SQLite

  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
**
** If an R*-tree "Reinsert" operation is required, the same number of

  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.
*/
#ifdef SQLITE_RTREE_INT_ONLY
# define DCOORD(coord) ((RtreeDValue)coord.i)
#else
# define DCOORD(coord) (                           \
    (pRtree->eCoordType==RTREE_COORD_REAL32) ?      \
      ((double)coord.f) :                           \
      ((double)coord.i)                             \
  )
#endif

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

/*
** 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

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]);

  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: 

  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;

  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;
}

  /* 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;

            ** 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;

  pIdxInfo->estimatedCost = (2000000.0 / (double)(iIdx + 1));
  return rc;
}

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

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

/*
** Store the union of cells p1 and p2 in p1.
*/

  }
  return 1;
}

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

#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.

  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;

    /* 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);

  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;
      }
    }
  }

  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;

  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;
      }
    }

**
** The aSpare array is used as temporary working space by the
** sorting algorithm.
*/
static void SortByDistance(
  int *aIdx, 
  int nIdx, 
  RtreeDValue *aDistance, 
  int *aSpare
){
  if( nIdx>1 ){
    int iLeft = 0;
    int iRight = 0;

    int nLeft = nIdx/2;

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

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

    SortByDimension(pRtree, aLeft, nLeft, iDim, aCell, aSpare);
    SortByDimension(pRtree, aRight, nRight, iDim, aCell, aSpare);

    memcpy(aSpare, aLeft, sizeof(int)*nLeft);
    aLeft = aSpare;
    while( iLeft<nLeft || iRight<nRight ){
      RtreeDValue xleft1 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2]);
      RtreeDValue xleft2 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2+1]);
      RtreeDValue xright1 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2]);
      RtreeDValue xright2 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2+1]);
      if( (iLeft!=nLeft) && ((iRight==nRight)
       || (xleft1<xright1)
       || (xleft1==xright1 && xleft2<xright2)
      )){
        aIdx[iLeft+iRight] = aLeft[iLeft];
        iLeft++;
      }else{
        aIdx[iLeft+iRight] = aRight[iRight];
        iRight++;
      }
    }

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

){
  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;
  }

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

  for(ii=0; ii<pRtree->nDim; ii++){
    RtreeDValue margin = 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++
    ){
      RtreeCell left;
      RtreeCell right;
      int kk;
      RtreeDValue overlap;
      RtreeDValue area;

      memcpy(&left, &aCell[aaSorted[ii][0]], sizeof(RtreeCell));
      memcpy(&right, &aCell[aaSorted[ii][nCell-1]], sizeof(RtreeCell));
      for(kk=1; kk<(nCell-1); kk++){
        if( kk<nLeft ){
          cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
        }else{

  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);

  RtreeNode *pNode, 
  RtreeCell *pCell, 
  int iHeight
){
  int *aOrder;
  int *aSpare;
  RtreeCell *aCell;
  RtreeDValue *aDistance;
  int nCell;
  RtreeDValue aCenterCoord[RTREE_MAX_DIMENSIONS];
  int iDim;
  int ii;
  int rc = SQLITE_OK;
  int n;

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

  nCell = NCELL(pNode)+1;
  n = (nCell+1)&(~1);

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

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

  for(ii=0; ii<nCell; ii++){
    aDistance[ii] = 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]);
    }
  }

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

  ** conflict-handling mode specified by the user.
  */
  if( nData>1 ){
    int ii;

    /* Populate the cell.aCoord[] array. The first coordinate is azData[3]. */
    assert( nData==(pRtree->nDim*2 + 3) );
#ifndef SQLITE_RTREE_INT_ONLY
    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
      for(ii=0; ii<(pRtree->nDim*2); ii+=2){
        cell.aCoord[ii].f = (RtreeValue)sqlite3_value_double(azData[ii+3]);
        cell.aCoord[ii+1].f = (RtreeValue)sqlite3_value_double(azData[ii+4]);
        if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
          rc = SQLITE_CONSTRAINT;
          goto constraint;
        }
      }
    }else
#endif
    {
      for(ii=0; ii<(pRtree->nDim*2); 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 = SQLITE_CONSTRAINT;
          goto constraint;
        }

    RtreeCell cell;
    int jj;

    nodeGetCell(&tree, &node, ii, &cell);
    sqlite3_snprintf(512-nCell,&zCell[nCell],"%lld", cell.iRowid);
    nCell = (int)strlen(zCell);
    for(jj=0; jj<tree.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);
    }

    if( zText ){
      char *zTextNew = sqlite3_mprintf("%s {%s}", zText, zCell);
      sqlite3_free(zText);
      zText = zTextNew;

  int rc;

  rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);
  if( rc==SQLITE_OK ){
    rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
  }
  if( rc==SQLITE_OK ){
#ifdef SQLITE_RTREE_INT_ONLY
    void *c = (void *)RTREE_COORD_INT32;
#else
    void *c = (void *)RTREE_COORD_REAL32;
#endif
    rc = sqlite3_create_module_v2(db, "rtree", &rtreeModule, c, 0);
  }
  if( rc==SQLITE_OK ){
    void *c = (void *)RTREE_COORD_INT32;
    rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
  }

** 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;

    catchsql " 
      CREATE VIRTUAL TABLE t1 USING rtree($columns);
    "
  } $X

  catchsql { DROP TABLE t1 }
}

# Like execsql except display output as integer where that can be
# done without loss of information.
#
proc execsql_intout {sql} {
  set out {}
  foreach term [execsql $sql] {
    regsub {\.0$} $term {} term
    lappend out $term
  }
  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 {
  execsql { DROP TABLE t1 }
} {}

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

# Force the r-tree constructor to fail.
#
do_test rtree-1.6.1 {

    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
    SELECT * FROM t1;
  }
} {}

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

do_test rtree-3.1.1 {
  execsql { 
    CREATE VIRTUAL TABLE t1 USING rtree(ii, x1, x2, y1, y2);
    SELECT * FROM t1;
  }
} {}
do_test rtree-3.1.2 {
  execsql_intout { 
    INSERT INTO t1 VALUES(5, 1, 3, 2, 4);
    SELECT * FROM t1;
  }
} {5 1 3 2 4}
do_test rtree-3.1.3 {
  execsql_intout {
    INSERT INTO t1 VALUES(6, 2, 6, 4, 8);
    SELECT * FROM t1;
  }
} {5 1 3 2 4 6 2 6 4 8}

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

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

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

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

# An error midway through a rename operation.
do_test rtree-7.2.1 {
  execsql { 
    CREATE TABLE t4_node(a);
  }
  catchsql { ALTER TABLE "abc 123" RENAME TO t4 }
} {1 {SQL logic error or missing database}}
do_test rtree-7.2.2 {
  execsql_intout { SELECT * FROM "abc 123" }
} {1 2 3 4 5 6 7}
do_test rtree-7.2.3 {
  execsql { 
    DROP TABLE t4_node;
    CREATE TABLE t4_rowid(a);
  }
  catchsql { ALTER TABLE "abc 123" RENAME TO t4 }
} {1 {SQL logic error or missing database}}
do_test rtree-7.2.4 {
  db close
  sqlite3 db test.db
  execsql_intout { SELECT * FROM "abc 123" }
} {1 2 3 4 5 6 7}
do_test rtree-7.2.5 {
  execsql { DROP TABLE t4_rowid }
  execsql { ALTER TABLE "abc 123" RENAME TO t4 }
  execsql_intout { SELECT * FROM t4 }
} {1 2 3 4 5 6 7}


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

# Test that the function to determine if a leaf cell is part of the

}

set ::NROW 2500
if {[info exists G(isquick)] && $G(isquick)} {
  set ::NROW 250
}

ifcapable !rtree_int_only {
  # Return a floating point number between -X and X.
  # 
  proc rand {X} {
    return [expr {int((rand()-0.5)*1024.0*$X)/512.0}]
  }
  
  # Return a positive floating point number less than or equal to X
  #
  proc randincr {X} {
    while 1 {
      set r [expr {int(rand()*$X*32.0)/32.0}]
      if {$r>0.0} {return $r}
    }
  }
} else {
  # For rtree_int_only, return an number between -X and X.
  # 
  proc rand {X} {
    return [expr {int((rand()-0.5)*2*$X)}]
  }
  
  # Return a positive integer less than or equal to X
  #
  proc randincr {X} {
    while 1 {
      set r [expr {int(rand()*$X)+1}]
      if {$r>0} {return $r}
    }
  }
}
  
# Scramble the $inlist into a random order.
#
proc scramble {inlist} {
  set y {}
  foreach x $inlist {
    lappend y [list [expr {rand()}] $x]
  }

do_test rtree5-1.6 { 
  execsql { SELECT x1==5.0 FROM t1 }
} {1}

do_test rtree5-1.7 { 
  execsql { SELECT count(*) FROM t1 WHERE x1==5 }
} {1}
ifcapable !rtree_int_only {
  do_test rtree5-1.8 { 
    execsql { SELECT count(*) FROM t1 WHERE x1==5.2 }
  } {0}
}
do_test rtree5-1.9 { 
  execsql { SELECT count(*) FROM t1 WHERE x1==5.0 }
} {1}

do_test rtree5-1.10 { 
  execsql { SELECT (1<<31)-5, (1<<31)-1, -1*(1<<31), -1*(1<<31)+5 }
} {2147483643 2147483647 -2147483648 -2147483643}

#

if {![info exists testdir]} {
  set testdir [file join [file dirname [info script]] .. .. test]
} 
source $testdir/tester.tcl

ifcapable !rtree || rtree_int_only {
  finish_test
  return
}

#   Operator    Byte Value
#   ----------------------
#      =        0x41 ('A')

} 
source $testdir/tester.tcl

ifcapable !rtree||!vacuum {
  finish_test
  return
}

# Like execsql except display output as integer where that can be
# done without loss of information.
#
proc execsql_intout {sql} {
  set out {}
  foreach term [execsql $sql] {
    regsub {\.0$} $term {} term
    lappend out $term
  }
  return $out
}

do_test rtree7-1.1 {
  execsql {
    PRAGMA page_size = 1024;
    CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2, y1, y2);
    INSERT INTO rt VALUES(1, 1, 2, 3, 4);
  }
} {}
do_test rtree7-1.2 {
  execsql_intout { SELECT * FROM rt }
} {1 1 2 3 4}
do_test rtree7-1.3 {
  execsql_intout { 
    PRAGMA page_size = 2048;
    VACUUM;
    SELECT * FROM rt;
  }
} {1 1 2 3 4}
do_test rtree7-1.4 {
  for {set i 2} {$i <= 51} {incr i} {
    execsql { INSERT INTO rt VALUES($i, 1, 2, 3, 4) }
  }
  execsql_intout { SELECT sum(x1), sum(x2), sum(y1), sum(y2) FROM rt }
} {51 102 153 204}
do_test rtree7-1.5 {
  execsql_intout { 
    PRAGMA page_size = 512;
    VACUUM;
    SELECT sum(x1), sum(x2), sum(y1), sum(y2) FROM rt
  }
} {51 102 153 204}

finish_test

# 

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 }

register_cube_geom db

do_execsql_test rtree9-1.1 {
  CREATE VIRTUAL TABLE rt USING rtree(id, x1, x2, y1, y2, z1, z2);
  INSERT INTO rt VALUES(1, 1, 2, 1, 2, 1, 2);
} {}

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 {
  do_test rtreeB-1.1-intonly {
    db eval {
      CREATE VIRTUAL TABLE t1 USING rtree(ii, x0, y0, x1, y1);
      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}}}
} else {  
  do_test rtreeB-1.1 {
    db eval {
      CREATE VIRTUAL TABLE t1 USING rtree(ii, x0, y0, x1, y1);
      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

** 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().

#endif

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

#ifdef SQLITE_RTREE_INT_ONLY
  Tcl_SetVar2(interp, "sqlite_options", "rtree_int_only", "1", TCL_GLOBAL_ONLY);
#else
  Tcl_SetVar2(interp, "sqlite_options", "rtree_int_only", "0", TCL_GLOBAL_ONLY);
#endif

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

/*
** 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 */

**
**   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 ){