}else{
      sqlite3VdbeAddOp3(v, OP_Column, iCur, idx, regBase+j);
      sqlite3ColumnDefault(v, pTab, idx, -1);
    }
  }
  if( doMakeRec ){
    const char *zAff;
    if( pTab->pSelect || (pParse->db->flags & SQLITE_IdxRealAsInt)!=0 ){


      zAff = 0;
    }else{
      zAff = sqlite3IndexAffinityStr(v, pIdx);
    }
    sqlite3VdbeAddOp3(v, OP_MakeRecord, regBase, nCol+1, regOut);
    sqlite3VdbeChangeP4(v, -1, zAff, P4_TRANSIENT);
  }
  sqlite3ReleaseTempRange(pParse, regBase, nCol+1);
  return regBase;
}

    }else{
      sqlite3VdbeAddOp3(v, OP_Column, iCur, idx, regBase+j);
      sqlite3ColumnDefault(v, pTab, idx, -1);
    }
  }
  if( doMakeRec ){
    const char *zAff;
    if( pTab->pSelect
     || OptimizationDisabled(pParse->db, SQLITE_IdxRealAsInt)
    ){
      zAff = 0;
    }else{
      zAff = sqlite3IndexAffinityStr(v, pIdx);
    }
    sqlite3VdbeAddOp3(v, OP_MakeRecord, regBase, nCol+1, regOut);
    sqlite3VdbeChangeP4(v, -1, zAff, P4_TRANSIENT);
  }
  sqlite3ReleaseTempRange(pParse, regBase, nCol+1);
  return regBase;
}

  assert( iReg>0 );  /* Register numbers are always positive */
  assert( iCol>=-1 && iCol<32768 );  /* Finite column numbers */

  /* The SQLITE_ColumnCache flag disables the column cache.  This is used
  ** for testing only - to verify that SQLite always gets the same answer
  ** with and without the column cache.
  */
  if( pParse->db->flags & SQLITE_ColumnCache ) return;

  /* First replace any existing entry.
  **
  ** Actually, the way the column cache is currently used, we are guaranteed
  ** that the object will never already be in cache.  Verify this guarantee.
  */
#ifndef NDEBUG
................................................................................
** interface.  This allows test logic to verify that the same answer is
** obtained for queries regardless of whether or not constants are
** precomputed into registers or if they are inserted in-line.
*/
void sqlite3ExprCodeConstants(Parse *pParse, Expr *pExpr){
  Walker w;
  if( pParse->cookieGoto ) return;
  if( (pParse->db->flags & SQLITE_FactorOutConst)!=0 ) return;
  w.xExprCallback = evalConstExpr;
  w.xSelectCallback = 0;
  w.pParse = pParse;
  sqlite3WalkExpr(&w, pExpr);
}

  assert( iReg>0 );  /* Register numbers are always positive */
  assert( iCol>=-1 && iCol<32768 );  /* Finite column numbers */

  /* The SQLITE_ColumnCache flag disables the column cache.  This is used
  ** for testing only - to verify that SQLite always gets the same answer
  ** with and without the column cache.
  */
  if( OptimizationDisabled(pParse->db, SQLITE_ColumnCache) ) return;

  /* First replace any existing entry.
  **
  ** Actually, the way the column cache is currently used, we are guaranteed
  ** that the object will never already be in cache.  Verify this guarantee.
  */
#ifndef NDEBUG
................................................................................
** interface.  This allows test logic to verify that the same answer is
** obtained for queries regardless of whether or not constants are
** precomputed into registers or if they are inserted in-line.
*/
void sqlite3ExprCodeConstants(Parse *pParse, Expr *pExpr){
  Walker w;
  if( pParse->cookieGoto ) return;
  if( OptimizationDisabled(pParse->db, SQLITE_FactorOutConst) ) return;
  w.xExprCallback = evalConstExpr;
  w.xSelectCallback = 0;
  w.pParse = pParse;
  sqlite3WalkExpr(&w, pExpr);
}

    ** operation N should be 0.  The idea is that a test program (like the
    ** SQL Logic Test or SLT test module) can run the same SQL multiple times
    ** with various optimizations disabled to verify that the same answer
    ** is obtained in every case.
    */
    case SQLITE_TESTCTRL_OPTIMIZATIONS: {
      sqlite3 *db = va_arg(ap, sqlite3*);
      int x = va_arg(ap,int);
      db->flags = (x & SQLITE_OptMask) | (db->flags & ~SQLITE_OptMask);
      break;
    }

#ifdef SQLITE_N_KEYWORD
    /* sqlite3_test_control(SQLITE_TESTCTRL_ISKEYWORD, const char *zWord)
    **
    ** If zWord is a keyword recognized by the parser, then return the

    ** operation N should be 0.  The idea is that a test program (like the
    ** SQL Logic Test or SLT test module) can run the same SQL multiple times
    ** with various optimizations disabled to verify that the same answer
    ** is obtained in every case.
    */
    case SQLITE_TESTCTRL_OPTIMIZATIONS: {
      sqlite3 *db = va_arg(ap, sqlite3*);
      db->dbOptFlags = (u16)(va_arg(ap, int) & 0xffff);

      break;
    }

#ifdef SQLITE_N_KEYWORD
    /* sqlite3_test_control(SQLITE_TESTCTRL_ISKEYWORD, const char *zWord)
    **
    ** If zWord is a keyword recognized by the parser, then return the

  struct SrcList_item *pSubitem;   /* The subquery */
  sqlite3 *db = pParse->db;

  /* Check to see if flattening is permitted.  Return 0 if not.
  */
  assert( p!=0 );
  assert( p->pPrior==0 );  /* Unable to flatten compound queries */
  if( db->flags & SQLITE_QueryFlattener ) return 0;
  pSrc = p->pSrc;
  assert( pSrc && iFrom>=0 && iFrom<pSrc->nSrc );
  pSubitem = &pSrc->a[iFrom];
  iParent = pSubitem->iCursor;
  pSub = pSubitem->pSelect;
  assert( pSub!=0 );
  if( isAgg && subqueryIsAgg ) return 0;                 /* Restriction (1)  */
................................................................................
  ** identical, then disable the ORDER BY clause since the GROUP BY
  ** will cause elements to come out in the correct order.  This is
  ** an optimization - the correct answer should result regardless.
  ** Use the SQLITE_GroupByOrder flag with SQLITE_TESTCTRL_OPTIMIZER
  ** to disable this optimization for testing purposes.
  */
  if( sqlite3ExprListCompare(p->pGroupBy, pOrderBy)==0
         && (db->flags & SQLITE_GroupByOrder)==0 ){
    pOrderBy = 0;
  }

  /* If the query is DISTINCT with an ORDER BY but is not an aggregate, and 
  ** if the select-list is the same as the ORDER BY list, then this query
  ** can be rewritten as a GROUP BY. In other words, this:
  **
................................................................................
        resetAccumulator(pParse, &sAggInfo);
        pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, pMinMax,0,flag,0);
        if( pWInfo==0 ){
          sqlite3ExprListDelete(db, pDel);
          goto select_end;
        }
        updateAccumulator(pParse, &sAggInfo);

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

  struct SrcList_item *pSubitem;   /* The subquery */
  sqlite3 *db = pParse->db;

  /* Check to see if flattening is permitted.  Return 0 if not.
  */
  assert( p!=0 );
  assert( p->pPrior==0 );  /* Unable to flatten compound queries */
  if( OptimizationDisabled(db, SQLITE_QueryFlattener) ) return 0;
  pSrc = p->pSrc;
  assert( pSrc && iFrom>=0 && iFrom<pSrc->nSrc );
  pSubitem = &pSrc->a[iFrom];
  iParent = pSubitem->iCursor;
  pSub = pSubitem->pSelect;
  assert( pSub!=0 );
  if( isAgg && subqueryIsAgg ) return 0;                 /* Restriction (1)  */
................................................................................
  ** identical, then disable the ORDER BY clause since the GROUP BY
  ** will cause elements to come out in the correct order.  This is
  ** an optimization - the correct answer should result regardless.
  ** Use the SQLITE_GroupByOrder flag with SQLITE_TESTCTRL_OPTIMIZER
  ** to disable this optimization for testing purposes.
  */
  if( sqlite3ExprListCompare(p->pGroupBy, pOrderBy)==0
         && OptimizationEnabled(db, SQLITE_GroupByOrder) ){
    pOrderBy = 0;
  }

  /* If the query is DISTINCT with an ORDER BY but is not an aggregate, and 
  ** if the select-list is the same as the ORDER BY list, then this query
  ** can be rewritten as a GROUP BY. In other words, this:
  **
................................................................................
        resetAccumulator(pParse, &sAggInfo);
        pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, pMinMax,0,flag,0);
        if( pWInfo==0 ){
          sqlite3ExprListDelete(db, pDel);
          goto select_end;
        }
        updateAccumulator(pParse, &sAggInfo);
        assert( pMinMax==0 || pMinMax->nExpr==1 );
        if( pWInfo->nOBSat>0 ){
          sqlite3VdbeAddOp2(v, OP_Goto, 0, pWInfo->iBreak);
          VdbeComment((v, "%s() by index",
                (flag==WHERE_ORDERBY_MIN?"min":"max")));
        }
        sqlite3WhereEnd(pWInfo);
        finalizeAggFunctions(pParse, &sAggInfo);

  Db *aDb;                      /* All backends */
  int nDb;                      /* Number of backends currently in use */
  int flags;                    /* Miscellaneous flags. See below */
  i64 lastRowid;                /* ROWID of most recent insert (see above) */
  unsigned int openFlags;       /* Flags passed to sqlite3_vfs.xOpen() */
  int errCode;                  /* Most recent error code (SQLITE_*) */
  int errMask;                  /* & result codes with this before returning */

  u8 autoCommit;                /* The auto-commit flag. */
  u8 temp_store;                /* 1: file 2: memory 0: default */
  u8 mallocFailed;              /* True if we have seen a malloc failure */
  u8 dfltLockMode;              /* Default locking-mode for attached dbs */
  signed char nextAutovac;      /* Autovac setting after VACUUM if >=0 */
  u8 suppressErr;               /* Do not issue error messages if true */
  u8 vtabOnConflict;            /* Value to return for s3_vtab_on_conflict() */
................................................................................
** A macro to discover the encoding of a database.
*/
#define ENC(db) ((db)->aDb[0].pSchema->enc)

/*
** Possible values for the sqlite3.flags.
*/
#define SQLITE_VdbeTrace      0x00000100  /* True to trace VDBE execution */
#define SQLITE_InternChanges  0x00000200  /* Uncommitted Hash table changes */
#define SQLITE_FullColNames   0x00000400  /* Show full column names on SELECT */
#define SQLITE_ShortColNames  0x00000800  /* Show short columns names */
#define SQLITE_CountRows      0x00001000  /* Count rows changed by INSERT, */
                                          /*   DELETE, or UPDATE and return */
                                          /*   the count using a callback. */
#define SQLITE_NullCallback   0x00002000  /* Invoke the callback once if the */
                                          /*   result set is empty */
#define SQLITE_SqlTrace       0x00004000  /* Debug print SQL as it executes */
#define SQLITE_VdbeListing    0x00008000  /* Debug listings of VDBE programs */
#define SQLITE_WriteSchema    0x00010000  /* OK to update SQLITE_MASTER */
                         /*   0x00020000  Unused */
#define SQLITE_IgnoreChecks   0x00040000  /* Do not enforce check constraints */
#define SQLITE_ReadUncommitted 0x0080000  /* For shared-cache mode */
#define SQLITE_LegacyFileFmt  0x00100000  /* Create new databases in format 1 */
#define SQLITE_FullFSync      0x00200000  /* Use full fsync on the backend */
#define SQLITE_CkptFullFSync  0x00400000  /* Use full fsync for checkpoint */
#define SQLITE_RecoveryMode   0x00800000  /* Ignore schema errors */
#define SQLITE_ReverseOrder   0x01000000  /* Reverse unordered SELECTs */
#define SQLITE_RecTriggers    0x02000000  /* Enable recursive triggers */
#define SQLITE_ForeignKeys    0x04000000  /* Enforce foreign key constraints  */
#define SQLITE_AutoIndex      0x08000000  /* Enable automatic indexes */
#define SQLITE_PreferBuiltin  0x10000000  /* Preference to built-in funcs */
#define SQLITE_LoadExtension  0x20000000  /* Enable load_extension */
#define SQLITE_EnableTrigger  0x40000000  /* True to enable triggers */

/*
** Bits of the sqlite3.flags field that are used by the
** sqlite3_test_control(SQLITE_TESTCTRL_OPTIMIZATIONS,...) interface.
** These must be the low-order bits of the flags field.
*/
#define SQLITE_QueryFlattener 0x01   /* Disable query flattening */
#define SQLITE_ColumnCache    0x02   /* Disable the column cache */
#define SQLITE_GroupByOrder   0x04   /* Disable GROUPBY cover of ORDERBY */
#define SQLITE_FactorOutConst 0x08   /* Disable factoring out constants */
#define SQLITE_IdxRealAsInt   0x10   /* Store REAL as INT in indices */
#define SQLITE_DistinctOpt    0x20   /* DISTINCT using indexes */
#define SQLITE_CoverIdxScan   0x40   /* Disable covering index scans */
#define SQLITE_OptMask        0xff   /* Mask of all disablable opts */













/*
** Possible values for the sqlite.magic field.
** The numbers are obtained at random and have no special meaning, other
** than being distinct from one another.
*/
#define SQLITE_MAGIC_OPEN     0xa029a697  /* Database is open */
................................................................................
** Within the union, pIdx is only used when wsFlags&WHERE_INDEXED is true.
** pTerm is only used when wsFlags&WHERE_MULTI_OR is true.  And pVtabIdx
** is only used when wsFlags&WHERE_VIRTUALTABLE is true.  It is never the
** case that more than one of these conditions is true.
*/
struct WherePlan {
  u32 wsFlags;                   /* WHERE_* flags that describe the strategy */
  u32 nEq;                       /* Number of == constraints */

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

  Db *aDb;                      /* All backends */
  int nDb;                      /* Number of backends currently in use */
  int flags;                    /* Miscellaneous flags. See below */
  i64 lastRowid;                /* ROWID of most recent insert (see above) */
  unsigned int openFlags;       /* Flags passed to sqlite3_vfs.xOpen() */
  int errCode;                  /* Most recent error code (SQLITE_*) */
  int errMask;                  /* & result codes with this before returning */
  u8 dbOptFlags;                /* Flags to enable/disable optimizations */
  u8 autoCommit;                /* The auto-commit flag. */
  u8 temp_store;                /* 1: file 2: memory 0: default */
  u8 mallocFailed;              /* True if we have seen a malloc failure */
  u8 dfltLockMode;              /* Default locking-mode for attached dbs */
  signed char nextAutovac;      /* Autovac setting after VACUUM if >=0 */
  u8 suppressErr;               /* Do not issue error messages if true */
  u8 vtabOnConflict;            /* Value to return for s3_vtab_on_conflict() */
................................................................................
** A macro to discover the encoding of a database.
*/
#define ENC(db) ((db)->aDb[0].pSchema->enc)

/*
** Possible values for the sqlite3.flags.
*/
#define SQLITE_VdbeTrace      0x00000001  /* True to trace VDBE execution */
#define SQLITE_InternChanges  0x00000002  /* Uncommitted Hash table changes */
#define SQLITE_FullColNames   0x00000004  /* Show full column names on SELECT */
#define SQLITE_ShortColNames  0x00000008  /* Show short columns names */
#define SQLITE_CountRows      0x00000010  /* Count rows changed by INSERT, */
                                          /*   DELETE, or UPDATE and return */
                                          /*   the count using a callback. */
#define SQLITE_NullCallback   0x00000020  /* Invoke the callback once if the */
                                          /*   result set is empty */
#define SQLITE_SqlTrace       0x00000040  /* Debug print SQL as it executes */
#define SQLITE_VdbeListing    0x00000080  /* Debug listings of VDBE programs */
#define SQLITE_WriteSchema    0x00000100  /* OK to update SQLITE_MASTER */
                         /*   0x00000200  Unused */
#define SQLITE_IgnoreChecks   0x00000400  /* Do not enforce check constraints */
#define SQLITE_ReadUncommitted 0x0000800  /* For shared-cache mode */
#define SQLITE_LegacyFileFmt  0x00001000  /* Create new databases in format 1 */
#define SQLITE_FullFSync      0x00002000  /* Use full fsync on the backend */
#define SQLITE_CkptFullFSync  0x00004000  /* Use full fsync for checkpoint */
#define SQLITE_RecoveryMode   0x00008000  /* Ignore schema errors */
#define SQLITE_ReverseOrder   0x00010000  /* Reverse unordered SELECTs */
#define SQLITE_RecTriggers    0x00020000  /* Enable recursive triggers */
#define SQLITE_ForeignKeys    0x00040000  /* Enforce foreign key constraints  */
#define SQLITE_AutoIndex      0x00080000  /* Enable automatic indexes */
#define SQLITE_PreferBuiltin  0x00100000  /* Preference to built-in funcs */
#define SQLITE_LoadExtension  0x00200000  /* Enable load_extension */
#define SQLITE_EnableTrigger  0x00400000  /* True to enable triggers */

/*
** Bits of the sqlite3.dbOptFlags field that are used by the
** sqlite3_test_control(SQLITE_TESTCTRL_OPTIMIZATIONS,...) interface to
** selectively disable various optimizations.
*/
#define SQLITE_QueryFlattener 0x0001   /* Query flattening */
#define SQLITE_ColumnCache    0x0002   /* Column cache */
#define SQLITE_GroupByOrder   0x0004   /* GROUPBY cover of ORDERBY */
#define SQLITE_FactorOutConst 0x0008   /* Constant factoring */
#define SQLITE_IdxRealAsInt   0x0010   /* Store REAL as INT in indices */
#define SQLITE_DistinctOpt    0x0020   /* DISTINCT using indexes */
#define SQLITE_CoverIdxScan   0x0040   /* Covering index scans */
#define SQLITE_OrderByIdxJoin 0x0080   /* ORDER BY of joins via index */
#define SQLITE_AllOpts        0x00ff   /* All optimizations */

/*
** Macros for testing whether or not optimizations are enabled or disabled.
*/
#ifndef SQLITE_OMIT_BUILTIN_TEST
#define OptimizationDisabled(db, mask)  (((db)->dbOptFlags&(mask))!=0)
#define OptimizationEnabled(db, mask)   (((db)->dbOptFlags&(mask))==0)
#else
#define OptimizationDisabled(db, mask)  0
#define OptimizationEnabled(db, mask)   1
#endif

/*
** Possible values for the sqlite.magic field.
** The numbers are obtained at random and have no special meaning, other
** than being distinct from one another.
*/
#define SQLITE_MAGIC_OPEN     0xa029a697  /* Database is open */
................................................................................
** Within the union, pIdx is only used when wsFlags&WHERE_INDEXED is true.
** pTerm is only used when wsFlags&WHERE_MULTI_OR is true.  And pVtabIdx
** is only used when wsFlags&WHERE_VIRTUALTABLE is true.  It is never the
** case that more than one of these conditions is true.
*/
struct WherePlan {
  u32 wsFlags;                   /* WHERE_* flags that describe the strategy */
  u16 nEq;                       /* Number of == constraints */
  u16 nOBSat;                    /* Number of ORDER BY terms satisfied */
  double nRow;                   /* Estimated number of rows (for EQP) */
  union {
    Index *pIdx;                   /* Index when WHERE_INDEXED is true */
    struct WhereTerm *pTerm;       /* WHERE clause term for OR-search */
    sqlite3_index_info *pVtabIdx;  /* Virtual table index to use */
  } u;
};

  const char *zOpt;
  int onoff;
  int mask = 0;
  static const struct {
    const char *zOptName;
    int mask;
  } aOpt[] = {
    { "all",              SQLITE_OptMask        },
    { "query-flattener",  SQLITE_QueryFlattener },
    { "column-cache",     SQLITE_ColumnCache    },
    { "groupby-order",    SQLITE_GroupByOrder   },
    { "factor-constants", SQLITE_FactorOutConst },
    { "real-as-int",      SQLITE_IdxRealAsInt   },
    { "distinct-opt",     SQLITE_DistinctOpt    },
    { "cover-idx-scan",   SQLITE_CoverIdxScan   },

  };

  if( objc!=4 ){
    Tcl_WrongNumArgs(interp, 1, objv, "DB OPT BOOLEAN");
    return TCL_ERROR;
  }
  if( getDbPointer(interp, Tcl_GetString(objv[1]), &db) ) return TCL_ERROR;

  const char *zOpt;
  int onoff;
  int mask = 0;
  static const struct {
    const char *zOptName;
    int mask;
  } aOpt[] = {
    { "all",              SQLITE_AllOpts        },
    { "query-flattener",  SQLITE_QueryFlattener },
    { "column-cache",     SQLITE_ColumnCache    },
    { "groupby-order",    SQLITE_GroupByOrder   },
    { "factor-constants", SQLITE_FactorOutConst },
    { "real-as-int",      SQLITE_IdxRealAsInt   },
    { "distinct-opt",     SQLITE_DistinctOpt    },
    { "cover-idx-scan",   SQLITE_CoverIdxScan   },
    { "order-by-idx-join",SQLITE_OrderByIdxJoin },
  };

  if( objc!=4 ){
    Tcl_WrongNumArgs(interp, 1, objv, "DB OPT BOOLEAN");
    return TCL_ERROR;
  }
  if( getDbPointer(interp, Tcl_GetString(objv[1]), &db) ) return TCL_ERROR;

#define WHERE_UNIQUE       0x04000000  /* Selects no more than one row */
#define WHERE_VIRTUALTABLE 0x08000000  /* Use virtual-table processing */
#define WHERE_MULTI_OR     0x10000000  /* OR using multiple indices */
#define WHERE_TEMP_INDEX   0x20000000  /* Uses an ephemeral index */
#define WHERE_DISTINCT     0x40000000  /* Correct order for DISTINCT */
#define WHERE_COVER_SCAN   0x80000000  /* Full scan of a covering index */























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

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

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

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

  return 0;
}

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

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

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




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

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

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

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


  sqlite3 *db = pParse->db;















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

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

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

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

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





      && (wsFlags & WHERE_COLUMN_NULL)==0
      && !referencesOtherTables(pOrderBy, pMaskSet, j, base) 



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






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

/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operations with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
................................................................................
#define TRACE_IDX_INPUTS(A)
#define TRACE_IDX_OUTPUTS(A)
#endif

/* 
** Required because bestIndex() is called by bestOrClauseIndex() 
*/
static void bestIndex(
    Parse*, WhereClause*, struct SrcList_item*,
    Bitmask, Bitmask, WhereCost*);

/*
** 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(
  Parse *pParse,              /* The parsing context */
  WhereClause *pWC,           /* The WHERE clause */
  struct SrcList_item *pSrc,  /* The FROM clause term to search */
  Bitmask notReady,           /* Mask of cursors not available for indexing */
  Bitmask notValid,           /* Cursors not available for any purpose */
  ExprList *pOrderBy,         /* The ORDER BY clause */
  WhereCost *pCost            /* Lowest cost query plan */
){
#ifndef SQLITE_OMIT_OR_OPTIMIZATION


  const int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  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 
     && ((pTerm->prereqAll & ~maskSrc) & notReady)==0
     && (pTerm->u.pOrInfo->indexable & maskSrc)!=0 
    ){
      WhereClause * const pOrWC = &pTerm->u.pOrInfo->wc;
      WhereTerm * const pOrWCEnd = &pOrWC->a[pOrWC->nTerm];
      WhereTerm *pOrTerm;
      int flags = WHERE_MULTI_OR;
      double rTotal = 0;
      double nRow = 0;
      Bitmask used = 0;






      for(pOrTerm=pOrWC->a; pOrTerm<pOrWCEnd; pOrTerm++){
        WhereCost sTermCost;
        WHERETRACE(("... Multi-index OR testing for term %d of %d....\n", 
          (pOrTerm - pOrWC->a), (pTerm - pWC->a)
        ));
        if( pOrTerm->eOperator==WO_AND ){
          WhereClause *pAndWC = &pOrTerm->u.pAndInfo->wc;
          bestIndex(pParse, pAndWC, pSrc, notReady, notValid, &sTermCost);
        }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;
          bestIndex(pParse, &tempWC, pSrc, notReady, notValid, &sTermCost);

        }else{
          continue;
        }
        rTotal += sTermCost.rCost;
        nRow += sTermCost.plan.nRow;
        used |= sTermCost.used;
        if( rTotal>=pCost->rCost ) break;
      }

      /* If there is an ORDER BY clause, increase the scan cost to account 
      ** for the cost of the sort. */
      if( 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<pCost->rCost ){
        pCost->rCost = rTotal;
        pCost->used = used;
        pCost->plan.nRow = nRow;
        pCost->plan.wsFlags = flags;
        pCost->plan.u.pTerm = pTerm;
      }
    }
  }
#endif /* SQLITE_OMIT_OR_OPTIMIZATION */
}

#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(
  Parse *pParse,              /* The parsing context */
  WhereClause *pWC,           /* The WHERE clause */
  struct SrcList_item *pSrc,  /* The FROM clause term to search */
  Bitmask notReady,           /* Mask of cursors that are not available */
  WhereCost *pCost            /* Lowest cost query plan */
){
  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( (pCost->plan.wsFlags & WHERE_NOT_FULLSCAN)!=0 ){
    /* We already have some kind of index in use for this query. */
    return;
  }
  if( pSrc->notIndexed ){
    /* The NOT INDEXED clause appears in the SQL. */
    return;
  }
................................................................................
  }

  assert( pParse->nQueryLoop >= (double)1 );
  pTable = pSrc->pTab;
  nTableRow = pTable->nRowEst;
  logN = estLog(nTableRow);
  costTempIdx = 2*logN*(nTableRow/pParse->nQueryLoop + 1);
  if( costTempIdx>=pCost->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, notReady) ){
      WHERETRACE(("auto-index reduces cost from %.1f to %.1f\n",
                    pCost->rCost, costTempIdx));
      pCost->rCost = costTempIdx;
      pCost->plan.nRow = logN + 1;
      pCost->plan.wsFlags = WHERE_TEMP_INDEX;
      pCost->used = pTerm->prereqRight;
      break;
    }
  }
}
#else
# define bestAutomaticIndex(A,B,C,D,E)  /* 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
................................................................................

#ifndef SQLITE_OMIT_VIRTUALTABLE
/*
** Allocate and populate an sqlite3_index_info structure. It is the 
** responsibility of the caller to eventually release the structure
** by passing the pointer returned by this function to sqlite3_free().
*/
static sqlite3_index_info *allocateIndexInfo(
  Parse *pParse, 
  WhereClause *pWC,
  struct SrcList_item *pSrc,
  ExprList *pOrderBy
){
  int i, j;
  int nTerm;
  struct sqlite3_index_constraint *pIdxCons;
  struct sqlite3_index_orderby *pIdxOrderBy;
  struct sqlite3_index_constraint_usage *pUsage;
  WhereTerm *pTerm;
  int nOrderBy;
................................................................................

  /* If the ORDER BY clause contains only columns in the current 
  ** virtual table then allocate space for the aOrderBy part of
  ** the sqlite3_index_info structure.
  */
  nOrderBy = 0;
  if( pOrderBy ){
    for(i=0; i<pOrderBy->nExpr; i++){

      Expr *pExpr = pOrderBy->a[i].pExpr;
      if( pExpr->op!=TK_COLUMN || pExpr->iTable!=pSrc->iCursor ) break;
    }
    if( i==pOrderBy->nExpr ){
      nOrderBy = pOrderBy->nExpr;
    }
  }

  /* Allocate the sqlite3_index_info structure
  */
  pIdxInfo = sqlite3DbMallocZero(pParse->db, sizeof(*pIdxInfo)
                           + (sizeof(*pIdxCons) + sizeof(*pUsage))*nTerm
................................................................................
** 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(
  Parse *pParse,                  /* The parsing context */
  WhereClause *pWC,               /* The WHERE clause */
  struct SrcList_item *pSrc,      /* The FROM clause term to search */
  Bitmask notReady,               /* Mask of cursors not available for index */
  Bitmask notValid,               /* Cursors not valid for any purpose */
  ExprList *pOrderBy,             /* The order by clause */
  WhereCost *pCost,               /* Lowest cost query plan */
  sqlite3_index_info **ppIdxInfo  /* Index information passed to xBestIndex */
){
  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;
  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(pCost, 0, sizeof(*pCost));
  pCost->plan.wsFlags = WHERE_VIRTUALTABLE;

  /* If the sqlite3_index_info structure has not been previously
  ** allocated and initialized, then allocate and initialize it now.
  */
  pIdxInfo = *ppIdxInfo;
  if( pIdxInfo==0 ){
    *ppIdxInfo = pIdxInfo = allocateIndexInfo(pParse, pWC, pSrc, 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
................................................................................
  ** 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];
    pIdxCons->usable = (pTerm->prereqRight&notReady) ? 0 : 1;
  }
  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( !pOrderBy ){
    pIdxInfo->nOrderBy = 0;
  }

  if( vtabBestIndex(pParse, pTab, pIdxInfo) ){
    return;
  }

  pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;
  for(i=0; i<pIdxInfo->nConstraint; i++){
    if( pUsage[i].argvIndex>0 ){
      pCost->used |= pWC->a[pIdxCons[i].iTermOffset].prereqRight;
    }
  }

  /* 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( 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 ){
    pCost->rCost = (SQLITE_BIG_DBL/((double)2));
  }else{
    pCost->rCost = rCost;
  }
  pCost->plan.u.pVtabIdx = pIdxInfo;
  if( pIdxInfo->orderByConsumed ){
    pCost->plan.wsFlags |= WHERE_ORDERBY;
  }
  pCost->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(pParse, pWC, pSrc, notReady, notValid, pOrderBy, pCost);
}
#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:
................................................................................
    *pnRow = nRowEst;
    WHERETRACE(("IN row estimate: est=%g\n", nRowEst));
  }
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT3) */

















































/*



























** Find the best query plan for accessing a particular table.  Write the
** best query plan and its cost into the WhereCost object supplied as the
** last parameter.
**
** 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.)
................................................................................
** then the cost is calculated in the usual way.
**
** If a NOT INDEXED clause (pSrc->notIndexed!=0) 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(
  Parse *pParse,              /* The parsing context */
  WhereClause *pWC,           /* The WHERE clause */
  struct SrcList_item *pSrc,  /* The FROM clause term to search */
  Bitmask notReady,           /* Mask of cursors not available for indexing */
  Bitmask notValid,           /* Cursors not available for any purpose */
  ExprList *pOrderBy,         /* The ORDER BY clause */
  ExprList *pDistinct,        /* The select-list if query is DISTINCT */
  WhereCost *pCost            /* Lowest cost query plan */
){
  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 pCost->plan.wsFlag */

  /* Initialize the cost to a worst-case value */
  memset(pCost, 0, sizeof(*pCost));
  pCost->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 ){
................................................................................
  /* Loop over all indices looking for the best one to use
  */
  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const tRowcnt * const aiRowEst = pProbe->aiRowEst;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    double log10N = (double)1;  /* base-10 logarithm of nRow (inexact) */
    int rev;                    /* True to scan in reverse order */
    int wsFlags = 0;
    Bitmask used = 0;

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




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




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

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


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





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



      }
#ifdef SQLITE_ENABLE_STAT3
      if( nEq==0 && pProbe->aSample ) pFirstTerm = pTerm;
#endif
      used |= pTerm->prereqRight;
    }
 
................................................................................
      testcase( wsFlags & WHERE_COLUMN_IN );
      testcase( wsFlags & WHERE_COLUMN_NULL );
      if( (wsFlags & (WHERE_COLUMN_IN|WHERE_COLUMN_NULL))==0 ){
        wsFlags |= WHERE_UNIQUE;
      }
    }else if( pProbe->bUnordered==0 ){
      int j = (nEq==pProbe->nColumn ? -1 : pProbe->aiColumn[nEq]);
      if( findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE|WO_GT|WO_GE, pIdx) ){

        WhereTerm *pTop = findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE, pIdx);
        WhereTerm *pBtm = findTerm(pWC, iCur, j, notReady, WO_GT|WO_GE, pIdx);
        whereRangeScanEst(pParse, pProbe, nEq, pBtm, pTop, &rangeDiv);
        if( pTop ){
          nBound = 1;
          wsFlags |= WHERE_TOP_LIMIT;
          used |= pTop->prereqRight;
          testcase( pTop->pWC!=pWC );
        }
................................................................................
      }
    }

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





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


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


    }

    /* If there is a DISTINCT qualifier and this index will scan rows in
    ** order of the DISTINCT expressions, clear bDist and set the appropriate
    ** flags in wsFlags. */

    if( isDistinctIndex(pParse, pWC, pProbe, iCur, pDistinct, nEq)
     && (wsFlags & WHERE_COLUMN_IN)==0
    ){
      bDist = 0;
      wsFlags |= WHERE_ROWID_RANGE|WHERE_COLUMN_RANGE|WHERE_DISTINCT;
    }

    /* If currently calculating the cost of using an index (not the IPK
................................................................................
    ** 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( wsFlags==WHERE_IDX_ONLY
     && (pWC->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
     && sqlite3GlobalConfig.bUseCis
#ifndef SQLITE_OMIT_BUILTIN_TEST
     && (pParse->db->flags & SQLITE_CoverIdxScan)==0
#endif
    ){
      /* 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. */
      cost = aiRowEst[0]*3 + pProbe->nColumn;
      wsFlags |= WHERE_COVER_SCAN|WHERE_COLUMN_RANGE;
................................................................................
    /* Add in the estimated cost of sorting the result.  Actual experimental
    ** measurements of sorting performance in SQLite show that sorting time
    ** adds C*N*log10(N) to the cost, where N is the number of rows to be 
    ** sorted and C is a factor between 1.95 and 4.3.  We will split the
    ** difference and select C of 3.0.
    */
    if( bSort ){
      cost += nRow*estLog(nRow)*3;
    }
    if( bDist ){
      cost += nRow*estLog(nRow)*3;
    }

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

................................................................................
    ** 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( nRow>2 && cost<=pCost->rCost ){
      int k;                       /* Loop counter */
      int nSkipEq = 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; nRow>2 && k; k--, pTerm++){
        if( pTerm->wtFlags & TERM_VIRTUAL ) continue;
        if( (pTerm->prereqAll & notValid)!=thisTab ) continue;
        if( pTerm->eOperator & (WO_EQ|WO_IN|WO_ISNULL) ){
          if( nSkipEq ){
            /* Ignore the first nEq equality matches since the index
            ** has already accounted for these */
            nSkipEq--;
          }else{
            /* Assume each additional equality match reduces the result
................................................................................
        }
      }
      if( nRow<2 ) nRow = 2;
    }


    WHERETRACE((

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

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

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

      pCost->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 */
................................................................................
  }

  /* 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 behaviour depends on the (undefined) order that
  ** SQLite outputs rows in in the absence of an ORDER BY clause.  */
  if( !pOrderBy && pParse->db->flags & SQLITE_ReverseOrder ){
    pCost->plan.wsFlags |= WHERE_REVERSE;
  }

  assert( pOrderBy || (pCost->plan.wsFlags&WHERE_ORDERBY)==0 );
  assert( pCost->plan.u.pIdx==0 || (pCost->plan.wsFlags&WHERE_ROWID_EQ)==0 );
  assert( pSrc->pIndex==0 
       || pCost->plan.u.pIdx==0 
       || pCost->plan.u.pIdx==pSrc->pIndex 
  );

  WHERETRACE(("best index is: %s\n", 
    ((pCost->plan.wsFlags & WHERE_NOT_FULLSCAN)==0 ? "none" : 
         pCost->plan.u.pIdx ? pCost->plan.u.pIdx->zName : "ipk")
  ));
  
  bestOrClauseIndex(pParse, pWC, pSrc, notReady, notValid, pOrderBy, pCost);
  bestAutomaticIndex(pParse, pWC, pSrc, notReady, pCost);
  pCost->plan.wsFlags |= eqTermMask;
}

/*
** 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(
  Parse *pParse,              /* The parsing context */
  WhereClause *pWC,           /* The WHERE clause */
  struct SrcList_item *pSrc,  /* The FROM clause term to search */
  Bitmask notReady,           /* Mask of cursors not available for indexing */
  Bitmask notValid,           /* Cursors not available for any purpose */
  WhereCost *pCost            /* Lowest cost query plan */
){
#ifndef SQLITE_OMIT_VIRTUALTABLE
  if( IsVirtual(pSrc->pTab) ){
    sqlite3_index_info *p = 0;

    bestVirtualIndex(pParse, pWC, pSrc, notReady, notValid, 0, pCost, &p);
    if( p->needToFreeIdxStr ){
      sqlite3_free(p->idxStr);
    }
    sqlite3DbFree(pParse->db, p);
  }else
#endif
  {
    bestBtreeIndex(pParse, pWC, pSrc, notReady, notValid, 0, 0, pCost);
  }
}

/*
** 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.
................................................................................
  SrcList *pTabList,    /* A list of all tables to be scanned */
  Expr *pWhere,         /* The WHERE clause */
  ExprList *pOrderBy,   /* An ORDER BY clause, or NULL */
  ExprList *pDistinct,  /* The select-list for DISTINCT queries - or NULL */
  u16 wctrlFlags,       /* One of the WHERE_* flags defined in sqliteInt.h */
  int iIdxCur           /* If WHERE_ONETABLE_ONLY is set, index cursor number */
){
  int i;                     /* Loop counter */
  int nByteWInfo;            /* Num. bytes allocated for WhereInfo struct */
  int nTabList;              /* Number of elements in pTabList */
  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 */

  WhereMaskSet *pMaskSet;    /* The expression mask set */
  WhereClause *pWC;               /* Decomposition of the WHERE clause */
  struct SrcList_item *pTabItem;  /* A single entry from pTabList */
  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 */

  sqlite3 *db;               /* Database connection */






  /* The number of tables in the FROM clause is limited by the number of
  ** bits in a Bitmask 
  */
  testcase( pTabList->nSrc==BMS );
  if( pTabList->nSrc>BMS ){
    sqlite3ErrorMsg(pParse, "at most %d tables in a join", BMS);
    return 0;
................................................................................
    pWInfo = 0;
    goto whereBeginError;
  }
  pWInfo->nLevel = nTabList;
  pWInfo->pParse = pParse;
  pWInfo->pTabList = pTabList;
  pWInfo->iBreak = sqlite3VdbeMakeLabel(v);
  pWInfo->pWC = pWC = (WhereClause *)&((u8 *)pWInfo)[nByteWInfo];
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  pMaskSet = (WhereMaskSet*)&pWC[1];


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

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.
  */
  initMaskSet(pMaskSet);
  whereClauseInit(pWC, pParse, pMaskSet, wctrlFlags);
  sqlite3ExprCodeConstants(pParse, pWhere);
  whereSplit(pWC, pWhere, TK_AND);   /* IMP: R-15842-53296 */
    
  /* Special case: a WHERE clause that is constant.  Evaluate the
  ** expression and either jump over all of the code or fall thru.
  */
  if( pWhere && (nTabList==0 || sqlite3ExprIsConstantNotJoin(pWhere)) ){
    sqlite3ExprIfFalse(pParse, pWhere, pWInfo->iBreak, SQLITE_JUMPIFNULL);
    pWhere = 0;
................................................................................
  ** with virtual tables.
  **
  ** Note that bitmasks are created for all pTabList->nSrc tables in
  ** pTabList, not just the first nTabList tables.  nTabList is normally
  ** equal to pTabList->nSrc but might be shortened to 1 if the
  ** WHERE_ONETABLE_ONLY flag is set.
  */
  assert( pWC->vmask==0 && pMaskSet->n==0 );
  for(i=0; i<pTabList->nSrc; i++){
    createMask(pMaskSet, pTabList->a[i].iCursor);
#ifndef SQLITE_OMIT_VIRTUALTABLE
    if( ALWAYS(pTabList->a[i].pTab) && IsVirtual(pTabList->a[i].pTab) ){
      pWC->vmask |= ((Bitmask)1 << i);
    }
#endif
  }
#ifndef NDEBUG
  {
    Bitmask toTheLeft = 0;
    for(i=0; i<pTabList->nSrc; i++){
      Bitmask m = getMask(pMaskSet, pTabList->a[i].iCursor);
      assert( (m-1)==toTheLeft );
      toTheLeft |= m;
    }
  }
#endif

  /* Analyze all of the subexpressions.  Note that exprAnalyze() might
  ** add new virtual terms onto the end of the WHERE clause.  We do not
  ** want to analyze these virtual terms, so start analyzing at the end
  ** and work forward so that the added virtual terms are never processed.
  */
  exprAnalyzeAll(pTabList, pWC);
  if( db->mallocFailed ){
    goto whereBeginError;
  }

  /* Check if the DISTINCT qualifier, if there is one, is redundant. 
  ** If it is, then set pDistinct to NULL and WhereInfo.eDistinct to
  ** WHERE_DISTINCT_UNIQUE to tell the caller to ignore the DISTINCT.
  */
  if( pDistinct && isDistinctRedundant(pParse, pTabList, pWC, pDistinct) ){
    pDistinct = 0;
    pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
  }

  /* Chose the best index to use for each table in the FROM clause.
  **
  ** This loop fills in the following fields:
................................................................................
  **   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.
  */
  notReady = ~(Bitmask)0;



  andFlags = ~0;
  WHERETRACE(("*** Optimizer Start ***\n"));
  for(i=iFrom=0, pLevel=pWInfo->a; i<nTabList; 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 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", 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
................................................................................
    ** 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 notReady.  If no notReady 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.  
    **
................................................................................
    ** 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;
    for(isOptimal=(iFrom<nTabList-1); isOptimal>=0 && bestJ<0; isOptimal--){
      Bitmask mask;             /* Mask of tables not yet ready */
      for(j=iFrom, pTabItem=&pTabList->a[j]; j<nTabList; j++, pTabItem++){
        int doNotReorder;    /* True if this table should not be reordered */
        WhereCost sCost;     /* Cost information from best[Virtual]Index() */
        ExprList *pOB;       /* ORDER BY clause for index to optimize */
        ExprList *pDist;     /* DISTINCT clause for index to optimize */
  
        doNotReorder =  (pTabItem->jointype & (JT_LEFT|JT_CROSS))!=0;
        if( j!=iFrom && doNotReorder ) break;
        m = getMask(pMaskSet, pTabItem->iCursor);
        if( (m & notReady)==0 ){

          if( j==iFrom ) iFrom++;
          continue;
        }
        mask = (isOptimal ? m : notReady);
        pOB = (i==0) ? pOrderBy : 0;
        pDist = (i==0 ? pDistinct : 0);
        if( pTabItem->pIndex==0 ) nUnconstrained++;
  
        WHERETRACE(("=== trying table %d with isOptimal=%d ===\n",
                    j, isOptimal));
        assert( pTabItem->pTab );
#ifndef SQLITE_OMIT_VIRTUALTABLE
        if( IsVirtual(pTabItem->pTab) ){
          sqlite3_index_info **pp = &pWInfo->a[j].pIdxInfo;
          bestVirtualIndex(pParse, pWC, pTabItem, mask, notReady, pOB,
                           &sCost, pp);
        }else 
#endif
        {
          bestBtreeIndex(pParse, pWC, pTabItem, mask, notReady, pOB,
              pDist, &sCost);
        }
        assert( isOptimal || (sCost.used&notReady)==0 );

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

        if( isOptimal && (sCost.plan.wsFlags & WHERE_NOT_FULLSCAN)==0 ){
          notIndexed |= m;
        }

        /* Conditions under which this table becomes the best so far:
        **
        **   (1) The table must not depend on other tables that have not
        **       yet run.

        **
        **   (2) A full-table-scan plan cannot supercede indexed plan unless
        **       the full-table-scan is an "optimal" plan as defined above.
        **
        **   (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
................................................................................
        **       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 or else the
        **       cost must be the same and the number of rows must be lower.
        */
        if( (sCost.used&notReady)==0                       /* (1) */
            && (bestJ<0 || (notIndexed&m)!=0               /* (2) */
                || (bestPlan.plan.wsFlags & WHERE_NOT_FULLSCAN)==0
                || (sCost.plan.wsFlags & WHERE_NOT_FULLSCAN)!=0)
            && (nUnconstrained==0 || pTabItem->pIndex==0   /* (3) */
                || NEVER((sCost.plan.wsFlags & WHERE_NOT_FULLSCAN)!=0))
            && (bestJ<0 || sCost.rCost<bestPlan.rCost      /* (4) */
                || (sCost.rCost<=bestPlan.rCost 
                 && sCost.plan.nRow<bestPlan.plan.nRow))
        ){
          WHERETRACE(("=== table %d is best so far"
                      " with cost=%g and nRow=%g\n",
                      j, sCost.rCost, sCost.plan.nRow));

          bestPlan = sCost;
          bestJ = j;
        }
        if( doNotReorder ) break;
      }
    }
    assert( bestJ>=0 );
    assert( notReady & getMask(pMaskSet, pTabList->a[bestJ].iCursor) );
    WHERETRACE(("*** Optimizer selects table %d for loop %d"
                " with cost=%g and nRow=%g\n",
                bestJ, pLevel-pWInfo->a, bestPlan.rCost, bestPlan.plan.nRow));

    if( (bestPlan.plan.wsFlags & WHERE_ORDERBY)!=0 ){
      pWInfo->nOBSat = pOrderBy->nExpr;
    }
    if( (bestPlan.plan.wsFlags & WHERE_DISTINCT)!=0 ){
      assert( pWInfo->eDistinct==0 );
      pWInfo->eDistinct = WHERE_DISTINCT_ORDERED;
    }
................................................................................
        pLevel->iIdxCur = iIdxCur;
      }else{
        pLevel->iIdxCur = pParse->nTab++;
      }
    }else{
      pLevel->iIdxCur = -1;
    }
    notReady &= ~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
................................................................................

  /* 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(i=0, pLevel=pWInfo->a; i<nTabList; i++, pLevel++){
    Table *pTab;     /* Table to open */
    int iDb;         /* Index of database containing table/index */


    pTabItem = &pTabList->a[pLevel->iFrom];
    pTab = pTabItem->pTab;
    pLevel->iTabCur = pTabItem->iCursor;
    pWInfo->nRowOut *= pLevel->plan.nRow;
    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);
    if( (pTab->tabFlags & TF_Ephemeral)!=0 || pTab->pSelect ){
................................................................................
        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, 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);
    notReady &= ~getMask(pWC->pMaskSet, pTabItem->iCursor);
  }
  pWInfo->iTop = sqlite3VdbeCurrentAddr(v);
  if( db->mallocFailed ) goto whereBeginError;

  /* Generate the code to do the search.  Each iteration of the for
  ** loop below generates code for a single nested loop of the VM
  ** program.
  */
  notReady = ~(Bitmask)0;
  for(i=0; i<nTabList; i++){
    pLevel = &pWInfo->a[i];
    explainOneScan(pParse, pTabList, pLevel, i, pLevel->iFrom, wctrlFlags);
    notReady = codeOneLoopStart(pWInfo, i, 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(i=0; i<nTabList; i++){
    char *z;
    int n;
    int w;


    pLevel = &pWInfo->a[i];
    w = pLevel->plan.wsFlags;
    pTabItem = &pTabList->a[pLevel->iFrom];
    z = pTabItem->zAlias;
    if( z==0 ) z = pTabItem->pTab->zName;
    n = sqlite3Strlen30(z);
    if( n+nQPlan < sizeof(sqlite3_query_plan)-10 ){
      if( (w & WHERE_IDX_ONLY)!=0 && (w & WHERE_COVER_SCAN)==0 ){

#define WHERE_UNIQUE       0x04000000  /* Selects no more than one row */
#define WHERE_VIRTUALTABLE 0x08000000  /* Use virtual-table processing */
#define WHERE_MULTI_OR     0x10000000  /* OR using multiple indices */
#define WHERE_TEMP_INDEX   0x20000000  /* Uses an ephemeral index */
#define WHERE_DISTINCT     0x40000000  /* Correct order for DISTINCT */
#define WHERE_COVER_SCAN   0x80000000  /* Full scan of a covering index */

/*
** This module contains many separate subroutines that work together to
** find the best indices to use for accessing a particular table in a query.
** An instance of the following structure holds context information about the
** index search so that it can be more easily passed between the various
** routines.
*/
typedef struct WhereBestIdx WhereBestIdx;
struct WhereBestIdx {
  Parse *pParse;                  /* Parser context */
  WhereClause *pWC;               /* The WHERE clause */
  struct SrcList_item *pSrc;      /* The FROM clause term to search */
  Bitmask notReady;               /* Mask of cursors not available */
  Bitmask notValid;               /* Cursors not available for any purpose */
  ExprList *pOrderBy;             /* The ORDER BY clause */
  ExprList *pDistinct;            /* The select-list if query is DISTINCT */
  sqlite3_index_info **ppIdxInfo; /* Index information passed to xBestIndex */
  int i, n;                       /* Which loop is being coded; # of loops */
  WhereLevel *aLevel;             /* Info about outer loops */
  WhereCost cost;                 /* Lowest cost query plan */
};

/*
** Initialize a preallocated WhereClause structure.
*/
static void whereClauseInit(
  WhereClause *pWC,        /* The WhereClause to be initialized */
  Parse *pParse,           /* The parsing context */
  WhereMaskSet *pMaskSet,  /* Mapping from table cursor numbers to bitmasks */
................................................................................
  /* Prevent ON clause terms of a LEFT JOIN from being used to drive
  ** an index for tables to the left of the join.
  */
  pTerm->prereqRight |= extraRight;
}

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

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



  }

  return 1;
}

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

  return 0;
}

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


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




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

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

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

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

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

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

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





    }
  }

  *pbRev = sortOrder;






  /* If there was an "ORDER BY rowid" term that matched, or it is only
  ** possible for a single row from this table to match, then skip over
  ** any additional ORDER BY terms dealing with this table.
  */
  if( seenRowid ||
     (   (wsFlags & WHERE_COLUMN_NULL)==0

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

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













  }


  return j;
}

/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operations with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
................................................................................
#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 
     && ((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;
      int flags = WHERE_MULTI_OR;
      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 ){
          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.wsFlags = flags;
        p->cost.plan.u.pTerm = pTerm;
      }
    }
  }
#endif /* SQLITE_OMIT_OR_OPTIMIZATION */
}

#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 ){
    /* We already have some kind of index in use for this query. */
    return;
  }
  if( pSrc->notIndexed ){
    /* The NOT INDEXED clause appears in the SQL. */
    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
................................................................................

#ifndef SQLITE_OMIT_VIRTUALTABLE
/*
** Allocate and populate an sqlite3_index_info structure. It is the 
** responsibility of the caller to eventually release the structure
** by passing the pointer returned by this function to sqlite3_free().
*/
static sqlite3_index_info *allocateIndexInfo(WhereBestIdx *p){
  Parse *pParse = p->pParse; 
  WhereClause *pWC = p->pWC;
  struct SrcList_item *pSrc = p->pSrc;
  ExprList *pOrderBy = p->pOrderBy;

  int i, j;
  int nTerm;
  struct sqlite3_index_constraint *pIdxCons;
  struct sqlite3_index_orderby *pIdxOrderBy;
  struct sqlite3_index_constraint_usage *pUsage;
  WhereTerm *pTerm;
  int nOrderBy;
................................................................................

  /* If the ORDER BY clause contains only columns in the current 
  ** virtual table then allocate space for the aOrderBy part of
  ** the sqlite3_index_info structure.
  */
  nOrderBy = 0;
  if( pOrderBy ){
    int n = pOrderBy->nExpr;
    for(i=0; i<n; i++){
      Expr *pExpr = pOrderBy->a[i].pExpr;
      if( pExpr->op!=TK_COLUMN || pExpr->iTable!=pSrc->iCursor ) break;
    }
    if( i==n){
      nOrderBy = n;
    }
  }

  /* Allocate the sqlite3_index_info structure
  */
  pIdxInfo = sqlite3DbMallocZero(pParse->db, sizeof(*pIdxInfo)
                           + (sizeof(*pIdxCons) + sizeof(*pUsage))*nTerm
................................................................................
** 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;
  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(p);
  }
  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
................................................................................
  ** 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];
    pIdxCons->usable = (pTerm->prereqRight&p->notReady) ? 0 : 1;
  }
  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++){
    if( pUsage[i].argvIndex>0 ){
      p->cost.used |= pWC->a[pIdxCons[i].iTermOffset].prereqRight;
    }
  }

  /* 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_ORDERBY;
  }
  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:
................................................................................
    *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 true if
** it will and false if not.  
**
** If *pbRev is initially 2 (meaning "unknown") then set *pbRev to the
** sort order of iTab.iCol.  If *pbRev is 0 or 1 but does not match
** the sort order of iTab.iCol, then consider the column to be unordered.
*/
static int isOrderedColumn(WhereBestIdx *p, int iTab, int iCol, int *pbRev){
  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_INDEXED)!=0 ){
      pIdx = pLevel->plan.u.pIdx;
      if( iCol<0 ){
        sortOrder = 0;
        testcase( (pLevel->plan.wsFlags & WHERE_REVERSE)!=0 );
      }else{
        for(j=0; j<pIdx->nColumn; j++){
          if( iCol==pIdx->aiColumn[j] ) break;
        }
        if( j>=pIdx->nColumn ) 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;
    }
    if( *pbRev==2 ){
      *pbRev = sortOrder;
      return 1;
    }
    return (*pbRev==sortOrder);
  }
  return 0;
}

/*
** pTerm is an == constraint.  Check to see if the other side of
** the == is a constant or a value that is guaranteed to be ordered
** by outer loops.  Return 1 if pTerm is ordered, and 0 if not.
*/
static int isOrderedTerm(WhereBestIdx *p, WhereTerm *pTerm, int *pbRev){
  Expr *pExpr = pTerm->pExpr;
  assert( pExpr->op==TK_EQ );
  assert( pExpr->pLeft!=0 && pExpr->pLeft->op==TK_COLUMN );
  assert( pExpr->pRight!=0 );
  if( p->i==0 ){
    return 1;  /* All == are ordered in the outer loop */
  }
  if( pTerm->prereqRight==0 ){
    return 1;  /* RHS of the == is a constant */
  }
  if( pExpr->pRight->op==TK_COLUMN 
   && isOrderedColumn(p, pExpr->pRight->iTable, pExpr->pRight->iColumn, pbRev)
  ){
    return 1;
  }

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


/*
** Find the best query plan for accessing a particular table.  Write the
** best query plan and its cost into the p->cost.

**
** The lowest cost plan wins.  The cost is an estimate of the amount of
** CPU and disk I/O needed to process the requested result.
** Factors that influence cost include:
**
**    *  The estimated number of rows that will be retrieved.  (The
**       fewer the better.)
................................................................................
** then the cost is calculated in the usual way.
**
** If a NOT INDEXED clause (pSrc->notIndexed!=0) 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 */

  /* 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 ){
................................................................................
  /* Loop over all indices looking for the best one to use
  */
  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const tRowcnt * const aiRowEst = pProbe->aiRowEst;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    double log10N = (double)1;  /* base-10 logarithm of nRow (inexact) */
    int bRev = 2;               /* 0=forward scan.  1=reverse.  2=undecided */
    int wsFlags = 0;
    Bitmask used = 0;

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

    nOrderBy = p->pOrderBy ? p->pOrderBy->nExpr : 0;
    bSort = nOrderBy>0 && (p->i==0 || p->aLevel[p->i-1].plan.nOBSat<nOrderBy);
    bDist = p->i==0 && p->pDistinct!=0;

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

    /* If there is an ORDER BY clause and the index being considered will
    ** naturally scan rows in the required order, set the appropriate flags
    ** in wsFlags. Otherwise, if there is an ORDER BY clause but the index
    ** will scan rows in a different order, set the bSort variable.  */
    assert( bRev>=0 && bRev<=2 );
    if( bSort ){
      testcase( bRev==0 );
      testcase( bRev==1 );
      testcase( bRev==2 );
      nOBSat = isSortingIndex(p, pProbe, iCur, nOrdered,


                              wsFlags, bRev&1, &bRev);
      if( nOrderBy==nOBSat ){
        bSort = 0;
        wsFlags |= WHERE_ROWID_RANGE|WHERE_COLUMN_RANGE|WHERE_ORDERBY;

      }
      if( bRev & 1 ) 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 wsFlags. */
    if( bDist
     && isDistinctIndex(pParse, pWC, pProbe, iCur, p->pDistinct, nEq)
     && (wsFlags & WHERE_COLUMN_IN)==0
    ){
      bDist = 0;
      wsFlags |= WHERE_ROWID_RANGE|WHERE_COLUMN_RANGE|WHERE_DISTINCT;
    }

    /* If currently calculating the cost of using an index (not the IPK
................................................................................
    ** 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( (wsFlags&~WHERE_REVERSE)==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. */
      cost = aiRowEst[0]*3 + pProbe->nColumn;
      wsFlags |= WHERE_COVER_SCAN|WHERE_COLUMN_RANGE;
................................................................................
    /* Add in the estimated cost of sorting the result.  Actual experimental
    ** measurements of sorting performance in SQLite show that sorting time
    ** adds C*N*log10(N) to the cost, where N is the number of rows to be 
    ** sorted and C is a factor between 1.95 and 4.3.  We will split the
    ** difference and select C of 3.0.
    */
    if( bSort ){
      cost += nRow*estLog(nRow*(nOrderBy - nOBSat)/nOrderBy)*3;
    }
    if( bDist ){
      cost += nRow*estLog(nRow)*3;
    }

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

................................................................................
    ** 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( nRow>2 && cost<=p->cost.rCost ){
      int k;                       /* Loop counter */
      int nSkipEq = 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; 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 nEq equality matches since the index
            ** has already accounted for these */
            nSkipEq--;
          }else{
            /* Assume each additional equality match reduces the result
................................................................................
        }
      }
      if( nRow<2 ) nRow = 2;
    }


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

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

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

    /* Reset masks for the next index in the loop */
................................................................................
  }

  /* 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 behaviour 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_ORDERBY)==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\n", 
    ((p->cost.plan.wsFlags & WHERE_NOT_FULLSCAN)==0 ? "none" : 
         p->cost.plan.u.pIdx ? p->cost.plan.u.pIdx->zName : "ipk")
  ));
  
  bestOrClauseIndex(p);
  bestAutomaticIndex(p);
  p->cost.plan.wsFlags |= eqTermMask;
}

/*
** 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);
    if( 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.
................................................................................
  SrcList *pTabList,    /* A list of all tables to be scanned */
  Expr *pWhere,         /* The WHERE clause */
  ExprList *pOrderBy,   /* An ORDER BY clause, or NULL */
  ExprList *pDistinct,  /* The select-list for DISTINCT queries - or NULL */
  u16 wctrlFlags,       /* One of the WHERE_* flags defined in sqliteInt.h */
  int iIdxCur           /* If WHERE_ONETABLE_ONLY is set, index cursor number */
){

  int nByteWInfo;            /* Num. bytes allocated for WhereInfo struct */
  int nTabList;              /* Number of elements in pTabList */
  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 */
  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 */


  /* Variable initialization */
  memset(&sWBI, 0, sizeof(sWBI));
  sWBI.pParse = pParse;

  /* The number of tables in the FROM clause is limited by the number of
  ** bits in a Bitmask 
  */
  testcase( pTabList->nSrc==BMS );
  if( pTabList->nSrc>BMS ){
    sqlite3ErrorMsg(pParse, "at most %d tables in a join", BMS);
    return 0;
................................................................................
    pWInfo = 0;
    goto whereBeginError;
  }
  pWInfo->nLevel = nTabList;
  pWInfo->pParse = pParse;
  pWInfo->pTabList = pTabList;
  pWInfo->iBreak = sqlite3VdbeMakeLabel(v);
  pWInfo->pWC = sWBI.pWC = (WhereClause *)&((u8 *)pWInfo)[nByteWInfo];
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  pMaskSet = (WhereMaskSet*)&sWBI.pWC[1];
  sWBI.aLevel = pWInfo->a;

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

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.
  */
  initMaskSet(pMaskSet);
  whereClauseInit(sWBI.pWC, pParse, pMaskSet, wctrlFlags);
  sqlite3ExprCodeConstants(pParse, pWhere);
  whereSplit(sWBI.pWC, pWhere, TK_AND);   /* IMP: R-15842-53296 */
    
  /* Special case: a WHERE clause that is constant.  Evaluate the
  ** expression and either jump over all of the code or fall thru.
  */
  if( pWhere && (nTabList==0 || sqlite3ExprIsConstantNotJoin(pWhere)) ){
    sqlite3ExprIfFalse(pParse, pWhere, pWInfo->iBreak, SQLITE_JUMPIFNULL);
    pWhere = 0;
................................................................................
  ** with virtual tables.
  **
  ** Note that bitmasks are created for all pTabList->nSrc tables in
  ** pTabList, not just the first nTabList tables.  nTabList is normally
  ** equal to pTabList->nSrc but might be shortened to 1 if the
  ** WHERE_ONETABLE_ONLY flag is set.
  */
  assert( sWBI.pWC->vmask==0 && pMaskSet->n==0 );
  for(ii=0; ii<pTabList->nSrc; ii++){
    createMask(pMaskSet, pTabList->a[ii].iCursor);
#ifndef SQLITE_OMIT_VIRTUALTABLE
    if( ALWAYS(pTabList->a[ii].pTab) && IsVirtual(pTabList->a[ii].pTab) ){
      sWBI.pWC->vmask |= ((Bitmask)1 << ii);
    }
#endif
  }
#ifndef NDEBUG
  {
    Bitmask toTheLeft = 0;
    for(ii=0; ii<pTabList->nSrc; ii++){
      Bitmask m = getMask(pMaskSet, pTabList->a[ii].iCursor);
      assert( (m-1)==toTheLeft );
      toTheLeft |= m;
    }
  }
#endif

  /* Analyze all of the subexpressions.  Note that exprAnalyze() might
  ** add new virtual terms onto the end of the WHERE clause.  We do not
  ** want to analyze these virtual terms, so start analyzing at the end
  ** and work forward so that the added virtual terms are never processed.
  */
  exprAnalyzeAll(pTabList, sWBI.pWC);
  if( db->mallocFailed ){
    goto whereBeginError;
  }

  /* Check if the DISTINCT qualifier, if there is one, is redundant. 
  ** If it is, then set pDistinct to NULL and WhereInfo.eDistinct to
  ** WHERE_DISTINCT_UNIQUE to tell the caller to ignore the DISTINCT.
  */
  if( pDistinct && isDistinctRedundant(pParse, pTabList, sWBI.pWC, pDistinct) ){
    pDistinct = 0;
    pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
  }

  /* Chose the best index to use for each table in the FROM clause.
  **
  ** This loop fills in the following fields:
................................................................................
  **   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;
  WHERETRACE(("*** Optimizer Start ***\n"));
  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 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
................................................................................
    ** 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.  
    **
................................................................................
    ** 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;
    for(isOptimal=(iFrom<nTabList-1); isOptimal>=0 && bestJ<0; isOptimal--){

      for(j=iFrom, sWBI.pSrc=&pTabList->a[j]; j<nTabList; j++, sWBI.pSrc++){
        int doNotReorder;    /* True if this table should not be reordered */



  
        doNotReorder =  (sWBI.pSrc->jointype & (JT_LEFT|JT_CROSS))!=0;
        if( j!=iFrom && doNotReorder ) break;
        m = getMask(pMaskSet, sWBI.pSrc->iCursor);

        if( (m & sWBI.notValid)==0 ){
          if( j==iFrom ) iFrom++;
          continue;
        }
        sWBI.notReady = (isOptimal ? m : sWBI.notValid);


        if( sWBI.pSrc->pIndex==0 ) nUnconstrained++;
  
        WHERETRACE(("=== trying table %d with isOptimal=%d ===\n",
                    j, 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;
        }

        /* 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) A full-table-scan plan cannot supercede indexed plan unless
        **       the full-table-scan is an "optimal" plan as defined above.
        **
        **   (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
................................................................................
        **       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 or else the
        **       cost must be the same and the number of rows must be lower.
        */
        if( (sWBI.cost.used&sWBI.notValid)==0                    /* (1) */
            && (bestJ<0 || (notIndexed&m)!=0                     /* (2) */
                || (bestPlan.plan.wsFlags & WHERE_NOT_FULLSCAN)==0
                || (sWBI.cost.plan.wsFlags & WHERE_NOT_FULLSCAN)!=0)
            && (nUnconstrained==0 || sWBI.pSrc->pIndex==0        /* (3) */
                || NEVER((sWBI.cost.plan.wsFlags & WHERE_NOT_FULLSCAN)!=0))
            && (bestJ<0 || sWBI.cost.rCost<bestPlan.rCost        /* (4) */
                || (sWBI.cost.rCost<=bestPlan.rCost 
                 && sWBI.cost.plan.nRow<bestPlan.plan.nRow))
        ){
          WHERETRACE(("=== table %d is best so far"
                      " with cost=%.1f, nRow=%.1f, nOBSat=%d\n",
                      j, sWBI.cost.rCost, sWBI.cost.plan.nRow,
                      sWBI.cost.plan.nOBSat));
          bestPlan = sWBI.cost;
          bestJ = j;
        }
        if( doNotReorder ) break;
      }
    }
    assert( bestJ>=0 );
    assert( sWBI.notValid & getMask(pMaskSet, pTabList->a[bestJ].iCursor) );
    WHERETRACE(("*** Optimizer selects table %d for loop %d with:\n"
                "    cost=%.1f, nRow=%.1f, nOBSat=%d wsFlags=0x%08x\n",
                bestJ, pLevel-pWInfo->a, bestPlan.rCost, bestPlan.plan.nRow,
                bestPlan.plan.nOBSat, bestPlan.plan.wsFlags));
    if( (bestPlan.plan.wsFlags & WHERE_ORDERBY)!=0 ){
      pWInfo->nOBSat = pOrderBy->nExpr;
    }
    if( (bestPlan.plan.wsFlags & WHERE_DISTINCT)!=0 ){
      assert( pWInfo->eDistinct==0 );
      pWInfo->eDistinct = WHERE_DISTINCT_ORDERED;
    }
................................................................................
        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
................................................................................

  /* 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;
    pLevel->iTabCur = pTabItem->iCursor;
    pWInfo->nRowOut *= pLevel->plan.nRow;
    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);
    if( (pTab->tabFlags & TF_Ephemeral)!=0 || pTab->pSelect ){
................................................................................
        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);
    notReady &= ~getMask(sWBI.pWC->pMaskSet, pTabItem->iCursor);
  }
  pWInfo->iTop = sqlite3VdbeCurrentAddr(v);
  if( db->mallocFailed ) goto whereBeginError;

  /* Generate the code to do the search.  Each iteration of the for
  ** loop below generates code for a single nested loop of the VM
  ** program.
  */
  notReady = ~(Bitmask)0;
  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++){
    char *z;
    int n;
    int w;
    struct SrcList_item *pTabItem;

    pLevel = &pWInfo->a[ii];
    w = pLevel->plan.wsFlags;
    pTabItem = &pTabList->a[pLevel->iFrom];
    z = pTabItem->zAlias;
    if( z==0 ) z = pTabItem->pTab->zName;
    n = sqlite3Strlen30(z);
    if( n+nQPlan < sizeof(sqlite3_query_plan)-10 ){
      if( (w & WHERE_IDX_ONLY)!=0 && (w & WHERE_COVER_SCAN)==0 ){

# These tests - collate5-3.* - focus on compound SELECT queries that 
# feature ORDER BY clauses.
#
do_test collate5-3.0 {
  execsql {
    SELECT a FROM collate5t1 UNION ALL SELECT a FROM collate5t2 ORDER BY 1;
  }
} {a A a A b B b B n N}
do_test collate5-3.1 {
  execsql {
    SELECT a FROM collate5t2 UNION ALL SELECT a FROM collate5t1 ORDER BY 1;
  }
} {A A B B N a a b b n}
do_test collate5-3.2 {
  execsql {
................................................................................
    SELECT a, count(*) FROM collate5t1 GROUP BY a;
  }]
} {a 2 b 2}
do_test collate5-4.2 {
  execsql {
    SELECT a, b, count(*) FROM collate5t1 GROUP BY a, b ORDER BY a, b;
  }
} {A 1.0 2 b 2 1 B 3 1}
do_test collate5-4.3 {
  execsql {
    DROP TABLE collate5t1;
  }
} {}

finish_test

# These tests - collate5-3.* - focus on compound SELECT queries that 
# feature ORDER BY clauses.
#
do_test collate5-3.0 {
  execsql {
    SELECT a FROM collate5t1 UNION ALL SELECT a FROM collate5t2 ORDER BY 1;
  }
} {/[aA] [aA] [aA] [aA] [bB] [bB] [bB] [bB] [nN] [nN]/}
do_test collate5-3.1 {
  execsql {
    SELECT a FROM collate5t2 UNION ALL SELECT a FROM collate5t1 ORDER BY 1;
  }
} {A A B B N a a b b n}
do_test collate5-3.2 {
  execsql {
................................................................................
    SELECT a, count(*) FROM collate5t1 GROUP BY a;
  }]
} {a 2 b 2}
do_test collate5-4.2 {
  execsql {
    SELECT a, b, count(*) FROM collate5t1 GROUP BY a, b ORDER BY a, b;
  }
} {/[aA] 1(.0)? 2 [bB] 2 1 [bB] 3 1/}
do_test collate5-4.3 {
  execsql {
    DROP TABLE collate5t1;
  }
} {}

finish_test

#   These tests also show that the following is not untrue:
#
# EVIDENCE-OF: R-25883-55063 The expressions in the GROUP BY clause do
# not have to be expressions that appear in the result.
#
do_select_tests e_select-4.9 {
  1  "SELECT group_concat(one), two FROM b1 GROUP BY two" {
    4,5 f   1 o   7,6   s 3,2 t
  }
  2  "SELECT group_concat(one), sum(one) FROM b1 GROUP BY (one>4)" {
    1,2,3,4 10    5,6,7 18
  }
  3  "SELECT group_concat(one) FROM b1 GROUP BY (two>'o'), one%2" {
    4  1,5    2,6   3,7
  }
................................................................................
  }
}

# EVIDENCE-OF: R-14926-50129 For the purposes of grouping rows, NULL
# values are considered equal.
#
do_select_tests e_select-4.10 {
  1  "SELECT group_concat(y) FROM b2 GROUP BY x" {0,1   3   2,4}
  2  "SELECT count(*) FROM b2 GROUP BY CASE WHEN y<4 THEN NULL ELSE 0 END" {4 1}
} 

# EVIDENCE-OF: R-10470-30318 The usual rules for selecting a collation
# sequence with which to compare text values apply when evaluating
# expressions in a GROUP BY clause.
#
................................................................................
     1 2 3    1 2 -20    1 4  93    1 5 -1   
  }
  7  "SELECT * FROM d1 ORDER BY 1 DESC, 2, 3" {
     2 4 93   2 5 -1     1 2 -20    1 2 3    
     1 2 7    1 2 8      1 4  93    1 5 -1   
  }
  8  "SELECT z, x FROM d1 ORDER BY 2" {
     3 1     8 1    7 1   -20 1 
     93 1   -1 1   -1 2   93 2
  }
  9  "SELECT z, x FROM d1 ORDER BY 1" {
     -20 1  -1 2   -1 1   3 1     
     7 1     8 1   93 2   93 1   
  }
}

# EVIDENCE-OF: R-63286-51977 If the ORDER BY expression is an identifier
# that corresponds to the alias of one of the output columns, then the
# expression is considered an alias for that column.
#
................................................................................
  1   "SELECT z+1 AS abc FROM d1 ORDER BY abc" {
    -19 0 0 4 8 9 94 94
  }
  2   "SELECT z+1 AS abc FROM d1 ORDER BY abc DESC" {
    94 94 9 8 4 0 0 -19
  }
  3  "SELECT z AS x, x AS z FROM d1 ORDER BY z" {
    3 1    8 1    7 1    -20 1    93 1    -1 1    -1 2    93 2
  }
  4  "SELECT z AS x, x AS z FROM d1 ORDER BY x" {
    -20 1    -1 2    -1 1    3 1    7 1    8 1    93 2    93 1
  }
}

# EVIDENCE-OF: R-65068-27207 Otherwise, if the ORDER BY expression is
# any other expression, it is evaluated and the returned value used to
# order the output rows.
#

#   These tests also show that the following is not untrue:
#
# EVIDENCE-OF: R-25883-55063 The expressions in the GROUP BY clause do
# not have to be expressions that appear in the result.
#
do_select_tests e_select-4.9 {
  1  "SELECT group_concat(one), two FROM b1 GROUP BY two" {
    /#,# f   1 o   #,#   s #,# t/
  }
  2  "SELECT group_concat(one), sum(one) FROM b1 GROUP BY (one>4)" {
    1,2,3,4 10    5,6,7 18
  }
  3  "SELECT group_concat(one) FROM b1 GROUP BY (two>'o'), one%2" {
    4  1,5    2,6   3,7
  }
................................................................................
  }
}

# EVIDENCE-OF: R-14926-50129 For the purposes of grouping rows, NULL
# values are considered equal.
#
do_select_tests e_select-4.10 {
  1  "SELECT group_concat(y) FROM b2 GROUP BY x" {/#,#   3   #,#/}
  2  "SELECT count(*) FROM b2 GROUP BY CASE WHEN y<4 THEN NULL ELSE 0 END" {4 1}
} 

# EVIDENCE-OF: R-10470-30318 The usual rules for selecting a collation
# sequence with which to compare text values apply when evaluating
# expressions in a GROUP BY clause.
#
................................................................................
     1 2 3    1 2 -20    1 4  93    1 5 -1   
  }
  7  "SELECT * FROM d1 ORDER BY 1 DESC, 2, 3" {
     2 4 93   2 5 -1     1 2 -20    1 2 3    
     1 2 7    1 2 8      1 4  93    1 5 -1   
  }
  8  "SELECT z, x FROM d1 ORDER BY 2" {
     /# 1    # 1    # 1   # 1 
      # 1    # 1    # 2   # 2/
  }
  9  "SELECT z, x FROM d1 ORDER BY 1" {
     /-20 1  -1 #   -1 #   3 1
     7 1     8 1   93 #   93 #/   
  }
}

# EVIDENCE-OF: R-63286-51977 If the ORDER BY expression is an identifier
# that corresponds to the alias of one of the output columns, then the
# expression is considered an alias for that column.
#
................................................................................
  1   "SELECT z+1 AS abc FROM d1 ORDER BY abc" {
    -19 0 0 4 8 9 94 94
  }
  2   "SELECT z+1 AS abc FROM d1 ORDER BY abc DESC" {
    94 94 9 8 4 0 0 -19
  }
  3  "SELECT z AS x, x AS z FROM d1 ORDER BY z" {
    /# 1    # 1    # 1    # 1    # 1    # 1    # 2    # 2/
  }
  4  "SELECT z AS x, x AS z FROM d1 ORDER BY x" {
    /-20 1    -1 #    -1 #    3 1    7 1    8 1    93 #    93 #/
  }
}

# EVIDENCE-OF: R-65068-27207 Otherwise, if the ORDER BY expression is
# any other expression, it is evaluated and the returned value used to
# order the output rows.
#

# 2012 Sept 27
#
# The author disclaims copyright to this source code.  In place of
# a legal notice, here is a blessing:
#
#    May you do good and not evil.
#    May you find forgiveness for yourself and forgive others.
#    May you share freely, never taking more than you give.
#
#***********************************************************************
# This file implements regression tests for SQLite library.  The
# focus of this file is testing that the optimizations that disable
# ORDER BY clauses when the natural order of a query is correct.
#


set testdir [file dirname $argv0]
source $testdir/tester.tcl
set ::testprefix orderby1

# Generate test data for a join.  Verify that the join gets the
# correct answer.
#
do_test 1.0 {
  db eval {
    BEGIN;
    CREATE TABLE album(
      aid INTEGER PRIMARY KEY,
      title TEXT UNIQUE NOT NULL
    );
    CREATE TABLE track(
      tid INTEGER PRIMARY KEY,
      aid INTEGER NOT NULL REFERENCES album,
      tn INTEGER NOT NULL,
      name TEXT,
      UNIQUE(aid, tn)
    );
    INSERT INTO album VALUES(1, '1-one'), (2, '2-two'), (3, '3-three');
    INSERT INTO track VALUES
        (NULL, 1, 1, 'one-a'),
        (NULL, 2, 2, 'two-b'),
        (NULL, 3, 3, 'three-c'),
        (NULL, 1, 3, 'one-c'),
        (NULL, 2, 1, 'two-a'),
        (NULL, 3, 1, 'three-a');
    COMMIT;
  }
} {}
do_test 1.1a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {one-a one-c two-a two-b three-a three-c}

# Verify that the ORDER BY clause is optimized out
#
do_test 1.1b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {~/ORDER BY/}  ;# ORDER BY optimized out

# The same query with ORDER BY clause optimization disabled via + operators
# should give exactly the same answer.
#
do_test 1.2a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn
  }
} {one-a one-c two-a two-b three-a three-c}

# The output is sorted manually in this case.
#
do_test 1.2b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn
  }
} {/ORDER BY/}   ;# separate sorting pass due to "+" on ORDER BY terms

# The same query with ORDER BY optimizations turned off via built-in test.
#
do_test 1.3a {
  optimization_control db order-by-idx-join 0
  db cache flush
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {one-a one-c two-a two-b three-a three-c}
do_test 1.3b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {/ORDER BY/}   ;# separate sorting pass due to disabled optimization
optimization_control db all 1
db cache flush

# Reverse order sorts
#
do_test 1.4a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn
  }
} {three-a three-c two-a two-b one-a one-c}
do_test 1.4b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title DESC, +tn
  }
} {three-a three-c two-a two-b one-a one-c}  ;# verify same order after sorting
do_test 1.4c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn
  }
} {/ORDER BY/}  ;# separate sorting pass due to mixed DESC/ASC


do_test 1.5a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn DESC
  }
} {one-c one-a two-b two-a three-c three-a}
do_test 1.5b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn DESC
  }
} {one-c one-a two-b two-a three-c three-a}  ;# verify same order after sorting
do_test 1.5c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn DESC
  }
} {/ORDER BY/}  ;# separate sorting pass due to mixed DESC/ASC

do_test 1.6a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn DESC
  }
} {three-c three-a two-b two-a one-c one-a}
do_test 1.6b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title DESC, +tn DESC
  }
} {three-c three-a two-b two-a one-c one-a}  ;# verify same order after sorting
do_test 1.6c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn DESC
  }
} {~/ORDER BY/}  ;# ORDER BY optimized-out


# Reconstruct the test data to use indices rather than integer primary keys.
#
do_test 2.0 {
  db eval {
    BEGIN;
    DROP TABLE album;
    DROP TABLE track;
    CREATE TABLE album(
      aid INT PRIMARY KEY,
      title TEXT NOT NULL
    );
    CREATE INDEX album_i1 ON album(title, aid);
    CREATE TABLE track(
      aid INTEGER NOT NULL REFERENCES album,
      tn INTEGER NOT NULL,
      name TEXT,
      UNIQUE(aid, tn)
    );
    INSERT INTO album VALUES(1, '1-one'), (2, '2-two'), (3, '3-three');
    INSERT INTO track VALUES
        (1, 1, 'one-a'),
        (2, 2, 'two-b'),
        (3, 3, 'three-c'),
        (1, 3, 'one-c'),
        (2, 1, 'two-a'),
        (3, 1, 'three-a');
    COMMIT;
  }
} {}
do_test 2.1a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {one-a one-c two-a two-b three-a three-c}

# Verify that the ORDER BY clause is optimized out
#
do_test 2.1b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {~/ORDER BY/}  ;# ORDER BY optimized out

# The same query with ORDER BY clause optimization disabled via + operators
# should give exactly the same answer.
#
do_test 2.2a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn
  }
} {one-a one-c two-a two-b three-a three-c}

# The output is sorted manually in this case.
#
do_test 2.2b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn
  }
} {/ORDER BY/}   ;# separate sorting pass due to "+" on ORDER BY terms

# The same query with ORDER BY optimizations turned off via built-in test.
#
do_test 2.3a {
  optimization_control db order-by-idx-join 0
  db cache flush
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {one-a one-c two-a two-b three-a three-c}
do_test 2.3b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {/ORDER BY/}   ;# separate sorting pass due to disabled optimization
optimization_control db all 1
db cache flush

# Reverse order sorts
#
do_test 2.4a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn
  }
} {three-a three-c two-a two-b one-a one-c}
do_test 2.4b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title DESC, +tn
  }
} {three-a three-c two-a two-b one-a one-c}  ;# verify same order after sorting
do_test 2.4c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn
  }
} {/ORDER BY/}  ;# separate sorting pass due to mixed DESC/ASC


do_test 2.5a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn DESC
  }
} {one-c one-a two-b two-a three-c three-a}
do_test 2.5b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn DESC
  }
} {one-c one-a two-b two-a three-c three-a}  ;# verify same order after sorting
do_test 2.5c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn DESC
  }
} {/ORDER BY/}  ;# separate sorting pass due to mixed ASC/DESC

do_test 2.6a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn DESC
  }
} {three-c three-a two-b two-a one-c one-a}
do_test 2.6b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title DESC, +tn DESC
  }
} {three-c three-a two-b two-a one-c one-a}  ;# verify same order after sorting
do_test 2.6c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn DESC
  }
} {~/ORDER BY/}  ;# ORDER BY optimized-out


# Generate another test dataset, but this time using mixed ASC/DESC indices.
#
do_test 3.0 {
  db eval {
    BEGIN;
    DROP TABLE album;
    DROP TABLE track;
    CREATE TABLE album(
      aid INTEGER PRIMARY KEY,
      title TEXT UNIQUE NOT NULL
    );
    CREATE TABLE track(
      tid INTEGER PRIMARY KEY,
      aid INTEGER NOT NULL REFERENCES album,
      tn INTEGER NOT NULL,
      name TEXT,
      UNIQUE(aid ASC, tn DESC)
    );
    INSERT INTO album VALUES(1, '1-one'), (2, '2-two'), (3, '3-three');
    INSERT INTO track VALUES
        (NULL, 1, 1, 'one-a'),
        (NULL, 2, 2, 'two-b'),
        (NULL, 3, 3, 'three-c'),
        (NULL, 1, 3, 'one-c'),
        (NULL, 2, 1, 'two-a'),
        (NULL, 3, 1, 'three-a');
    COMMIT;
  }
} {}
do_test 3.1a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn DESC
  }
} {one-c one-a two-b two-a three-c three-a}

# Verify that the ORDER BY clause is optimized out
#
do_test 3.1b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn DESC
  }
} {~/ORDER BY/}  ;# ORDER BY optimized out

# The same query with ORDER BY clause optimization disabled via + operators
# should give exactly the same answer.
#
do_test 3.2a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn DESC
  }
} {one-c one-a two-b two-a three-c three-a}

# The output is sorted manually in this case.
#
do_test 3.2b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn DESC
  }
} {/ORDER BY/}   ;# separate sorting pass due to "+" on ORDER BY terms

# The same query with ORDER BY optimizations turned off via built-in test.
#
do_test 3.3a {
  optimization_control db order-by-idx-join 0
  db cache flush
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn DESC
  }
} {one-c one-a two-b two-a three-c three-a}
do_test 3.3b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn DESC
  }
} {/ORDER BY/}   ;# separate sorting pass due to disabled optimization
optimization_control db all 1
db cache flush

# Without the mixed ASC/DESC on ORDER BY
#
do_test 3.4a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {one-a one-c two-a two-b three-a three-c}
do_test 3.4b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title, +tn
  }
} {one-a one-c two-a two-b three-a three-c}  ;# verify same order after sorting
do_test 3.4c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title, tn
  }
} {/ORDER BY/}  ;# separate sorting pass due to mismatched DESC/ASC


do_test 3.5a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn DESC
  }
} {three-c three-a two-b two-a one-c one-a}
do_test 3.5b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title DESC, +tn DESC
  }
} {three-c three-a two-b two-a one-c one-a}  ;# verify same order after sorting
do_test 3.5c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn DESC
  }
} {/ORDER BY/}  ;# separate sorting pass due to mismatched ASC/DESC


do_test 3.6a {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn
  }
} {three-a three-c two-a two-b one-a one-c}
do_test 3.6b {
  db eval {
    SELECT name FROM album JOIN track USING (aid) ORDER BY +title DESC, +tn
  }
} {three-a three-c two-a two-b one-a one-c}  ;# verify same order after sorting
do_test 3.6c {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT name FROM album JOIN track USING (aid) ORDER BY title DESC, tn
  }
} {~/ORDER BY/}  ;# inverted ASC/DESC is optimized out


finish_test

  if {![info exists ::G(match)] || [string match $::G(match) $name]} {
    if {[catch {uplevel #0 "$cmd;\n"} result]} {
      puts "\nError: $result"
      fail_test $name
    } else {
      if {[regexp {^~?/.*/$} $expected]} {
        if {[string index $expected 0]=="~"} {
          set re [string range $expected 2 end-1]
          set ok [expr {![regexp $re $result]}]
        } else {
          set re [string range $expected 1 end-1]
          set ok [regexp $re $result]
        }
      } else {
        set ok [expr {[string compare $result $expected]==0}]
      }
      if {!$ok} {
        # if {![info exists ::testprefix] || $::testprefix eq ""} {

  if {![info exists ::G(match)] || [string match $::G(match) $name]} {
    if {[catch {uplevel #0 "$cmd;\n"} result]} {
      puts "\nError: $result"
      fail_test $name
    } else {
      if {[regexp {^~?/.*/$} $expected]} {
        if {[string index $expected 0]=="~"} {
          set re [string map {# {[-0-9.]+}} [string range $expected 2 end-1]]
          set ok [expr {![regexp $re $result]}]
        } else {
          set re [string map {# {[-0-9.]+}} [string range $expected 1 end-1]]
          set ok [regexp $re $result]
        }
      } else {
        set ok [expr {[string compare $result $expected]==0}]
      }
      if {!$ok} {
        # if {![info exists ::testprefix] || $::testprefix eq ""} {

do_test tkt-cbd05-1.3 {
  execsql { 
    SELECT tbl,idx,group_concat(sample,' ') 
    FROM sqlite_stat3 
    WHERE idx = 't1_x' 
    GROUP BY tbl,idx
  }
} {t1 t1_x { A B C D E F G H I}}

do_test tkt-cbd05-2.1 {
  db eval {
    DROP TABLE t1;
    CREATE TABLE t1(a INTEGER PRIMARY KEY, b BLOB UNIQUE NOT NULL);
    CREATE INDEX t1_x ON t1(b);
    INSERT INTO t1 VALUES(NULL, X'');
................................................................................
do_test tkt-cbd05-2.3 {
  execsql { 
    SELECT tbl,idx,group_concat(sample,' ') 
    FROM sqlite_stat3 
    WHERE idx = 't1_x' 
    GROUP BY tbl,idx
  }
} {t1 t1_x { A B C D E F G H I}}

finish_test

do_test tkt-cbd05-1.3 {
  execsql { 
    SELECT tbl,idx,group_concat(sample,' ') 
    FROM sqlite_stat3 
    WHERE idx = 't1_x' 
    GROUP BY tbl,idx
  }
} {/t1 t1_x .[ ABCDEFGHI]{10}./}

do_test tkt-cbd05-2.1 {
  db eval {
    DROP TABLE t1;
    CREATE TABLE t1(a INTEGER PRIMARY KEY, b BLOB UNIQUE NOT NULL);
    CREATE INDEX t1_x ON t1(b);
    INSERT INTO t1 VALUES(NULL, X'');
................................................................................
do_test tkt-cbd05-2.3 {
  execsql { 
    SELECT tbl,idx,group_concat(sample,' ') 
    FROM sqlite_stat3 
    WHERE idx = 't1_x' 
    GROUP BY tbl,idx
  }
} {/t1 t1_x .[ ABCDEFGHI]{10}./}

finish_test

  } 
} {1/4 1/1 4/4 4/1 nosort}
do_test where-14.5 {
  # This test case changed from "nosort" to "sort". See ticket 2a5629202f.
  cksort {
    SELECT x.a || '/' || y.a FROM t8 x, t8 y ORDER BY x.b, x.a||x.b
  } 
} {4/4 4/1 1/4 1/1 sort}
do_test where-14.6 {
  # This test case changed from "nosort" to "sort". See ticket 2a5629202f.
  cksort {
    SELECT x.a || '/' || y.a FROM t8 x, t8 y ORDER BY x.b, x.a||x.b DESC
  } 
} {4/4 4/1 1/4 1/1 sort}
do_test where-14.7 {
  cksort {
    SELECT x.a || '/' || y.a FROM t8 x, t8 y ORDER BY x.b, y.a||y.b
  } 
} {4/1 4/4 1/1 1/4 sort}
do_test where-14.7.1 {
  cksort {

  } 
} {1/4 1/1 4/4 4/1 nosort}
do_test where-14.5 {
  # This test case changed from "nosort" to "sort". See ticket 2a5629202f.
  cksort {
    SELECT x.a || '/' || y.a FROM t8 x, t8 y ORDER BY x.b, x.a||x.b
  } 
} {/4/[14] 4/[14] 1/[14] 1/[14] sort/}
do_test where-14.6 {
  # This test case changed from "nosort" to "sort". See ticket 2a5629202f.
  cksort {
    SELECT x.a || '/' || y.a FROM t8 x, t8 y ORDER BY x.b, x.a||x.b DESC
  } 
} {/4/[14] 4/[14] 1/[14] 1/[14] sort/}
do_test where-14.7 {
  cksort {
    SELECT x.a || '/' || y.a FROM t8 x, t8 y ORDER BY x.b, y.a||y.b
  } 
} {4/1 4/4 1/1 1/4 sort}
do_test where-14.7.1 {
  cksort {