resetAccumulator(pParse, &sAggInfo);
        pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, pMinMax,0,flag,0);
        if( pWInfo==0 ){
          sqlite3ExprListDelete(db, pDel);
          goto select_end;
        }
        updateAccumulator(pParse, &sAggInfo);

        if( pWInfo->nOBSat>0 ){
          sqlite3VdbeAddOp2(v, OP_Goto, 0, pWInfo->iBreak);
          VdbeComment((v, "%s() by index",
                (flag==WHERE_ORDERBY_MIN?"min":"max")));
        }
        sqlite3WhereEnd(pWInfo);
        finalizeAggFunctions(pParse, &sAggInfo);

        resetAccumulator(pParse, &sAggInfo);
        pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, pMinMax,0,flag,0);
        if( pWInfo==0 ){
          sqlite3ExprListDelete(db, pDel);
          goto select_end;
        }
        updateAccumulator(pParse, &sAggInfo);
        assert( pMinMax==0 || pMinMax->nExpr==1 );
        if( pWInfo->nOBSat>0 ){
          sqlite3VdbeAddOp2(v, OP_Goto, 0, pWInfo->iBreak);
          VdbeComment((v, "%s() by index",
                (flag==WHERE_ORDERBY_MIN?"min":"max")));
        }
        sqlite3WhereEnd(pWInfo);
        finalizeAggFunctions(pParse, &sAggInfo);

** Within the union, pIdx is only used when wsFlags&WHERE_INDEXED is true.
** pTerm is only used when wsFlags&WHERE_MULTI_OR is true.  And pVtabIdx
** is only used when wsFlags&WHERE_VIRTUALTABLE is true.  It is never the
** case that more than one of these conditions is true.
*/
struct WherePlan {
  u32 wsFlags;                   /* WHERE_* flags that describe the strategy */
  u32 nEq;                       /* Number of == constraints */

  double nRow;                   /* Estimated number of rows (for EQP) */
  union {
    Index *pIdx;                   /* Index when WHERE_INDEXED is true */
    struct WhereTerm *pTerm;       /* WHERE clause term for OR-search */
    sqlite3_index_info *pVtabIdx;  /* Virtual table index to use */
  } u;
};

** Within the union, pIdx is only used when wsFlags&WHERE_INDEXED is true.
** pTerm is only used when wsFlags&WHERE_MULTI_OR is true.  And pVtabIdx
** is only used when wsFlags&WHERE_VIRTUALTABLE is true.  It is never the
** case that more than one of these conditions is true.
*/
struct WherePlan {
  u32 wsFlags;                   /* WHERE_* flags that describe the strategy */
  u16 nEq;                       /* Number of == constraints */
  u16 nOBSat;                    /* Number of ORDER BY terms satisfied */
  double nRow;                   /* Estimated number of rows (for EQP) */
  union {
    Index *pIdx;                   /* Index when WHERE_INDEXED is true */
    struct WhereTerm *pTerm;       /* WHERE clause term for OR-search */
    sqlite3_index_info *pVtabIdx;  /* Virtual table index to use */
  } u;
};

  struct SrcList_item *pSrc;      /* The FROM clause term to search */
  Bitmask notReady;               /* Mask of cursors not available */
  Bitmask notValid;               /* Cursors not available for any purpose */
  ExprList *pOrderBy;             /* The ORDER BY clause */
  ExprList *pDistinct;            /* The select-list if query is DISTINCT */
  sqlite3_index_info **ppIdxInfo; /* Index information passed to xBestIndex */
  int i, n;                       /* Which loop is being coded; # of loops */
  WhereLevel *a;                  /* Info about outer loops */
  WhereCost cost;                 /* Lowest cost query plan */
};

/*
** Initialize a preallocated WhereClause structure.
*/
static void whereClauseInit(
................................................................................
  /* Prevent ON clause terms of a LEFT JOIN from being used to drive
  ** an index for tables to the left of the join.
  */
  pTerm->prereqRight |= extraRight;
}

/*
** Return TRUE if any of the expressions in pList->a[iFirst...] contain
** a reference to any table other than the iBase table.
*/
static int referencesOtherTables(
  ExprList *pList,          /* Search expressions in ths list */
  WhereMaskSet *pMaskSet,   /* Mapping from tables to bitmaps */
  int iFirst,               /* Be searching with the iFirst-th expression */
  int iBase                 /* Ignore references to this table */
){

  Bitmask allowed = ~getMask(pMaskSet, iBase);
  while( iFirst<pList->nExpr ){
    if( (exprTableUsage(pMaskSet, pList->a[iFirst++].pExpr)&allowed)!=0 ){
      return 1;
    }
  }
  return 0;
}

/*
** This function searches the expression list passed as the second argument
** for an expression of type TK_COLUMN that refers to the same column and
** uses the same collation sequence as the iCol'th column of index pIdx.
** Argument iBase is the cursor number used for the table that pIdx refers
................................................................................
  }

  return 0;
}

/*
** This routine decides if pIdx can be used to satisfy the ORDER BY
** clause.  If it can, it returns 1.  If pIdx cannot satisfy the
** ORDER BY clause, this routine returns 0.

**
** pOrderBy is an ORDER BY clause from a SELECT statement.  pTab is the
** left-most table in the FROM clause of that same SELECT statement and
** the table has a cursor number of "base".  pIdx is an index on pTab.

**
** nEqCol is the number of columns of pIdx that are used as equality
** constraints.  Any of these columns may be missing from the ORDER BY




** clause and the match can still be a success.
**
** All terms of the ORDER BY that match against the index must be either
** ASC or DESC.  (Terms of the ORDER BY clause past the end of a UNIQUE
** index do not need to satisfy this constraint.)  The *pbRev value is
** set to 1 if the ORDER BY clause is all DESC and it is set to 0 if
** the ORDER BY clause is all ASC.

*/
static int isSortingIndex(
  Parse *pParse,          /* Parsing context */
  WhereMaskSet *pMaskSet, /* Mapping from table cursor numbers to bitmaps */
  Index *pIdx,            /* The index we are testing */
  int base,               /* Cursor number for the table to be sorted */
  ExprList *pOrderBy,     /* The ORDER BY clause */
  int nEqCol,             /* Number of index columns with == constraints */
  int wsFlags,            /* Index usages flags */

  int *pbRev              /* Set to 1 if ORDER BY is DESC */
){

  int i, j;                       /* Loop counters */
  int sortOrder = 0;              /* XOR of index and ORDER BY sort direction */
  int nTerm;                      /* Number of ORDER BY terms */
  struct ExprList_item *pTerm;    /* A term of the ORDER BY clause */


  sqlite3 *db = pParse->db;










  if( !pOrderBy ) return 0;
  if( wsFlags & WHERE_COLUMN_IN ) return 0;
  if( pIdx->bUnordered ) return 0;

  nTerm = pOrderBy->nExpr;
  assert( nTerm>0 );

  /* Argument pIdx must either point to a 'real' named index structure, 
  ** or an index structure allocated on the stack by bestBtreeIndex() to
  ** represent the rowid index that is part of every table.  */
  assert( pIdx->zName || (pIdx->nColumn==1 && pIdx->aiColumn[0]==-1) );
................................................................................
  ** the index.
  **
  ** Note that indices have pIdx->nColumn regular columns plus
  ** one additional column containing the rowid.  The rowid column
  ** of the index is also allowed to match against the ORDER BY
  ** clause.
  */
  for(i=j=0, pTerm=pOrderBy->a; j<nTerm && i<=pIdx->nColumn; i++){
    Expr *pExpr;       /* The expression of the ORDER BY pTerm */
    CollSeq *pColl;    /* The collating sequence of pExpr */
    int termSortOrder; /* Sort order for this term */
    int iColumn;       /* The i-th column of the index.  -1 for rowid */
    int iSortOrder;    /* 1 for DESC, 0 for ASC on the i-th index term */
    const char *zColl; /* Name of the collating sequence for i-th index term */

................................................................................
      }else if( i==pIdx->nColumn ){
        /* Index column i is the rowid.  All other terms match. */
        break;
      }else{
        /* If an index column fails to match and is not constrained by ==
        ** then the index cannot satisfy the ORDER BY constraint.
        */
        return 0;
      }
    }
    assert( pIdx->aSortOrder!=0 || iColumn==-1 );
    assert( pTerm->sortOrder==0 || pTerm->sortOrder==1 );
    assert( iSortOrder==0 || iSortOrder==1 );
    termSortOrder = iSortOrder ^ pTerm->sortOrder;
    if( i>nEqCol ){
      if( termSortOrder!=sortOrder ){
        /* Indices can only be used if all ORDER BY terms past the
        ** equality constraints are all either DESC or ASC. */
        return 0;
      }
    }else{
      sortOrder = termSortOrder;
    }
    j++;
    pTerm++;
    if( iColumn<0 && !referencesOtherTables(pOrderBy, pMaskSet, j, base) ){
      /* If the indexed column is the primary key and everything matches
      ** so far and none of the ORDER BY terms to the right reference other
      ** tables in the join, then we are assured that the index can be used 
      ** to sort because the primary key is unique and so none of the other
      ** columns will make any difference
      */
      j = nTerm;
    }
  }






  *pbRev = sortOrder!=0;
  if( j>=nTerm ){
    /* All terms of the ORDER BY clause are covered by this index so
    ** this index can be used for sorting. */
    return 1;
  }
  if( pIdx->onError!=OE_None && i==pIdx->nColumn
      && (wsFlags & WHERE_COLUMN_NULL)==0
      && !referencesOtherTables(pOrderBy, pMaskSet, j, base) 



  ){
    Column *aCol = pIdx->pTable->aCol;






    /* All terms of this index match some prefix of the ORDER BY clause,
    ** the index is UNIQUE, and no terms on the tail of the ORDER BY
    ** refer to other tables in a join. So, assuming that the index entries
    ** visited contain no NULL values, then this index delivers rows in
    ** the required order.
    **
    ** It is not possible for any of the first nEqCol index fields to be
    ** NULL (since the corresponding "=" operator in the WHERE clause would 
    ** not be true). So if all remaining index columns have NOT NULL 
    ** constaints attached to them, we can be confident that the visited
    ** index entries are free of NULLs.  */
    for(i=nEqCol; i<pIdx->nColumn; i++){
      if( aCol[pIdx->aiColumn[i]].notNull==0 ) break;
    }
    return (i==pIdx->nColumn);
  }
  return 0;
}

/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operations with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
................................................................................
    *pnRow = nRowEst;
    WHERETRACE(("IN row estimate: est=%g\n", nRowEst));
  }
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT3) */


















/*
** Find the best query plan for accessing a particular table.  Write the
** best query plan and its cost into the p->cost.
**
** The lowest cost plan wins.  The cost is an estimate of the amount of
** CPU and disk I/O needed to process the requested result.
................................................................................
  /* Loop over all indices looking for the best one to use
  */
  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const tRowcnt * const aiRowEst = pProbe->aiRowEst;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    double log10N = (double)1;  /* base-10 logarithm of nRow (inexact) */
    int rev;                    /* True to scan in reverse order */
    int wsFlags = 0;
    Bitmask used = 0;

    /* The following variables are populated based on the properties of
    ** index being evaluated. They are then used to determine the expected
    ** cost and number of rows returned.
    **
................................................................................
    **
    **    nInMul is set to 1.
    **
    **    If there exists a WHERE term of the form "x IN (SELECT ...)", then 
    **    the sub-select is assumed to return 25 rows for the purposes of 
    **    determining nInMul.
    **




    **  bInEst:  
    **    Set to true if there was at least one "x IN (SELECT ...)" term used 
    **    in determining the value of nInMul.  Note that the RHS of the
    **    IN operator must be a SELECT, not a value list, for this variable
    **    to be true.
    **
    **  rangeDiv:
................................................................................
    **    space to 1/16th of its original size (rangeDiv==16).
    **
    **  bSort:   
    **    Boolean. True if there is an ORDER BY clause that will require an 
    **    external sort (i.e. scanning the index being evaluated will not 
    **    correctly order records).
    **




    **  bLookup: 
    **    Boolean. True if a table lookup is required for each index entry
    **    visited.  In other words, true if this is not a covering index.
    **    This is always false for the rowid primary key index of a table.
    **    For other indexes, it is true unless all the columns of the table
    **    used by the SELECT statement are present in the index (such an
    **    index is sometimes described as a covering index).
................................................................................
    **    of column c, but the first does not because columns a and b are
    **    both available in the index.
    **
    **             SELECT a, b    FROM tbl WHERE a = 1;
    **             SELECT a, b, c FROM tbl WHERE a = 1;
    */
    int nEq;                      /* Number of == or IN terms matching index */

    int bInEst = 0;               /* True if "x IN (SELECT...)" seen */
    int nInMul = 1;               /* Number of distinct equalities to lookup */
    double rangeDiv = (double)1;  /* Estimated reduction in search space */
    int nBound = 0;               /* Number of range constraints seen */
    int bSort;                    /* True if external sort required */
    int bDist;                    /* True if index cannot help with DISTINCT */
    int bLookup = 0;              /* True if not a covering index */


    WhereTerm *pTerm;             /* A single term of the WHERE clause */
#ifdef SQLITE_ENABLE_STAT3
    WhereTerm *pFirstTerm = 0;    /* First term matching the index */
#endif


    if( (p->i) > 0 ){
      bSort = 0;
      bDist = 0;
    }else{
      bSort = p->pOrderBy!=0;
      bDist = p->pDistinct!=0;
    }

    /* Determine the values of nEq and nInMul */
    for(nEq=0; nEq<pProbe->nColumn; nEq++){
      int j = pProbe->aiColumn[nEq];
      pTerm = findTerm(pWC, iCur, j, p->notReady, eqTermMask, pIdx);
      if( pTerm==0 ) break;
      wsFlags |= (WHERE_COLUMN_EQ|WHERE_ROWID_EQ);
      testcase( pTerm->pWC!=pWC );
      if( pTerm->eOperator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
................................................................................
          bInEst = 1;
        }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
          /* "x IN (value, value, ...)" */
          nInMul *= pExpr->x.pList->nExpr;
        }
      }else if( pTerm->eOperator & WO_ISNULL ){
        wsFlags |= WHERE_COLUMN_NULL;


      }
#ifdef SQLITE_ENABLE_STAT3
      if( nEq==0 && pProbe->aSample ) pFirstTerm = pTerm;
#endif
      used |= pTerm->prereqRight;
    }
 
................................................................................
      }
    }

    /* If there is an ORDER BY clause and the index being considered will
    ** naturally scan rows in the required order, set the appropriate flags
    ** in wsFlags. Otherwise, if there is an ORDER BY clause but the index
    ** will scan rows in a different order, set the bSort variable.  */

    if( bSort && isSortingIndex(
          pParse, pWC->pMaskSet, pProbe, iCur, p->pOrderBy, nEq, wsFlags, &rev)
    ){





      bSort = 0;
      wsFlags |= WHERE_ROWID_RANGE|WHERE_COLUMN_RANGE|WHERE_ORDERBY;
      wsFlags |= (rev ? WHERE_REVERSE : 0);

    }

    /* If there is a DISTINCT qualifier and this index will scan rows in
    ** order of the DISTINCT expressions, clear bDist and set the appropriate
    ** flags in wsFlags. */
    if( bDist
     && isDistinctIndex(pParse, pWC, pProbe, iCur, p->pDistinct, nEq)
................................................................................
    /* Add in the estimated cost of sorting the result.  Actual experimental
    ** measurements of sorting performance in SQLite show that sorting time
    ** adds C*N*log10(N) to the cost, where N is the number of rows to be 
    ** sorted and C is a factor between 1.95 and 4.3.  We will split the
    ** difference and select C of 3.0.
    */
    if( bSort ){
      cost += nRow*estLog(nRow)*3;
    }
    if( bDist ){
      cost += nRow*estLog(nRow)*3;
    }

    /**** Cost of using this index has now been computed ****/

................................................................................
      }
      if( nRow<2 ) nRow = 2;
    }


    WHERETRACE((
      "%s(%s): nEq=%d nInMul=%d rangeDiv=%d bSort=%d bLookup=%d wsFlags=0x%x\n"
      "         notReady=0x%llx log10N=%.1f nRow=%.1f cost=%.1f used=0x%llx\n",

      pSrc->pTab->zName, (pIdx ? pIdx->zName : "ipk"), 
      nEq, nInMul, (int)rangeDiv, bSort, bLookup, wsFlags,
      p->notReady, log10N, nRow, cost, used
    ));

    /* If this index is the best we have seen so far, then record this
    ** index and its cost in the pCost structure.
    */
    if( (!pIdx || wsFlags)
     && (cost<p->cost.rCost || (cost<=p->cost.rCost && nRow<p->cost.plan.nRow))
    ){
      p->cost.rCost = cost;
      p->cost.used = used;
      p->cost.plan.nRow = nRow;
      p->cost.plan.wsFlags = (wsFlags&wsFlagMask);
      p->cost.plan.nEq = nEq;

      p->cost.plan.u.pIdx = pIdx;
    }

    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;

................................................................................
  pWInfo->pParse = pParse;
  pWInfo->pTabList = pTabList;
  pWInfo->iBreak = sqlite3VdbeMakeLabel(v);
  pWInfo->pWC = sWBI.pWC = (WhereClause *)&((u8 *)pWInfo)[nByteWInfo];
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  pMaskSet = (WhereMaskSet*)&sWBI.pWC[1];
  sWBI.a = pWInfo->a;

  /* Disable the DISTINCT optimization if SQLITE_DistinctOpt is set via
  ** sqlite3_test_ctrl(SQLITE_TESTCTRL_OPTIMIZATIONS,...) */
  if( db->flags & SQLITE_DistinctOpt ) pDistinct = 0;

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.

  struct SrcList_item *pSrc;      /* The FROM clause term to search */
  Bitmask notReady;               /* Mask of cursors not available */
  Bitmask notValid;               /* Cursors not available for any purpose */
  ExprList *pOrderBy;             /* The ORDER BY clause */
  ExprList *pDistinct;            /* The select-list if query is DISTINCT */
  sqlite3_index_info **ppIdxInfo; /* Index information passed to xBestIndex */
  int i, n;                       /* Which loop is being coded; # of loops */
  WhereLevel *aLevel;             /* Info about outer loops */
  WhereCost cost;                 /* Lowest cost query plan */
};

/*
** Initialize a preallocated WhereClause structure.
*/
static void whereClauseInit(
................................................................................
  /* Prevent ON clause terms of a LEFT JOIN from being used to drive
  ** an index for tables to the left of the join.
  */
  pTerm->prereqRight |= extraRight;
}

/*
** Return TRUE if the given index is UNIQUE and all columns past the
** first nSkip columns are NOT NULL.
*/
static int indexIsUniqueNotNull(Index *pIdx, int nSkip){
  Table *pTab = pIdx->pTable;
  int i;
  if( pIdx->onError==OE_None ) return 0;
  for(i=nSkip; i<pIdx->nColumn; i++){

    int j = pIdx->aiColumn[i];
    if( j>=0 && pTab->aCol[j].notNull==0 ) return 0;



  }

  return 1;
}

/*
** This function searches the expression list passed as the second argument
** for an expression of type TK_COLUMN that refers to the same column and
** uses the same collation sequence as the iCol'th column of index pIdx.
** Argument iBase is the cursor number used for the table that pIdx refers
................................................................................
  }

  return 0;
}

/*
** This routine decides if pIdx can be used to satisfy the ORDER BY
** clause, either in whole or in part.  The return value is the 
** cumulative number of terms in the ORDER BY clause that are satisfied
** by the index pIdx and other indices in outer loops.
**


** The table being queried has a cursor number of "base".  pIdx is the
** index that is postulated for use to access the table.
**
** nEqCol is the number of columns of pIdx that are used as equality
** constraints and where the other side of the == is an ordered column
** or constant.  An "order column" in the previous sentence means a column
** in table from an outer loop whose values will always appear in the 
** correct order due to othre index, or because the outer loop generates
** a unique result.  Any of the first nEqCol columns of pIdx may be missing
** from the ORDER BY clause and the match can still be a success.
**




** The *pbRev value is set to 0 order 1 depending on whether or not
** pIdx should be run in the forward order or in reverse order.
*/
static int isSortingIndex(

  WhereBestIdx *p,    /* Best index search context */
  Index *pIdx,        /* The index we are testing */
  int base,           /* Cursor number for the table to be sorted */

  int nEqCol,         /* Number of index columns with ordered == constraints */
  int wsFlags,        /* Index usages flags */
  int bOuterRev,      /* True if outer loops scan in reverse order */
  int *pbRev          /* Set to 1 for reverse-order scan of pIdx */
){
  int i;                        /* Number of pIdx terms used */
  int j;                        /* Number of ORDER BY terms satisfied */
  int sortOrder = 0;            /* XOR of index and ORDER BY sort direction */
  int nTerm;                    /* Number of ORDER BY terms */
  struct ExprList_item *pTerm;  /* A term of the ORDER BY clause */
  ExprList *pOrderBy;           /* The ORDER BY clause */
  Parse *pParse = p->pParse;    /* Parser context */
  sqlite3 *db = pParse->db;     /* Database connection */
  int nPriorSat;                /* ORDER BY terms satisfied by outer loops */
  int seenRowid = 0;            /* True if an ORDER BY rowid term is seen */

  if( p->i==0 ){
    nPriorSat = 0;
  }else{
    nPriorSat = p->aLevel[p->i-1].plan.nOBSat;
  }
  if( p->i>0 && nEqCol==0 /*&& !allOuterLoopsUnique(p)*/ ) return nPriorSat;
  pOrderBy = p->pOrderBy;
  if( !pOrderBy ) return nPriorSat;
  if( wsFlags & WHERE_COLUMN_IN ) return nPriorSat;
  if( pIdx->bUnordered ) return nPriorSat;

  nTerm = pOrderBy->nExpr;
  assert( nTerm>0 );

  /* Argument pIdx must either point to a 'real' named index structure, 
  ** or an index structure allocated on the stack by bestBtreeIndex() to
  ** represent the rowid index that is part of every table.  */
  assert( pIdx->zName || (pIdx->nColumn==1 && pIdx->aiColumn[0]==-1) );
................................................................................
  ** the index.
  **
  ** Note that indices have pIdx->nColumn regular columns plus
  ** one additional column containing the rowid.  The rowid column
  ** of the index is also allowed to match against the ORDER BY
  ** clause.
  */
  for(i=0,j=nPriorSat,pTerm=&pOrderBy->a[j]; j<nTerm && i<=pIdx->nColumn; i++){
    Expr *pExpr;       /* The expression of the ORDER BY pTerm */
    CollSeq *pColl;    /* The collating sequence of pExpr */
    int termSortOrder; /* Sort order for this term */
    int iColumn;       /* The i-th column of the index.  -1 for rowid */
    int iSortOrder;    /* 1 for DESC, 0 for ASC on the i-th index term */
    const char *zColl; /* Name of the collating sequence for i-th index term */

................................................................................
      }else if( i==pIdx->nColumn ){
        /* Index column i is the rowid.  All other terms match. */
        break;
      }else{
        /* If an index column fails to match and is not constrained by ==
        ** then the index cannot satisfy the ORDER BY constraint.
        */
        return nPriorSat;
      }
    }
    assert( pIdx->aSortOrder!=0 || iColumn==-1 );
    assert( pTerm->sortOrder==0 || pTerm->sortOrder==1 );
    assert( iSortOrder==0 || iSortOrder==1 );
    termSortOrder = iSortOrder ^ pTerm->sortOrder;
    if( i>nEqCol ){
      if( termSortOrder!=sortOrder ){
        /* Indices can only be used if all ORDER BY terms past the
        ** equality constraints are all either DESC or ASC. */
        break;
      }
    }else{
      sortOrder = termSortOrder;
    }
    j++;
    pTerm++;
    if( iColumn<0 ){
      seenRowid = 1;
      break;





    }
  }
  *pbRev = bOuterRev ^ sortOrder;

  /* If there was an "ORDER BY rowid" term that matched, or it is only
  ** possible for a single row from this table to match, then skip over
  ** any additional ORDER BY terms dealing with this table.
  */
  if( seenRowid ||






     (   (wsFlags & WHERE_COLUMN_NULL)==0

      && i>=pIdx->nColumn
      && indexIsUniqueNotNull(pIdx, nEqCol)
     )
  ){

    /* Advance j over additional ORDER BY terms associated with base */
    WhereMaskSet *pMS = p->pWC->pMaskSet;
    Bitmask m = ~getMask(pMS, base);
    while( j<nTerm && (exprTableUsage(pMS, pOrderBy->a[j].pExpr)&m)==0 ){
      j++;
    }













  }


  return j;
}

/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operations with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
................................................................................
    *pnRow = nRowEst;
    WHERETRACE(("IN row estimate: est=%g\n", nRowEst));
  }
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT3) */

/*
** pTerm is an == constraint.  Check to see if the other side of
** the == is a constant or a value that is guaranteed to be ordered
** by outer loops.  Return 1 if pTerm is ordered, and 0 if not.
*/
static int isOrderedTerm(WhereBestIdx *p, WhereTerm *pTerm, int *pbRev){
  if( p->i==0 ){
    return 1;  /* All == are ordered in the outer loop */
  }



  /* If we cannot prove that the constraint is ordered, assume it is not */
  return 0;
}


/*
** Find the best query plan for accessing a particular table.  Write the
** best query plan and its cost into the p->cost.
**
** The lowest cost plan wins.  The cost is an estimate of the amount of
** CPU and disk I/O needed to process the requested result.
................................................................................
  /* Loop over all indices looking for the best one to use
  */
  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const tRowcnt * const aiRowEst = pProbe->aiRowEst;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    double log10N = (double)1;  /* base-10 logarithm of nRow (inexact) */
    int bRev = 2;               /* 0=forward scan.  1=reverse.  2=undecided */
    int wsFlags = 0;
    Bitmask used = 0;

    /* The following variables are populated based on the properties of
    ** index being evaluated. They are then used to determine the expected
    ** cost and number of rows returned.
    **
................................................................................
    **
    **    nInMul is set to 1.
    **
    **    If there exists a WHERE term of the form "x IN (SELECT ...)", then 
    **    the sub-select is assumed to return 25 rows for the purposes of 
    **    determining nInMul.
    **
    **  nOrdered:
    **    The number of equality terms that are constrainted by outer loop
    **    variables that are well-ordered.
    **
    **  bInEst:  
    **    Set to true if there was at least one "x IN (SELECT ...)" term used 
    **    in determining the value of nInMul.  Note that the RHS of the
    **    IN operator must be a SELECT, not a value list, for this variable
    **    to be true.
    **
    **  rangeDiv:
................................................................................
    **    space to 1/16th of its original size (rangeDiv==16).
    **
    **  bSort:   
    **    Boolean. True if there is an ORDER BY clause that will require an 
    **    external sort (i.e. scanning the index being evaluated will not 
    **    correctly order records).
    **
    **  bDistinct:
    **    Boolean. True if there is a DISTINCT clause that will require an 
    **    external btree.
    **
    **  bLookup: 
    **    Boolean. True if a table lookup is required for each index entry
    **    visited.  In other words, true if this is not a covering index.
    **    This is always false for the rowid primary key index of a table.
    **    For other indexes, it is true unless all the columns of the table
    **    used by the SELECT statement are present in the index (such an
    **    index is sometimes described as a covering index).
................................................................................
    **    of column c, but the first does not because columns a and b are
    **    both available in the index.
    **
    **             SELECT a, b    FROM tbl WHERE a = 1;
    **             SELECT a, b, c FROM tbl WHERE a = 1;
    */
    int nEq;                      /* Number of == or IN terms matching index */
    int nOrdered;                 /* Number of ordered terms matching index */
    int bInEst = 0;               /* True if "x IN (SELECT...)" seen */
    int nInMul = 1;               /* Number of distinct equalities to lookup */
    double rangeDiv = (double)1;  /* Estimated reduction in search space */
    int nBound = 0;               /* Number of range constraints seen */
    int bSort;                    /* True if external sort required */
    int bDist;                    /* True if index cannot help with DISTINCT */
    int bLookup = 0;              /* True if not a covering index */
    int nOBSat = 0;               /* Number of ORDER BY terms satisfied */
    int nOrderBy;                 /* Number of ORDER BY terms */
    WhereTerm *pTerm;             /* A single term of the WHERE clause */
#ifdef SQLITE_ENABLE_STAT3
    WhereTerm *pFirstTerm = 0;    /* First term matching the index */
#endif

    nOrderBy = p->pOrderBy ? p->pOrderBy->nExpr : 0;
    if( (p->i) > 0 ){
      bSort = 0;
      bDist = 0;
    }else{
      bSort = p->pOrderBy!=0;
      bDist = p->pDistinct!=0;
    }

    /* Determine the values of nEq and nInMul */
    for(nEq=nOrdered=0; nEq<pProbe->nColumn; nEq++){
      int j = pProbe->aiColumn[nEq];
      pTerm = findTerm(pWC, iCur, j, p->notReady, eqTermMask, pIdx);
      if( pTerm==0 ) break;
      wsFlags |= (WHERE_COLUMN_EQ|WHERE_ROWID_EQ);
      testcase( pTerm->pWC!=pWC );
      if( pTerm->eOperator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
................................................................................
          bInEst = 1;
        }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
          /* "x IN (value, value, ...)" */
          nInMul *= pExpr->x.pList->nExpr;
        }
      }else if( pTerm->eOperator & WO_ISNULL ){
        wsFlags |= WHERE_COLUMN_NULL;
      }else if( bSort && nEq==nOrdered && isOrderedTerm(p, pTerm, &bRev) ){
        nOrdered++;
      }
#ifdef SQLITE_ENABLE_STAT3
      if( nEq==0 && pProbe->aSample ) pFirstTerm = pTerm;
#endif
      used |= pTerm->prereqRight;
    }
 
................................................................................
      }
    }

    /* If there is an ORDER BY clause and the index being considered will
    ** naturally scan rows in the required order, set the appropriate flags
    ** in wsFlags. Otherwise, if there is an ORDER BY clause but the index
    ** will scan rows in a different order, set the bSort variable.  */
    assert( bRev>=0 && bRev<=2 );
    if( bSort ){

      testcase( bRev==0 );
      testcase( bRev==1 );
      testcase( bRev==2 );
      nOBSat = isSortingIndex(p, pProbe, iCur, nOrdered,
                              wsFlags, bRev&1, &bRev);
      if( nOrderBy==nOBSat ){
        bSort = 0;
        wsFlags |= WHERE_ROWID_RANGE|WHERE_COLUMN_RANGE|WHERE_ORDERBY;
        wsFlags |= (bRev==1 ? WHERE_REVERSE : 0);
      }
    }

    /* If there is a DISTINCT qualifier and this index will scan rows in
    ** order of the DISTINCT expressions, clear bDist and set the appropriate
    ** flags in wsFlags. */
    if( bDist
     && isDistinctIndex(pParse, pWC, pProbe, iCur, p->pDistinct, nEq)
................................................................................
    /* Add in the estimated cost of sorting the result.  Actual experimental
    ** measurements of sorting performance in SQLite show that sorting time
    ** adds C*N*log10(N) to the cost, where N is the number of rows to be 
    ** sorted and C is a factor between 1.95 and 4.3.  We will split the
    ** difference and select C of 3.0.
    */
    if( bSort ){
      cost += nRow*estLog(nRow*(nOrderBy - nOBSat)/nOrderBy)*3;
    }
    if( bDist ){
      cost += nRow*estLog(nRow)*3;
    }

    /**** Cost of using this index has now been computed ****/

................................................................................
      }
      if( nRow<2 ) nRow = 2;
    }


    WHERETRACE((
      "%s(%s): nEq=%d nInMul=%d rangeDiv=%d bSort=%d bLookup=%d wsFlags=0x%x\n"
      "         notReady=0x%llx log10N=%.1f nRow=%.1f cost=%.1f used=0x%llx\n"
      "         nOrdered=%d nOBSat=%d\n",
      pSrc->pTab->zName, (pIdx ? pIdx->zName : "ipk"), 
      nEq, nInMul, (int)rangeDiv, bSort, bLookup, wsFlags,
      p->notReady, log10N, nRow, cost, used, nOrdered, nOBSat
    ));

    /* If this index is the best we have seen so far, then record this
    ** index and its cost in the pCost structure.
    */
    if( (!pIdx || wsFlags)
     && (cost<p->cost.rCost || (cost<=p->cost.rCost && nRow<p->cost.plan.nRow))
    ){
      p->cost.rCost = cost;
      p->cost.used = used;
      p->cost.plan.nRow = nRow;
      p->cost.plan.wsFlags = (wsFlags&wsFlagMask);
      p->cost.plan.nEq = nEq;
      p->cost.plan.nOBSat = nOBSat;
      p->cost.plan.u.pIdx = pIdx;
    }

    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;

................................................................................
  pWInfo->pParse = pParse;
  pWInfo->pTabList = pTabList;
  pWInfo->iBreak = sqlite3VdbeMakeLabel(v);
  pWInfo->pWC = sWBI.pWC = (WhereClause *)&((u8 *)pWInfo)[nByteWInfo];
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  pMaskSet = (WhereMaskSet*)&sWBI.pWC[1];
  sWBI.aLevel = pWInfo->a;

  /* Disable the DISTINCT optimization if SQLITE_DistinctOpt is set via
  ** sqlite3_test_ctrl(SQLITE_TESTCTRL_OPTIMIZATIONS,...) */
  if( db->flags & SQLITE_DistinctOpt ) pDistinct = 0;

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.