** index.  Store the results in aStat as follows:
**
**    aStat[0]      Est. number of rows less than pVal
**    aStat[1]      Est. number of rows equal to pVal
**
** Return SQLITE_OK on success.
*/
static int whereKeyStats(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  UnpackedRecord *pRec,       /* Vector of values to consider */
  int roundUp,                /* Round up if true.  Round down if false */
  tRowcnt *aStat              /* OUT: stats written here */
){
  IndexSample *aSample = pIdx->aSample;
................................................................................
    if( roundUp ){
      iGap = (iGap*2)/3;
    }else{
      iGap = iGap/3;
    }
    aStat[0] = iLower + iGap;
  }
  return SQLITE_OK;
}
#endif /* SQLITE_ENABLE_STAT4 */

/*
** This function is used to estimate the number of rows that will be visited
** by scanning an index for a range of values. The range may have an upper
** bound, a lower bound, or both. The WHERE clause terms that set the upper
................................................................................
  int nEq = pBuilder->pNew->u.btree.nEq;

  if( nEq==pBuilder->nRecValid 
   && p->nSample 
   && OptimizationEnabled(pParse->db, SQLITE_Stat3) 
  ){
    UnpackedRecord *pRec = pBuilder->pRec;
    tRowcnt iLower = 0;
    tRowcnt iUpper = p->aiRowEst[0];
    tRowcnt a[2];
    u8 aff = p->pTable->aCol[p->aiColumn[0]].affinity;


































    if( pLower ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pLower->pExpr->pRight;
      assert( (pLower->eOperator & (WO_GT|WO_GE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk

       && whereKeyStats(pParse, p, pRec, 0, a)==SQLITE_OK
      ){
        iLower = a[0];
        if( (pLower->eOperator & WO_GT)!=0 ) iLower += a[1];

      }
    }


    if( rc==SQLITE_OK && pUpper ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pUpper->pExpr->pRight;
      assert( (pUpper->eOperator & (WO_LT|WO_LE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk

       && whereKeyStats(pParse, p, pRec, 1, a)==SQLITE_OK
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];

      }
    }

    pBuilder->pRec = pRec;
    if( rc==SQLITE_OK ){
      WhereCost nNew;
      if( iUpper>iLower ){
        nNew = whereCost(iUpper - iLower);
      }else{
        nNew = whereCost(2);      /* Small number */
      }
      if( nNew<nOut ){
        nOut = nNew;
      }
      *pnOut = (WhereCost)nOut;
      WHERETRACE(0x100, ("range scan regions: %u..%u  est=%d\n",
                         (u32)iLower, (u32)iUpper, nOut));
................................................................................
  aff = p->pTable->aCol[p->aiColumn[nEq-1]].affinity;
  rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq-1, &bOk);
  pBuilder->pRec = pRec;
  if( rc!=SQLITE_OK ) return rc;
  if( bOk==0 ) return SQLITE_NOTFOUND;
  pBuilder->nRecValid = nEq;

  rc = whereKeyStats(pParse, p, pRec, 0, a);
  if( rc==SQLITE_OK ){
    WHERETRACE(0x100,("equality scan regions: %d\n", (int)a[1]));
    *pnRow = a[1];
  }
  
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT4) */

#ifdef SQLITE_ENABLE_STAT4
/*

** index.  Store the results in aStat as follows:
**
**    aStat[0]      Est. number of rows less than pVal
**    aStat[1]      Est. number of rows equal to pVal
**
** Return SQLITE_OK on success.
*/
static void whereKeyStats(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  UnpackedRecord *pRec,       /* Vector of values to consider */
  int roundUp,                /* Round up if true.  Round down if false */
  tRowcnt *aStat              /* OUT: stats written here */
){
  IndexSample *aSample = pIdx->aSample;
................................................................................
    if( roundUp ){
      iGap = (iGap*2)/3;
    }else{
      iGap = iGap/3;
    }
    aStat[0] = iLower + iGap;
  }

}
#endif /* SQLITE_ENABLE_STAT4 */

/*
** This function is used to estimate the number of rows that will be visited
** by scanning an index for a range of values. The range may have an upper
** bound, a lower bound, or both. The WHERE clause terms that set the upper
................................................................................
  int nEq = pBuilder->pNew->u.btree.nEq;

  if( nEq==pBuilder->nRecValid 
   && p->nSample 
   && OptimizationEnabled(pParse->db, SQLITE_Stat3) 
  ){
    UnpackedRecord *pRec = pBuilder->pRec;


    tRowcnt a[2];
    u8 aff = p->pTable->aCol[p->aiColumn[0]].affinity;

    /* Variable iLower will be set to the estimate of the number of rows in 
    ** the index that are less than the lower bound of the range query. The
    ** lower bound being the concatenation of $P and $L, where $P is the
    ** key-prefix formed by the nEq values matched against the nEq left-most
    ** columns of the index, and $L is the value in pLower.
    **
    ** Or, if pLower is NULL or $L cannot be extracted from it (because it
    ** is not a simple variable or literal value), the lower bound of the
    ** range is $P. Due to a quirk in the way whereKeyStats() works, even
    ** if $L is available, whereKeyStats() is called for both ($P) and 
    ** ($P:$L) and the larger of the two returned values used.
    **
    ** Similarly, iUpper is to be set to the estimate of the number of rows
    ** less than the upper bound of the range query. Where the upper bound
    ** is either ($P) or ($P:$U). Again, even if $U is available, both values
    ** of iUpper are requested of whereKeyStats() and the smaller used.
    */
    tRowcnt iLower;
    tRowcnt iUpper;

    /* Determine iLower and iUpper using ($P) only. */
    if( nEq==0 ){
      iLower = 0;
      iUpper = p->aiRowEst[0];
    }else{
      /* Note: this call could be optimized away - since the same values must 
      ** have been requested when testing key $P in whereEqualScanEst().  */
      whereKeyStats(pParse, p, pRec, 0, a);
      iLower = a[0];
      iUpper = a[0] + a[1];
    }

    /* If possible, improve on the iLower estimate using ($P:$L). */
    if( pLower ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pLower->pExpr->pRight;
      assert( (pLower->eOperator & (WO_GT|WO_GE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk ){
        tRowcnt iNew;
        whereKeyStats(pParse, p, pRec, 0, a);


        iNew = a[0] + ((pLower->eOperator & WO_GT) ? a[1] : 0);
        if( iNew>iLower ) iLower = iNew;
      }
    }

    /* If possible, improve on the iUpper estimate using ($P:$U). */
    if( pUpper ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pUpper->pExpr->pRight;
      assert( (pUpper->eOperator & (WO_LT|WO_LE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk ){
        tRowcnt iNew;
        whereKeyStats(pParse, p, pRec, 1, a);


        iNew = a[0] + ((pUpper->eOperator & WO_LE) ? a[1] : 0);
        if( iNew<iUpper ) iUpper = iNew;
      }
    }

    pBuilder->pRec = pRec;
    if( rc==SQLITE_OK ){
      WhereCost nNew;
      if( iUpper>iLower ){
        nNew = whereCost(iUpper - iLower);
      }else{
        nNew = 10;        assert( 10==whereCost(2) );
      }
      if( nNew<nOut ){
        nOut = nNew;
      }
      *pnOut = (WhereCost)nOut;
      WHERETRACE(0x100, ("range scan regions: %u..%u  est=%d\n",
                         (u32)iLower, (u32)iUpper, nOut));
................................................................................
  aff = p->pTable->aCol[p->aiColumn[nEq-1]].affinity;
  rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq-1, &bOk);
  pBuilder->pRec = pRec;
  if( rc!=SQLITE_OK ) return rc;
  if( bOk==0 ) return SQLITE_NOTFOUND;
  pBuilder->nRecValid = nEq;

  whereKeyStats(pParse, p, pRec, 0, a);

  WHERETRACE(0x100,("equality scan regions: %d\n", (int)a[1]));
  *pnRow = a[1];

  
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT4) */

#ifdef SQLITE_ENABLE_STAT4
/*