** The data structure for a single virtual r-tree table is stored in three 
** native SQLite tables declared as follows. In each case, the '%' character
** in the table name is replaced with the user-supplied name of the r-tree
** table.
**
**   CREATE TABLE %_node(nodeno INTEGER PRIMARY KEY, data BLOB)
**   CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)
**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER)
**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER, ...)
**
** The data for each node of the r-tree structure is stored in the %_node
** table. For each node that is not the root node of the r-tree, there is
** an entry in the %_parent table associating the node with its parent.
** And for each row of data in the table, there is an entry in the %_rowid
** table that maps from the entries rowid to the id of the node that it
** is stored on.
** is stored on.  If the r-tree contains auxiliary columns, those are stored
** on the end of the %_rowid table.
**
** The root node of an r-tree always exists, even if the r-tree table is
** empty. The nodeno of the root node is always 1. All other nodes in the
** table must be the same size as the root node. The content of each node
** is formatted as follows:
**
**   1. If the node is the root node (node 1), then the first 2 bytes

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

/* Maximum number of auxiliary columns */
#define RTREE_MAX_AUX_COLUMN 100

/* 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

  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.

  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{
  }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

){
  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
  RtreeNode *pRoot = 0;
  int ii;
  int rc = SQLITE_OK;
  int iCell = 0;
  sqlite3_stmt *pStmt;

  rtreeReference(pRtree);

  /* Reset the cursor to the same state as rtreeOpen() leaves it in. */
  freeCursorConstraints(pCsr);
  sqlite3_free(pCsr->aPoint);
  pStmt = pCsr->pReadAux;
  memset(pCsr, 0, sizeof(RtreeCursor));
  pCsr->base.pVtab = (sqlite3_vtab*)pRtree;
  pCsr->pReadAux = pStmt;

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

      ** a single row.
      */ 
      pIdxInfo->estimatedCost = 30.0;
      pIdxInfo->estimatedRows = 1;
      return SQLITE_OK;
    }

    if( p->usable
    && ((p->iColumn>0 && p->iColumn<=pRtree->nDim2)
    if( p->usable && (p->iColumn>0 || p->op==SQLITE_INDEX_CONSTRAINT_MATCH) ){
        || p->op==SQLITE_INDEX_CONSTRAINT_MATCH)
    ){
      u8 op;
      switch( p->op ){
        case SQLITE_INDEX_CONSTRAINT_EQ: op = RTREE_EQ; break;
        case SQLITE_INDEX_CONSTRAINT_GT: op = RTREE_GT; break;
        case SQLITE_INDEX_CONSTRAINT_LE: op = RTREE_LE; break;
        case SQLITE_INDEX_CONSTRAINT_LT: op = RTREE_LT; break;
        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;

/*
** The xUpdate method for rtree module virtual tables.
*/
static int rtreeUpdate(
  sqlite3_vtab *pVtab, 
  int nData, 
  sqlite3_value **azData, 
  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 azData[3].
    /* 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.
    */
    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]);
      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<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]);
      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(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
    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 ){
            rc = rtreeDeleteRowid(pRtree, cell.iRowid);
          }else{
            rc = rtreeConstraintError(pRtree, 0);
            goto constraint;
          }
        }
      }
      bHaveRowid = 1;
    }
  }

  /* If azData[0] is not an SQL NULL value, it is the rowid of a
  /* 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(azData[0])!=SQLITE_NULL ){
    rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(azData[0]));
  if( sqlite3_value_type(aData[0])!=SQLITE_NULL ){
    rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(aData[0]));
  }

  /* If the azData[] array contains more than one element, elements
  ** (azData[2]..azData[argc-1]) contain a new record to insert into
  /* 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",
    "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",
    "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"
    "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
    );
    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 = sqlite3_mprintf(azSql[i], zDb, zPrefix);
    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 */
    "Too many columns for an rtree table",                /* 3 */
    "Auxiliary rtree columns must be last"                /* 4 */
  };

  int iErr = (argc<6) ? 2 : argc>(RTREE_MAX_DIMENSIONS*2+4) ? 3 : argc%2;
  if( aErrMsg[iErr] ){
    *pzErr = sqlite3_mprintf("%s", aErrMsg[iErr]);
  assert( RTREE_MAX_AUX_COLUMN<256 ); /* Aux columns counted by a u8 */
  if( argc>RTREE_MAX_AUX_COLUMN+3 ){
    *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]);
  nName = (int)strlen(argv[2]);
  pRtree = (Rtree *)sqlite3_malloc(sizeof(Rtree)+nDb+nName+2);
  if( !pRtree ){
    return SQLITE_NOMEM;
  }
  memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);
  pRtree->nBusy = 1;
  pRtree->base.pModule = &rtreeModule;
  pRtree->zDb = (char *)&pRtree[1];
  pRtree->zName = &pRtree->zDb[nDb+1];
  pRtree->nDim = (u8)((argc-4)/2);
  pRtree->nDim2 = pRtree->nDim*2;
  pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;
  pRtree->eCoordType = (u8)eCoordType;
  memcpy(pRtree->zDb, argv[1], nDb);
  memcpy(pRtree->zName, argv[2], nName);

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

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

  if( rc==SQLITE_OK ){
    *ppVtab = (sqlite3_vtab *)pRtree;
  }else{
    assert( *ppVtab==0 );
    assert( pRtree->nBusy==1 );
    rtreeRelease(pRtree);
  *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.

/*
** This function is used to check that the %_parent (if bLeaf==0) or %_rowid
** (if bLeaf==1) table contains a specified entry. The schemas of the
** two tables are:
**
**   CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)
**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER)
**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER, ...)
**
** In both cases, this function checks that there exists an entry with
** IPK value iKey and the second column set to iVal.
**
*/
static void rtreeCheckMapping(
  RtreeCheck *pCheck,             /* RtreeCheck object */
  int bLeaf,                      /* True for a leaf cell, false for interior */
  i64 iKey,                       /* Key for mapping */
  i64 iVal                        /* Expected value for mapping */
){
  int rc;
  sqlite3_stmt *pStmt;
  const char *azSql[2] = {
    "SELECT parentnode FROM %Q.'%q_parent' WHERE nodeno=?",
    "SELECT nodeno FROM %Q.'%q_rowid' WHERE rowid=?"
    "SELECT parentnode FROM %Q.'%q_parent' WHERE nodeno=?1",
    "SELECT nodeno FROM %Q.'%q_rowid' WHERE rowid=?1"
  };

  assert( bLeaf==0 || bLeaf==1 );
  if( pCheck->aCheckMapping[bLeaf]==0 ){
    pCheck->aCheckMapping[bLeaf] = rtreeCheckPrepare(pCheck,
        azSql[bLeaf], pCheck->zDb, pCheck->zTab
    );

  const char *zDb,                /* Name of db ("main", "temp" etc.) */
  const char *zTab,               /* Name of rtree table to check */
  char **pzReport                 /* OUT: sqlite3_malloc'd report text */
){
  RtreeCheck check;               /* Common context for various routines */
  sqlite3_stmt *pStmt = 0;        /* Used to find column count of rtree table */
  int bEnd = 0;                   /* True if transaction should be closed */
  int nAux = 0;                   /* Number of extra columns. */

  /* Initialize the context object */
  memset(&check, 0, sizeof(check));
  check.db = db;
  check.zDb = zDb;
  check.zTab = zTab;

  /* If there is not already an open transaction, open one now. This is
  ** to ensure that the queries run as part of this integrity-check operate
  ** on a consistent snapshot.  */
  if( sqlite3_get_autocommit(db) ){
    check.rc = sqlite3_exec(db, "BEGIN", 0, 0, 0);
    bEnd = 1;
  }

  /* Find the number of auxiliary columns */
  if( check.rc==SQLITE_OK ){
    pStmt = rtreeCheckPrepare(&check, "SELECT * FROM %Q.'%q_rowid'", zDb, zTab);
    if( pStmt ){
      nAux = sqlite3_column_count(pStmt) - 2;
      sqlite3_finalize(pStmt);
    }
    check.rc = SQLITE_OK;
  }

  /* Find number of dimensions in the rtree table. */
  pStmt = rtreeCheckPrepare(&check, "SELECT * FROM %Q.%Q", zDb, zTab);
  if( pStmt ){
    int rc;
    check.nDim = (sqlite3_column_count(pStmt) - 1) / 2;
    check.nDim = (sqlite3_column_count(pStmt) - 1 - nAux) / 2;
    if( check.nDim<1 ){
      rtreeCheckAppendMsg(&check, "Schema corrupt or not an rtree");
    }else if( SQLITE_ROW==sqlite3_step(pStmt) ){
      check.bInt = (sqlite3_column_type(pStmt, 1)==SQLITE_INTEGER);
    }
    rc = sqlite3_finalize(pStmt);
    if( rc!=SQLITE_CORRUPT ) check.rc = rc;

  INSERT INTO rt VALUES(1,2,3,4,5);
}
do_execsql_test 15.2 {
  DROP TABLE t13;
  COMMIT;
}

# Test cases for the new auxiliary columns feature
#
do_catchsql_test 16.100 {
  CREATE VIRTUAL TABLE t16 USING rtree(id,x0,x1,y0,+aux1,x1);
} {1 {Auxiliary rtree columns must be last}}
do_test 16.110 {
  set sql {
    CREATE VIRTUAL TABLE t16 USING rtree(
      id, x00, x01, x10, x11, x20, x21, x30, x31, x40, x41
  }
  for {set i 12} {$i<=100} {incr i} {
     append sql ", +a$i"
  }
  append sql ");"
  execsql $sql
} {}
do_test 16.120 {
  set sql {
    CREATE VIRTUAL TABLE t16b USING rtree(
      id, x00, x01, x10, x11, x20, x21, x30, x31, x40, x41
  }
  for {set i 12} {$i<=101} {incr i} {
     append sql ", +a$i"
  }
  append sql ");"
  catchsql $sql
} {1 {Too many columns for an rtree table}}

do_execsql_test 16.130 {
  DROP TABLE IF EXISTS rt1;
  CREATE VIRTUAL TABLE rt1 USING rtree(id, x1, x2, +aux);
  INSERT INTO rt1 VALUES(1, 1, 2, 'aux1');
  INSERT INTO rt1 VALUES(2, 2, 3, 'aux2');
  INSERT INTO rt1 VALUES(3, 3, 4, 'aux3');
  INSERT INTO rt1 VALUES(4, 4, 5, 'aux4');
  SELECT * FROM rt1 WHERE id IN (1, 2, 3, 4);
} {1 1.0 2.0 aux1 2 2.0 3.0 aux2 3 3.0 4.0 aux3 4 4.0 5.0 aux4}

expand_all_sql db
finish_test

} -body {
  execsql { DROP TABLE rt } 
}

do_malloc_test rtree3-3.prep {
  faultsim_delete_and_reopen
  execsql {
    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2);
    CREATE VIRTUAL TABLE rt USING rtree(ii, x1, x2, y1, y2, +a1, +a2);
    INSERT INTO rt VALUES(NULL, 3, 5, 7, 9);
  }
  faultsim_save_and_close
} {}

do_faultsim_test rtree3-3a -faults oom* -prep {
  faultsim_restore_and_reopen

#--------------------------------------------------------------------
# Test that the sqlite_stat1 data is used correctly.
#
reset_db
do_execsql_test 5.1 {
  CREATE TABLE t1(x PRIMARY KEY, y);
  CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2);
  CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2, +d1);

  INSERT INTO t1(x) VALUES(1);
  INSERT INTO t1(x) SELECT x+1 FROM t1;   --   2
  INSERT INTO t1(x) SELECT x+2 FROM t1;   --   4
  INSERT INTO t1(x) SELECT x+4 FROM t1;   --   8
  INSERT INTO t1(x) SELECT x+8 FROM t1;   --  16
  INSERT INTO t1(x) SELECT x+16 FROM t1;  --  32
  INSERT INTO t1(x) SELECT x+32 FROM t1;  --  64
  INSERT INTO t1(x) SELECT x+64 FROM t1;  -- 128
  INSERT INTO t1(x) SELECT x+128 FROM t1; -- 256
  INSERT INTO t1(x) SELECT x+256 FROM t1; -- 512
  INSERT INTO t1(x) SELECT x+512 FROM t1; --1024

  INSERT INTO rt SELECT x, x, x+1 FROM t1 WHERE x<=5;
  INSERT INTO rt SELECT x, x, x+1, printf('x%04xy',x) FROM t1 WHERE x<=5;
}
do_rtree_integrity_test 5.1.1 rt

# First test a query with no ANALYZE data at all. The outer loop is
# real table "t1".
#
do_eqp_test 5.2 {

# 2018-05-16
#
# 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 the
# auxiliary column mechanism.

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

do_execsql_test rtreeH-100 {
  CREATE VIRTUAL TABLE t1 USING rtree(id,x0,x1,y0,y1,+label,+other);
  INSERT INTO t1(x0,x1,y0,y1,label) VALUES
    (0,10,0,10,'lower-left corner'),
    (0,10,90,100,'upper-left corner'),
    (90,100,0,10,'lower-right corner'),
    (90,100,90,100,'upper-right corner'),
    (40,60,40,60,'center'),
    (0,5,0,100,'left edge'),
    (95,100,0,100,'right edge'),
    (0,100,0,5,'bottom edge'),
    (0,100,95,100,'top edge'),
    (0,100,0,100,'the whole thing'),
    (0,50,0,100,'left half'),
    (51,100,0,100,'right half'),
    (0,100,0,50,'bottom half'),
    (0,100,51,100,'top half');
} {}
do_execsql_test rtreeH-101 {
  SELECT * FROM t1_rowid ORDER BY rowid
} {1 1 {lower-left corner} {} 2 1 {upper-left corner} {} 3 1 {lower-right corner} {} 4 1 {upper-right corner} {} 5 1 center {} 6 1 {left edge} {} 7 1 {right edge} {} 8 1 {bottom edge} {} 9 1 {top edge} {} 10 1 {the whole thing} {} 11 1 {left half} {} 12 1 {right half} {} 13 1 {bottom half} {} 14 1 {top half} {}}

do_execsql_test rtreeH-102 {
  SELECT * FROM t1 WHERE rowid=5;
} {5 40.0 60.0 40.0 60.0 center {}}
do_execsql_test rtreeH-103 {
  SELECT * FROM t1 WHERE label='center';
} {5 40.0 60.0 40.0 60.0 center {}}

do_rtree_integrity_test rtreeH-110 t1

do_execsql_test rtreeH-120 {
  SELECT label FROM t1 WHERE x1<=50 ORDER BY id
} {{lower-left corner} {upper-left corner} {left edge} {left half}}
do_execsql_test rtreeH-121 {
  SELECT label FROM t1 WHERE x1<=50 AND label NOT LIKE '%corner%' ORDER BY id
} {{left edge} {left half}}

do_execsql_test rtreeH-200 {
  WITH RECURSIVE
    c1(x) AS (VALUES(0) UNION ALL SELECT x+1 FROM c1 WHERE x<99),
    c2(y) AS (VALUES(0) UNION ALL SELECT y+1 FROM c2 WHERE y<99)
  INSERT INTO t1(id, x0,x1,y0,y1,label)
    SELECT 1000+x+y*100, x, x+1, y, y+1, printf('box-%d,%d',x,y) FROM c1, c2;
} {}

do_execsql_test rtreeH-210 {
  SELECT label FROM t1 WHERE x0>=48 AND x1<=50 AND y0>=48 AND y1<=50
     ORDER BY id;
} {box-48,48 box-49,48 box-48,49 box-49,49}

do_execsql_test rtreeH-300 {
  UPDATE t1 SET label='x'||label
    WHERE x0>=49 AND x1<=50 AND y0>=49 AND y1<=50;
  SELECT label FROM t1 WHERE x0>=48 AND x1<=50 AND y0>=48 AND y1<=50
     ORDER BY id;
} {box-48,48 box-49,48 box-48,49 xbox-49,49}


finish_test