** virtual table.  The pIdxInfo pointer contains indexing
** information for the i-th table in the FROM clause before reordering.
** All the pIdxInfo pointers are freed by whereInfoFree() in where.c.
** All other information in the i-th WhereLevel object for the i-th table
** after FROM clause ordering.
*/
struct WhereLevel {
  WherePlan plan;       /* query plan for this element of the FROM clause */
  int iLeftJoin;        /* Memory cell used to implement LEFT OUTER JOIN */
  int iTabCur;          /* The VDBE cursor used to access the table */
  int iIdxCur;          /* The VDBE cursor used to access pIdx */
  int addrBrk;          /* Jump here to break out of the loop */
  int addrNxt;          /* Jump here to start the next IN combination */
  int addrCont;         /* Jump here to continue with the next loop cycle */
  int addrFirst;        /* First instruction of interior of the loop */
  u8 iFrom;             /* Which entry in the FROM clause */
  u8 op, p5;            /* Opcode and P5 of the opcode that ends the loop */
  int p1, p2;           /* Operands of the opcode used to ends the loop */
  union {               /* Information that depends on plan.wsFlags */
    struct {
      int nIn;              /* Number of entries in aInLoop[] */
      struct InLoop {
        int iCur;              /* The VDBE cursor used by this IN operator */
        int addrInTop;         /* Top of the IN loop */
        u8 eEndLoopOp;         /* IN Loop terminator. OP_Next or OP_Prev */
      } *aInLoop;           /* Information about each nested IN operator */
    } in;                 /* Used when plan.wsFlags&WHERE_IN_ABLE */
    Index *pCovidx;       /* Possible covering index for WHERE_MULTI_OR */
  } u;
  double rOptCost;      /* "Optimal" cost for this level */
  struct WhereLoop *pWLoop;  /* The selected WhereLoop object */

  /* The following field is really not part of the current level.  But
  ** we need a place to cache virtual table index information for each
  ** virtual table in the FROM clause and the WhereLevel structure is
  ** a convenient place since there is one WhereLevel for each FROM clause
  ** element.
  */
  sqlite3_index_info *pIdxInfo;  /* Index info for n-th source table */
};

/*
** Flags appropriate for the wctrlFlags parameter of sqlite3WhereBegin()
** and the WhereInfo.wctrlFlags member.
*/
#define WHERE_ORDERBY_NORMAL   0x0000 /* No-op */

** virtual table.  The pIdxInfo pointer contains indexing
** information for the i-th table in the FROM clause before reordering.
** All the pIdxInfo pointers are freed by whereInfoFree() in where.c.
** All other information in the i-th WhereLevel object for the i-th table
** after FROM clause ordering.
*/
struct WhereLevel {

  int iLeftJoin;        /* Memory cell used to implement LEFT OUTER JOIN */
  int iTabCur;          /* The VDBE cursor used to access the table */
  int iIdxCur;          /* The VDBE cursor used to access pIdx */
  int addrBrk;          /* Jump here to break out of the loop */
  int addrNxt;          /* Jump here to start the next IN combination */
  int addrCont;         /* Jump here to continue with the next loop cycle */
  int addrFirst;        /* First instruction of interior of the loop */
  u8 iFrom;       /* FIXME: Which entry in the FROM clause */
  u8 op, p5;            /* Opcode and P5 of the opcode that ends the loop */
  int p1, p2;           /* Operands of the opcode used to ends the loop */
  union {               /* Information that depends on plan.wsFlags */
    struct {
      int nIn;              /* Number of entries in aInLoop[] */
      struct InLoop {
        int iCur;              /* The VDBE cursor used by this IN operator */
        int addrInTop;         /* Top of the IN loop */
        u8 eEndLoopOp;         /* IN Loop terminator. OP_Next or OP_Prev */
      } *aInLoop;           /* Information about each nested IN operator */
    } in;                 /* Used when plan.wsFlags&WHERE_IN_ABLE */
    Index *pCovidx;       /* Possible covering index for WHERE_MULTI_OR */
  } u;

  struct WhereLoop *pWLoop;  /* The selected WhereLoop object */








};

/*
** Flags appropriate for the wctrlFlags parameter of sqlite3WhereBegin()
** and the WhereInfo.wctrlFlags member.
*/
#define WHERE_ORDERBY_NORMAL   0x0000 /* No-op */

*/
struct WhereLoop {
  Bitmask prereq;       /* Bitmask of other loops that must run first */
  Bitmask maskSelf;     /* Bitmask identifying table iTab */
#ifdef SQLITE_DEBUG
  char cId;             /* Symbolic ID of this loop for debugging use */
#endif
  u8 iTab;              /* Position in FROM clause of table coded by this loop */
  u8 iSortIdx;          /* Sorting index number.  0==None */
  u16 nTerm;            /* Number of entries in aTerm[] */
  u32 wsFlags;          /* WHERE_* flags describing the plan */
  double rSetup;        /* One-time setup cost (ex: create transient index) */
  double rRun;          /* Cost of running each loop */
  double nOut;          /* Estimated number of output rows */
  union {
................................................................................
** An instance of the WhereScan object is used as an iterator for locating
** terms in the WHERE clause that are useful to the query planner.
*/
struct WhereScan {
  WhereTerm *pCurrent;       /* Most recent match */
  WhereClause *pOrigWC;      /* Original, innermost WhereClause */
  WhereClause *pWC;          /* WhereClause currently being scanned */
  char *zCollName;           /* Must have this collating sequence, if not NULL */
  char idxaff;               /* Must match this affinity, if zCollName!=NULL */
  unsigned char nEquiv;      /* Number of entries in aEquiv[] */
  unsigned char iEquiv;      /* Next unused slot in aEquiv[] */
  u32 opMask;                /* Acceptable operators */
  int k;                     /* Resume scanning at this->pWC->a[this->k] */
  int aEquiv[22];            /* Cursor,Column pairs for equivalence classes */
};
................................................................................
  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 */
};

/*
** Return TRUE if the probe cost is less than the baseline cost
*/
static int compareCost(const WhereCost *pProbe, const WhereCost *pBaseline){
  if( pProbe->rCost<pBaseline->rCost ) return 1;
  if( pProbe->rCost>pBaseline->rCost ) return 0;
  if( pProbe->plan.nOBSat>pBaseline->plan.nOBSat ) return 1;
  if( pProbe->plan.nRow<pBaseline->plan.nRow ) return 1;
  return 0;
}

/*
** Initialize a preallocated WhereClause structure.
*/
static void whereClauseInit(
  WhereClause *pWC,        /* The WhereClause to be initialized */
  Parse *pParse,           /* The parsing context */
  WhereMaskSet *pMaskSet,  /* Mapping from table cursor numbers to bitmasks */
................................................................................
        return i;
      }
    }
  }

  return -1;
}

/*
** This routine determines if pIdx can be used to assist in processing a
** DISTINCT qualifier. In other words, it tests whether or not using this
** index for the outer loop guarantees that rows with equal values for
** all expressions in the pDistinct list are delivered grouped together.
**
** For example, the query 
**
**   SELECT DISTINCT a, b, c FROM tbl WHERE a = ?
**
** can benefit from any index on columns "b" and "c".
*/
static int isDistinctIndex(
  Parse *pParse,                  /* Parsing context */
  WhereClause *pWC,               /* The WHERE clause */
  Index *pIdx,                    /* The index being considered */
  int base,                       /* Cursor number for the table pIdx is on */
  ExprList *pDistinct,            /* The DISTINCT expressions */
  int nEqCol                      /* Number of index columns with == */
){
  Bitmask mask = 0;               /* Mask of unaccounted for pDistinct exprs */
  int i;                          /* Iterator variable */

  assert( pDistinct!=0 );
  if( pIdx->zName==0 || pDistinct->nExpr>=BMS ) return 0;
  testcase( pDistinct->nExpr==BMS-1 );

  /* Loop through all the expressions in the distinct list. If any of them
  ** are not simple column references, return early. Otherwise, test if the
  ** WHERE clause contains a "col=X" clause. If it does, the expression
  ** can be ignored. If it does not, and the column does not belong to the
  ** same table as index pIdx, return early. Finally, if there is no
  ** matching "col=X" expression and the column is on the same table as pIdx,
  ** set the corresponding bit in variable mask.
  */
  for(i=0; i<pDistinct->nExpr; i++){
    WhereTerm *pTerm;
    Expr *p = sqlite3ExprSkipCollate(pDistinct->a[i].pExpr);
    if( p->op!=TK_COLUMN ) return 0;
    pTerm = findTerm(pWC, p->iTable, p->iColumn, ~(Bitmask)0, WO_EQ, 0);
    if( pTerm ){
      Expr *pX = pTerm->pExpr;
      CollSeq *p1 = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);
      CollSeq *p2 = sqlite3ExprCollSeq(pParse, p);
      if( p1==p2 ) continue;
    }
    if( p->iTable!=base ) return 0;
    mask |= (((Bitmask)1) << i);
  }

  for(i=nEqCol; mask && i<pIdx->nColumn; i++){
    int iExpr = findIndexCol(pParse, pDistinct, base, pIdx, i);
    if( iExpr<0 ) break;
    mask &= ~(((Bitmask)1) << iExpr);
  }

  return (mask==0);
}


/*
** Return true if the DISTINCT expression-list passed as the third argument
** is redundant. A DISTINCT list is redundant if the database contains a
** UNIQUE index that guarantees that the result of the query will be distinct
** anyway.
*/
................................................................................
  sqlite3DebugPrintf("  estimatedCost=%g\n", p->estimatedCost);
}
#else
#define TRACE_IDX_INPUTS(A)
#define TRACE_IDX_OUTPUTS(A)
#endif

/* 
** Required because bestIndex() is called by bestOrClauseIndex() 
*/
static void bestIndex(WhereBestIdx*);

/*
** This routine attempts to find an scanning strategy that can be used 
** to optimize an 'OR' expression that is part of a WHERE clause. 
**
** The table associated with FROM clause term pSrc may be either a
** regular B-Tree table or a virtual table.
*/
static void bestOrClauseIndex(WhereBestIdx *p){
#ifndef SQLITE_OMIT_OR_OPTIMIZATION
  WhereClause *pWC = p->pWC;           /* The WHERE clause */
  struct SrcList_item *pSrc = p->pSrc; /* The FROM clause term to search */
  const int iCur = pSrc->iCursor;      /* The cursor of the table  */
  const Bitmask maskSrc = getMask(pWC->pMaskSet, iCur);  /* Bitmask for pSrc */
  WhereTerm * const pWCEnd = &pWC->a[pWC->nTerm];        /* End of pWC->a[] */
  WhereTerm *pTerm;                    /* A single term of the WHERE clause */

  /* The OR-clause optimization is disallowed if the INDEXED BY or
  ** NOT INDEXED clauses are used or if the WHERE_AND_ONLY bit is set. */
  if( pSrc->notIndexed || pSrc->pIndex!=0 ){
    return;
  }
  if( pWC->wctrlFlags & WHERE_AND_ONLY ){
    return;
  }

  /* Search the WHERE clause terms for a usable WO_OR term. */
  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){
    if( (pTerm->eOperator & WO_OR)!=0
     && ((pTerm->prereqAll & ~maskSrc) & p->notReady)==0
     && (pTerm->u.pOrInfo->indexable & maskSrc)!=0 
    ){
      WhereClause * const pOrWC = &pTerm->u.pOrInfo->wc;
      WhereTerm * const pOrWCEnd = &pOrWC->a[pOrWC->nTerm];
      WhereTerm *pOrTerm;
      double rTotal = 0;
      double nRow = 0;
      Bitmask used = 0;
      WhereBestIdx sBOI;

      sBOI = *p;
      sBOI.pOrderBy = 0;
      sBOI.pDistinct = 0;
      sBOI.ppIdxInfo = 0;
      for(pOrTerm=pOrWC->a; pOrTerm<pOrWCEnd; pOrTerm++){
        /*WHERETRACE(("... Multi-index OR testing for term %d of %d....\n", 
          (pOrTerm - pOrWC->a), (pTerm - pWC->a)
        ));*/
        if( (pOrTerm->eOperator& WO_AND)!=0 ){
          sBOI.pWC = &pOrTerm->u.pAndInfo->wc;
          bestIndex(&sBOI);
        }else if( pOrTerm->leftCursor==iCur ){
          WhereClause tempWC;
          tempWC.pParse = pWC->pParse;
          tempWC.pMaskSet = pWC->pMaskSet;
          tempWC.pOuter = pWC;
          tempWC.op = TK_AND;
          tempWC.a = pOrTerm;
          tempWC.wctrlFlags = 0;
          tempWC.nTerm = 1;
          sBOI.pWC = &tempWC;
          bestIndex(&sBOI);
        }else{
          continue;
        }
        rTotal += sBOI.cost.rCost;
        nRow += sBOI.cost.plan.nRow;
        used |= sBOI.cost.used;
        if( rTotal>=p->cost.rCost ) break;
      }

      /* If there is an ORDER BY clause, increase the scan cost to account 
      ** for the cost of the sort. */
      if( p->pOrderBy!=0 ){
        /*WHERETRACE(("... sorting increases OR cost %.9g to %.9g\n",
                    rTotal, rTotal+nRow*estLog(nRow)));*/
        rTotal += nRow*estLog(nRow);
      }

      /* If the cost of scanning using this OR term for optimization is
      ** less than the current cost stored in pCost, replace the contents
      ** of pCost. */
      /*WHERETRACE(("... multi-index OR cost=%.9g nrow=%.9g\n", rTotal, nRow));*/
      if( rTotal<p->cost.rCost ){
        p->cost.rCost = rTotal;
        p->cost.used = used;
        p->cost.plan.nRow = nRow;
        p->cost.plan.nOBSat = p->i ? p->aLevel[p->i-1].plan.nOBSat : 0;
        p->cost.plan.wsFlags = WHERE_MULTI_OR;
        p->cost.plan.u.pTerm = pTerm;
      }
    }
  }
#endif /* SQLITE_OMIT_OR_OPTIMIZATION */
}

#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
/*
** Return TRUE if the WHERE clause term pTerm is of a form where it
** could be used with an index to access pSrc, assuming an appropriate
** index existed.
*/
static int termCanDriveIndex(
................................................................................
  if( pTerm->u.leftColumn<0 ) return 0;
  aff = pSrc->pTab->aCol[pTerm->u.leftColumn].affinity;
  if( !sqlite3IndexAffinityOk(pTerm->pExpr, aff) ) return 0;
  return 1;
}
#endif

#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
/*
** If the query plan for pSrc specified in pCost is a full table scan
** and indexing is allows (if there is no NOT INDEXED clause) and it
** possible to construct a transient index that would perform better
** than a full table scan even when the cost of constructing the index
** is taken into account, then alter the query plan to use the
** transient index.
*/
static void bestAutomaticIndex(WhereBestIdx *p){
  Parse *pParse = p->pParse;            /* The parsing context */
  WhereClause *pWC = p->pWC;            /* The WHERE clause */
  struct SrcList_item *pSrc = p->pSrc;  /* The FROM clause term to search */
  double nTableRow;                     /* Rows in the input table */
  double logN;                          /* log(nTableRow) */
  double costTempIdx;         /* per-query cost of the transient index */
  WhereTerm *pTerm;           /* A single term of the WHERE clause */
  WhereTerm *pWCEnd;          /* End of pWC->a[] */
  Table *pTable;              /* Table tht might be indexed */

  if( pParse->nQueryLoop<=(double)1 ){
    /* There is no point in building an automatic index for a single scan */
    return;
  }
  if( (pParse->db->flags & SQLITE_AutoIndex)==0 ){
    /* Automatic indices are disabled at run-time */
    return;
  }
  if( (p->cost.plan.wsFlags & WHERE_NOT_FULLSCAN)!=0
   && (p->cost.plan.wsFlags & WHERE_COVER_SCAN)==0
  ){
    /* We already have some kind of index in use for this query. */
    return;
  }
  if( pSrc->viaCoroutine ){
    /* Cannot index a co-routine */
    return;
  }
  if( pSrc->notIndexed ){
    /* The NOT INDEXED clause appears in the SQL. */
    return;
  }
  if( pSrc->isCorrelated ){
    /* The source is a correlated sub-query. No point in indexing it. */
    return;
  }

  assert( pParse->nQueryLoop >= (double)1 );
  pTable = pSrc->pTab;
  nTableRow = pTable->nRowEst;
  logN = estLog(nTableRow);
  costTempIdx = 2*logN*(nTableRow/pParse->nQueryLoop + 1);
  if( costTempIdx>=p->cost.rCost ){
    /* The cost of creating the transient table would be greater than
    ** doing the full table scan */
    return;
  }

  /* Search for any equality comparison term */
  pWCEnd = &pWC->a[pWC->nTerm];
  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){
    if( termCanDriveIndex(pTerm, pSrc, p->notReady) ){
      /*WHERETRACE(("auto-index reduces cost from %.1f to %.1f\n",
                    p->cost.rCost, costTempIdx));*/
      p->cost.rCost = costTempIdx;
      p->cost.plan.nRow = logN + 1;
      p->cost.plan.wsFlags = WHERE_TEMP_INDEX;
      p->cost.used = pTerm->prereqRight;
      break;
    }
  }
}
#else
# define bestAutomaticIndex(A)  /* no-op */
#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */


#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
/*
** Generate code to construct the Index object for an automatic index
** and to set up the WhereLevel object pLevel so that the code generator
** makes use of the automatic index.
*/
................................................................................
  KeyInfo *pKeyinfo;          /* Key information for the index */   
  int addrTop;                /* Top of the index fill loop */
  int regRecord;              /* Register holding an index record */
  int n;                      /* Column counter */
  int i;                      /* Loop counter */
  int mxBitCol;               /* Maximum column in pSrc->colUsed */
  CollSeq *pColl;             /* Collating sequence to on a column */

  Bitmask idxCols;            /* Bitmap of columns used for indexing */
  Bitmask extraCols;          /* Bitmap of additional columns */

  /* Generate code to skip over the creation and initialization of the
  ** transient index on 2nd and subsequent iterations of the loop. */
  v = pParse->pVdbe;
  assert( v!=0 );
................................................................................
  addrInit = sqlite3CodeOnce(pParse);

  /* Count the number of columns that will be added to the index
  ** and used to match WHERE clause constraints */
  nColumn = 0;
  pTable = pSrc->pTab;
  pWCEnd = &pWC->a[pWC->nTerm];

  idxCols = 0;
  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){
    if( termCanDriveIndex(pTerm, pSrc, notReady) ){
      int iCol = pTerm->u.leftColumn;
      Bitmask cMask = iCol>=BMS ? ((Bitmask)1)<<(BMS-1) : ((Bitmask)1)<<iCol;
      testcase( iCol==BMS );
      testcase( iCol==BMS-1 );
................................................................................
      if( (idxCols & cMask)==0 ){
        nColumn++;
        idxCols |= cMask;
      }
    }
  }
  assert( nColumn>0 );
  pLevel->plan.nEq = nColumn;

  /* Count the number of additional columns needed to create a
  ** covering index.  A "covering index" is an index that contains all
  ** columns that are needed by the query.  With a covering index, the
  ** original table never needs to be accessed.  Automatic indices must
  ** be a covering index because the index will not be updated if the
  ** original table changes and the index and table cannot both be used
................................................................................
  testcase( pTable->nCol==BMS-2 );
  for(i=0; i<mxBitCol; i++){
    if( extraCols & (((Bitmask)1)<<i) ) nColumn++;
  }
  if( pSrc->colUsed & (((Bitmask)1)<<(BMS-1)) ){
    nColumn += pTable->nCol - BMS + 1;
  }
  pLevel->plan.wsFlags |= WHERE_COLUMN_EQ | WHERE_IDX_ONLY;

  /* Construct the Index object to describe this index */
  nByte = sizeof(Index);
  nByte += nColumn*sizeof(int);     /* Index.aiColumn */
  nByte += nColumn*sizeof(char*);   /* Index.azColl */
  nByte += nColumn;                 /* Index.aSortOrder */
  pIdx = sqlite3DbMallocZero(pParse->db, nByte);
  if( pIdx==0 ) return;
  pLevel->plan.u.pIdx = pIdx;
  pIdx->azColl = (char**)&pIdx[1];
  pIdx->aiColumn = (int*)&pIdx->azColl[nColumn];
  pIdx->aSortOrder = (u8*)&pIdx->aiColumn[nColumn];
  pIdx->zName = "auto-index";
  pIdx->nColumn = nColumn;
  pIdx->pTable = pTable;
  n = 0;
................................................................................
        pIdx->aiColumn[n] = pTerm->u.leftColumn;
        pColl = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);
        pIdx->azColl[n] = ALWAYS(pColl) ? pColl->zName : "BINARY";
        n++;
      }
    }
  }
  assert( (u32)n==pLevel->plan.nEq );

  /* Add additional columns needed to make the automatic index into
  ** a covering index */
  for(i=0; i<mxBitCol; i++){
    if( extraCols & (((Bitmask)1)<<i) ){
      pIdx->aiColumn[n] = i;
      pIdx->azColl[n] = "BINARY";
................................................................................
      sqlite3ErrorMsg(pParse, 
          "table %s: xBestIndex returned an invalid plan", pTab->zName);
    }
  }

  return pParse->nErr;
}



/*
** Compute the best index for a virtual table.
**
** The best index is computed by the xBestIndex method of the virtual
** table module.  This routine is really just a wrapper that sets up
** the sqlite3_index_info structure that is used to communicate with
** xBestIndex.
**
** In a join, this routine might be called multiple times for the
** same virtual table.  The sqlite3_index_info structure is created
** and initialized on the first invocation and reused on all subsequent
** invocations.  The sqlite3_index_info structure is also used when
** code is generated to access the virtual table.  The whereInfoDelete() 
** routine takes care of freeing the sqlite3_index_info structure after
** everybody has finished with it.
*/
static void bestVirtualIndex(WhereBestIdx *p){
  Parse *pParse = p->pParse;      /* The parsing context */
  WhereClause *pWC = p->pWC;      /* The WHERE clause */
  struct SrcList_item *pSrc = p->pSrc; /* The FROM clause term to search */
  Table *pTab = pSrc->pTab;
  sqlite3_index_info *pIdxInfo;
  struct sqlite3_index_constraint *pIdxCons;
  struct sqlite3_index_constraint_usage *pUsage;
  WhereTerm *pTerm;
  int i, j;
  int nOrderBy;
  int bAllowIN;                   /* Allow IN optimizations */
  double rCost;

  /* Make sure wsFlags is initialized to some sane value. Otherwise, if the 
  ** malloc in allocateIndexInfo() fails and this function returns leaving
  ** wsFlags in an uninitialized state, the caller may behave unpredictably.
  */
  memset(&p->cost, 0, sizeof(p->cost));
  p->cost.plan.wsFlags = WHERE_VIRTUALTABLE;

  /* If the sqlite3_index_info structure has not been previously
  ** allocated and initialized, then allocate and initialize it now.
  */
  pIdxInfo = *p->ppIdxInfo;
  if( pIdxInfo==0 ){
    *p->ppIdxInfo = pIdxInfo = allocateIndexInfo(pParse,pWC,pSrc,p->pOrderBy);
  }
  if( pIdxInfo==0 ){
    return;
  }

  /* At this point, the sqlite3_index_info structure that pIdxInfo points
  ** to will have been initialized, either during the current invocation or
  ** during some prior invocation.  Now we just have to customize the
  ** details of pIdxInfo for the current invocation and pass it to
  ** xBestIndex.
  */

  /* The module name must be defined. Also, by this point there must
  ** be a pointer to an sqlite3_vtab structure. Otherwise
  ** sqlite3ViewGetColumnNames() would have picked up the error. 
  */
  assert( pTab->azModuleArg && pTab->azModuleArg[0] );
  assert( sqlite3GetVTable(pParse->db, pTab) );

  /* Try once or twice.  On the first attempt, allow IN optimizations.
  ** If an IN optimization is accepted by the virtual table xBestIndex
  ** method, but the  pInfo->aConstrainUsage.omit flag is not set, then
  ** the query will not work because it might allow duplicate rows in
  ** output.  In that case, run the xBestIndex method a second time
  ** without the IN constraints.  Usually this loop only runs once.
  ** The loop will exit using a "break" statement.
  */
  for(bAllowIN=1; 1; bAllowIN--){
    assert( bAllowIN==0 || bAllowIN==1 );

    /* Set the aConstraint[].usable fields and initialize all 
    ** output variables to zero.
    **
    ** aConstraint[].usable is true for constraints where the right-hand
    ** side contains only references to tables to the left of the current
    ** table.  In other words, if the constraint is of the form:
    **
    **           column = expr
    **
    ** and we are evaluating a join, then the constraint on column is 
    ** only valid if all tables referenced in expr occur to the left
    ** of the table containing column.
    **
    ** The aConstraints[] array contains entries for all constraints
    ** on the current table.  That way we only have to compute it once
    ** even though we might try to pick the best index multiple times.
    ** For each attempt at picking an index, the order of tables in the
    ** join might be different so we have to recompute the usable flag
    ** each time.
    */
    pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;
    pUsage = pIdxInfo->aConstraintUsage;
    for(i=0; i<pIdxInfo->nConstraint; i++, pIdxCons++){
      j = pIdxCons->iTermOffset;
      pTerm = &pWC->a[j];
      if( (pTerm->prereqRight&p->notReady)==0
       && (bAllowIN || (pTerm->eOperator & WO_IN)==0)
      ){
        pIdxCons->usable = 1;
      }else{
        pIdxCons->usable = 0;
      }
    }
    memset(pUsage, 0, sizeof(pUsage[0])*pIdxInfo->nConstraint);
    if( pIdxInfo->needToFreeIdxStr ){
      sqlite3_free(pIdxInfo->idxStr);
    }
    pIdxInfo->idxStr = 0;
    pIdxInfo->idxNum = 0;
    pIdxInfo->needToFreeIdxStr = 0;
    pIdxInfo->orderByConsumed = 0;
    /* ((double)2) In case of SQLITE_OMIT_FLOATING_POINT... */
    pIdxInfo->estimatedCost = SQLITE_BIG_DBL / ((double)2);
    nOrderBy = pIdxInfo->nOrderBy;
    if( !p->pOrderBy ){
      pIdxInfo->nOrderBy = 0;
    }
  
    if( vtabBestIndex(pParse, pTab, pIdxInfo) ){
      return;
    }
  
    pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;
    for(i=0; i<pIdxInfo->nConstraint; i++, pIdxCons++){
      if( pUsage[i].argvIndex>0 ){
        j = pIdxCons->iTermOffset;
        pTerm = &pWC->a[j];
        p->cost.used |= pTerm->prereqRight;
        if( (pTerm->eOperator & WO_IN)!=0 ){
          if( pUsage[i].omit==0 ){
            /* Do not attempt to use an IN constraint if the virtual table
            ** says that the equivalent EQ constraint cannot be safely omitted.
            ** If we do attempt to use such a constraint, some rows might be
            ** repeated in the output. */
            break;
          }
          /* A virtual table that is constrained by an IN clause may not
          ** consume the ORDER BY clause because (1) the order of IN terms
          ** is not necessarily related to the order of output terms and
          ** (2) Multiple outputs from a single IN value will not merge
          ** together.  */
          pIdxInfo->orderByConsumed = 0;
        }
      }
    }
    if( i>=pIdxInfo->nConstraint ) break;
  }

  /* The orderByConsumed signal is only valid if all outer loops collectively
  ** generate just a single row of output.
  */
  if( pIdxInfo->orderByConsumed ){
    for(i=0; i<p->i; i++){
      if( (p->aLevel[i].plan.wsFlags & WHERE_UNIQUE)==0 ){
        pIdxInfo->orderByConsumed = 0;
      }
    }
  }
  
  /* If there is an ORDER BY clause, and the selected virtual table index
  ** does not satisfy it, increase the cost of the scan accordingly. This
  ** matches the processing for non-virtual tables in bestBtreeIndex().
  */
  rCost = pIdxInfo->estimatedCost;
  if( p->pOrderBy && pIdxInfo->orderByConsumed==0 ){
    rCost += estLog(rCost)*rCost;
  }

  /* The cost is not allowed to be larger than SQLITE_BIG_DBL (the
  ** inital value of lowestCost in this loop. If it is, then the
  ** (cost<lowestCost) test below will never be true.
  ** 
  ** Use "(double)2" instead of "2.0" in case OMIT_FLOATING_POINT 
  ** is defined.
  */
  if( (SQLITE_BIG_DBL/((double)2))<rCost ){
    p->cost.rCost = (SQLITE_BIG_DBL/((double)2));
  }else{
    p->cost.rCost = rCost;
  }
  p->cost.plan.u.pVtabIdx = pIdxInfo;
  if( pIdxInfo->orderByConsumed ){
    p->cost.plan.wsFlags |= WHERE_ORDERED;
    p->cost.plan.nOBSat = nOrderBy;
  }else{
    p->cost.plan.nOBSat = p->i ? p->aLevel[p->i-1].plan.nOBSat : 0;
  }
  p->cost.plan.nEq = 0;
  pIdxInfo->nOrderBy = nOrderBy;

  /* Try to find a more efficient access pattern by using multiple indexes
  ** to optimize an OR expression within the WHERE clause. 
  */
  bestOrClauseIndex(p);
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the location of a particular key among all keys in an
** index.  Store the results in aStat as follows:
**
**    aStat[0]      Est. number of rows less than pVal
................................................................................
    *pnRow = nRowEst;
    /*WHERETRACE(("IN row estimate: est=%g\n", nRowEst));*/
  }
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT3) */

/*
** Check to see if column iCol of the table with cursor iTab will appear
** in sorted order according to the current query plan.
**
** Return values:
**
**    0   iCol is not ordered
**    1   iCol has only a single value
**    2   iCol is in ASC order
**    3   iCol is in DESC order
*/
static int isOrderedColumn(
  WhereBestIdx *p,
  int iTab,
  int iCol
){
  int i, j;
  WhereLevel *pLevel = &p->aLevel[p->i-1];
  Index *pIdx;
  u8 sortOrder;
  for(i=p->i-1; i>=0; i--, pLevel--){
    if( pLevel->iTabCur!=iTab ) continue;
    if( (pLevel->plan.wsFlags & WHERE_ALL_UNIQUE)!=0 ){
      return 1;
    }
    assert( (pLevel->plan.wsFlags & WHERE_ORDERED)!=0 );
    if( (pIdx = pLevel->plan.u.pIdx)!=0 ){
      if( iCol<0 ){
        sortOrder = 0;
        testcase( (pLevel->plan.wsFlags & WHERE_REVERSE)!=0 );
      }else{
        int n = pIdx->nColumn;
        for(j=0; j<n; j++){
          if( iCol==pIdx->aiColumn[j] ) break;
        }
        if( j>=n ) return 0;
        sortOrder = pIdx->aSortOrder[j];
        testcase( (pLevel->plan.wsFlags & WHERE_REVERSE)!=0 );
      }
    }else{
      if( iCol!=(-1) ) return 0;
      sortOrder = 0;
      testcase( (pLevel->plan.wsFlags & WHERE_REVERSE)!=0 );
    }
    if( (pLevel->plan.wsFlags & WHERE_REVERSE)!=0 ){
      assert( sortOrder==0 || sortOrder==1 );
      testcase( sortOrder==1 );
      sortOrder = 1 - sortOrder;
    }
    return sortOrder+2;
  }
  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.
**
** 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 *pbRev,         /* Set to 1 for reverse-order scan of pIdx */
  int *pbObUnique     /* ORDER BY column values will different in every row */
){
  int i;                        /* Number of pIdx terms used */
  int j;                        /* Number of ORDER BY terms satisfied */
  int sortOrder = 2;            /* 0: forward.  1: backward.  2: unknown */
  int nTerm;                    /* Number of ORDER BY terms */
  struct ExprList_item *pOBItem;/* A term of the ORDER BY clause */
  Table *pTab = pIdx->pTable;   /* Table that owns index pIdx */
  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 */
  int uniqueNotNull;            /* pIdx is UNIQUE with all terms are NOT NULL */
  int outerObUnique;            /* Outer loops generate different values in
                                ** every row for the ORDER BY columns */

  if( p->i==0 ){
    nPriorSat = 0;
    outerObUnique = 1;
  }else{
    u32 wsFlags = p->aLevel[p->i-1].plan.wsFlags;
    nPriorSat = p->aLevel[p->i-1].plan.nOBSat;
    if( (wsFlags & WHERE_ORDERED)==0 ){
      /* This loop cannot be ordered unless the next outer loop is
      ** also ordered */
      return nPriorSat;
    }
    if( OptimizationDisabled(db, SQLITE_OrderByIdxJoin) ){
      /* Only look at the outer-most loop if the OrderByIdxJoin
      ** optimization is disabled */
      return nPriorSat;
    }
    testcase( wsFlags & WHERE_OB_UNIQUE );
    testcase( wsFlags & WHERE_ALL_UNIQUE );
    outerObUnique = (wsFlags & (WHERE_OB_UNIQUE|WHERE_ALL_UNIQUE))!=0;
  }
  pOrderBy = p->pOrderBy;
  assert( pOrderBy!=0 );
  if( pIdx->bUnordered ){
    /* Hash indices (indicated by the "unordered" tag on sqlite_stat1) cannot
    ** be used for sorting */
    return nPriorSat;
  }
  nTerm = pOrderBy->nExpr;
  uniqueNotNull = pIdx->onError!=OE_None;
  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) );

  /* Match terms of the ORDER BY clause against columns of
  ** 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.
  */
  j = nPriorSat;
  for(i=0,pOBItem=&pOrderBy->a[j]; j<nTerm && i<=pIdx->nColumn; i++){
    Expr *pOBExpr;          /* The expression of the ORDER BY pOBItem */
    CollSeq *pColl;         /* The collating sequence of pOBExpr */
    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 */
    int isEq;               /* Subject to an == or IS NULL constraint */
    int isMatch;            /* ORDER BY term matches the index term */
    const char *zColl;      /* Name of collating sequence for i-th index term */
    WhereTerm *pConstraint; /* A constraint in the WHERE clause */

    /* If the next term of the ORDER BY clause refers to anything other than
    ** a column in the "base" table, then this index will not be of any
    ** further use in handling the ORDER BY. */
    pOBExpr = sqlite3ExprSkipCollate(pOBItem->pExpr);
    if( pOBExpr->op!=TK_COLUMN || pOBExpr->iTable!=base ){
      break;
    }

    /* Find column number and collating sequence for the next entry
    ** in the index */
    if( pIdx->zName && i<pIdx->nColumn ){
      iColumn = pIdx->aiColumn[i];
      if( iColumn==pIdx->pTable->iPKey ){
        iColumn = -1;
      }
      iSortOrder = pIdx->aSortOrder[i];
      zColl = pIdx->azColl[i];
      assert( zColl!=0 );
    }else{
      iColumn = -1;
      iSortOrder = 0;
      zColl = 0;
    }

    /* Check to see if the column number and collating sequence of the
    ** index match the column number and collating sequence of the ORDER BY
    ** clause entry.  Set isMatch to 1 if they both match. */
    if( pOBExpr->iColumn==iColumn ){
      if( zColl ){
        pColl = sqlite3ExprCollSeq(pParse, pOBItem->pExpr);
        if( !pColl ) pColl = db->pDfltColl;
        isMatch = sqlite3StrICmp(pColl->zName, zColl)==0;
      }else{
        isMatch = 1;
      }
    }else{
      isMatch = 0;
    }

    /* termSortOrder is 0 or 1 for whether or not the access loop should
    ** run forward or backwards (respectively) in order to satisfy this 
    ** term of the ORDER BY clause. */
    assert( pOBItem->sortOrder==0 || pOBItem->sortOrder==1 );
    assert( iSortOrder==0 || iSortOrder==1 );
    termSortOrder = iSortOrder ^ pOBItem->sortOrder;

    /* If X is the column in the index and ORDER BY clause, check to see
    ** if there are any X= or X IS NULL constraints in the WHERE clause. */
    pConstraint = findTerm(p->pWC, base, iColumn, p->notReady,
                           WO_EQ|WO_ISNULL|WO_IN, pIdx);
    if( pConstraint==0 ){
      isEq = 0;
    }else if( (pConstraint->eOperator & WO_IN)!=0 ){
      isEq = 0;
    }else if( (pConstraint->eOperator & WO_ISNULL)!=0 ){
      uniqueNotNull = 0;
      isEq = 1;  /* "X IS NULL" means X has only a single value */
    }else if( pConstraint->prereqRight==0 ){
      isEq = 1;  /* Constraint "X=constant" means X has only a single value */
    }else{
      Expr *pRight = pConstraint->pExpr->pRight;
      if( pRight->op==TK_COLUMN ){
        /*WHERETRACE(("       .. isOrderedColumn(tab=%d,col=%d)",
                    pRight->iTable, pRight->iColumn));*/
        isEq = isOrderedColumn(p, pRight->iTable, pRight->iColumn);
        /*WHERETRACE((" -> isEq=%d\n", isEq));*/

        /* If the constraint is of the form X=Y where Y is an ordered value
        ** in an outer loop, then make sure the sort order of Y matches the
        ** sort order required for X. */
        if( isMatch && isEq>=2 && isEq!=pOBItem->sortOrder+2 ){
          testcase( isEq==2 );
          testcase( isEq==3 );
          break;
        }
      }else{
        isEq = 0;  /* "X=expr" places no ordering constraints on X */
      }
    }
    if( !isMatch ){
      if( isEq==0 ){
        break;
      }else{
        continue;
      }
    }else if( isEq!=1 ){
      if( sortOrder==2 ){
        sortOrder = termSortOrder;
      }else if( termSortOrder!=sortOrder ){
        break;
      }
    }
    j++;
    pOBItem++;
    if( iColumn<0 ){
      seenRowid = 1;
      break;
    }else if( pTab->aCol[iColumn].notNull==0 && isEq!=1 ){
      testcase( isEq==0 );
      testcase( isEq==2 );
      testcase( isEq==3 );
      uniqueNotNull = 0;
    }
  }
  if( seenRowid ){
    uniqueNotNull = 1;
  }else if( uniqueNotNull==0 || i<pIdx->nColumn ){
    uniqueNotNull = 0;
  }

  /* If we have not found at least one ORDER BY term that matches the
  ** index, then show no progress. */
  if( pOBItem==&pOrderBy->a[nPriorSat] ) return nPriorSat;

  /* Either the outer queries must generate rows where there are no two
  ** rows with the same values in all ORDER BY columns, or else this
  ** loop must generate just a single row of output.  Example:  Suppose
  ** the outer loops generate A=1 and A=1, and this loop generates B=3
  ** and B=4.  Then without the following test, ORDER BY A,B would 
  ** generate the wrong order output: 1,3 1,4 1,3 1,4
  */
  if( outerObUnique==0 && uniqueNotNull==0 ) return nPriorSat;
  *pbObUnique = uniqueNotNull;

  /* Return the necessary scan order back to the caller */
  *pbRev = sortOrder & 1;

  /* 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( uniqueNotNull ){
    /* 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;
}

/*
** 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.
** Factors that influence cost include:
**
**    *  The estimated number of rows that will be retrieved.  (The
**       fewer the better.)
**
**    *  Whether or not sorting must occur.
**
**    *  Whether or not there must be separate lookups in the
**       index and in the main table.
**
** If there was an INDEXED BY clause (pSrc->pIndex) attached to the table in
** the SQL statement, then this function only considers plans using the 
** named index. If no such plan is found, then the returned cost is
** SQLITE_BIG_DBL. If a plan is found that uses the named index, 
** then the cost is calculated in the usual way.
**
** If a NOT INDEXED clause was attached to the table 
** in the SELECT statement, then no indexes are considered. However, the 
** selected plan may still take advantage of the built-in rowid primary key
** index.
*/
static void bestBtreeIndex(WhereBestIdx *p){
  Parse *pParse = p->pParse;  /* The parsing context */
  WhereClause *pWC = p->pWC;  /* The WHERE clause */
  struct SrcList_item *pSrc = p->pSrc; /* The FROM clause term to search */
  int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  Index *pProbe;              /* An index we are evaluating */
  Index *pIdx;                /* Copy of pProbe, or zero for IPK index */
  int eqTermMask;             /* Current mask of valid equality operators */
  int idxEqTermMask;          /* Index mask of valid equality operators */
  Index sPk;                  /* A fake index object for the primary key */
  tRowcnt aiRowEstPk[2];      /* The aiRowEst[] value for the sPk index */
  int aiColumnPk = -1;        /* The aColumn[] value for the sPk index */
  int wsFlagMask;             /* Allowed flags in p->cost.plan.wsFlag */
  int nPriorSat;              /* ORDER BY terms satisfied by outer loops */
  int nOrderBy;               /* Number of ORDER BY terms */
  char bSortInit;             /* Initializer for bSort in inner loop */
  char bDistInit;             /* Initializer for bDist in inner loop */


  /* Initialize the cost to a worst-case value */
  memset(&p->cost, 0, sizeof(p->cost));
  p->cost.rCost = SQLITE_BIG_DBL;

  /* If the pSrc table is the right table of a LEFT JOIN then we may not
  ** use an index to satisfy IS NULL constraints on that table.  This is
  ** because columns might end up being NULL if the table does not match -
  ** a circumstance which the index cannot help us discover.  Ticket #2177.
  */
  if( pSrc->jointype & JT_LEFT ){
    idxEqTermMask = WO_EQ|WO_IN;
  }else{
    idxEqTermMask = WO_EQ|WO_IN|WO_ISNULL;
  }

  if( pSrc->pIndex ){
    /* An INDEXED BY clause specifies a particular index to use */
    pIdx = pProbe = pSrc->pIndex;
    wsFlagMask = ~(WHERE_ROWID_EQ|WHERE_ROWID_RANGE);
    eqTermMask = idxEqTermMask;
  }else{
    /* There is no INDEXED BY clause.  Create a fake Index object in local
    ** variable sPk to represent the rowid primary key index.  Make this
    ** fake index the first in a chain of Index objects with all of the real
    ** indices to follow */
    Index *pFirst;                  /* First of real indices on the table */
    memset(&sPk, 0, sizeof(Index));
    sPk.nColumn = 1;
    sPk.aiColumn = &aiColumnPk;
    sPk.aiRowEst = aiRowEstPk;
    sPk.onError = OE_Replace;
    sPk.pTable = pSrc->pTab;
    aiRowEstPk[0] = pSrc->pTab->nRowEst;
    aiRowEstPk[1] = 1;
    pFirst = pSrc->pTab->pIndex;
    if( pSrc->notIndexed==0 ){
      /* The real indices of the table are only considered if the
      ** NOT INDEXED qualifier is omitted from the FROM clause */
      sPk.pNext = pFirst;
    }
    pProbe = &sPk;
    wsFlagMask = ~(
        WHERE_COLUMN_IN|WHERE_COLUMN_EQ|WHERE_COLUMN_NULL|WHERE_COLUMN_RANGE
    );
    eqTermMask = WO_EQ|WO_IN;
    pIdx = 0;
  }

  nOrderBy = p->pOrderBy ? p->pOrderBy->nExpr : 0;
  if( p->i ){
    nPriorSat = p->aLevel[p->i-1].plan.nOBSat;
    bSortInit = nPriorSat<nOrderBy;
    bDistInit = 0;
  }else{
    nPriorSat = 0;
    bSortInit = nOrderBy>0;
    bDistInit = p->pDistinct!=0;
  }

  /* Loop over all indices looking for the best one to use
  */
  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const tRowcnt * const aiRowEst = pProbe->aiRowEst;
    WhereCost pc;               /* Cost of using pProbe */
    double log10N = (double)1;  /* base-10 logarithm of nRow (inexact) */

    /* 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.
    **
    **  pc.plan.nEq: 
    **    Number of equality terms that can be implemented using the index.
    **    In other words, the number of initial fields in the index that
    **    are used in == or IN or NOT NULL constraints of the WHERE clause.
    **
    **  nInMul:  
    **    The "in-multiplier". This is an estimate of how many seek operations 
    **    SQLite must perform on the index in question. For example, if the 
    **    WHERE clause is:
    **
    **      WHERE a IN (1, 2, 3) AND b IN (4, 5, 6)
    **
    **    SQLite must perform 9 lookups on an index on (a, b), so nInMul is 
    **    set to 9. Given the same schema and either of the following WHERE 
    **    clauses:
    **
    **      WHERE a =  1
    **      WHERE a >= 2
    **
    **    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:
    **    An estimate of a divisor by which to reduce the search space due
    **    to inequality constraints.  In the absence of sqlite_stat3 ANALYZE
    **    data, a single inequality reduces the search space to 1/4rd its
    **    original size (rangeDiv==4).  Two inequalities reduce the search
    **    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).
    **
    **  bDist:
    **    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).
    **    For example, given the index on (a, b), the second of the following 
    **    two queries requires table b-tree lookups in order to find the value
    **    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 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 */
    char bSort = bSortInit;       /* True if external sort required */
    char bDist = bDistInit;       /* True if index cannot help with DISTINCT */
    char 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

    /*WHERETRACE((
      "   %s(%s):\n",
      pSrc->pTab->zName, (pIdx ? pIdx->zName : "ipk")
    ));*/
    memset(&pc, 0, sizeof(pc));
    pc.plan.nOBSat = nPriorSat;

    /* Determine the values of pc.plan.nEq and nInMul */
    for(pc.plan.nEq=0; pc.plan.nEq<pProbe->nColumn; pc.plan.nEq++){
      int j = pProbe->aiColumn[pc.plan.nEq];
      pTerm = findTerm(pWC, iCur, j, p->notReady, eqTermMask, pIdx);
      if( pTerm==0 ) break;
      pc.plan.wsFlags |= (WHERE_COLUMN_EQ|WHERE_ROWID_EQ);
      testcase( pTerm->pWC!=pWC );
      if( pTerm->eOperator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
        pc.plan.wsFlags |= WHERE_COLUMN_IN;
        if( ExprHasProperty(pExpr, EP_xIsSelect) ){
          /* "x IN (SELECT ...)":  Assume the SELECT returns 25 rows */
          nInMul *= 25;
          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 ){
        pc.plan.wsFlags |= WHERE_COLUMN_NULL;
      }
#ifdef SQLITE_ENABLE_STAT3
      if( pc.plan.nEq==0 && pProbe->aSample ) pFirstTerm = pTerm;
#endif
      pc.used |= pTerm->prereqRight;
    }
 
    /* If the index being considered is UNIQUE, and there is an equality 
    ** constraint for all columns in the index, then this search will find
    ** at most a single row. In this case set the WHERE_UNIQUE flag to 
    ** indicate this to the caller.
    **
    ** Otherwise, if the search may find more than one row, test to see if
    ** there is a range constraint on indexed column (pc.plan.nEq+1) that
    ** can be optimized using the index. 
    */
    if( pc.plan.nEq==pProbe->nColumn && pProbe->onError!=OE_None ){
      testcase( pc.plan.wsFlags & WHERE_COLUMN_IN );
      testcase( pc.plan.wsFlags & WHERE_COLUMN_NULL );
      if( (pc.plan.wsFlags & (WHERE_COLUMN_IN|WHERE_COLUMN_NULL))==0 ){
        pc.plan.wsFlags |= WHERE_UNIQUE;
        if( p->i==0 || (p->aLevel[p->i-1].plan.wsFlags & WHERE_ALL_UNIQUE)!=0 ){
          pc.plan.wsFlags |= WHERE_ALL_UNIQUE;
        }
      }
    }else if( pProbe->bUnordered==0 ){
      int j;
      j = (pc.plan.nEq==pProbe->nColumn ? -1 : pProbe->aiColumn[pc.plan.nEq]);
      if( findTerm(pWC, iCur, j, p->notReady, WO_LT|WO_LE|WO_GT|WO_GE, pIdx) ){
        WhereTerm *pTop, *pBtm;
        pTop = findTerm(pWC, iCur, j, p->notReady, WO_LT|WO_LE, pIdx);
        pBtm = findTerm(pWC, iCur, j, p->notReady, WO_GT|WO_GE, pIdx);
        whereRangeScanEst(pParse, pProbe, pc.plan.nEq, pBtm, pTop, &rangeDiv);
        if( pTop ){
          nBound = 1;
          pc.plan.wsFlags |= WHERE_TOP_LIMIT;
          pc.used |= pTop->prereqRight;
          testcase( pTop->pWC!=pWC );
        }
        if( pBtm ){
          nBound++;
          pc.plan.wsFlags |= WHERE_BTM_LIMIT;
          pc.used |= pBtm->prereqRight;
          testcase( pBtm->pWC!=pWC );
        }
        pc.plan.wsFlags |= (WHERE_COLUMN_RANGE|WHERE_ROWID_RANGE);
      }
    }

    /* 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 pc.plan.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 && (pSrc->jointype & JT_LEFT)==0 ){
      int bRev = 2;
      int bObUnique = 0;
      /*WHERETRACE(("      --> before isSortIndex: nPriorSat=%d\n",nPriorSat));*/
      pc.plan.nOBSat = isSortingIndex(p, pProbe, iCur, &bRev, &bObUnique);
      /*WHERETRACE(("      --> after  isSortIndex: bRev=%d bObU=%d nOBSat=%d\n",
                  bRev, bObUnique, pc.plan.nOBSat));*/
      if( nPriorSat<pc.plan.nOBSat || (pc.plan.wsFlags & WHERE_ALL_UNIQUE)!=0 ){
        pc.plan.wsFlags |= WHERE_ORDERED;
        if( bObUnique ) pc.plan.wsFlags |= WHERE_OB_UNIQUE;
      }
      if( nOrderBy==pc.plan.nOBSat ){
        bSort = 0;
        pc.plan.wsFlags |= WHERE_ROWID_RANGE|WHERE_COLUMN_RANGE;
      }
      if( bRev & 1 ) pc.plan.wsFlags |= WHERE_REVERSE;
    }

    /* 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 pc.plan.wsFlags. */
    if( bDist
     && isDistinctIndex(pParse, pWC, pProbe, iCur, p->pDistinct, pc.plan.nEq)
     && (pc.plan.wsFlags & WHERE_COLUMN_IN)==0
    ){
      bDist = 0;
      pc.plan.wsFlags |= WHERE_ROWID_RANGE|WHERE_COLUMN_RANGE|WHERE_DISTINCT;
    }

    /* If currently calculating the cost of using an index (not the IPK
    ** index), determine if all required column data may be obtained without 
    ** using the main table (i.e. if the index is a covering
    ** index for this query). If it is, set the WHERE_IDX_ONLY flag in
    ** pc.plan.wsFlags. Otherwise, set the bLookup variable to true.  */
    if( pIdx ){
      Bitmask m = pSrc->colUsed;
      int j;
      for(j=0; j<pIdx->nColumn; j++){
        int x = pIdx->aiColumn[j];
        if( x<BMS-1 ){
          m &= ~(((Bitmask)1)<<x);
        }
      }
      if( m==0 ){
        pc.plan.wsFlags |= WHERE_IDX_ONLY;
      }else{
        bLookup = 1;
      }
    }

    /*
    ** Estimate the number of rows of output.  For an "x IN (SELECT...)"
    ** constraint, do not let the estimate exceed half the rows in the table.
    */
    pc.plan.nRow = (double)(aiRowEst[pc.plan.nEq] * nInMul);
    if( bInEst && pc.plan.nRow*2>aiRowEst[0] ){
      pc.plan.nRow = aiRowEst[0]/2;
      nInMul = (int)(pc.plan.nRow / aiRowEst[pc.plan.nEq]);
    }

#ifdef SQLITE_ENABLE_STAT3
    /* If the constraint is of the form x=VALUE or x IN (E1,E2,...)
    ** and we do not think that values of x are unique and if histogram
    ** data is available for column x, then it might be possible
    ** to get a better estimate on the number of rows based on
    ** VALUE and how common that value is according to the histogram.
    */
    if( pc.plan.nRow>(double)1 && pc.plan.nEq==1
     && pFirstTerm!=0 && aiRowEst[1]>1 ){
      assert( (pFirstTerm->eOperator & (WO_EQ|WO_ISNULL|WO_IN))!=0 );
      if( pFirstTerm->eOperator & (WO_EQ|WO_ISNULL) ){
        testcase( pFirstTerm->eOperator & WO_EQ );
        testcase( pFirstTerm->eOperator & WO_EQUIV );
        testcase( pFirstTerm->eOperator & WO_ISNULL );
        whereEqualScanEst(pParse, pProbe, pFirstTerm->pExpr->pRight,
                          &pc.plan.nRow);
      }else if( bInEst==0 ){
        assert( pFirstTerm->eOperator & WO_IN );
        whereInScanEst(pParse, pProbe, pFirstTerm->pExpr->x.pList,
                       &pc.plan.nRow);
      }
    }
#endif /* SQLITE_ENABLE_STAT3 */

    /* Adjust the number of output rows and downward to reflect rows
    ** that are excluded by range constraints.
    */
    pc.plan.nRow = pc.plan.nRow/rangeDiv;
    if( pc.plan.nRow<1 ) pc.plan.nRow = 1;

    /* Experiments run on real SQLite databases show that the time needed
    ** to do a binary search to locate a row in a table or index is roughly
    ** log10(N) times the time to move from one row to the next row within
    ** a table or index.  The actual times can vary, with the size of
    ** records being an important factor.  Both moves and searches are
    ** slower with larger records, presumably because fewer records fit
    ** on one page and hence more pages have to be fetched.
    **
    ** The ANALYZE command and the sqlite_stat1 and sqlite_stat3 tables do
    ** not give us data on the relative sizes of table and index records.
    ** So this computation assumes table records are about twice as big
    ** as index records
    */
    if( (pc.plan.wsFlags&~(WHERE_REVERSE|WHERE_ORDERED|WHERE_OB_UNIQUE))
                                                              ==WHERE_IDX_ONLY
     && (pWC->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
     && sqlite3GlobalConfig.bUseCis
     && OptimizationEnabled(pParse->db, SQLITE_CoverIdxScan)
    ){
      /* This index is not useful for indexing, but it is a covering index.
      ** A full-scan of the index might be a little faster than a full-scan
      ** of the table, so give this case a cost slightly less than a table
      ** scan. */
      pc.rCost = aiRowEst[0]*3 + pProbe->nColumn;
      pc.plan.wsFlags |= WHERE_COVER_SCAN|WHERE_COLUMN_RANGE;
    }else if( (pc.plan.wsFlags & WHERE_NOT_FULLSCAN)==0 ){
      /* The cost of a full table scan is a number of move operations equal
      ** to the number of rows in the table.
      **
      ** We add an additional 4x penalty to full table scans.  This causes
      ** the cost function to err on the side of choosing an index over
      ** choosing a full scan.  This 4x full-scan penalty is an arguable
      ** decision and one which we expect to revisit in the future.  But
      ** it seems to be working well enough at the moment.
      */
      pc.rCost = aiRowEst[0]*4;
      pc.plan.wsFlags &= ~WHERE_IDX_ONLY;
      if( pIdx ){
        pc.plan.wsFlags &= ~WHERE_ORDERED;
        pc.plan.nOBSat = nPriorSat;
      }
    }else{
      log10N = estLog(aiRowEst[0]);
      pc.rCost = pc.plan.nRow;
      if( pIdx ){
        if( bLookup ){
          /* For an index lookup followed by a table lookup:
          **    nInMul index searches to find the start of each index range
          **  + nRow steps through the index
          **  + nRow table searches to lookup the table entry using the rowid
          */
          pc.rCost += (nInMul + pc.plan.nRow)*log10N;
        }else{
          /* For a covering index:
          **     nInMul index searches to find the initial entry 
          **   + nRow steps through the index
          */
          pc.rCost += nInMul*log10N;
        }
      }else{
        /* For a rowid primary key lookup:
        **    nInMult table searches to find the initial entry for each range
        **  + nRow steps through the table
        */
        pc.rCost += nInMul*log10N;
      }
    }

    /* 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 ){
      double m = estLog(pc.plan.nRow*(nOrderBy - pc.plan.nOBSat)/nOrderBy);
      m *= (double)(pc.plan.nOBSat ? 2 : 3);
      pc.rCost += pc.plan.nRow*m;
    }
    if( bDist ){
      pc.rCost += pc.plan.nRow*estLog(pc.plan.nRow)*3;
    }

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

    /* If there are additional constraints on this table that cannot
    ** be used with the current index, but which might lower the number
    ** of output rows, adjust the nRow value accordingly.  This only 
    ** matters if the current index is the least costly, so do not bother
    ** with this step if we already know this index will not be chosen.
    ** Also, never reduce the output row count below 2 using this step.
    **
    ** It is critical that the notValid mask be used here instead of
    ** the notReady mask.  When computing an "optimal" index, the notReady
    ** mask will only have one bit set - the bit for the current table.
    ** The notValid mask, on the other hand, always has all bits set for
    ** tables that are not in outer loops.  If notReady is used here instead
    ** of notValid, then a optimal index that depends on inner joins loops
    ** might be selected even when there exists an optimal index that has
    ** no such dependency.
    */
    if( pc.plan.nRow>2 && pc.rCost<=p->cost.rCost ){
      int k;                       /* Loop counter */
      int nSkipEq = pc.plan.nEq;   /* Number of == constraints to skip */
      int nSkipRange = nBound;     /* Number of < constraints to skip */
      Bitmask thisTab;             /* Bitmap for pSrc */

      thisTab = getMask(pWC->pMaskSet, iCur);
      for(pTerm=pWC->a, k=pWC->nTerm; pc.plan.nRow>2 && k; k--, pTerm++){
        if( pTerm->wtFlags & TERM_VIRTUAL ) continue;
        if( (pTerm->prereqAll & p->notValid)!=thisTab ) continue;
        if( pTerm->eOperator & (WO_EQ|WO_IN|WO_ISNULL) ){
          if( nSkipEq ){
            /* Ignore the first pc.plan.nEq equality matches since the index
            ** has already accounted for these */
            nSkipEq--;
          }else{
            /* Assume each additional equality match reduces the result
            ** set size by a factor of 10 */
            pc.plan.nRow /= 10;
          }
        }else if( pTerm->eOperator & (WO_LT|WO_LE|WO_GT|WO_GE) ){
          if( nSkipRange ){
            /* Ignore the first nSkipRange range constraints since the index
            ** has already accounted for these */
            nSkipRange--;
          }else{
            /* Assume each additional range constraint reduces the result
            ** set size by a factor of 3.  Indexed range constraints reduce
            ** the search space by a larger factor: 4.  We make indexed range
            ** more selective intentionally because of the subjective 
            ** observation that indexed range constraints really are more
            ** selective in practice, on average. */
            pc.plan.nRow /= 3;
          }
        }else if( (pTerm->eOperator & WO_NOOP)==0 ){
          /* Any other expression lowers the output row count by half */
          pc.plan.nRow /= 2;
        }
      }
      if( pc.plan.nRow<2 ) pc.plan.nRow = 2;
    }


    /*WHERETRACE((
      "      nEq=%d nInMul=%d rangeDiv=%d bSort=%d bLookup=%d wsFlags=0x%08x\n"
      "      notReady=0x%llx log10N=%.1f nRow=%.1f cost=%.1f\n"
      "      used=0x%llx nOBSat=%d\n",
      pc.plan.nEq, nInMul, (int)rangeDiv, bSort, bLookup, pc.plan.wsFlags,
      p->notReady, log10N, pc.plan.nRow, pc.rCost, pc.used,
      pc.plan.nOBSat
    ));*/

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

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

    /* Reset masks for the next index in the loop */
    wsFlagMask = ~(WHERE_ROWID_EQ|WHERE_ROWID_RANGE);
    eqTermMask = idxEqTermMask;
  }

  /* If there is no ORDER BY clause and the SQLITE_ReverseOrder flag
  ** is set, then reverse the order that the index will be scanned
  ** in. This is used for application testing, to help find cases
  ** where application behavior depends on the (undefined) order that
  ** SQLite outputs rows in in the absence of an ORDER BY clause.  */
  if( !p->pOrderBy && pParse->db->flags & SQLITE_ReverseOrder ){
    p->cost.plan.wsFlags |= WHERE_REVERSE;
  }

  assert( p->pOrderBy || (p->cost.plan.wsFlags&WHERE_ORDERED)==0 );
  assert( p->cost.plan.u.pIdx==0 || (p->cost.plan.wsFlags&WHERE_ROWID_EQ)==0 );
  assert( pSrc->pIndex==0 
       || p->cost.plan.u.pIdx==0 
       || p->cost.plan.u.pIdx==pSrc->pIndex 
  );

  /*WHERETRACE(("   best index is %s cost=%.1f\n",
         p->cost.plan.u.pIdx ? p->cost.plan.u.pIdx->zName : "ipk",
         p->cost.rCost));*/
  
  bestOrClauseIndex(p);
  bestAutomaticIndex(p);
  if( eqTermMask & WO_ISNULL ) p->cost.plan.wsFlags |= WHERE_NULL_OK;
}

/*
** Find the query plan for accessing table pSrc->pTab. Write the
** best query plan and its cost into the WhereCost object supplied 
** as the last parameter. This function may calculate the cost of
** both real and virtual table scans.
**
** This function does not take ORDER BY or DISTINCT into account.  Nor
** does it remember the virtual table query plan.  All it does is compute
** the cost while determining if an OR optimization is applicable.  The
** details will be reconsidered later if the optimization is found to be
** applicable.
*/
static void bestIndex(WhereBestIdx *p){
#ifndef SQLITE_OMIT_VIRTUALTABLE
  if( IsVirtual(p->pSrc->pTab) ){
    sqlite3_index_info *pIdxInfo = 0;
    p->ppIdxInfo = &pIdxInfo;
    bestVirtualIndex(p);
    assert( pIdxInfo!=0 || p->pParse->db->mallocFailed );
    if( pIdxInfo && pIdxInfo->needToFreeIdxStr ){
      sqlite3_free(pIdxInfo->idxStr);
    }
    sqlite3DbFree(p->pParse->db, pIdxInfo);
  }else
#endif
  {
    bestBtreeIndex(p);
  }
}

/*
** Disable a term in the WHERE clause.  Except, do not disable the term
** if it controls a LEFT OUTER JOIN and it did not originate in the ON
** or USING clause of that join.
**
** Consider the term t2.z='ok' in the following queries:
**
................................................................................
** this routine sets up a loop that will iterate over all values of X.
*/
static int codeEqualityTerm(
  Parse *pParse,      /* The parsing context */
  WhereTerm *pTerm,   /* The term of the WHERE clause to be coded */
  WhereLevel *pLevel, /* The level of the FROM clause we are working on */
  int iEq,            /* Index of the equality term within this level */

  int iTarget         /* Attempt to leave results in this register */
){
  Expr *pX = pTerm->pExpr;
  Vdbe *v = pParse->pVdbe;
  int iReg;                  /* Register holding results */

  assert( iTarget>0 );
................................................................................
    iReg = iTarget;
    sqlite3VdbeAddOp2(v, OP_Null, 0, iReg);
#ifndef SQLITE_OMIT_SUBQUERY
  }else{
    int eType;
    int iTab;
    struct InLoop *pIn;
    u8 bRev = (pLevel->plan.wsFlags & WHERE_REVERSE)!=0;

    if( (pLevel->plan.wsFlags & WHERE_INDEXED)!=0 

      && pLevel->plan.u.pIdx->aSortOrder[iEq]
    ){
      testcase( iEq==0 );
      testcase( iEq==pLevel->plan.u.pIdx->nColumn-1 );
      testcase( iEq>0 && iEq+1<pLevel->plan.u.pIdx->nColumn );
      testcase( bRev );
      bRev = !bRev;
    }
................................................................................
    eType = sqlite3FindInIndex(pParse, pX, 0);
    if( eType==IN_INDEX_INDEX_DESC ){
      testcase( bRev );
      bRev = !bRev;
    }
    iTab = pX->iTable;
    sqlite3VdbeAddOp2(v, bRev ? OP_Last : OP_Rewind, iTab, 0);
    assert( pLevel->plan.wsFlags & WHERE_IN_ABLE );
    if( pLevel->u.in.nIn==0 ){
      pLevel->addrNxt = sqlite3VdbeMakeLabel(v);
    }
    pLevel->u.in.nIn++;
    pLevel->u.in.aInLoop =
       sqlite3DbReallocOrFree(pParse->db, pLevel->u.in.aInLoop,
                              sizeof(pLevel->u.in.aInLoop[0])*pLevel->u.in.nIn);
................................................................................
** string in this example would be set to SQLITE_AFF_NONE.
*/
static int codeAllEqualityTerms(
  Parse *pParse,        /* Parsing context */
  WhereLevel *pLevel,   /* Which nested loop of the FROM we are coding */
  WhereClause *pWC,     /* The WHERE clause */
  Bitmask notReady,     /* Which parts of FROM have not yet been coded */

  int nExtraReg,        /* Number of extra registers to allocate */
  char **pzAff          /* OUT: Set to point to affinity string */
){
  int nEq = pLevel->plan.nEq;   /* The number of == or IN constraints to code */
  Vdbe *v = pParse->pVdbe;      /* The vm under construction */
  Index *pIdx;                  /* The index being used for this loop */
  int iCur = pLevel->iTabCur;   /* The cursor of the table */
  WhereTerm *pTerm;             /* A single constraint term */

  int j;                        /* Loop counter */
  int regBase;                  /* Base register */
  int nReg;                     /* Number of registers to allocate */
  char *zAff;                   /* Affinity string to return */
  int eqFlags;                  /* WO_EQ|WO_IN and maybe also WO_ISNULL */

  /* This module is only called on query plans that use an index. */

  assert( pLevel->plan.wsFlags & WHERE_INDEXED );
  pIdx = pLevel->plan.u.pIdx;



  /* Figure out how many memory cells we will need then allocate them.
  */
  regBase = pParse->nMem + 1;
  nReg = pLevel->plan.nEq + nExtraReg;
  pParse->nMem += nReg;

  zAff = sqlite3DbStrDup(pParse->db, sqlite3IndexAffinityStr(v, pIdx));
  if( !zAff ){
    pParse->db->mallocFailed = 1;
  }

  /* Evaluate the equality constraints
  */
  assert( pIdx->nColumn>=nEq );
  eqFlags = (pLevel->plan.wsFlags&WHERE_NULL_OK) ? (WO_EQ|WO_IN|WO_ISNULL)
                                                 : (WO_EQ|WO_IN);
  for(j=0; j<nEq; j++){
    int r1;
    int k = pIdx->aiColumn[j];
    pTerm = findTerm(pWC, iCur, k, notReady, eqFlags, pIdx);
    if( pTerm==0 ) break;


    /* The following true for indices with redundant columns. 
    ** Ex: CREATE INDEX i1 ON t1(a,b,a); SELECT * FROM t1 WHERE a=0 AND b=0; */
    testcase( (pTerm->wtFlags & TERM_CODED)!=0 );
    testcase( pTerm->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
    r1 = codeEqualityTerm(pParse, pTerm, pLevel, j, regBase+j);
    if( r1!=regBase+j ){
      if( nReg==1 ){
        sqlite3ReleaseTempReg(pParse, regBase);
        regBase = r1;
      }else{
        sqlite3VdbeAddOp2(v, OP_SCopy, r1, regBase+j);
      }
................................................................................
){
  int j, k;            /* Loop counters */
  int iCur;            /* The VDBE cursor for the table */
  int addrNxt;         /* Where to jump to continue with the next IN case */
  int omitTable;       /* True if we use the index only */
  int bRev;            /* True if we need to scan in reverse order */
  WhereLevel *pLevel;  /* The where level to be coded */

  WhereClause *pWC;    /* Decomposition of the entire WHERE clause */
  WhereTerm *pTerm;               /* A WHERE clause term */
  Parse *pParse;                  /* Parsing context */
  Vdbe *v;                        /* The prepared stmt under constructions */
  struct SrcList_item *pTabItem;  /* FROM clause term being coded */
  int addrBrk;                    /* Jump here to break out of the loop */
  int addrCont;                   /* Jump here to continue with next cycle */
................................................................................
  int iReleaseReg = 0;      /* Temp register to free before returning */
  Bitmask newNotReady;      /* Return value */

  pParse = pWInfo->pParse;
  v = pParse->pVdbe;
  pWC = pWInfo->pWC;
  pLevel = &pWInfo->a[iLevel];

  pTabItem = &pWInfo->pTabList->a[pLevel->iFrom];
  iCur = pTabItem->iCursor;
  bRev = (pLevel->plan.wsFlags & WHERE_REVERSE)!=0;

  omitTable = (pLevel->plan.wsFlags & WHERE_IDX_ONLY)!=0 
           && (wctrlFlags & WHERE_FORCE_TABLE)==0;
  VdbeNoopComment((v, "Begin Join Loop %d", iLevel));

  /* Create labels for the "break" and "continue" instructions
  ** for the current loop.  Jump to addrBrk to break out of a loop.
  ** Jump to cont to go immediately to the next iteration of the
  ** loop.
................................................................................
    pLevel->p2 =  sqlite3VdbeAddOp1(v, OP_Yield, regYield);
    VdbeComment((v, "next row of co-routine %s", pTabItem->pTab->zName));
    sqlite3VdbeAddOp2(v, OP_If, regYield+1, addrBrk);
    pLevel->op = OP_Goto;
  }else

#ifndef SQLITE_OMIT_VIRTUALTABLE
  if(  (pLevel->plan.wsFlags & WHERE_VIRTUALTABLE)!=0 ){
    /* Case 0:  The table is a virtual-table.  Use the VFilter and VNext
    **          to access the data.
    */
    int iReg;   /* P3 Value for OP_VFilter */
    int addrNotFound;
    sqlite3_index_info *pVtabIdx = pLevel->plan.u.pVtabIdx;
    int nConstraint = pVtabIdx->nConstraint;
    struct sqlite3_index_constraint_usage *aUsage =
                                                pVtabIdx->aConstraintUsage;
    const struct sqlite3_index_constraint *aConstraint =
                                                pVtabIdx->aConstraint;

    sqlite3ExprCachePush(pParse);
    iReg = sqlite3GetTempRange(pParse, nConstraint+2);
    addrNotFound = pLevel->addrBrk;
    for(j=1; j<=nConstraint; j++){
      for(k=0; k<nConstraint; k++){
        if( aUsage[k].argvIndex==j ){
          int iTarget = iReg+j+1;
          pTerm = &pWC->a[aConstraint[k].iTermOffset];

          if( pTerm->eOperator & WO_IN ){
            codeEqualityTerm(pParse, pTerm, pLevel, k, iTarget);
            addrNotFound = pLevel->addrNxt;
          }else{
            sqlite3ExprCode(pParse, pTerm->pExpr->pRight, iTarget);
          }
          break;
        }
      }
      if( k==nConstraint ) break;
    }
    sqlite3VdbeAddOp2(v, OP_Integer, pVtabIdx->idxNum, iReg);
    sqlite3VdbeAddOp2(v, OP_Integer, j-1, iReg+1);
    sqlite3VdbeAddOp4(v, OP_VFilter, iCur, addrNotFound, iReg, pVtabIdx->idxStr,

                      pVtabIdx->needToFreeIdxStr ? P4_MPRINTF : P4_STATIC);
    pVtabIdx->needToFreeIdxStr = 0;

    for(j=0; j<nConstraint; j++){
      if( aUsage[j].omit ){
        int iTerm = aConstraint[j].iTermOffset;

        disableTerm(pLevel, &pWC->a[iTerm]);
      }
    }
    pLevel->op = OP_VNext;
    pLevel->p1 = iCur;
    pLevel->p2 = sqlite3VdbeCurrentAddr(v);
    sqlite3ReleaseTempRange(pParse, iReg, nConstraint+2);
    sqlite3ExprCachePop(pParse, 1);
  }else
#endif /* SQLITE_OMIT_VIRTUALTABLE */

  if( pLevel->plan.wsFlags & WHERE_ROWID_EQ ){


    /* Case 1:  We can directly reference a single row using an
    **          equality comparison against the ROWID field.  Or
    **          we reference multiple rows using a "rowid IN (...)"
    **          construct.
    */

    iReleaseReg = sqlite3GetTempReg(pParse);
    pTerm = findTerm(pWC, iCur, -1, notReady, WO_EQ|WO_IN, 0);

    assert( pTerm!=0 );
    assert( pTerm->pExpr!=0 );
    assert( omitTable==0 );
    testcase( pTerm->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
    iRowidReg = codeEqualityTerm(pParse, pTerm, pLevel, 0, iReleaseReg);
    addrNxt = pLevel->addrNxt;
    sqlite3VdbeAddOp2(v, OP_MustBeInt, iRowidReg, addrNxt);
    sqlite3VdbeAddOp3(v, OP_NotExists, iCur, addrNxt, iRowidReg);
    sqlite3ExprCacheAffinityChange(pParse, iRowidReg, 1);
    sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
    VdbeComment((v, "pk"));
    pLevel->op = OP_Noop;
  }else if( pLevel->plan.wsFlags & WHERE_ROWID_RANGE ){


    /* Case 2:  We have an inequality comparison against the ROWID field.
    */
    int testOp = OP_Noop;
    int start;
    int memEndValue = 0;
    WhereTerm *pStart, *pEnd;

    assert( omitTable==0 );
    pStart = findTerm(pWC, iCur, -1, notReady, WO_GT|WO_GE, 0);
    pEnd = findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE, 0);


    if( bRev ){
      pTerm = pStart;
      pStart = pEnd;
      pEnd = pTerm;
    }
    if( pStart ){
      Expr *pX;             /* The expression that defines the start bound */
................................................................................
    if( testOp!=OP_Noop ){
      iRowidReg = iReleaseReg = sqlite3GetTempReg(pParse);
      sqlite3VdbeAddOp2(v, OP_Rowid, iCur, iRowidReg);
      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
      sqlite3VdbeAddOp3(v, testOp, memEndValue, addrBrk, iRowidReg);
      sqlite3VdbeChangeP5(v, SQLITE_AFF_NUMERIC | SQLITE_JUMPIFNULL);
    }
  }else if( pLevel->plan.wsFlags & (WHERE_COLUMN_RANGE|WHERE_COLUMN_EQ) ){
    /* Case 3: A scan using an index.
    **
    **         The WHERE clause may contain zero or more equality 
    **         terms ("==" or "IN" operators) that refer to the N
    **         left-most columns of the index. It may also contain
    **         inequality constraints (>, <, >= or <=) on the indexed
    **         column that immediately follows the N equalities. Only 
    **         the right-most column can be an inequality - the rest must
................................................................................
      OP_SeekLe            /* 7: (start_constraints  &&  startEq &&  bRev) */
    };
    static const u8 aEndOp[] = {
      OP_Noop,             /* 0: (!end_constraints) */
      OP_IdxGE,            /* 1: (end_constraints && !bRev) */
      OP_IdxLT             /* 2: (end_constraints && bRev) */
    };
    int nEq = pLevel->plan.nEq;  /* Number of == or IN terms */
    int isMinQuery = 0;          /* If this is an optimized SELECT min(x).. */
    int regBase;                 /* Base register holding constraint values */
    int r1;                      /* Temp register */
    WhereTerm *pRangeStart = 0;  /* Inequality constraint at range start */
    WhereTerm *pRangeEnd = 0;    /* Inequality constraint at range end */
    int startEq;                 /* True if range start uses ==, >= or <= */
    int endEq;                   /* True if range end uses ==, >= or <= */
    int start_constraints;       /* Start of range is constrained */
................................................................................
    Index *pIdx;                 /* The index we will be using */
    int iIdxCur;                 /* The VDBE cursor for the index */
    int nExtraReg = 0;           /* Number of extra registers needed */
    int op;                      /* Instruction opcode */
    char *zStartAff;             /* Affinity for start of range constraint */
    char *zEndAff;               /* Affinity for end of range constraint */

    pIdx = pLevel->plan.u.pIdx;
    iIdxCur = pLevel->iIdxCur;
    k = (nEq==pIdx->nColumn ? -1 : pIdx->aiColumn[nEq]);

    /* If this loop satisfies a sort order (pOrderBy) request that 
    ** was passed to this function to implement a "SELECT min(x) ..." 
    ** query, then the caller will only allow the loop to run for
    ** a single iteration. This means that the first row returned
    ** should not have a NULL value stored in 'x'. If column 'x' is
    ** the first one after the nEq equality constraints in the index,
    ** this requires some special handling.
    */
    if( (wctrlFlags&WHERE_ORDERBY_MIN)!=0
     && (pLevel->plan.wsFlags&WHERE_ORDERED)
     && (pIdx->nColumn>nEq)
    ){
      /* assert( pOrderBy->nExpr==1 ); */
      /* assert( pOrderBy->a[0].pExpr->iColumn==pIdx->aiColumn[nEq] ); */
      isMinQuery = 1;
      nExtraReg = 1;
    }

    /* Find any inequality constraint terms for the start and end 
    ** of the range. 
    */
    if( pLevel->plan.wsFlags & WHERE_TOP_LIMIT ){
      pRangeEnd = findTerm(pWC, iCur, k, notReady, (WO_LT|WO_LE), pIdx);
      nExtraReg = 1;
    }
    if( pLevel->plan.wsFlags & WHERE_BTM_LIMIT ){
      pRangeStart = findTerm(pWC, iCur, k, notReady, (WO_GT|WO_GE), pIdx);

      nExtraReg = 1;
    }

    /* Generate code to evaluate all constraint terms using == or IN
    ** and store the values of those terms in an array of registers
    ** starting at regBase.
    */
    regBase = codeAllEqualityTerms(
        pParse, pLevel, pWC, notReady, nExtraReg, &zStartAff
    );
    zEndAff = sqlite3DbStrDup(pParse->db, zStartAff);
    addrNxt = pLevel->addrNxt;

    /* If we are doing a reverse order scan on an ascending index, or
    ** a forward order scan on a descending index, interchange the 
    ** start and end terms (pRangeStart and pRangeEnd).
................................................................................
    /* If there are inequality constraints, check that the value
    ** of the table column that the inequality contrains is not NULL.
    ** If it is, jump to the next iteration of the loop.
    */
    r1 = sqlite3GetTempReg(pParse);
    testcase( pLevel->plan.wsFlags & WHERE_BTM_LIMIT );
    testcase( pLevel->plan.wsFlags & WHERE_TOP_LIMIT );
    if( (pLevel->plan.wsFlags & (WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))!=0 ){
      sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, nEq, r1);
      sqlite3VdbeAddOp2(v, OP_IsNull, r1, addrCont);
    }
    sqlite3ReleaseTempReg(pParse, r1);

    /* Seek the table cursor, if required */
    disableTerm(pLevel, pRangeStart);
................................................................................
      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
      sqlite3VdbeAddOp2(v, OP_Seek, iCur, iRowidReg);  /* Deferred seek */
    }

    /* Record the instruction used to terminate the loop. Disable 
    ** WHERE clause terms made redundant by the index range scan.
    */
    if( pLevel->plan.wsFlags & WHERE_UNIQUE ){
      pLevel->op = OP_Noop;
    }else if( bRev ){
      pLevel->op = OP_Prev;
    }else{
      pLevel->op = OP_Next;
    }
    pLevel->p1 = iIdxCur;
    if( pLevel->plan.wsFlags & WHERE_COVER_SCAN ){
      pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;
    }else{
      assert( pLevel->p5==0 );
    }
  }else

#ifndef SQLITE_OMIT_OR_OPTIMIZATION
  if( pLevel->plan.wsFlags & WHERE_MULTI_OR ){
    /* Case 4:  Two or more separately indexed terms connected by OR
    **
    ** Example:
    **
    **   CREATE TABLE t1(a,b,c,d);
    **   CREATE INDEX i1 ON t1(a);
    **   CREATE INDEX i2 ON t1(b);
    **   CREATE INDEX i3 ON t1(c);
................................................................................
    int regRowid = 0;                         /* Register holding rowid */
    int iLoopBody = sqlite3VdbeMakeLabel(v);  /* Start of loop body */
    int iRetInit;                             /* Address of regReturn init */
    int untestedTerms = 0;             /* Some terms not completely tested */
    int ii;                            /* Loop counter */
    Expr *pAndExpr = 0;                /* An ".. AND (...)" expression */
   
    pTerm = pLevel->plan.u.pTerm;
    assert( pTerm!=0 );
    assert( pTerm->eOperator & WO_OR );
    assert( (pTerm->wtFlags & TERM_ORINFO)!=0 );
    pOrWc = &pTerm->u.pOrInfo->wc;
    pLevel->op = OP_Return;
    pLevel->p1 = regReturn;

................................................................................
        }
        /* Loop through table entries that match term pOrTerm. */
        pSubWInfo = sqlite3WhereBegin(pParse, pOrTab, pOrExpr, 0, 0,
                        WHERE_OMIT_OPEN_CLOSE | WHERE_AND_ONLY |
                        WHERE_FORCE_TABLE | WHERE_ONETABLE_ONLY, iCovCur);
        assert( pSubWInfo || pParse->nErr || pParse->db->mallocFailed );
        if( pSubWInfo ){
          WhereLevel *pLvl;
          explainOneScan(
              pParse, pOrTab, &pSubWInfo->a[0], iLevel, pLevel->iFrom, 0
          );
          if( (wctrlFlags & WHERE_DUPLICATES_OK)==0 ){
            int iSet = ((ii==pOrWc->nTerm-1)?-1:ii);
            int r;
            r = sqlite3ExprCodeGetColumn(pParse, pTabItem->pTab, -1, iCur, 
................................................................................
          ** If the call to sqlite3WhereBegin() above resulted in a scan that
          ** uses an index, and this is either the first OR-connected term
          ** processed or the index is the same as that used by all previous
          ** terms, set pCov to the candidate covering index. Otherwise, set 
          ** pCov to NULL to indicate that no candidate covering index will 
          ** be available.
          */
          pLvl = &pSubWInfo->a[0];
          if( (pLvl->plan.wsFlags & WHERE_INDEXED)!=0
           && (pLvl->plan.wsFlags & WHERE_TEMP_INDEX)==0
           && (ii==0 || pLvl->plan.u.pIdx==pCov)
          ){
            assert( pLvl->iIdxCur==iCovCur );
            pCov = pLvl->plan.u.pIdx;
          }else{
            pCov = 0;
          }

          /* Finish the loop through table entries that match term pOrTerm. */
          sqlite3WhereEnd(pSubWInfo);
        }
................................................................................

    if( pWInfo->nLevel>1 ) sqlite3StackFree(pParse->db, pOrTab);
    if( !untestedTerms ) disableTerm(pLevel, pTerm);
  }else
#endif /* SQLITE_OMIT_OR_OPTIMIZATION */

  {
    /* Case 5:  There is no usable index.  We must do a complete
    **          scan of the entire table.
    */
    static const u8 aStep[] = { OP_Next, OP_Prev };
    static const u8 aStart[] = { OP_Rewind, OP_Last };
    assert( bRev==0 || bRev==1 );
    assert( omitTable==0 );
    pLevel->op = aStep[bRev];
    pLevel->p1 = iCur;
    pLevel->p2 = 1 + sqlite3VdbeAddOp2(v, aStart[bRev], iCur, addrBrk);
    pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;
  }
  newNotReady = notReady & ~getMask(pWC->pMaskSet, iCur);

................................................................................
/*
** Free a WhereInfo structure
*/
static void whereInfoFree(sqlite3 *db, WhereInfo *pWInfo){
  if( ALWAYS(pWInfo) ){
    int i;
    for(i=0; i<pWInfo->nLevel; i++){
      sqlite3_index_info *pInfo = pWInfo->a[i].pIdxInfo;
      if( pInfo ){
        /* assert( pInfo->needToFreeIdxStr==0 || db->mallocFailed ); */
        if( pInfo->needToFreeIdxStr ){
          sqlite3_free(pInfo->idxStr);
        }
        sqlite3DbFree(db, pInfo);
      }
      if( pWInfo->a[i].plan.wsFlags & WHERE_TEMP_INDEX ){
        Index *pIdx = pWInfo->a[i].plan.u.pIdx;
        if( pIdx ){
          sqlite3DbFree(db, pIdx->zColAff);
          sqlite3DbFree(db, pIdx);
        }
      }
    }
    whereClauseClear(pWInfo->pWC);
................................................................................
  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  savedLoop = *pNew;
  pNew->rSetup = (double)0;
  rLogSize = estLog(pProbe->aiRowEst[0]);
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 1;

    pNew->u.btree.nEq = savedLoop.u.btree.nEq;
    pNew->nTerm = savedLoop.nTerm;
    if( pNew->nTerm>=pBuilder->mxTerm ) break; /* Repeated column in index */
    pNew->aTerm[pNew->nTerm++] = pTerm;
    pNew->prereq = (savedLoop.prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    if( pTerm->eOperator & WO_IN ){
      Expr *pExpr = pTerm->pExpr;
................................................................................
  pFrom = aFrom;
  for(ii=1; ii<nFrom; ii++){
    if( pFrom->rCost>aFrom[ii].rCost ) pFrom = &aFrom[ii];
  }
  assert( pWInfo->nLevel==nLoop );
  /* Load the lowest cost path into pWInfo */
  for(iLoop=0; iLoop<nLoop; iLoop++){

    pWInfo->a[iLoop].pWLoop = pFrom->aLoop[iLoop];


  }
  if( pFrom->isOrdered ){
    pWInfo->nOBSat = pWInfo->pOrderBy->nExpr;
    pWInfo->revMask = pFrom->revLoop;
  }
  pWInfo->nRowOut = pFrom->nRow;

................................................................................
  WhereInfo *pWInfo;         /* Will become the return value of this function */
  Vdbe *v = pParse->pVdbe;   /* The virtual database engine */
  Bitmask notReady;          /* Cursors that are not yet positioned */
  WhereBestIdx sWBI;         /* Best index search context */
  WhereLoopBuilder sWLB;     /* The WhereLoop builder */
  WhereMaskSet *pMaskSet;    /* The expression mask set */
  WhereLevel *pLevel;        /* A single level in pWInfo->a[] */
  int iFrom;                 /* First unused FROM clause element */
  int andFlags;              /* AND-ed combination of all pWC->a[].wtFlags */
  int ii;                    /* Loop counter */
  sqlite3 *db;               /* Database connection */
  int rc;                    /* Return code */


  /* Variable initialization */
  memset(&sWBI, 0, sizeof(sWBI));
................................................................................
    }
    for(ii=0; ii<nTabList; ii++){
      whereLoopPrint(pWInfo->a[ii].pWLoop, pTabList);
    }
  }
#endif

  /* Chose the best index to use for each table in the FROM clause.
  **
  ** This loop fills in the following fields:
  **
  **   pWInfo->a[].pIdx      The index to use for this level of the loop.
  **   pWInfo->a[].wsFlags   WHERE_xxx flags associated with pIdx
  **   pWInfo->a[].nEq       The number of == and IN constraints
  **   pWInfo->a[].iFrom     Which term of the FROM clause is being coded
  **   pWInfo->a[].iTabCur   The VDBE cursor for the database table
  **   pWInfo->a[].iIdxCur   The VDBE cursor for the index
  **   pWInfo->a[].pTerm     When wsFlags==WO_OR, the OR-clause term
  **
  ** This loop also figures out the nesting order of tables in the FROM
  ** clause.
  */
  sWBI.notValid = ~(Bitmask)0;
  sWBI.pOrderBy = pOrderBy;
  sWBI.n = nTabList;
  sWBI.pDistinct = pDistinct;
  andFlags = ~0;
  for(sWBI.i=iFrom=0, pLevel=pWInfo->a; sWBI.i<nTabList; sWBI.i++, pLevel++){
    WhereCost bestPlan;         /* Most efficient plan seen so far */
    Index *pIdx;                /* Index for FROM table at pTabItem */
    int j;                      /* For looping over FROM tables */
    int bestJ = -1;             /* The value of j */
    Bitmask m;                  /* Bitmask value for j or bestJ */
    int isOptimal;              /* Iterator for optimal/non-optimal search */
    int ckOptimal;              /* Do the optimal scan check */
    int nUnconstrained;         /* Number tables without INDEXED BY */
    Bitmask notIndexed;         /* Mask of tables that cannot use an index */

    memset(&bestPlan, 0, sizeof(bestPlan));
    bestPlan.rCost = SQLITE_BIG_DBL;
    /*WHERETRACE(("*** Begin search for loop %d ***\n", sWBI.i));*/

    /* Loop through the remaining entries in the FROM clause to find the
    ** next nested loop. The loop tests all FROM clause entries
    ** either once or twice. 
    **
    ** The first test is always performed if there are two or more entries
    ** remaining and never performed if there is only one FROM clause entry
    ** to choose from.  The first test looks for an "optimal" scan.  In
    ** this context an optimal scan is one that uses the same strategy
    ** for the given FROM clause entry as would be selected if the entry
    ** were used as the innermost nested loop.  In other words, a table
    ** is chosen such that the cost of running that table cannot be reduced
    ** by waiting for other tables to run first.  This "optimal" test works
    ** by first assuming that the FROM clause is on the inner loop and finding
    ** its query plan, then checking to see if that query plan uses any
    ** other FROM clause terms that are sWBI.notValid.  If no notValid terms
    ** are used then the "optimal" query plan works.
    **
    ** Note that the WhereCost.nRow parameter for an optimal scan might
    ** not be as small as it would be if the table really were the innermost
    ** join.  The nRow value can be reduced by WHERE clause constraints
    ** that do not use indices.  But this nRow reduction only happens if the
    ** table really is the innermost join.  
    **
    ** The second loop iteration is only performed if no optimal scan
    ** strategies were found by the first iteration. This second iteration
    ** is used to search for the lowest cost scan overall.
    **
    ** Without the optimal scan step (the first iteration) a suboptimal
    ** plan might be chosen for queries like this:
    **   
    **   CREATE TABLE t1(a, b); 
    **   CREATE TABLE t2(c, d);
    **   SELECT * FROM t2, t1 WHERE t2.rowid = t1.a;
    **
    ** The best strategy is to iterate through table t1 first. However it
    ** is not possible to determine this with a simple greedy algorithm.
    ** Since the cost of a linear scan through table t2 is the same 
    ** as the cost of a linear scan through table t1, a simple greedy 
    ** algorithm may choose to use t2 for the outer loop, which is a much
    ** costlier approach.
    */
    nUnconstrained = 0;
    notIndexed = 0;

    /* The optimal scan check only occurs if there are two or more tables
    ** available to be reordered */
    if( iFrom==nTabList-1 ){
      ckOptimal = 0;  /* Common case of just one table in the FROM clause */
    }else{
      ckOptimal = -1;
      for(j=iFrom, sWBI.pSrc=&pTabList->a[j]; j<nTabList; j++, sWBI.pSrc++){
        m = getMask(pMaskSet, sWBI.pSrc->iCursor);
        if( (m & sWBI.notValid)==0 ){
          if( j==iFrom ) iFrom++;
          continue;
        }
        if( j>iFrom && (sWBI.pSrc->jointype & (JT_LEFT|JT_CROSS))!=0 ) break;
        if( ++ckOptimal ) break;
        if( (sWBI.pSrc->jointype & JT_LEFT)!=0 ) break;
      }
    }
    assert( ckOptimal==0 || ckOptimal==1 );

    for(isOptimal=ckOptimal; isOptimal>=0 && bestJ<0; isOptimal--){
      for(j=iFrom, sWBI.pSrc=&pTabList->a[j]; j<nTabList; j++, sWBI.pSrc++){
        if( j>iFrom && (sWBI.pSrc->jointype & (JT_LEFT|JT_CROSS))!=0 ){
          /* This break and one like it in the ckOptimal computation loop
          ** above prevent table reordering across LEFT and CROSS JOINs.
          ** The LEFT JOIN case is necessary for correctness.  The prohibition
          ** against reordering across a CROSS JOIN is an SQLite feature that
          ** allows the developer to control table reordering */
          break;
        }
        m = getMask(pMaskSet, sWBI.pSrc->iCursor);
        if( (m & sWBI.notValid)==0 ){
          assert( j>iFrom );
          continue;
        }
        sWBI.notReady = (isOptimal ? m : sWBI.notValid);
        if( sWBI.pSrc->pIndex==0 ) nUnconstrained++;
  
        /*WHERETRACE(("   === trying table %d (%s) with isOptimal=%d ===\n",
                    j, sWBI.pSrc->pTab->zName, isOptimal));*/
        assert( sWBI.pSrc->pTab );
#ifndef SQLITE_OMIT_VIRTUALTABLE
        if( IsVirtual(sWBI.pSrc->pTab) ){
          sWBI.ppIdxInfo = &pWInfo->a[j].pIdxInfo;
          bestVirtualIndex(&sWBI);
        }else 
#endif
        {
          bestBtreeIndex(&sWBI);
        }
        assert( isOptimal || (sWBI.cost.used&sWBI.notValid)==0 );

        /* If an INDEXED BY clause is present, then the plan must use that
        ** index if it uses any index at all */
        assert( sWBI.pSrc->pIndex==0 
                  || (sWBI.cost.plan.wsFlags & WHERE_NOT_FULLSCAN)==0
                  || sWBI.cost.plan.u.pIdx==sWBI.pSrc->pIndex );

        if( isOptimal && (sWBI.cost.plan.wsFlags & WHERE_NOT_FULLSCAN)==0 ){
          notIndexed |= m;
        }
        if( isOptimal ){
          pWInfo->a[j].rOptCost = sWBI.cost.rCost;
        }else if( ckOptimal ){
          /* If two or more tables have nearly the same outer loop cost, but
          ** very different inner loop (optimal) cost, we want to choose
          ** for the outer loop that table which benefits the least from
          ** being in the inner loop.  The following code scales the 
          ** outer loop cost estimate to accomplish that. */
          /*WHERETRACE(("   scaling cost from %.1f to %.1f\n",
                      sWBI.cost.rCost,
                      sWBI.cost.rCost/pWInfo->a[j].rOptCost));*/
          sWBI.cost.rCost /= pWInfo->a[j].rOptCost;
        }

        /* Conditions under which this table becomes the best so far:
        **
        **   (1) The table must not depend on other tables that have not
        **       yet run.  (In other words, it must not depend on tables
        **       in inner loops.)
        **
        **   (2) (This rule was removed on 2012-11-09.  The scaling of the
        **       cost using the optimal scan cost made this rule obsolete.)
        **
        **   (3) All tables have an INDEXED BY clause or this table lacks an
        **       INDEXED BY clause or this table uses the specific
        **       index specified by its INDEXED BY clause.  This rule ensures
        **       that a best-so-far is always selected even if an impossible
        **       combination of INDEXED BY clauses are given.  The error
        **       will be detected and relayed back to the application later.
        **       The NEVER() comes about because rule (2) above prevents
        **       An indexable full-table-scan from reaching rule (3).
        **
        **   (4) The plan cost must be lower than prior plans, where "cost"
        **       is defined by the compareCost() function above. 
        */
        if( (sWBI.cost.used&sWBI.notValid)==0                    /* (1) */
            && (nUnconstrained==0 || sWBI.pSrc->pIndex==0        /* (3) */
                || NEVER((sWBI.cost.plan.wsFlags & WHERE_NOT_FULLSCAN)!=0))
            && (bestJ<0 || compareCost(&sWBI.cost, &bestPlan))   /* (4) */
        ){
          /*WHERETRACE(("   === table %d (%s) is best so far\n"
                      "       cost=%.1f, nRow=%.1f, nOBSat=%d, wsFlags=%08x\n",
                      j, sWBI.pSrc->pTab->zName,
                      sWBI.cost.rCost, sWBI.cost.plan.nRow,
                      sWBI.cost.plan.nOBSat, sWBI.cost.plan.wsFlags));*/
          bestPlan = sWBI.cost;
          bestJ = j;
        }

        /* In a join like "w JOIN x LEFT JOIN y JOIN z"  make sure that
        ** table y (and not table z) is always the next inner loop inside
        ** of table x. */
        if( (sWBI.pSrc->jointype & JT_LEFT)!=0 ) break;
      }
    }
    assert( bestJ>=0 );
    assert( sWBI.notValid & getMask(pMaskSet, pTabList->a[bestJ].iCursor) );
    assert( bestJ==iFrom || (pTabList->a[iFrom].jointype & JT_LEFT)==0 );
    testcase( bestJ>iFrom && (pTabList->a[iFrom].jointype & JT_CROSS)!=0 );
    testcase( bestJ>iFrom && bestJ<nTabList-1
                          && (pTabList->a[bestJ+1].jointype & JT_LEFT)!=0 );
    /*WHERETRACE(("*** Optimizer selects table %d (%s) for loop %d with:\n"
                "    cost=%.1f, nRow=%.1f, nOBSat=%d, wsFlags=0x%08x\n",
                bestJ, pTabList->a[bestJ].pTab->zName,
                pLevel-pWInfo->a, bestPlan.rCost, bestPlan.plan.nRow,
                bestPlan.plan.nOBSat, bestPlan.plan.wsFlags));*/
    if( (bestPlan.plan.wsFlags & WHERE_DISTINCT)!=0 ){
      assert( pWInfo->eDistinct==0 );
      pWInfo->eDistinct = WHERE_DISTINCT_ORDERED;
    }
    andFlags &= bestPlan.plan.wsFlags;
    pLevel->plan = bestPlan.plan;
    pLevel->iTabCur = pTabList->a[bestJ].iCursor;
    testcase( bestPlan.plan.wsFlags & WHERE_INDEXED );
    testcase( bestPlan.plan.wsFlags & WHERE_TEMP_INDEX );
    if( bestPlan.plan.wsFlags & (WHERE_INDEXED|WHERE_TEMP_INDEX) ){
      if( (wctrlFlags & WHERE_ONETABLE_ONLY) 
       && (bestPlan.plan.wsFlags & WHERE_TEMP_INDEX)==0 
      ){
        pLevel->iIdxCur = iIdxCur;
      }else{
        pLevel->iIdxCur = pParse->nTab++;
      }
    }else{
      pLevel->iIdxCur = -1;
    }
    sWBI.notValid &= ~getMask(pMaskSet, pTabList->a[bestJ].iCursor);
    pLevel->iFrom = (u8)bestJ;
    if( bestPlan.plan.nRow>=(double)1 ){
      pParse->nQueryLoop *= bestPlan.plan.nRow;
    }

    /* Check that if the table scanned by this loop iteration had an
    ** INDEXED BY clause attached to it, that the named index is being
    ** used for the scan. If not, then query compilation has failed.
    ** Return an error.
    */
    pIdx = pTabList->a[bestJ].pIndex;
    if( pIdx ){
      if( (bestPlan.plan.wsFlags & WHERE_INDEXED)==0 ){
        sqlite3ErrorMsg(pParse, "cannot use index: %s", pIdx->zName);
        goto whereBeginError;
      }else{
        /* If an INDEXED BY clause is used, the bestIndex() function is
        ** guaranteed to find the index specified in the INDEXED BY clause
        ** if it find an index at all. */
        assert( bestPlan.plan.u.pIdx==pIdx );
      }
    }
  }
  WHERETRACE(("*** Optimizer Finished ***\n"));
  if( pParse->nErr || db->mallocFailed ){
    goto whereBeginError;
  }
  if( nTabList ){
    pLevel--;
    pWInfo->nOBSat = pLevel->plan.nOBSat;
  }else{
    pWInfo->nOBSat = 0;
  }

  /* If the total query only selects a single row, then the ORDER BY
  ** clause is irrelevant.
  */
  if( (andFlags & WHERE_UNIQUE)!=0 && pOrderBy ){
    assert( nTabList==0 || (pLevel->plan.wsFlags & WHERE_ALL_UNIQUE)!=0 );
    pWInfo->nOBSat = pOrderBy->nExpr;
  }

  /* If the caller is an UPDATE or DELETE statement that is requesting
  ** to use a one-pass algorithm, determine if this is appropriate.
  ** The one-pass algorithm only works if the WHERE clause constraints
  ** the statement to update a single row.
  */
  assert( (wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || pWInfo->nLevel==1 );
  if( (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 && (andFlags & WHERE_UNIQUE)!=0 ){
    pWInfo->okOnePass = 1;
    pWInfo->a[0].plan.wsFlags &= ~WHERE_IDX_ONLY;
  }

#if 1
  /* Scaffolding:  Check the new query plan against the old.  Report any
  ** discrepencies */
  for(ii=0; ii<nTabList; ii++){
    if( pWInfo->a[ii].iFrom!=pWInfo->a[ii].pWLoop->iTab ){
      sqlite3DebugPrintf("(QP-Mismatch)");
      break;
    }
  }
#endif

  /* Open all tables in the pTabList and any indices selected for
  ** searching those tables.
  */
  sqlite3CodeVerifySchema(pParse, -1); /* Insert the cookie verifier Goto */
  notReady = ~(Bitmask)0;
  pWInfo->nRowOut = (double)1;
  for(ii=0, pLevel=pWInfo->a; ii<nTabList; ii++, pLevel++){
    Table *pTab;     /* Table to open */
    int iDb;         /* Index of database containing table/index */
    struct SrcList_item *pTabItem;


    pTabItem = &pTabList->a[pLevel->iFrom];
    pTab = pTabItem->pTab;
    pWInfo->nRowOut *= pLevel->plan.nRow;
    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);

    if( (pTab->tabFlags & TF_Ephemeral)!=0 || pTab->pSelect ){
      /* Do nothing */
    }else
#ifndef SQLITE_OMIT_VIRTUALTABLE
    if( (pLevel->plan.wsFlags & WHERE_VIRTUALTABLE)!=0 ){
      const char *pVTab = (const char *)sqlite3GetVTable(db, pTab);
      int iCur = pTabItem->iCursor;
      sqlite3VdbeAddOp4(v, OP_VOpen, iCur, 0, 0, pVTab, P4_VTAB);
    }else if( IsVirtual(pTab) ){
      /* noop */
    }else
#endif
    if( (pLevel->plan.wsFlags & WHERE_IDX_ONLY)==0
         && (wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0 ){
      int op = pWInfo->okOnePass ? OP_OpenWrite : OP_OpenRead;
      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, op);
      testcase( pTab->nCol==BMS-1 );
      testcase( pTab->nCol==BMS );
      if( !pWInfo->okOnePass && pTab->nCol<BMS ){
        Bitmask b = pTabItem->colUsed;
................................................................................
                            SQLITE_INT_TO_PTR(n), P4_INT32);
        assert( n<=pTab->nCol );
      }
    }else{
      sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);
    }
#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
    if( (pLevel->plan.wsFlags & WHERE_TEMP_INDEX)!=0 ){
      constructAutomaticIndex(pParse, sWBI.pWC, pTabItem, notReady, pLevel);
    }else
#endif
    if( (pLevel->plan.wsFlags & WHERE_INDEXED)!=0 ){
      Index *pIx = pLevel->plan.u.pIdx;
      KeyInfo *pKey = sqlite3IndexKeyinfo(pParse, pIx);


      int iIndexCur = pLevel->iIdxCur;
      assert( pIx->pSchema==pTab->pSchema );
      assert( iIndexCur>=0 );
      sqlite3VdbeAddOp4(v, OP_OpenRead, iIndexCur, pIx->tnum, iDb,
                        (char*)pKey, P4_KEYINFO_HANDOFF);
      VdbeComment((v, "%s", pIx->zName));
    }
    sqlite3CodeVerifySchema(pParse, iDb);
................................................................................
  for(ii=0; ii<nTabList; ii++){
    pLevel = &pWInfo->a[ii];
    explainOneScan(pParse, pTabList, pLevel, ii, pLevel->iFrom, wctrlFlags);
    notReady = codeOneLoopStart(pWInfo, ii, wctrlFlags, notReady);
    pWInfo->iContinue = pLevel->addrCont;
  }

#ifdef SQLITE_TEST  /* For testing and debugging use only */
  /* Record in the query plan information about the current table
  ** and the index used to access it (if any).  If the table itself
  ** is not used, its name is just '{}'.  If no index is used
  ** the index is listed as "{}".  If the primary key is used the
  ** index name is '*'.
  */
  for(ii=0; ii<nTabList; ii++){
................................................................................
** sqlite3WhereBegin() for additional information.
*/
void sqlite3WhereEnd(WhereInfo *pWInfo){
  Parse *pParse = pWInfo->pParse;
  Vdbe *v = pParse->pVdbe;
  int i;
  WhereLevel *pLevel;

  SrcList *pTabList = pWInfo->pTabList;
  sqlite3 *db = pParse->db;

  /* Generate loop termination code.
  */
  sqlite3ExprCacheClear(pParse);
  for(i=pWInfo->nLevel-1; i>=0; i--){
    pLevel = &pWInfo->a[i];

    sqlite3VdbeResolveLabel(v, pLevel->addrCont);
    if( pLevel->op!=OP_Noop ){
      sqlite3VdbeAddOp2(v, pLevel->op, pLevel->p1, pLevel->p2);
      sqlite3VdbeChangeP5(v, pLevel->p5);
    }
    if( pLevel->plan.wsFlags & WHERE_IN_ABLE && pLevel->u.in.nIn>0 ){
      struct InLoop *pIn;
      int j;
      sqlite3VdbeResolveLabel(v, pLevel->addrNxt);
      for(j=pLevel->u.in.nIn, pIn=&pLevel->u.in.aInLoop[j-1]; j>0; j--, pIn--){
        sqlite3VdbeJumpHere(v, pIn->addrInTop+1);
        sqlite3VdbeAddOp2(v, pIn->eEndLoopOp, pIn->iCur, pIn->addrInTop);
        sqlite3VdbeJumpHere(v, pIn->addrInTop-1);
................................................................................
      }
      sqlite3DbFree(db, pLevel->u.in.aInLoop);
    }
    sqlite3VdbeResolveLabel(v, pLevel->addrBrk);
    if( pLevel->iLeftJoin ){
      int addr;
      addr = sqlite3VdbeAddOp1(v, OP_IfPos, pLevel->iLeftJoin);
      assert( (pLevel->plan.wsFlags & WHERE_IDX_ONLY)==0
           || (pLevel->plan.wsFlags & WHERE_INDEXED)!=0 );
      if( (pLevel->plan.wsFlags & WHERE_IDX_ONLY)==0 ){
        sqlite3VdbeAddOp1(v, OP_NullRow, pTabList->a[i].iCursor);
      }
      if( pLevel->iIdxCur>=0 ){
        sqlite3VdbeAddOp1(v, OP_NullRow, pLevel->iIdxCur);
      }
      if( pLevel->op==OP_Return ){
        sqlite3VdbeAddOp2(v, OP_Gosub, pLevel->p1, pLevel->addrFirst);
................................................................................
  */
  assert( pWInfo->nLevel==1 || pWInfo->nLevel==pTabList->nSrc );
  for(i=0, pLevel=pWInfo->a; i<pWInfo->nLevel; i++, pLevel++){
    Index *pIdx = 0;
    struct SrcList_item *pTabItem = &pTabList->a[pLevel->iFrom];
    Table *pTab = pTabItem->pTab;
    assert( pTab!=0 );

    if( (pTab->tabFlags & TF_Ephemeral)==0
     && pTab->pSelect==0
     && (pWInfo->wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0
    ){
      int ws = pLevel->plan.wsFlags;
      if( !pWInfo->okOnePass && (ws & WHERE_IDX_ONLY)==0 ){
        sqlite3VdbeAddOp1(v, OP_Close, pTabItem->iCursor);
      }
      if( (ws & WHERE_INDEXED)!=0 && (ws & WHERE_TEMP_INDEX)==0 ){
        sqlite3VdbeAddOp1(v, OP_Close, pLevel->iIdxCur);
      }
    }

    /* If this scan uses an index, make code substitutions to read data
    ** from the index in preference to the table. Sometimes, this means
    ** the table need never be read from. This is a performance boost,
................................................................................
    ** 
    ** Calls to the code generator in between sqlite3WhereBegin and
    ** sqlite3WhereEnd will have created code that references the table
    ** directly.  This loop scans all that code looking for opcodes
    ** that reference the table and converts them into opcodes that
    ** reference the index.
    */
    if( pLevel->plan.wsFlags & WHERE_INDEXED ){
      pIdx = pLevel->plan.u.pIdx;
    }else if( pLevel->plan.wsFlags & WHERE_MULTI_OR ){
      pIdx = pLevel->u.pCovidx;
    }
    if( pIdx && !db->mallocFailed){
      int k, j, last;
      VdbeOp *pOp;

      pOp = sqlite3VdbeGetOp(v, pWInfo->iTop);
      last = sqlite3VdbeCurrentAddr(v);
      for(k=pWInfo->iTop; k<last; k++, pOp++){
        if( pOp->p1!=pLevel->iTabCur ) continue;
................................................................................
          for(j=0; j<pIdx->nColumn; j++){
            if( pOp->p2==pIdx->aiColumn[j] ){
              pOp->p2 = j;
              pOp->p1 = pLevel->iIdxCur;
              break;
            }
          }
          assert( (pLevel->plan.wsFlags & WHERE_IDX_ONLY)==0
               || j<pIdx->nColumn );
        }else if( pOp->opcode==OP_Rowid ){
          pOp->p1 = pLevel->iIdxCur;
          pOp->opcode = OP_IdxRowid;
        }
      }
    }
  }

*/
struct WhereLoop {
  Bitmask prereq;       /* Bitmask of other loops that must run first */
  Bitmask maskSelf;     /* Bitmask identifying table iTab */
#ifdef SQLITE_DEBUG
  char cId;             /* Symbolic ID of this loop for debugging use */
#endif
  u8 iTab;              /* Position in FROM clause of table for this loop */
  u8 iSortIdx;          /* Sorting index number.  0==None */
  u16 nTerm;            /* Number of entries in aTerm[] */
  u32 wsFlags;          /* WHERE_* flags describing the plan */
  double rSetup;        /* One-time setup cost (ex: create transient index) */
  double rRun;          /* Cost of running each loop */
  double nOut;          /* Estimated number of output rows */
  union {
................................................................................
** An instance of the WhereScan object is used as an iterator for locating
** terms in the WHERE clause that are useful to the query planner.
*/
struct WhereScan {
  WhereTerm *pCurrent;       /* Most recent match */
  WhereClause *pOrigWC;      /* Original, innermost WhereClause */
  WhereClause *pWC;          /* WhereClause currently being scanned */
  char *zCollName;           /* Required collating sequence, if not NULL */
  char idxaff;               /* Must match this affinity, if zCollName!=NULL */
  unsigned char nEquiv;      /* Number of entries in aEquiv[] */
  unsigned char iEquiv;      /* Next unused slot in aEquiv[] */
  u32 opMask;                /* Acceptable operators */
  int k;                     /* Resume scanning at this->pWC->a[this->k] */
  int aEquiv[22];            /* Cursor,Column pairs for equivalence classes */
};
................................................................................
  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(
  WhereClause *pWC,        /* The WhereClause to be initialized */
  Parse *pParse,           /* The parsing context */
  WhereMaskSet *pMaskSet,  /* Mapping from table cursor numbers to bitmasks */
................................................................................
        return i;
      }
    }
  }

  return -1;
}





























































/*
** Return true if the DISTINCT expression-list passed as the third argument
** is redundant. A DISTINCT list is redundant if the database contains a
** UNIQUE index that guarantees that the result of the query will be distinct
** anyway.
*/
................................................................................
  sqlite3DebugPrintf("  estimatedCost=%g\n", p->estimatedCost);
}
#else
#define TRACE_IDX_INPUTS(A)
#define TRACE_IDX_OUTPUTS(A)
#endif





































































































#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
/*
** Return TRUE if the WHERE clause term pTerm is of a form where it
** could be used with an index to access pSrc, assuming an appropriate
** index existed.
*/
static int termCanDriveIndex(
................................................................................
  if( pTerm->u.leftColumn<0 ) return 0;
  aff = pSrc->pTab->aCol[pTerm->u.leftColumn].affinity;
  if( !sqlite3IndexAffinityOk(pTerm->pExpr, aff) ) return 0;
  return 1;
}
#endif














































































#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
/*
** Generate code to construct the Index object for an automatic index
** and to set up the WhereLevel object pLevel so that the code generator
** makes use of the automatic index.
*/
................................................................................
  KeyInfo *pKeyinfo;          /* Key information for the index */   
  int addrTop;                /* Top of the index fill loop */
  int regRecord;              /* Register holding an index record */
  int n;                      /* Column counter */
  int i;                      /* Loop counter */
  int mxBitCol;               /* Maximum column in pSrc->colUsed */
  CollSeq *pColl;             /* Collating sequence to on a column */
  WhereLoop *pLoop;           /* The Loop object */
  Bitmask idxCols;            /* Bitmap of columns used for indexing */
  Bitmask extraCols;          /* Bitmap of additional columns */

  /* Generate code to skip over the creation and initialization of the
  ** transient index on 2nd and subsequent iterations of the loop. */
  v = pParse->pVdbe;
  assert( v!=0 );
................................................................................
  addrInit = sqlite3CodeOnce(pParse);

  /* Count the number of columns that will be added to the index
  ** and used to match WHERE clause constraints */
  nColumn = 0;
  pTable = pSrc->pTab;
  pWCEnd = &pWC->a[pWC->nTerm];
  pLoop = pLevel->pWLoop;
  idxCols = 0;
  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){
    if( termCanDriveIndex(pTerm, pSrc, notReady) ){
      int iCol = pTerm->u.leftColumn;
      Bitmask cMask = iCol>=BMS ? ((Bitmask)1)<<(BMS-1) : ((Bitmask)1)<<iCol;
      testcase( iCol==BMS );
      testcase( iCol==BMS-1 );
................................................................................
      if( (idxCols & cMask)==0 ){
        nColumn++;
        idxCols |= cMask;
      }
    }
  }
  assert( nColumn>0 );
  pLoop->u.btree.nEq = nColumn;

  /* Count the number of additional columns needed to create a
  ** covering index.  A "covering index" is an index that contains all
  ** columns that are needed by the query.  With a covering index, the
  ** original table never needs to be accessed.  Automatic indices must
  ** be a covering index because the index will not be updated if the
  ** original table changes and the index and table cannot both be used
................................................................................
  testcase( pTable->nCol==BMS-2 );
  for(i=0; i<mxBitCol; i++){
    if( extraCols & (((Bitmask)1)<<i) ) nColumn++;
  }
  if( pSrc->colUsed & (((Bitmask)1)<<(BMS-1)) ){
    nColumn += pTable->nCol - BMS + 1;
  }
  pLoop->wsFlags |= WHERE_COLUMN_EQ | WHERE_IDX_ONLY;

  /* Construct the Index object to describe this index */
  nByte = sizeof(Index);
  nByte += nColumn*sizeof(int);     /* Index.aiColumn */
  nByte += nColumn*sizeof(char*);   /* Index.azColl */
  nByte += nColumn;                 /* Index.aSortOrder */
  pIdx = sqlite3DbMallocZero(pParse->db, nByte);
  if( pIdx==0 ) return;
  pLoop->u.btree.pIndex = pIdx;
  pIdx->azColl = (char**)&pIdx[1];
  pIdx->aiColumn = (int*)&pIdx->azColl[nColumn];
  pIdx->aSortOrder = (u8*)&pIdx->aiColumn[nColumn];
  pIdx->zName = "auto-index";
  pIdx->nColumn = nColumn;
  pIdx->pTable = pTable;
  n = 0;
................................................................................
        pIdx->aiColumn[n] = pTerm->u.leftColumn;
        pColl = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);
        pIdx->azColl[n] = ALWAYS(pColl) ? pColl->zName : "BINARY";
        n++;
      }
    }
  }
  assert( (u32)n==pLoop->u.btree.nEq );

  /* Add additional columns needed to make the automatic index into
  ** a covering index */
  for(i=0; i<mxBitCol; i++){
    if( extraCols & (((Bitmask)1)<<i) ){
      pIdx->aiColumn[n] = i;
      pIdx->azColl[n] = "BINARY";
................................................................................
      sqlite3ErrorMsg(pParse, 
          "table %s: xBestIndex returned an invalid plan", pTab->zName);
    }
  }

  return pParse->nErr;
}
#endif /* !defined(SQLITE_OMIT_VIRTUALTABLE) */










































































































































































































#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the location of a particular key among all keys in an
** index.  Store the results in aStat as follows:
**
**    aStat[0]      Est. number of rows less than pVal
................................................................................
    *pnRow = nRowEst;
    /*WHERETRACE(("IN row estimate: est=%g\n", nRowEst));*/
  }
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT3) */










































































































































































































































































































































































































































































































































































































































































































































































































































































































/*
** Disable a term in the WHERE clause.  Except, do not disable the term
** if it controls a LEFT OUTER JOIN and it did not originate in the ON
** or USING clause of that join.
**
** Consider the term t2.z='ok' in the following queries:
**
................................................................................
** this routine sets up a loop that will iterate over all values of X.
*/
static int codeEqualityTerm(
  Parse *pParse,      /* The parsing context */
  WhereTerm *pTerm,   /* The term of the WHERE clause to be coded */
  WhereLevel *pLevel, /* The level of the FROM clause we are working on */
  int iEq,            /* Index of the equality term within this level */
  int bRev,           /* True for reverse-order IN operations */
  int iTarget         /* Attempt to leave results in this register */
){
  Expr *pX = pTerm->pExpr;
  Vdbe *v = pParse->pVdbe;
  int iReg;                  /* Register holding results */

  assert( iTarget>0 );
................................................................................
    iReg = iTarget;
    sqlite3VdbeAddOp2(v, OP_Null, 0, iReg);
#ifndef SQLITE_OMIT_SUBQUERY
  }else{
    int eType;
    int iTab;
    struct InLoop *pIn;
    WhereLoop *pLoop = pLevel->pWLoop;

    if( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0
      && pLoop->u.btree.pIndex!=0
      && pLoop->u.btree.pIndex->aSortOrder[iEq]
    ){
      testcase( iEq==0 );
      testcase( iEq==pLevel->plan.u.pIdx->nColumn-1 );
      testcase( iEq>0 && iEq+1<pLevel->plan.u.pIdx->nColumn );
      testcase( bRev );
      bRev = !bRev;
    }
................................................................................
    eType = sqlite3FindInIndex(pParse, pX, 0);
    if( eType==IN_INDEX_INDEX_DESC ){
      testcase( bRev );
      bRev = !bRev;
    }
    iTab = pX->iTable;
    sqlite3VdbeAddOp2(v, bRev ? OP_Last : OP_Rewind, iTab, 0);
    assert( pLoop->wsFlags & WHERE_IN_ABLE );
    if( pLevel->u.in.nIn==0 ){
      pLevel->addrNxt = sqlite3VdbeMakeLabel(v);
    }
    pLevel->u.in.nIn++;
    pLevel->u.in.aInLoop =
       sqlite3DbReallocOrFree(pParse->db, pLevel->u.in.aInLoop,
                              sizeof(pLevel->u.in.aInLoop[0])*pLevel->u.in.nIn);
................................................................................
** string in this example would be set to SQLITE_AFF_NONE.
*/
static int codeAllEqualityTerms(
  Parse *pParse,        /* Parsing context */
  WhereLevel *pLevel,   /* Which nested loop of the FROM we are coding */
  WhereClause *pWC,     /* The WHERE clause */
  Bitmask notReady,     /* Which parts of FROM have not yet been coded */
  int bRev,             /* Reverse the order of IN operators */
  int nExtraReg,        /* Number of extra registers to allocate */
  char **pzAff          /* OUT: Set to point to affinity string */
){
  int nEq;                      /* The number of == or IN constraints to code */
  Vdbe *v = pParse->pVdbe;      /* The vm under construction */
  Index *pIdx;                  /* The index being used for this loop */

  WhereTerm *pTerm;             /* A single constraint term */
  WhereLoop *pLoop;             /* The WhereLoop object */
  int j;                        /* Loop counter */
  int regBase;                  /* Base register */
  int nReg;                     /* Number of registers to allocate */
  char *zAff;                   /* Affinity string to return */


  /* This module is only called on query plans that use an index. */
  pLoop = pLevel->pWLoop;
  assert( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0 );
  nEq = pLoop->u.btree.nEq;
  pIdx = pLoop->u.btree.pIndex;
  assert( pIdx!=0 );

  /* Figure out how many memory cells we will need then allocate them.
  */
  regBase = pParse->nMem + 1;
  nReg = pLoop->u.btree.nEq + nExtraReg;
  pParse->nMem += nReg;

  zAff = sqlite3DbStrDup(pParse->db, sqlite3IndexAffinityStr(v, pIdx));
  if( !zAff ){
    pParse->db->mallocFailed = 1;
  }

  /* Evaluate the equality constraints
  */
  assert( pIdx->nColumn>=nEq );


  for(j=0; j<nEq; j++){
    int r1;



    pTerm = pLoop->aTerm[j];
    assert( pTerm!=0 );
    /* The following true for indices with redundant columns. 
    ** Ex: CREATE INDEX i1 ON t1(a,b,a); SELECT * FROM t1 WHERE a=0 AND b=0; */
    testcase( (pTerm->wtFlags & TERM_CODED)!=0 );
    testcase( pTerm->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
    r1 = codeEqualityTerm(pParse, pTerm, pLevel, j, bRev, regBase+j);
    if( r1!=regBase+j ){
      if( nReg==1 ){
        sqlite3ReleaseTempReg(pParse, regBase);
        regBase = r1;
      }else{
        sqlite3VdbeAddOp2(v, OP_SCopy, r1, regBase+j);
      }
................................................................................
){
  int j, k;            /* Loop counters */
  int iCur;            /* The VDBE cursor for the table */
  int addrNxt;         /* Where to jump to continue with the next IN case */
  int omitTable;       /* True if we use the index only */
  int bRev;            /* True if we need to scan in reverse order */
  WhereLevel *pLevel;  /* The where level to be coded */
  WhereLoop *pLoop;    /* The WhereLoop object being coded */
  WhereClause *pWC;    /* Decomposition of the entire WHERE clause */
  WhereTerm *pTerm;               /* A WHERE clause term */
  Parse *pParse;                  /* Parsing context */
  Vdbe *v;                        /* The prepared stmt under constructions */
  struct SrcList_item *pTabItem;  /* FROM clause term being coded */
  int addrBrk;                    /* Jump here to break out of the loop */
  int addrCont;                   /* Jump here to continue with next cycle */
................................................................................
  int iReleaseReg = 0;      /* Temp register to free before returning */
  Bitmask newNotReady;      /* Return value */

  pParse = pWInfo->pParse;
  v = pParse->pVdbe;
  pWC = pWInfo->pWC;
  pLevel = &pWInfo->a[iLevel];
  pLoop = pLevel->pWLoop;
  pTabItem = &pWInfo->pTabList->a[pLevel->iFrom];
  iCur = pTabItem->iCursor;

  bRev = (pWInfo->revMask>>iLevel)&1;
  omitTable = (pLoop->wsFlags & WHERE_IDX_ONLY)!=0 
           && (wctrlFlags & WHERE_FORCE_TABLE)==0;
  VdbeNoopComment((v, "Begin Join Loop %d", iLevel));

  /* Create labels for the "break" and "continue" instructions
  ** for the current loop.  Jump to addrBrk to break out of a loop.
  ** Jump to cont to go immediately to the next iteration of the
  ** loop.
................................................................................
    pLevel->p2 =  sqlite3VdbeAddOp1(v, OP_Yield, regYield);
    VdbeComment((v, "next row of co-routine %s", pTabItem->pTab->zName));
    sqlite3VdbeAddOp2(v, OP_If, regYield+1, addrBrk);
    pLevel->op = OP_Goto;
  }else

#ifndef SQLITE_OMIT_VIRTUALTABLE
  if(  (pLoop->wsFlags & WHERE_VIRTUALTABLE)!=0 ){
    /* Case 1:  The table is a virtual-table.  Use the VFilter and VNext
    **          to access the data.
    */
    int iReg;   /* P3 Value for OP_VFilter */
    int addrNotFound;

    int nConstraint = pLoop->nTerm;





    sqlite3ExprCachePush(pParse);
    iReg = sqlite3GetTempRange(pParse, nConstraint+2);
    addrNotFound = pLevel->addrBrk;
    for(j=0; j<nConstraint; j++){


      int iTarget = iReg+j+1;

      pTerm = pLoop->aTerm[j];
      if( pTerm->eOperator & WO_IN ){
        codeEqualityTerm(pParse, pTerm, pLevel, j, bRev, iTarget);
        addrNotFound = pLevel->addrNxt;
      }else{
        sqlite3ExprCode(pParse, pTerm->pExpr->pRight, iTarget);
      }

    }



    sqlite3VdbeAddOp2(v, OP_Integer, pLoop->u.vtab.idxNum, iReg);
    sqlite3VdbeAddOp2(v, OP_Integer, j-1, iReg+1);
    sqlite3VdbeAddOp4(v, OP_VFilter, iCur, addrNotFound, iReg,
                      pLoop->u.vtab.idxStr,
                      pLoop->u.vtab.needFree ? P4_MPRINTF : P4_STATIC);

    pLoop->u.vtab.needFree = 0;
    for(j=0; j<nConstraint && j<16; j++){


      if( (pLoop->u.vtab.omitMask>>j)&1 ){
        disableTerm(pLevel, pLoop->aTerm[j]);
      }
    }
    pLevel->op = OP_VNext;
    pLevel->p1 = iCur;
    pLevel->p2 = sqlite3VdbeCurrentAddr(v);
    sqlite3ReleaseTempRange(pParse, iReg, nConstraint+2);
    sqlite3ExprCachePop(pParse, 1);
  }else
#endif /* SQLITE_OMIT_VIRTUALTABLE */

  if( (pLoop->wsFlags & WHERE_IPK)!=0
   && (pLoop->wsFlags & (WHERE_COLUMN_IN|WHERE_COLUMN_EQ))!=0
  ){
    /* Case 2:  We can directly reference a single row using an
    **          equality comparison against the ROWID field.  Or
    **          we reference multiple rows using a "rowid IN (...)"
    **          construct.
    */
    assert( pLoop->u.btree.nEq==1 );
    iReleaseReg = sqlite3GetTempReg(pParse);

    pTerm = pLoop->aTerm[0];
    assert( pTerm!=0 );
    assert( pTerm->pExpr!=0 );
    assert( omitTable==0 );
    testcase( pTerm->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
    iRowidReg = codeEqualityTerm(pParse, pTerm, pLevel, 0, bRev, iReleaseReg);
    addrNxt = pLevel->addrNxt;
    sqlite3VdbeAddOp2(v, OP_MustBeInt, iRowidReg, addrNxt);
    sqlite3VdbeAddOp3(v, OP_NotExists, iCur, addrNxt, iRowidReg);
    sqlite3ExprCacheAffinityChange(pParse, iRowidReg, 1);
    sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
    VdbeComment((v, "pk"));
    pLevel->op = OP_Noop;
  }else if( (pLoop->wsFlags & WHERE_IPK)!=0
         && (pLoop->wsFlags & WHERE_COLUMN_RANGE)!=0
  ){
    /* Case 3:  We have an inequality comparison against the ROWID field.
    */
    int testOp = OP_Noop;
    int start;
    int memEndValue = 0;
    WhereTerm *pStart, *pEnd;

    assert( omitTable==0 );
    j = 0;
    pStart = pEnd = 0;
    if( pLoop->wsFlags & WHERE_BTM_LIMIT ) pStart = pLoop->aTerm[j++];
    if( pLoop->wsFlags & WHERE_TOP_LIMIT ) pEnd = pLoop->aTerm[j++];
    if( bRev ){
      pTerm = pStart;
      pStart = pEnd;
      pEnd = pTerm;
    }
    if( pStart ){
      Expr *pX;             /* The expression that defines the start bound */
................................................................................
    if( testOp!=OP_Noop ){
      iRowidReg = iReleaseReg = sqlite3GetTempReg(pParse);
      sqlite3VdbeAddOp2(v, OP_Rowid, iCur, iRowidReg);
      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
      sqlite3VdbeAddOp3(v, testOp, memEndValue, addrBrk, iRowidReg);
      sqlite3VdbeChangeP5(v, SQLITE_AFF_NUMERIC | SQLITE_JUMPIFNULL);
    }
  }else if( pLoop->wsFlags & (WHERE_COLUMN_RANGE|WHERE_COLUMN_EQ|WHERE_IDX_ONLY) ){
    /* Case 4: A scan using an index.
    **
    **         The WHERE clause may contain zero or more equality 
    **         terms ("==" or "IN" operators) that refer to the N
    **         left-most columns of the index. It may also contain
    **         inequality constraints (>, <, >= or <=) on the indexed
    **         column that immediately follows the N equalities. Only 
    **         the right-most column can be an inequality - the rest must
................................................................................
      OP_SeekLe            /* 7: (start_constraints  &&  startEq &&  bRev) */
    };
    static const u8 aEndOp[] = {
      OP_Noop,             /* 0: (!end_constraints) */
      OP_IdxGE,            /* 1: (end_constraints && !bRev) */
      OP_IdxLT             /* 2: (end_constraints && bRev) */
    };
    int nEq = pLoop->u.btree.nEq;  /* Number of == or IN terms */
    int isMinQuery = 0;            /* If this is an optimized SELECT min(x).. */
    int regBase;                 /* Base register holding constraint values */
    int r1;                      /* Temp register */
    WhereTerm *pRangeStart = 0;  /* Inequality constraint at range start */
    WhereTerm *pRangeEnd = 0;    /* Inequality constraint at range end */
    int startEq;                 /* True if range start uses ==, >= or <= */
    int endEq;                   /* True if range end uses ==, >= or <= */
    int start_constraints;       /* Start of range is constrained */
................................................................................
    Index *pIdx;                 /* The index we will be using */
    int iIdxCur;                 /* The VDBE cursor for the index */
    int nExtraReg = 0;           /* Number of extra registers needed */
    int op;                      /* Instruction opcode */
    char *zStartAff;             /* Affinity for start of range constraint */
    char *zEndAff;               /* Affinity for end of range constraint */

    pIdx = pLoop->u.btree.pIndex;
    iIdxCur = pLevel->iIdxCur;
    k = (nEq==pIdx->nColumn ? -1 : pIdx->aiColumn[nEq]);

    /* If this loop satisfies a sort order (pOrderBy) request that 
    ** was passed to this function to implement a "SELECT min(x) ..." 
    ** query, then the caller will only allow the loop to run for
    ** a single iteration. This means that the first row returned
    ** should not have a NULL value stored in 'x'. If column 'x' is
    ** the first one after the nEq equality constraints in the index,
    ** this requires some special handling.
    */
    if( (wctrlFlags&WHERE_ORDERBY_MIN)!=0
     && (pWInfo->nOBSat>0)
     && (pIdx->nColumn>nEq)
    ){
      /* assert( pOrderBy->nExpr==1 ); */
      /* assert( pOrderBy->a[0].pExpr->iColumn==pIdx->aiColumn[nEq] ); */
      isMinQuery = 1;
      nExtraReg = 1;
    }

    /* Find any inequality constraint terms for the start and end 
    ** of the range. 
    */
    j = nEq;
    if( pLoop->wsFlags & WHERE_BTM_LIMIT ){
      pRangeStart = pLoop->aTerm[j++];
      nExtraReg = 1;
    }
    if( pLoop->wsFlags & WHERE_TOP_LIMIT ){
      pRangeEnd = pLoop->aTerm[j++];
      nExtraReg = 1;
    }

    /* Generate code to evaluate all constraint terms using == or IN
    ** and store the values of those terms in an array of registers
    ** starting at regBase.
    */
    regBase = codeAllEqualityTerms(
        pParse, pLevel, pWC, notReady, bRev, nExtraReg, &zStartAff
    );
    zEndAff = sqlite3DbStrDup(pParse->db, zStartAff);
    addrNxt = pLevel->addrNxt;

    /* If we are doing a reverse order scan on an ascending index, or
    ** a forward order scan on a descending index, interchange the 
    ** start and end terms (pRangeStart and pRangeEnd).
................................................................................
    /* If there are inequality constraints, check that the value
    ** of the table column that the inequality contrains is not NULL.
    ** If it is, jump to the next iteration of the loop.
    */
    r1 = sqlite3GetTempReg(pParse);
    testcase( pLevel->plan.wsFlags & WHERE_BTM_LIMIT );
    testcase( pLevel->plan.wsFlags & WHERE_TOP_LIMIT );
    if( (pLoop->wsFlags & (WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))!=0 ){
      sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, nEq, r1);
      sqlite3VdbeAddOp2(v, OP_IsNull, r1, addrCont);
    }
    sqlite3ReleaseTempReg(pParse, r1);

    /* Seek the table cursor, if required */
    disableTerm(pLevel, pRangeStart);
................................................................................
      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
      sqlite3VdbeAddOp2(v, OP_Seek, iCur, iRowidReg);  /* Deferred seek */
    }

    /* Record the instruction used to terminate the loop. Disable 
    ** WHERE clause terms made redundant by the index range scan.
    */
    if( pLoop->wsFlags & WHERE_UNIQUE ){
      pLevel->op = OP_Noop;
    }else if( bRev ){
      pLevel->op = OP_Prev;
    }else{
      pLevel->op = OP_Next;
    }
    pLevel->p1 = iIdxCur;
    if( pLoop->wsFlags & WHERE_COVER_SCAN ){
      pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;
    }else{
      assert( pLevel->p5==0 );
    }
  }else

#ifndef SQLITE_OMIT_OR_OPTIMIZATION
  if( pLoop->wsFlags & WHERE_MULTI_OR ){
    /* Case 5:  Two or more separately indexed terms connected by OR
    **
    ** Example:
    **
    **   CREATE TABLE t1(a,b,c,d);
    **   CREATE INDEX i1 ON t1(a);
    **   CREATE INDEX i2 ON t1(b);
    **   CREATE INDEX i3 ON t1(c);
................................................................................
    int regRowid = 0;                         /* Register holding rowid */
    int iLoopBody = sqlite3VdbeMakeLabel(v);  /* Start of loop body */
    int iRetInit;                             /* Address of regReturn init */
    int untestedTerms = 0;             /* Some terms not completely tested */
    int ii;                            /* Loop counter */
    Expr *pAndExpr = 0;                /* An ".. AND (...)" expression */
   
    pTerm = pLoop->aTerm[0];
    assert( pTerm!=0 );
    assert( pTerm->eOperator & WO_OR );
    assert( (pTerm->wtFlags & TERM_ORINFO)!=0 );
    pOrWc = &pTerm->u.pOrInfo->wc;
    pLevel->op = OP_Return;
    pLevel->p1 = regReturn;

................................................................................
        }
        /* Loop through table entries that match term pOrTerm. */
        pSubWInfo = sqlite3WhereBegin(pParse, pOrTab, pOrExpr, 0, 0,
                        WHERE_OMIT_OPEN_CLOSE | WHERE_AND_ONLY |
                        WHERE_FORCE_TABLE | WHERE_ONETABLE_ONLY, iCovCur);
        assert( pSubWInfo || pParse->nErr || pParse->db->mallocFailed );
        if( pSubWInfo ){
          WhereLoop *pSubLoop;
          explainOneScan(
              pParse, pOrTab, &pSubWInfo->a[0], iLevel, pLevel->iFrom, 0
          );
          if( (wctrlFlags & WHERE_DUPLICATES_OK)==0 ){
            int iSet = ((ii==pOrWc->nTerm-1)?-1:ii);
            int r;
            r = sqlite3ExprCodeGetColumn(pParse, pTabItem->pTab, -1, iCur, 
................................................................................
          ** If the call to sqlite3WhereBegin() above resulted in a scan that
          ** uses an index, and this is either the first OR-connected term
          ** processed or the index is the same as that used by all previous
          ** terms, set pCov to the candidate covering index. Otherwise, set 
          ** pCov to NULL to indicate that no candidate covering index will 
          ** be available.
          */
          pSubLoop = pSubWInfo->a[0].pWLoop;
          if( (pSubLoop->wsFlags & WHERE_INDEXED)!=0
           && (pSubLoop->wsFlags & WHERE_TEMP_INDEX)==0
           && (ii==0 || pSubLoop->u.btree.pIndex==pCov)
          ){
            assert( pSubWInfo->a[0].iIdxCur==iCovCur );
            pCov = pLoop->u.btree.pIndex;
          }else{
            pCov = 0;
          }

          /* Finish the loop through table entries that match term pOrTerm. */
          sqlite3WhereEnd(pSubWInfo);
        }
................................................................................

    if( pWInfo->nLevel>1 ) sqlite3StackFree(pParse->db, pOrTab);
    if( !untestedTerms ) disableTerm(pLevel, pTerm);
  }else
#endif /* SQLITE_OMIT_OR_OPTIMIZATION */

  {
    /* Case 6:  There is no usable index.  We must do a complete
    **          scan of the entire table.
    */
    static const u8 aStep[] = { OP_Next, OP_Prev };
    static const u8 aStart[] = { OP_Rewind, OP_Last };
    assert( bRev==0 || bRev==1 );

    pLevel->op = aStep[bRev];
    pLevel->p1 = iCur;
    pLevel->p2 = 1 + sqlite3VdbeAddOp2(v, aStart[bRev], iCur, addrBrk);
    pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;
  }
  newNotReady = notReady & ~getMask(pWC->pMaskSet, iCur);

................................................................................
/*
** Free a WhereInfo structure
*/
static void whereInfoFree(sqlite3 *db, WhereInfo *pWInfo){
  if( ALWAYS(pWInfo) ){
    int i;
    for(i=0; i<pWInfo->nLevel; i++){








      if( pWInfo->a[i].pWLoop->wsFlags & WHERE_TEMP_INDEX ){
        Index *pIdx = pWInfo->a[i].pWLoop->u.btree.pIndex;
        if( pIdx ){
          sqlite3DbFree(db, pIdx->zColAff);
          sqlite3DbFree(db, pIdx);
        }
      }
    }
    whereClauseClear(pWInfo->pWC);
................................................................................
  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  savedLoop = *pNew;
  pNew->rSetup = (double)0;
  rLogSize = estLog(pProbe->aiRowEst[0]);
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 1;
    pNew->wsFlags = savedLoop.wsFlags;
    pNew->u.btree.nEq = savedLoop.u.btree.nEq;
    pNew->nTerm = savedLoop.nTerm;
    if( pNew->nTerm>=pBuilder->mxTerm ) break; /* Repeated column in index */
    pNew->aTerm[pNew->nTerm++] = pTerm;
    pNew->prereq = (savedLoop.prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    if( pTerm->eOperator & WO_IN ){
      Expr *pExpr = pTerm->pExpr;
................................................................................
  pFrom = aFrom;
  for(ii=1; ii<nFrom; ii++){
    if( pFrom->rCost>aFrom[ii].rCost ) pFrom = &aFrom[ii];
  }
  assert( pWInfo->nLevel==nLoop );
  /* Load the lowest cost path into pWInfo */
  for(iLoop=0; iLoop<nLoop; iLoop++){
    WhereLevel *pLevel = pWInfo->a + iLoop;
    pLevel->pWLoop = pWLoop = pFrom->aLoop[iLoop];
    pLevel->iFrom = pWLoop->iTab; /* FIXME: Omit the iFrom field */
    pLevel->iTabCur = pWInfo->pTabList->a[pLevel->iFrom].iCursor;
  }
  if( pFrom->isOrdered ){
    pWInfo->nOBSat = pWInfo->pOrderBy->nExpr;
    pWInfo->revMask = pFrom->revLoop;
  }
  pWInfo->nRowOut = pFrom->nRow;

................................................................................
  WhereInfo *pWInfo;         /* Will become the return value of this function */
  Vdbe *v = pParse->pVdbe;   /* The virtual database engine */
  Bitmask notReady;          /* Cursors that are not yet positioned */
  WhereBestIdx sWBI;         /* Best index search context */
  WhereLoopBuilder sWLB;     /* The WhereLoop builder */
  WhereMaskSet *pMaskSet;    /* The expression mask set */
  WhereLevel *pLevel;        /* A single level in pWInfo->a[] */


  int ii;                    /* Loop counter */
  sqlite3 *db;               /* Database connection */
  int rc;                    /* Return code */


  /* Variable initialization */
  memset(&sWBI, 0, sizeof(sWBI));
................................................................................
    }
    for(ii=0; ii<nTabList; ii++){
      whereLoopPrint(pWInfo->a[ii].pWLoop, pTabList);
    }
  }
#endif

#if 0  /* FIXME: Add this back in? */











































































































































































































































































  /* If the caller is an UPDATE or DELETE statement that is requesting
  ** to use a one-pass algorithm, determine if this is appropriate.
  ** The one-pass algorithm only works if the WHERE clause constraints
  ** the statement to update a single row.
  */
  assert( (wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || pWInfo->nLevel==1 );
  if( (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 && (andFlags & WHERE_UNIQUE)!=0 ){
    pWInfo->okOnePass = 1;
    pWInfo->a[0].plan.wsFlags &= ~WHERE_IDX_ONLY;
  }










#endif

  /* Open all tables in the pTabList and any indices selected for
  ** searching those tables.
  */
  sqlite3CodeVerifySchema(pParse, -1); /* Insert the cookie verifier Goto */
  notReady = ~(Bitmask)0;
  pWInfo->nRowOut = (double)1;
  for(ii=0, pLevel=pWInfo->a; ii<nTabList; ii++, pLevel++){
    Table *pTab;     /* Table to open */
    int iDb;         /* Index of database containing table/index */
    struct SrcList_item *pTabItem;
    WhereLoop *pLoop;

    pTabItem = &pTabList->a[pLevel->iFrom];
    pTab = pTabItem->pTab;

    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);
    pLoop = pLevel->pWLoop;
    if( (pTab->tabFlags & TF_Ephemeral)!=0 || pTab->pSelect ){
      /* Do nothing */
    }else
#ifndef SQLITE_OMIT_VIRTUALTABLE
    if( (pLoop->wsFlags & WHERE_VIRTUALTABLE)!=0 ){
      const char *pVTab = (const char *)sqlite3GetVTable(db, pTab);
      int iCur = pTabItem->iCursor;
      sqlite3VdbeAddOp4(v, OP_VOpen, iCur, 0, 0, pVTab, P4_VTAB);
    }else if( IsVirtual(pTab) ){
      /* noop */
    }else
#endif
    if( (pLoop->wsFlags & WHERE_IDX_ONLY)==0
         && (wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0 ){
      int op = pWInfo->okOnePass ? OP_OpenWrite : OP_OpenRead;
      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, op);
      testcase( pTab->nCol==BMS-1 );
      testcase( pTab->nCol==BMS );
      if( !pWInfo->okOnePass && pTab->nCol<BMS ){
        Bitmask b = pTabItem->colUsed;
................................................................................
                            SQLITE_INT_TO_PTR(n), P4_INT32);
        assert( n<=pTab->nCol );
      }
    }else{
      sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);
    }
#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
    if( (pLoop->wsFlags & WHERE_TEMP_INDEX)!=0 ){
      constructAutomaticIndex(pParse, sWBI.pWC, pTabItem, notReady, pLevel);
    }else
#endif
    if( pLoop->u.btree.pIndex!=0 ){
      Index *pIx = pLoop->u.btree.pIndex;
      KeyInfo *pKey = sqlite3IndexKeyinfo(pParse, pIx);
      /* FIXME:  Might need to be the iIdxCur parameter.  As an optimization
      ** use pTabItem->iCursor if WHERE_IDX_ONLY */
      int iIndexCur = pLevel->iIdxCur = pParse->nTab++;
      assert( pIx->pSchema==pTab->pSchema );
      assert( iIndexCur>=0 );
      sqlite3VdbeAddOp4(v, OP_OpenRead, iIndexCur, pIx->tnum, iDb,
                        (char*)pKey, P4_KEYINFO_HANDOFF);
      VdbeComment((v, "%s", pIx->zName));
    }
    sqlite3CodeVerifySchema(pParse, iDb);
................................................................................
  for(ii=0; ii<nTabList; ii++){
    pLevel = &pWInfo->a[ii];
    explainOneScan(pParse, pTabList, pLevel, ii, pLevel->iFrom, wctrlFlags);
    notReady = codeOneLoopStart(pWInfo, ii, wctrlFlags, notReady);
    pWInfo->iContinue = pLevel->addrCont;
  }

#if defined(SQLITE_TEST) && 0  /* For testing and debugging use only */
  /* Record in the query plan information about the current table
  ** and the index used to access it (if any).  If the table itself
  ** is not used, its name is just '{}'.  If no index is used
  ** the index is listed as "{}".  If the primary key is used the
  ** index name is '*'.
  */
  for(ii=0; ii<nTabList; ii++){
................................................................................
** sqlite3WhereBegin() for additional information.
*/
void sqlite3WhereEnd(WhereInfo *pWInfo){
  Parse *pParse = pWInfo->pParse;
  Vdbe *v = pParse->pVdbe;
  int i;
  WhereLevel *pLevel;
  WhereLoop *pLoop;
  SrcList *pTabList = pWInfo->pTabList;
  sqlite3 *db = pParse->db;

  /* Generate loop termination code.
  */
  sqlite3ExprCacheClear(pParse);
  for(i=pWInfo->nLevel-1; i>=0; i--){
    pLevel = &pWInfo->a[i];
    pLoop = pLevel->pWLoop;
    sqlite3VdbeResolveLabel(v, pLevel->addrCont);
    if( pLevel->op!=OP_Noop ){
      sqlite3VdbeAddOp2(v, pLevel->op, pLevel->p1, pLevel->p2);
      sqlite3VdbeChangeP5(v, pLevel->p5);
    }
    if( pLoop->wsFlags & WHERE_IN_ABLE && pLevel->u.in.nIn>0 ){
      struct InLoop *pIn;
      int j;
      sqlite3VdbeResolveLabel(v, pLevel->addrNxt);
      for(j=pLevel->u.in.nIn, pIn=&pLevel->u.in.aInLoop[j-1]; j>0; j--, pIn--){
        sqlite3VdbeJumpHere(v, pIn->addrInTop+1);
        sqlite3VdbeAddOp2(v, pIn->eEndLoopOp, pIn->iCur, pIn->addrInTop);
        sqlite3VdbeJumpHere(v, pIn->addrInTop-1);
................................................................................
      }
      sqlite3DbFree(db, pLevel->u.in.aInLoop);
    }
    sqlite3VdbeResolveLabel(v, pLevel->addrBrk);
    if( pLevel->iLeftJoin ){
      int addr;
      addr = sqlite3VdbeAddOp1(v, OP_IfPos, pLevel->iLeftJoin);
      assert( (pLoop->wsFlags & WHERE_IDX_ONLY)==0
           || (pLoop->wsFlags & WHERE_INDEXED)!=0 );
      if( (pLoop->wsFlags & WHERE_IDX_ONLY)==0 ){
        sqlite3VdbeAddOp1(v, OP_NullRow, pTabList->a[i].iCursor);
      }
      if( pLevel->iIdxCur>=0 ){
        sqlite3VdbeAddOp1(v, OP_NullRow, pLevel->iIdxCur);
      }
      if( pLevel->op==OP_Return ){
        sqlite3VdbeAddOp2(v, OP_Gosub, pLevel->p1, pLevel->addrFirst);
................................................................................
  */
  assert( pWInfo->nLevel==1 || pWInfo->nLevel==pTabList->nSrc );
  for(i=0, pLevel=pWInfo->a; i<pWInfo->nLevel; i++, pLevel++){
    Index *pIdx = 0;
    struct SrcList_item *pTabItem = &pTabList->a[pLevel->iFrom];
    Table *pTab = pTabItem->pTab;
    assert( pTab!=0 );
    pLoop = pLevel->pWLoop;
    if( (pTab->tabFlags & TF_Ephemeral)==0
     && pTab->pSelect==0
     && (pWInfo->wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0
    ){
      int ws = pLoop->wsFlags;
      if( !pWInfo->okOnePass && (ws & WHERE_IDX_ONLY)==0 ){
        sqlite3VdbeAddOp1(v, OP_Close, pTabItem->iCursor);
      }
      if( (ws & WHERE_INDEXED)!=0 && (ws & (WHERE_IPK|WHERE_TEMP_INDEX))==0 ){
        sqlite3VdbeAddOp1(v, OP_Close, pLevel->iIdxCur);
      }
    }

    /* If this scan uses an index, make code substitutions to read data
    ** from the index in preference to the table. Sometimes, this means
    ** the table need never be read from. This is a performance boost,
................................................................................
    ** 
    ** Calls to the code generator in between sqlite3WhereBegin and
    ** sqlite3WhereEnd will have created code that references the table
    ** directly.  This loop scans all that code looking for opcodes
    ** that reference the table and converts them into opcodes that
    ** reference the index.
    */
    if( pLoop->wsFlags & (WHERE_INDEXED|WHERE_IDX_ONLY) ){
      pIdx = pLoop->u.btree.pIndex;
    }else if( pLoop->wsFlags & WHERE_MULTI_OR ){
      pIdx = pLevel->u.pCovidx;
    }
    if( pIdx && !db->mallocFailed ){
      int k, j, last;
      VdbeOp *pOp;

      pOp = sqlite3VdbeGetOp(v, pWInfo->iTop);
      last = sqlite3VdbeCurrentAddr(v);
      for(k=pWInfo->iTop; k<last; k++, pOp++){
        if( pOp->p1!=pLevel->iTabCur ) continue;
................................................................................
          for(j=0; j<pIdx->nColumn; j++){
            if( pOp->p2==pIdx->aiColumn[j] ){
              pOp->p2 = j;
              pOp->p1 = pLevel->iIdxCur;
              break;
            }
          }
          assert( (pLoop->wsFlags & WHERE_IDX_ONLY)==0 || j<pIdx->nColumn );

        }else if( pOp->opcode==OP_Rowid ){
          pOp->p1 = pLevel->iIdxCur;
          pOp->opcode = OP_IdxRowid;
        }
      }
    }
  }