Dan wrote:
> On Jul 12, 2008, at 2:42 AM, Steve Friedman wrote:
> 
>>
>> Filip Navara wrote:
>>> how about actually attaching the patch? :)
>>>
>>> - Filip
>>>
>>> On Fri, Jul 11, 2008 at 9:23 PM, Steve Friedman  
>>> <[EMAIL PROTECTED]> wrote:
>>>> I've just started using the rtree extension, and have found that  
>>>> the 32-bit
>>>> float for the range keys is not appropriate for me.  Please find  
>>>> attached a
>>>> patch for rtree.c (based on v1.5) that allows for int -OR-  
>>>> unsigned int -OR-
>>>> float operation.
> 
> What kind of advantages does using int over float have here?
> 
> With a little work it might be possible to select int or float at
> runtime. Do other people who know about such things think that this
> would be a good option to have?

Dan,

I think the need for integer support is to avoid floating point rounding 
errors that might cause you to miss a key otherwise.

I think this would be a nice feature to have. I think it should be 
implemented at runtime because if I ever have an application that need 
both say time (int) and spatial rtrees (floats) then it puts me into a 
problem of not being able to support both in a single build.

-Steve

>>>> Steve Friedman
>> Not sure where it got deleted (since my inbox shows the attachment).
>> Included inline...
>>
>> --- rtree.c     2008-07-11 15:04:42.000000000 -0400
>> +++ rtreemod.c  2008-07-11 15:04:31.000000000 -0400
>> @@ -149,13 +149,36 @@
>>     RtreeConstraint *aConstraint;     /* Search constraints. */
>>   };
>>
>> +#if defined( SQLITE_RTREE_TYPE_INT)
>> +typedef int ConstraintType;
>> +# define sqlite3_result_ConstraintType  sqlite3_result_int
>> +# define sqlite3_value_ConstraintType(x)  ((int) sqlite3_value_int 
>> ((x)))
>> +# define sqlite3_snprintf_ConstraintType( a, b, c) \
>> +         sqlite3_snprintf( (a), (b), " %d", (c))
>> +
>> +#elif defined(SQLITE_RTREE_TYPE_UINT)
>> +typedef u32 ConstraintType;
>> +# define sqlite3_result_ConstraintType  sqlite3_result_int64
>> +# define sqlite3_value_ConstraintType(x)  ((u32)  
>> sqlite3_value_int64((x)))
>> +# define sqlite3_snprintf_ConstraintType( a, b, c) \
>> +         sqlite3_snprintf( (a), (b), " %u", (c))
>> +
>> +#else
>> +typedef float ConstraintType;
>> +# define sqlite3_result_ConstraintType  sqlite3_result_double
>> +# define sqlite3_value_ConstraintType(x)  ((float)
>> sqlite3_value_double((x)))
>> +# define sqlite3_snprintf_ConstraintType( a, b, c) \
>> +         sqlite3_snprintf( (a), (b), " %f", (double) (c))
>> +#endif
>> +
>> +
>>   /*
>>   ** A search constraint.
>>   */
>>   struct RtreeConstraint {
>>     int iCoord;                       /* Index of constrained  
>> coordinate */
>>     int op;                           /* Constraining operation */
>> -  float rValue;                     /* Constraint value. */
>> +  ConstraintType rValue;            /* Constraint value. */
>>   };
>>
>>   /* Possible values for RtreeConstraint.op */
>> @@ -198,7 +221,7 @@
>>   */
>>   struct RtreeCell {
>>     i64 iRowid;
>> -  float aCoord[RTREE_MAX_DIMENSIONS*2];
>> +  ConstraintType aCoord[RTREE_MAX_DIMENSIONS*2];
>>   };
>>
>>   #define MAX(x,y) ((x) < (y) ? (y) : (x))
>> @@ -211,14 +234,14 @@
>>   static int readInt16(u8 *p){
>>     return (p[0]<<8) + p[1];
>>   }
>> -static float readReal32(u8 *p){
>> +static ConstraintType readReal32(u8 *p){
>>     u32 i = (
>>       (((u32)p[0]) << 24) +
>>       (((u32)p[1]) << 16) +
>>       (((u32)p[2]) <<  8) +
>>       (((u32)p[3]) <<  0)
>>     );
>> -  return *(float *)&i;
>> +  return *(ConstraintType *)&i;
>>   }
>>   static i64 readInt64(u8 *p){
>>     return (
>> @@ -243,9 +266,9 @@
>>     p[1] = (i>> 0)&0xFF;
>>     return 2;
>>   }
>> -static int writeReal32(u8 *p, float f){
>> +static int writeReal32(u8 *p, ConstraintType f){
>>     u32 i;
>> -  assert( sizeof(float)==4 );
>> +  assert( sizeof(ConstraintType)==4 );
>>     assert( sizeof(u32)==4 );
>>     i = *(u32 *)&f;
>>     p[0] = (i>>24)&0xFF;
>> @@ -543,7 +566,7 @@
>>   /*
>>   ** Return coordinate iCoord from cell iCell in node pNode.
>>   */
>> -static float nodeGetCoord(
>> +static ConstraintType nodeGetCoord(
>>     Rtree *pRtree,
>>     RtreeNode *pNode,
>>     int iCell,
>> @@ -721,8 +744,8 @@
>>     for(ii=0; ii<pCursor->nConstraint; ii++){
>>       RtreeConstraint *p = &pCursor->aConstraint[ii];
>>
>> -    float cell_min = cell.aCoord[(p->iCoord>>1)*2];
>> -    float cell_max = cell.aCoord[(p->iCoord>>1)*2+1];
>> +    ConstraintType cell_min = cell.aCoord[(p->iCoord>>1)*2];
>> +    ConstraintType cell_max = cell.aCoord[(p->iCoord>>1)*2+1];
>>       assert( cell_min<=cell_max );
>>
>>       switch( p->op ){
>> @@ -769,7 +792,7 @@
>>     nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
>>     for(ii=0; ii<pCursor->nConstraint; ii++){
>>       RtreeConstraint *p = &pCursor->aConstraint[ii];
>> -    float cell_val = cell.aCoord[p->iCoord];
>> +    ConstraintType cell_val = cell.aCoord[p->iCoord];
>>       int res;
>>       switch( p->op ){
>>         case RTREE_LE: res = (cell_val<=p->rValue); break;
>> @@ -935,8 +958,8 @@
>>       i64 iRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
>>       sqlite3_result_int64(ctx, iRowid);
>>     }else{
>> -    float fCoord = nodeGetCoord(pRtree, pCsr->pNode, pCsr->iCell,  
>> i-1);
>> -    sqlite3_result_double(ctx, fCoord);
>> +    ConstraintType fCoord = nodeGetCoord(pRtree, pCsr->pNode,
>> pCsr->iCell, i-1);
>> +    sqlite3_result_ConstraintType(ctx, fCoord);
>>     }
>>
>>     return SQLITE_OK;
>> @@ -1009,7 +1032,7 @@
>>             RtreeConstraint *p = &pCsr->aConstraint[ii];
>>             p->op = idxStr[ii*2];
>>             p->iCoord = idxStr[ii*2+1]-'a';
>> -          p->rValue = sqlite3_value_double(argv[ii]);
>> +          p->rValue = sqlite3_value_ConstraintType(argv[ii]);
>>           }
>>         }
>>       }
>> @@ -1157,8 +1180,8 @@
>>   /*
>>   ** Return the N-dimensional volumn of the cell stored in *p.
>>   */
>> -static float cellArea(Rtree *pRtree, RtreeCell *p){
>> -  float area = 1.0;
>> +static ConstraintType cellArea(Rtree *pRtree, RtreeCell *p){
>> +  ConstraintType area = 1.0;
>>     int ii;
>>     for(ii=0; ii<(pRtree->nDim*2); ii+=2){
>>       area = area * (p->aCoord[ii+1] - p->aCoord[ii]);
>> @@ -1170,8 +1193,8 @@
>>   ** Return the margin length of cell p. The margin length is the sum
>>   ** of the objects size in each dimension.
>>   */
>> -static float cellMargin(Rtree *pRtree, RtreeCell *p){
>> -  float margin = 0.0;
>> +static ConstraintType cellMargin(Rtree *pRtree, RtreeCell *p){
>> +  ConstraintType margin = 0.0;
>>     int ii;
>>     for(ii=0; ii<(pRtree->nDim*2); ii+=2){
>>       margin += (p->aCoord[ii+1] - p->aCoord[ii]);
>> @@ -1193,8 +1216,8 @@
>>   /*
>>   ** Return the amount cell p would grow by if it were unioned with  
>> pCell.
>>   */
>> -static float cellGrowth(Rtree *pRtree, RtreeCell *p, RtreeCell  
>> *pCell){
>> -  float area;
>> +static ConstraintType cellGrowth(Rtree *pRtree, RtreeCell *p,  
>> RtreeCell
>> *pCell){
>> +  ConstraintType area;
>>     RtreeCell cell;
>>     memcpy(&cell, p, sizeof(RtreeCell));
>>     area = cellArea(pRtree, &cell);
>> @@ -1203,7 +1226,7 @@
>>   }
>>
>>   #if VARIANT_RSTARTREE_CHOOSESUBTREE || VARIANT_RSTARTREE_SPLIT
>> -static float cellOverlap(
>> +static ConstraintType cellOverlap(
>>     Rtree *pRtree,
>>     RtreeCell *p,
>>     RtreeCell *aCell,
>> @@ -1211,15 +1234,15 @@
>>     int iExclude
>>   ){
>>     int ii;
>> -  float overlap = 0.0;
>> +  ConstraintType overlap = 0.0;
>>     for(ii=0; ii<nCell; ii++){
>>       if( ii!=iExclude ){
>>         int jj;
>> -      float o = 1.0;
>> +      ConstraintType o = 1.0;
>>         for(jj=0; jj<(pRtree->nDim*2); jj+=2){
>>
>> -        float x1 = MAX(p->aCoord[jj], aCell[ii].aCoord[jj]);
>> -        float x2 = MIN(p->aCoord[jj+1], aCell[ii].aCoord[jj+1]);
>> +        ConstraintType x1 = MAX(p->aCoord[jj], aCell[ii].aCoord[jj]);
>> +        ConstraintType x2 = MIN(p->aCoord[jj+1], aCell[ii].aCoord 
>> [jj+1]);
>>
>>           if( x2<x1 ){
>>             o = 0.0;
>> @@ -1236,7 +1259,7 @@
>>   #endif
>>
>>   #if VARIANT_RSTARTREE_CHOOSESUBTREE
>> -static float cellOverlapEnlargement(
>> +static ConstraintType cellOverlapEnlargement(
>>     Rtree *pRtree,
>>     RtreeCell *p,
>>     RtreeCell *pInsert,
>> @@ -1244,8 +1267,8 @@
>>     int nCell,
>>     int iExclude
>>   ){
>> -  float before;
>> -  float after;
>> +  ConstraintType before;
>> +  ConstraintType after;
>>     before = cellOverlap(pRtree, p, aCell, nCell, iExclude);
>>     cellUnion(pRtree, p, pInsert);
>>     after = cellOverlap(pRtree, p, aCell, nCell, iExclude);
>> @@ -1273,9 +1296,9 @@
>>       int iCell;
>>       sqlite3_int64 iBest;
>>
>> -    float fMinGrowth;
>> -    float fMinArea;
>> -    float fMinOverlap;
>> +    ConstraintType fMinGrowth;
>> +    ConstraintType fMinArea;
>> +    ConstraintType fMinOverlap;
>>
>>       int nCell = NCELL(pNode);
>>       RtreeCell cell;
>> @@ -1304,9 +1327,9 @@
>>       ** the smallest area.
>>       */
>>       for(iCell=0; iCell<nCell; iCell++){
>> -      float growth;
>> -      float area;
>> -      float overlap = 0.0;
>> +      ConstraintType growth;
>> +      ConstraintType area;
>> +      ConstraintType overlap = 0.0;
>>         nodeGetCell(pRtree, pNode, iCell, &cell);
>>         growth = cellGrowth(pRtree, &cell, pCell);
>>         area = cellArea(pRtree, &cell);
>> @@ -1418,7 +1441,7 @@
>>     int i;
>>     int iLeftSeed = 0;
>>     int iRightSeed = 1;
>> -  float maxNormalInnerWidth = 0.0;
>> +  ConstraintType maxNormalInnerWidth = 0.0;
>>
>>     /* Pick two "seed" cells from the array of cells. The algorithm  
>> used
>>     ** here is the LinearPickSeeds algorithm from Gutman[1984]. The
>> @@ -1426,18 +1449,18 @@
>>     ** variables iLeftSeek and iRightSeed.
>>     */
>>     for(i=0; i<pRtree->nDim; i++){
>> -    float x1 = aCell[0].aCoord[i*2];
>> -    float x2 = aCell[0].aCoord[i*2+1];
>> -    float x3 = x1;
>> -    float x4 = x2;
>> +    ConstraintType x1 = aCell[0].aCoord[i*2];
>> +    ConstraintType x2 = aCell[0].aCoord[i*2+1];
>> +    ConstraintType x3 = x1;
>> +    ConstraintType x4 = x2;
>>       int jj;
>>
>>       int iCellLeft = 0;
>>       int iCellRight = 0;
>>
>>       for(jj=1; jj<nCell; jj++){
>> -      float left = aCell[jj].aCoord[i*2];
>> -      float right = aCell[jj].aCoord[i*2+1];
>> +      ConstraintType left = aCell[jj].aCoord[i*2];
>> +      ConstraintType right = aCell[jj].aCoord[i*2+1];
>>
>>         if( left<x1 ) x1 = left;
>>         if( right>x4 ) x4 = right;
>> @@ -1452,7 +1475,7 @@
>>       }
>>
>>       if( x4!=x1 ){
>> -      float normalwidth = (x3 - x2) / (x4 - x1);
>> +      ConstraintType normalwidth = (x3 - x2) / (x4 - x1);
>>         if( normalwidth>maxNormalInnerWidth ){
>>           iLeftSeed = iCellLeft;
>>           iRightSeed = iCellRight;
>> @@ -1481,13 +1504,13 @@
>>     #define FABS(a) ((a)<0.0?-1.0*(a):(a))
>>
>>     int iSelect = -1;
>> -  float fDiff;
>> +  ConstraintType fDiff;
>>     int ii;
>>     for(ii=0; ii<nCell; ii++){
>>       if( aiUsed[ii]==0 ){
>> -      float left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
>> -      float right = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
>> -      float diff = FABS(right-left);
>> +      ConstraintType left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
>> +      ConstraintType right = cellGrowth(pRtree, pLeftBox, &aCell 
>> [ii]);
>> +      ConstraintType diff = FABS(right-left);
>>         if( iSelect<0 || diff>fDiff ){
>>           fDiff = diff;
>>           iSelect = ii;
>> @@ -1514,13 +1537,13 @@
>>
>>     int iLeftSeed = 0;
>>     int iRightSeed = 1;
>> -  float fWaste = 0.0;
>> +  ConstraintType fWaste = 0.0;
>>
>>     for(ii=0; ii<nCell; ii++){
>>       for(jj=ii+1; jj<nCell; jj++){
>> -      float right = cellArea(pRtree, &aCell[jj]);
>> -      float growth = cellGrowth(pRtree, &aCell[ii], &aCell[jj]);
>> -      float waste = growth - right;
>> +      ConstraintType right = cellArea(pRtree, &aCell[jj]);
>> +      ConstraintType growth = cellGrowth(pRtree, &aCell[ii], &aCell 
>> [jj]);
>> +      ConstraintType waste = growth - right;
>>
>>         if( waste>fWaste ){
>>           iLeftSeed = ii;
>> @@ -1555,7 +1578,7 @@
>>   static void SortByDistance(
>>     int *aIdx,
>>     int nIdx,
>> -  float *aDistance,
>> +  ConstraintType *aDistance,
>>     int *aSpare
>>   ){
>>     if( nIdx>1 ){
>> @@ -1581,8 +1604,8 @@
>>           aIdx[iLeft+iRight] = aLeft[iLeft];
>>           iLeft++;
>>         }else{
>> -        float fLeft = aDistance[aLeft[iLeft]];
>> -        float fRight = aDistance[aRight[iRight]];
>> +        ConstraintType fLeft = aDistance[aLeft[iLeft]];
>> +        ConstraintType fRight = aDistance[aRight[iRight]];
>>           if( fLeft<fRight ){
>>             aIdx[iLeft+iRight] = aLeft[iLeft];
>>             iLeft++;
>> @@ -1598,8 +1621,8 @@
>>       {
>>         int jj;
>>         for(jj=1; jj<nIdx; jj++){
>> -        float left = aDistance[aIdx[jj-1]];
>> -        float right = aDistance[aIdx[jj]];
>> +        ConstraintType left = aDistance[aIdx[jj-1]];
>> +        ConstraintType right = aDistance[aIdx[jj]];
>>           assert( left<=right );
>>         }
>>       }
>> @@ -1641,10 +1664,10 @@
>>       memcpy(aSpare, aLeft, sizeof(int)*nLeft);
>>       aLeft = aSpare;
>>       while( iLeft<nLeft || iRight<nRight ){
>> -      float xleft1 = aCell[aLeft[iLeft]].aCoord[iDim*2];
>> -      float xleft2 = aCell[aLeft[iLeft]].aCoord[iDim*2+1];
>> -      float xright1 = aCell[aRight[iRight]].aCoord[iDim*2];
>> -      float xright2 = aCell[aRight[iRight]].aCoord[iDim*2+1];
>> +      ConstraintType xleft1 = aCell[aLeft[iLeft]].aCoord[iDim*2];
>> +      ConstraintType xleft2 = aCell[aLeft[iLeft]].aCoord[iDim*2+1];
>> +      ConstraintType xright1 = aCell[aRight[iRight]].aCoord[iDim*2];
>> +      ConstraintType xright2 = aCell[aRight[iRight]].aCoord[iDim*2 
>> +1];
>>
>>         if( (iLeft!=nLeft) && ((iRight==nRight)
>>          || (xleft1<xright1)
>> @@ -1663,10 +1686,10 @@
>>       {
>>         int jj;
>>         for(jj=1; jj<nIdx; jj++){
>> -        float xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
>> -        float xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
>> -        float xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
>> -        float xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
>> +        ConstraintType xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
>> +        ConstraintType xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
>> +        ConstraintType xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
>> +        ConstraintType xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
>>           assert( xleft1<=xright1 && (xleft1<xright1 ||  
>> xleft2<=xright2) );
>>         }
>>       }
>> @@ -1693,7 +1716,7 @@
>>
>>     int iBestDim;
>>     int iBestSplit;
>> -  float fBestMargin;
>> +  ConstraintType fBestMargin;
>>
>>     int nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));
>>
>> @@ -1714,9 +1737,9 @@
>>     }
>>
>>     for(ii=0; ii<pRtree->nDim; ii++){
>> -    float margin = 0.0;
>> -    float fBestOverlap;
>> -    float fBestArea;
>> +    ConstraintType margin = 0.0;
>> +    ConstraintType fBestOverlap;
>> +    ConstraintType fBestArea;
>>       int iBestLeft;
>>       int nLeft;
>>
>> @@ -1728,8 +1751,8 @@
>>         RtreeCell left;
>>         RtreeCell right;
>>         int kk;
>> -      float overlap;
>> -      float area;
>> +      ConstraintType overlap;
>> +      ConstraintType area;
>>
>>         memcpy(&left, &aCell[aaSorted[ii][0]], sizeof(RtreeCell));
>>         memcpy(&right, &aCell[aaSorted[ii][nCell-1]], sizeof 
>> (RtreeCell));
>> @@ -1809,7 +1832,7 @@
>>     for(i=nCell-2; i>0; i--){
>>       RtreeCell *pNext;
>>       pNext = PickNext(pRtree, aCell, nCell, pBboxLeft, pBboxRight,  
>> aiUsed);
>> -    float diff =
>> +    ConstraintType diff =
>>         cellGrowth(pRtree, pBboxLeft, pNext) -
>>         cellGrowth(pRtree, pBboxRight, pNext)
>>       ;
>> @@ -2099,14 +2122,14 @@
>>     int *aOrder;
>>     int *aSpare;
>>     RtreeCell *aCell;
>> -  float *aDistance;
>> +  ConstraintType *aDistance;
>>     int nCell;
>> -  float aCenterCoord[RTREE_MAX_DIMENSIONS];
>> +  ConstraintType aCenterCoord[RTREE_MAX_DIMENSIONS];
>>     int iDim;
>>     int ii;
>>     int rc = SQLITE_OK;
>>
>> -  memset(aCenterCoord, 0, sizeof(float)*RTREE_MAX_DIMENSIONS);
>> +  memset(aCenterCoord, 0, sizeof(ConstraintType) 
>> *RTREE_MAX_DIMENSIONS);
>>
>>     nCell = NCELL(pNode)+1;
>>
>> @@ -2117,14 +2140,14 @@
>>       sizeof(RtreeCell) +         /* aCell array */
>>       sizeof(int)       +         /* aOrder array */
>>       sizeof(int)       +         /* aSpare array */
>> -    sizeof(float)               /* aDistance array */
>> +    sizeof(ConstraintType)               /* aDistance array */
>>     ));
>>     if( !aCell ){
>>       return SQLITE_NOMEM;
>>     }
>>     aOrder    = (int *)&aCell[nCell];
>>     aSpare    = (int *)&aOrder[nCell];
>> -  aDistance = (float *)&aSpare[nCell];
>> +  aDistance = (ConstraintType *)&aSpare[nCell];
>>
>>     for(ii=0; ii<nCell; ii++){
>>       if( ii==(nCell-1) ){
>> @@ -2139,13 +2162,13 @@
>>       }
>>     }
>>     for(iDim=0; iDim<pRtree->nDim; iDim++){
>> -    aCenterCoord[iDim] = aCenterCoord[iDim]/((float)nCell*2.0);
>> +    aCenterCoord[iDim] = aCenterCoord[iDim]/((ConstraintType) 
>> nCell*2.0);
>>     }
>>
>>     for(ii=0; ii<nCell; ii++){
>>       aDistance[ii] = 0.0;
>>       for(iDim=0; iDim<pRtree->nDim; iDim++){
>> -      float coord = aCell[ii].aCoord[iDim*2+1] - aCell[ii].aCoord 
>> [iDim*2];
>> +      ConstraintType coord = aCell[ii].aCoord[iDim*2+1] -
>> aCell[ii].aCoord[iDim*2];
>>         aDistance[ii] +=
>> (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);
>>       }
>>     }
>> @@ -2388,8 +2411,8 @@
>>       /* Populate the cell.aCoord[] array. The first coordinate is
>> azData[3]. */
>>       assert( nData==(pRtree->nDim*2 + 3) );
>>       for(ii=0; ii<(pRtree->nDim*2); ii+=2){
>> -      cell.aCoord[ii] = (float)sqlite3_value_double(azData[ii+3]);
>> -      cell.aCoord[ii+1] = (float)sqlite3_value_double(azData[ii+4]);
>> +      cell.aCoord[ii] = sqlite3_value_ConstraintType(azData[ii+3]);
>> +      cell.aCoord[ii+1] = sqlite3_value_ConstraintType(azData[ii+4]);
>>         if( cell.aCoord[ii]>cell.aCoord[ii+1] ){
>>           rc = SQLITE_CONSTRAINT;
>>           goto constraint;
>> @@ -2716,7 +2739,7 @@
>>       sqlite3_snprintf(512-nCell,&zCell[nCell],"%d", cell.iRowid);
>>       nCell = strlen(zCell);
>>       for(jj=0; jj<tree.nDim*2; jj++){
>> -      sqlite3_snprintf(512-nCell,&zCell[nCell],"
>> %f",(double)cell.aCoord[jj]);
>> +      sqlite3_snprintf_ConstraintType(512-nCell,&zCell[nCell],
>> cell.aCoord[jj]);
>>         nCell = strlen(zCell);
>>       }
>>
>>
>>
>> _______________________________________________
>> sqlite-users mailing list
>> sqlite-users@sqlite.org
>> http://sqlite.org:8080/cgi-bin/mailman/listinfo/sqlite-users
> 
> _______________________________________________
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