELETE FROM '%q'.'%q_node' WHERE nodeno = ?1",

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

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

  pRtree->db = db;

  if( isCreate ){
    char *zCreate;
    sqlite3_str *p = sqlite3_str_new(db);
    int ii;
    sqlite3_str_appendf(p,
       "CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY,nodeno",
       zDb, zPrefix);
    for(ii=0; ii<pRtree->nAux; ii++){
      sqlite3_str_appendf(p,",a%d",ii);
    }
    sqlite3_str_appendf(p,
      ");CREATE TABLE \"%w\".\"%w_node\"(nodeno INTEGER PRIMARY KEY,data);",
      zDb, zPrefix);
    sqlite3_str_appendf(p,
    "CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY,parentnode);",


      zDb, zPrefix);
    sqlite3_str_appendf(p,
       "INSERT INTO \"%w\".\"%w_node\"VALUES(1,zeroblob(%d))",
       zDb, zPrefix, pRtree->iNodeSize);

    zCreate = sqlite3_str_finish(p);
    if( !zCreate ){
      return SQLITE_NOMEM;
    }
    rc = sqlite3_exec(db, zCreate, 0, 0, 0);
    sqlite3_free(zCreate);
    if( rc!=SQLITE_OK ){
      return rc;
................................................................................
  appStmt[4] = &pRtree->pDeleteRowid;
  appStmt[5] = &pRtree->pReadParent;
  appStmt[6] = &pRtree->pWriteParent;
  appStmt[7] = &pRtree->pDeleteParent;

  rc = rtreeQueryStat1(db, pRtree);
  for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){
    char *zSql;
    const char *zFormat;
    if( i!=3 || pRtree->nAux==0 ){
       zFormat = azSql[i];
    }else {
       /* An UPSERT is very slightly slower than REPLACE, but it is needed
       ** if there are auxiliary columns */
       zFormat = "INSERT INTO\"%w\".\"%w_rowid\"(rowid,nodeno)VALUES(?1,?2)"
                  "ON CONFLICT(rowid)DO UPDATE SET nodeno=excluded.nodeno";
    }
    zSql = sqlite3_mprintf(zFormat, zDb, zPrefix);
    if( zSql ){
      rc = sqlite3_prepare_v3(db, zSql, -1, SQLITE_PREPARE_PERSISTENT,
                              appStmt[i], 0); 
    }else{
      rc = SQLITE_NOMEM;
    }
    sqlite3_free(zSql);
  }
  if( pRtree->nAux ){
    pRtree->zReadAuxSql = sqlite3_mprintf(
       "SELECT * FROM \"%w\".\"%w_rowid\" WHERE rowid=?1",
       zDb, zPrefix);
    if( pRtree->zReadAuxSql==0 ){
      rc = SQLITE_NOMEM;
    }else{
      sqlite3_str *p = sqlite3_str_new(db);
      int ii;
      char *zSql;
      sqlite3_str_appendf(p, "UPDATE \"%w\".\"%w_rowid\"SET ", zDb, zPrefix);
      for(ii=0; ii<pRtree->nAux; ii++){
        if( ii ) sqlite3_str_append(p, ",", 1);
        sqlite3_str_appendf(p,"a%d=?%d",ii,ii+2);
      }
      sqlite3_str_appendf(p, " WHERE rowid=?1");
      zSql = sqlite3_str_finish(p);
      if( zSql==0 ){
        rc = SQLITE_NOMEM;
      }else{
        rc = sqlite3_prepare_v3(db, zSql, -1, SQLITE_PREPARE_PERSISTENT,
                                &pRtree->pWriteAux, 0); 
        sqlite3_free(zSql);
      }
    }
  }

  return rc;
}

/*
** The second argument to this function contains the text of an SQL statement
................................................................................
  int isCreate                        /* True for xCreate, false for xConnect */
){
  int rc = SQLITE_OK;
  Rtree *pRtree;
  int nDb;              /* Length of string argv[1] */
  int nName;            /* Length of string argv[2] */
  int eCoordType = (pAux ? RTREE_COORD_INT32 : RTREE_COORD_REAL32);
  sqlite3_str *pSql;
  char *zSql;
  int ii = 4;
  int iErr;

  const char *aErrMsg[] = {
    0,                                                    /* 0 */
    "Wrong number of columns for an rtree table",         /* 1 */
    "Too few columns for an rtree table",                 /* 2 */
    "Too many columns for an rtree table",                /* 3 */
    "AUX: columns must be last"                           /* 4 */
  };


  if( argc>=256 ){
    *pzErr = sqlite3_mprintf("%s", aErrMsg[3]);
    return SQLITE_ERROR;
  }

  sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);

  /* Allocate the sqlite3_vtab structure */
  nDb = (int)strlen(argv[1]);
................................................................................
    return SQLITE_NOMEM;
  }
  memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);
  pRtree->nBusy = 1;
  pRtree->base.pModule = &rtreeModule;
  pRtree->zDb = (char *)&pRtree[1];
  pRtree->zName = &pRtree->zDb[nDb+1];



  pRtree->eCoordType = (u8)eCoordType;
  memcpy(pRtree->zDb, argv[1], nDb);
  memcpy(pRtree->zName, argv[2], nName);




  /* Create/Connect to the underlying relational database schema. If
  ** that is successful, call sqlite3_declare_vtab() to configure
  ** the r-tree table schema.
  */




  pSql = sqlite3_str_new(db);





  sqlite3_str_appendf(pSql, "CREATE TABLE x(%s", argv[3]);
  for(ii=4; ii<argc; ii++){
    if( sqlite3_strlike("aux:%", argv[ii], 0)==0 ){
      pRtree->nAux++;
      sqlite3_str_appendf(pSql, ",%s", argv[ii]+4);
    }else if( pRtree->nAux>0 ){
      break;
    }else{
      pRtree->nDim2++;
      sqlite3_str_appendf(pSql, ",%s", argv[ii]);
    }
  }
  sqlite3_str_appendf(pSql, ");");
  zSql = sqlite3_str_finish(pSql);

  if( !zSql ){
    rc = SQLITE_NOMEM;
  }else if( ii<argc ){
    *pzErr = sqlite3_mprintf("%s", aErrMsg[4]);
    rc = SQLITE_ERROR;
  }else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){
    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
  }
  sqlite3_free(zSql);
  if( rc ) goto rtreeInit_fail;
  pRtree->nDim = pRtree->nDim2/2;
  if( pRtree->nDim<1 ){
    iErr = 2;
  }else if( pRtree->nDim2>RTREE_MAX_DIMENSIONS*2 ){
    iErr = 3;
  }else if( pRtree->nDim2 % 2 ){
    iErr = 1;
  }else{
    iErr = 0;
  }
  if( iErr ){
    *pzErr = sqlite3_mprintf("%s", aErrMsg[iErr]);
    goto rtreeInit_fail;
  }
  pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;

  /* Figure out the node size to use. */
  rc = getNodeSize(db, pRtree, isCreate, pzErr);
  if( rc ) goto rtreeInit_fail;
  rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate);
  if( rc ){
    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
    goto rtreeInit_fail;
  }

  *ppVtab = (sqlite3_vtab *)pRtree;

  return SQLITE_OK;

rtreeInit_fail:
  if( rc==SQLITE_OK ) rc = SQLITE_ERROR;
  assert( *ppVtab==0 );
  assert( pRtree->nBusy==1 );
  rtreeRelease(pRtree);

  return rc;
}


/*
** Implementation of a scalar function that decodes r-tree nodes to
** human readable strings. This can be used for debugging and analysis.