/*
** 2001 September 15
**
** 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 module contains C code that generates VDBE code used to process
** the WHERE clause of SQL statements.  This module is responsible for
** generating the code that loops through a table looking for applicable
** rows.  Indices are selected and used to speed the search when doing
** so is applicable.  Because this module is responsible for selecting
** indices, you might also think of this module as the "query optimizer".
*/
#include "sqliteInt.h"


/*
** Trace output macros
*/
#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)
int sqlite3WhereTrace = 0;
#endif
#if defined(SQLITE_TEST) && defined(SQLITE_DEBUG)
# define WHERETRACE(X)  if(sqlite3WhereTrace) sqlite3DebugPrintf X
#else
# define WHERETRACE(X)
#endif

/* Forward reference
*/
typedef struct WhereClause WhereClause;
typedef struct WhereMaskSet WhereMaskSet;
typedef struct WhereOrInfo WhereOrInfo;
typedef struct WhereAndInfo WhereAndInfo;
typedef struct WhereCost WhereCost;

/*
** The query generator uses an array of instances of this structure to
** help it analyze the subexpressions of the WHERE clause.  Each WHERE
** clause subexpression is separated from the others by AND operators,
** usually, or sometimes subexpressions separated by OR.
**
** All WhereTerms are collected into a single WhereClause structure.  
** The following identity holds:
**
**        WhereTerm.pWC->a[WhereTerm.idx] == WhereTerm
**
** When a term is of the form:
**
**              X <op> <expr>
**
** where X is a column name and <op> is one of certain operators,
** then WhereTerm.leftCursor and WhereTerm.u.leftColumn record the
** cursor number and column number for X.  WhereTerm.eOperator records
** the <op> using a bitmask encoding defined by WO_xxx below.  The
** use of a bitmask encoding for the operator allows us to search
** quickly for terms that match any of several different operators.
**
** A WhereTerm might also be two or more subterms connected by OR:
**
**         (t1.X <op> <expr>) OR (t1.Y <op> <expr>) OR ....
**
** In this second case, wtFlag as the TERM_ORINFO set and eOperator==WO_OR
** and the WhereTerm.u.pOrInfo field points to auxiliary information that
** is collected about the
**
** If a term in the WHERE clause does not match either of the two previous
** categories, then eOperator==0.  The WhereTerm.pExpr field is still set
** to the original subexpression content and wtFlags is set up appropriately
** but no other fields in the WhereTerm object are meaningful.
**
** When eOperator!=0, prereqRight and prereqAll record sets of cursor numbers,
** but they do so indirectly.  A single WhereMaskSet structure translates
** cursor number into bits and the translated bit is stored in the prereq
** fields.  The translation is used in order to maximize the number of
** bits that will fit in a Bitmask.  The VDBE cursor numbers might be
** spread out over the non-negative integers.  For example, the cursor
** numbers might be 3, 8, 9, 10, 20, 23, 41, and 45.  The WhereMaskSet
** translates these sparse cursor numbers into consecutive integers
** beginning with 0 in order to make the best possible use of the available
** bits in the Bitmask.  So, in the example above, the cursor numbers
** would be mapped into integers 0 through 7.
**
** The number of terms in a join is limited by the number of bits
** in prereqRight and prereqAll.  The default is 64 bits, hence SQLite
** is only able to process joins with 64 or fewer tables.
*/
typedef struct WhereTerm WhereTerm;
struct WhereTerm {
  Expr *pExpr;            /* Pointer to the subexpression that is this term */
  int iParent;            /* Disable pWC->a[iParent] when this term disabled */
  int leftCursor;         /* Cursor number of X in "X <op> <expr>" */
  union {
    int leftColumn;         /* Column number of X in "X <op> <expr>" */
    WhereOrInfo *pOrInfo;   /* Extra information if eOperator==WO_OR */
    WhereAndInfo *pAndInfo; /* Extra information if eOperator==WO_AND */
  } u;
  u16 eOperator;          /* A WO_xx value describing <op> */
  u8 wtFlags;             /* TERM_xxx bit flags.  See below */
  u8 nChild;              /* Number of children that must disable us */
  WhereClause *pWC;       /* The clause this term is part of */
  Bitmask prereqRight;    /* Bitmask of tables used by pExpr->pRight */
  Bitmask prereqAll;      /* Bitmask of tables referenced by pExpr */
};

/*
** Allowed values of WhereTerm.wtFlags
*/
#define TERM_DYNAMIC    0x01   /* Need to call sqlite3ExprDelete(db, pExpr) */
#define TERM_VIRTUAL    0x02   /* Added by the optimizer.  Do not code */
#define TERM_CODED      0x04   /* This term is already coded */
#define TERM_COPIED     0x08   /* Has a child */
#define TERM_ORINFO     0x10   /* Need to free the WhereTerm.u.pOrInfo object */
#define TERM_ANDINFO    0x20   /* Need to free the WhereTerm.u.pAndInfo obj */
#define TERM_OR_OK      0x40   /* Used during OR-clause processing */
#ifdef SQLITE_ENABLE_STAT2
#  define TERM_VNULL    0x80   /* Manufactured x>NULL or x<=NULL term */
#else
#  define TERM_VNULL    0x00   /* Disabled if not using stat2 */
#endif

/*
** An instance of the following structure holds all information about a
** WHERE clause.  Mostly this is a container for one or more WhereTerms.
*/
struct WhereClause {
  Parse *pParse;           /* The parser context */
  WhereMaskSet *pMaskSet;  /* Mapping of table cursor numbers to bitmasks */
  Bitmask vmask;           /* Bitmask identifying virtual table cursors */
  u8 op;                   /* Split operator.  TK_AND or TK_OR */
  int nTerm;               /* Number of terms */
  int nSlot;               /* Number of entries in a[] */
  WhereTerm *a;            /* Each a[] describes a term of the WHERE cluase */
#if defined(SQLITE_SMALL_STACK)
  WhereTerm aStatic[1];    /* Initial static space for a[] */
#else
  WhereTerm aStatic[8];    /* Initial static space for a[] */
#endif
};

/*
** A WhereTerm with eOperator==WO_OR has its u.pOrInfo pointer set to
** a dynamically allocated instance of the following structure.
*/
struct WhereOrInfo {
  WhereClause wc;          /* Decomposition into subterms */
  Bitmask indexable;       /* Bitmask of all indexable tables in the clause */
};

/*
** A WhereTerm with eOperator==WO_AND has its u.pAndInfo pointer set to
** a dynamically allocated instance of the following structure.
*/
struct WhereAndInfo {
  WhereClause wc;          /* The subexpression broken out */
};

/*
** An instance of the following structure keeps track of a mapping
** between VDBE cursor numbers and bits of the bitmasks in WhereTerm.
**
** The VDBE cursor numbers are small integers contained in 
** SrcList_item.iCursor and Expr.iTable fields.  For any given WHERE 
** clause, the cursor numbers might not begin with 0 and they might
** contain gaps in the numbering sequence.  But we want to make maximum
** use of the bits in our bitmasks.  This structure provides a mapping
** from the sparse cursor numbers into consecutive integers beginning
** with 0.
**
** If WhereMaskSet.ix[A]==B it means that The A-th bit of a Bitmask
** corresponds VDBE cursor number B.  The A-th bit of a bitmask is 1<<A.
**
** For example, if the WHERE clause expression used these VDBE
** cursors:  4, 5, 8, 29, 57, 73.  Then the  WhereMaskSet structure
** would map those cursor numbers into bits 0 through 5.
**
** Note that the mapping is not necessarily ordered.  In the example
** above, the mapping might go like this:  4->3, 5->1, 8->2, 29->0,
** 57->5, 73->4.  Or one of 719 other combinations might be used. It
** does not really matter.  What is important is that sparse cursor
** numbers all get mapped into bit numbers that begin with 0 and contain
** no gaps.
*/
struct WhereMaskSet {
  int n;                        /* Number of assigned cursor values */
  int ix[BMS];                  /* Cursor assigned to each bit */
};

/*
** A WhereCost object records a lookup strategy and the estimated
** cost of pursuing that strategy.
*/
struct WhereCost {
  WherePlan plan;    /* The lookup strategy */
  double rCost;      /* Overall cost of pursuing this search strategy */
  Bitmask used;      /* Bitmask of cursors used by this plan */
};

/*
** Bitmasks for the operators that indices are able to exploit.  An
** OR-ed combination of these values can be used when searching for
** terms in the where clause.
*/
#define WO_IN     0x001
#define WO_EQ     0x002
#define WO_LT     (WO_EQ<<(TK_LT-TK_EQ))
#define WO_LE     (WO_EQ<<(TK_LE-TK_EQ))
#define WO_GT     (WO_EQ<<(TK_GT-TK_EQ))
#define WO_GE     (WO_EQ<<(TK_GE-TK_EQ))
#define WO_MATCH  0x040
#define WO_ISNULL 0x080
#define WO_OR     0x100       /* Two or more OR-connected terms */
#define WO_AND    0x200       /* Two or more AND-connected terms */
#define WO_NOOP   0x800       /* This term does not restrict search space */

#define WO_ALL    0xfff       /* Mask of all possible WO_* values */
#define WO_SINGLE 0x0ff       /* Mask of all non-compound WO_* values */

/*
** Value for wsFlags returned by bestIndex() and stored in
** WhereLevel.wsFlags.  These flags determine which search
** strategies are appropriate.
**
** The least significant 12 bits is reserved as a mask for WO_ values above.
** The WhereLevel.wsFlags field is usually set to WO_IN|WO_EQ|WO_ISNULL.
** But if the table is the right table of a left join, WhereLevel.wsFlags
** is set to WO_IN|WO_EQ.  The WhereLevel.wsFlags field can then be used as
** the "op" parameter to findTerm when we are resolving equality constraints.
** ISNULL constraints will then not be used on the right table of a left
** join.  Tickets #2177 and #2189.
*/
#define WHERE_ROWID_EQ     0x00001000  /* rowid=EXPR or rowid IN (...) */
#define WHERE_ROWID_RANGE  0x00002000  /* rowid<EXPR and/or rowid>EXPR */
#define WHERE_COLUMN_EQ    0x00010000  /* x=EXPR or x IN (...) or x IS NULL */
#define WHERE_COLUMN_RANGE 0x00020000  /* x<EXPR and/or x>EXPR */
#define WHERE_COLUMN_IN    0x00040000  /* x IN (...) */
#define WHERE_COLUMN_NULL  0x00080000  /* x IS NULL */
#define WHERE_INDEXED      0x000f0000  /* Anything that uses an index */
#define WHERE_NOT_FULLSCAN 0x100f3000  /* Does not do a full table scan */
#define WHERE_IN_ABLE      0x000f1000  /* Able to support an IN operator */
#define WHERE_TOP_LIMIT    0x00100000  /* x<EXPR or x<=EXPR constraint */
#define WHERE_BTM_LIMIT    0x00200000  /* x>EXPR or x>=EXPR constraint */
#define WHERE_BOTH_LIMIT   0x00300000  /* Both x>EXPR and x<EXPR */
#define WHERE_IDX_ONLY     0x00800000  /* Use index only - omit table */
#define WHERE_ORDERBY      0x01000000  /* Output will appear in correct order */
#define WHERE_REVERSE      0x02000000  /* Scan in reverse order */
#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 */

/*
** 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 */
){
  pWC->pParse = pParse;
  pWC->pMaskSet = pMaskSet;
  pWC->nTerm = 0;
  pWC->nSlot = ArraySize(pWC->aStatic);
  pWC->a = pWC->aStatic;
  pWC->vmask = 0;
}

/* Forward reference */
static void whereClauseClear(WhereClause*);

/*
** Deallocate all memory associated with a WhereOrInfo object.
*/
static void whereOrInfoDelete(sqlite3 *db, WhereOrInfo *p){
  whereClauseClear(&p->wc);
  sqlite3DbFree(db, p);
}

/*
** Deallocate all memory associated with a WhereAndInfo object.
*/
static void whereAndInfoDelete(sqlite3 *db, WhereAndInfo *p){
  whereClauseClear(&p->wc);
  sqlite3DbFree(db, p);
}

/*
** Deallocate a WhereClause structure.  The WhereClause structure
** itself is not freed.  This routine is the inverse of whereClauseInit().
*/
static void whereClauseClear(WhereClause *pWC){
  int i;
  WhereTerm *a;
  sqlite3 *db = pWC->pParse->db;
  for(i=pWC->nTerm-1, a=pWC->a; i>=0; i--, a++){
    if( a->wtFlags & TERM_DYNAMIC ){
      sqlite3ExprDelete(db, a->pExpr);
    }
    if( a->wtFlags & TERM_ORINFO ){
      whereOrInfoDelete(db, a->u.pOrInfo);
    }else if( a->wtFlags & TERM_ANDINFO ){
      whereAndInfoDelete(db, a->u.pAndInfo);
    }
  }
  if( pWC->a!=pWC->aStatic ){
    sqlite3DbFree(db, pWC->a);
  }
}

/*
** Add a single new WhereTerm entry to the WhereClause object pWC.
** The new WhereTerm object is constructed from Expr p and with wtFlags.
** The index in pWC->a[] of the new WhereTerm is returned on success.
** 0 is returned if the new WhereTerm could not be added due to a memory
** allocation error.  The memory allocation failure will be recorded in
** the db->mallocFailed flag so that higher-level functions can detect it.
**
** This routine will increase the size of the pWC->a[] array as necessary.
**
** If the wtFlags argument includes TERM_DYNAMIC, then responsibility
** for freeing the expression p is assumed by the WhereClause object pWC.
** This is true even if this routine fails to allocate a new WhereTerm.
**
** WARNING:  This routine might reallocate the space used to store
** WhereTerms.  All pointers to WhereTerms should be invalidated after
** calling this routine.  Such pointers may be reinitialized by referencing
** the pWC->a[] array.
*/
static int whereClauseInsert(WhereClause *pWC, Expr *p, u8 wtFlags){
  WhereTerm *pTerm;
  int idx;
  testcase( wtFlags & TERM_VIRTUAL );  /* EV: R-00211-15100 */
  if( pWC->nTerm>=pWC->nSlot ){
    WhereTerm *pOld = pWC->a;
    sqlite3 *db = pWC->pParse->db;
    pWC->a = sqlite3DbMallocRaw(db, sizeof(pWC->a[0])*pWC->nSlot*2 );
    if( pWC->a==0 ){
      if( wtFlags & TERM_DYNAMIC ){
        sqlite3ExprDelete(db, p);
      }
      pWC->a = pOld;
      return 0;
    }
    memcpy(pWC->a, pOld, sizeof(pWC->a[0])*pWC->nTerm);
    if( pOld!=pWC->aStatic ){
      sqlite3DbFree(db, pOld);
    }
    pWC->nSlot = sqlite3DbMallocSize(db, pWC->a)/sizeof(pWC->a[0]);
  }
  pTerm = &pWC->a[idx = pWC->nTerm++];
  pTerm->pExpr = p;
  pTerm->wtFlags = wtFlags;
  pTerm->pWC = pWC;
  pTerm->iParent = -1;
  return idx;
}

/*
** This routine identifies subexpressions in the WHERE clause where
** each subexpression is separated by the AND operator or some other
** operator specified in the op parameter.  The WhereClause structure
** is filled with pointers to subexpressions.  For example:
**
**    WHERE  a=='hello' AND coalesce(b,11)<10 AND (c+12!=d OR c==22)
**           \________/     \_______________/     \________________/
**            slot[0]            slot[1]               slot[2]
**
** The original WHERE clause in pExpr is unaltered.  All this routine
** does is make slot[] entries point to substructure within pExpr.
**
** In the previous sentence and in the diagram, "slot[]" refers to
** the WhereClause.a[] array.  The slot[] array grows as needed to contain
** all terms of the WHERE clause.
*/
static void whereSplit(WhereClause *pWC, Expr *pExpr, int op){
  pWC->op = (u8)op;
  if( pExpr==0 ) return;
  if( pExpr->op!=op ){
    whereClauseInsert(pWC, pExpr, 0);
  }else{
    whereSplit(pWC, pExpr->pLeft, op);
    whereSplit(pWC, pExpr->pRight, op);
  }
}

/*
** Initialize an expression mask set (a WhereMaskSet object)
*/
#define initMaskSet(P)  memset(P, 0, sizeof(*P))

/*
** Return the bitmask for the given cursor number.  Return 0 if
** iCursor is not in the set.
*/
static Bitmask getMask(WhereMaskSet *pMaskSet, int iCursor){
  int i;
  assert( pMaskSet->n<=(int)sizeof(Bitmask)*8 );
  for(i=0; i<pMaskSet->n; i++){
    if( pMaskSet->ix[i]==iCursor ){
      return ((Bitmask)1)<<i;
    }
  }
  return 0;
}

/*
** Create a new mask for cursor iCursor.
**
** There is one cursor per table in the FROM clause.  The number of
** tables in the FROM clause is limited by a test early in the
** sqlite3WhereBegin() routine.  So we know that the pMaskSet->ix[]
** array will never overflow.
*/
static void createMask(WhereMaskSet *pMaskSet, int iCursor){
  assert( pMaskSet->n < ArraySize(pMaskSet->ix) );
  pMaskSet->ix[pMaskSet->n++] = iCursor;
}

/*
** This routine walks (recursively) an expression tree and generates
** a bitmask indicating which tables are used in that expression
** tree.
**
** In order for this routine to work, the calling function must have
** previously invoked sqlite3ResolveExprNames() on the expression.  See
** the header comment on that routine for additional information.
** The sqlite3ResolveExprNames() routines looks for column names and
** sets their opcodes to TK_COLUMN and their Expr.iTable fields to
** the VDBE cursor number of the table.  This routine just has to
** translate the cursor numbers into bitmask values and OR all
** the bitmasks together.
*/
static Bitmask exprListTableUsage(WhereMaskSet*, ExprList*);
static Bitmask exprSelectTableUsage(WhereMaskSet*, Select*);
static Bitmask exprTableUsage(WhereMaskSet *pMaskSet, Expr *p){
  Bitmask mask = 0;
  if( p==0 ) return 0;
  if( p->op==TK_COLUMN ){
    mask = getMask(pMaskSet, p->iTable);
    return mask;
  }
  mask = exprTableUsage(pMaskSet, p->pRight);
  mask |= exprTableUsage(pMaskSet, p->pLeft);
  if( ExprHasProperty(p, EP_xIsSelect) ){
    mask |= exprSelectTableUsage(pMaskSet, p->x.pSelect);
  }else{
    mask |= exprListTableUsage(pMaskSet, p->x.pList);
  }
  return mask;
}
static Bitmask exprListTableUsage(WhereMaskSet *pMaskSet, ExprList *pList){
  int i;
  Bitmask mask = 0;
  if( pList ){
    for(i=0; i<pList->nExpr; i++){
      mask |= exprTableUsage(pMaskSet, pList->a[i].pExpr);
    }
  }
  return mask;
}
static Bitmask exprSelectTableUsage(WhereMaskSet *pMaskSet, Select *pS){
  Bitmask mask = 0;
  while( pS ){
    mask |= exprListTableUsage(pMaskSet, pS->pEList);
    mask |= exprListTableUsage(pMaskSet, pS->pGroupBy);
    mask |= exprListTableUsage(pMaskSet, pS->pOrderBy);
    mask |= exprTableUsage(pMaskSet, pS->pWhere);
    mask |= exprTableUsage(pMaskSet, pS->pHaving);
    pS = pS->pPrior;
  }
  return mask;
}

/*
** Return TRUE if the given operator is one of the operators that is
** allowed for an indexable WHERE clause term.  The allowed operators are
** "=", "<", ">", "<=", ">=", and "IN".
**
** IMPLEMENTATION-OF: R-59926-26393 To be usable by an index a term must be
** of one of the following forms: column = expression column > expression
** column >= expression column < expression column <= expression
** expression = column expression > column expression >= column
** expression < column expression <= column column IN
** (expression-list) column IN (subquery) column IS NULL
*/
static int allowedOp(int op){
  assert( TK_GT>TK_EQ && TK_GT<TK_GE );
  assert( TK_LT>TK_EQ && TK_LT<TK_GE );
  assert( TK_LE>TK_EQ && TK_LE<TK_GE );
  assert( TK_GE==TK_EQ+4 );
  return op==TK_IN || (op>=TK_EQ && op<=TK_GE) || op==TK_ISNULL;
}

/*
** Swap two objects of type TYPE.
*/
#define SWAP(TYPE,A,B) {TYPE t=A; A=B; B=t;}

/*
** Commute a comparison operator.  Expressions of the form "X op Y"
** are converted into "Y op X".
**
** If a collation sequence is associated with either the left or right
** side of the comparison, it remains associated with the same side after
** the commutation. So "Y collate NOCASE op X" becomes 
** "X collate NOCASE op Y". This is because any collation sequence on
** the left hand side of a comparison overrides any collation sequence 
** attached to the right. For the same reason the EP_ExpCollate flag
** is not commuted.
*/
static void exprCommute(Parse *pParse, Expr *pExpr){
  u16 expRight = (pExpr->pRight->flags & EP_ExpCollate);
  u16 expLeft = (pExpr->pLeft->flags & EP_ExpCollate);
  assert( allowedOp(pExpr->op) && pExpr->op!=TK_IN );
  pExpr->pRight->pColl = sqlite3ExprCollSeq(pParse, pExpr->pRight);
  pExpr->pLeft->pColl = sqlite3ExprCollSeq(pParse, pExpr->pLeft);
  SWAP(CollSeq*,pExpr->pRight->pColl,pExpr->pLeft->pColl);
  pExpr->pRight->flags = (pExpr->pRight->flags & ~EP_ExpCollate) | expLeft;
  pExpr->pLeft->flags = (pExpr->pLeft->flags & ~EP_ExpCollate) | expRight;
  SWAP(Expr*,pExpr->pRight,pExpr->pLeft);
  if( pExpr->op>=TK_GT ){
    assert( TK_LT==TK_GT+2 );
    assert( TK_GE==TK_LE+2 );
    assert( TK_GT>TK_EQ );
    assert( TK_GT<TK_LE );
    assert( pExpr->op>=TK_GT && pExpr->op<=TK_GE );
    pExpr->op = ((pExpr->op-TK_GT)^2)+TK_GT;
  }
}

/*
** Translate from TK_xx operator to WO_xx bitmask.
*/
static u16 operatorMask(int op){
  u16 c;
  assert( allowedOp(op) );
  if( op==TK_IN ){
    c = WO_IN;
  }else if( op==TK_ISNULL ){
    c = WO_ISNULL;
  }else{
    assert( (WO_EQ<<(op-TK_EQ)) < 0x7fff );
    c = (u16)(WO_EQ<<(op-TK_EQ));
  }
  assert( op!=TK_ISNULL || c==WO_ISNULL );
  assert( op!=TK_IN || c==WO_IN );
  assert( op!=TK_EQ || c==WO_EQ );
  assert( op!=TK_LT || c==WO_LT );
  assert( op!=TK_LE || c==WO_LE );
  assert( op!=TK_GT || c==WO_GT );
  assert( op!=TK_GE || c==WO_GE );
  return c;
}

/*
** Search for a term in the WHERE clause that is of the form "X <op> <expr>"
** where X is a reference to the iColumn of table iCur and <op> is one of
** the WO_xx operator codes specified by the op parameter.
** Return a pointer to the term.  Return 0 if not found.
*/
static WhereTerm *findTerm(
  WhereClause *pWC,     /* The WHERE clause to be searched */
  int iCur,             /* Cursor number of LHS */
  int iColumn,          /* Column number of LHS */
  Bitmask notReady,     /* RHS must not overlap with this mask */
  u32 op,               /* Mask of WO_xx values describing operator */
  Index *pIdx           /* Must be compatible with this index, if not NULL */
){
  WhereTerm *pTerm;
  int k;
  assert( iCur>=0 );
  op &= WO_ALL;
  for(pTerm=pWC->a, k=pWC->nTerm; k; k--, pTerm++){
    if( pTerm->leftCursor==iCur
       && (pTerm->prereqRight & notReady)==0
       && pTerm->u.leftColumn==iColumn
       && (pTerm->eOperator & op)!=0
    ){
      if( pIdx && pTerm->eOperator!=WO_ISNULL ){
        Expr *pX = pTerm->pExpr;
        CollSeq *pColl;
        char idxaff;
        int j;
        Parse *pParse = pWC->pParse;

        idxaff = pIdx->pTable->aCol[iColumn].affinity;
        if( !sqlite3IndexAffinityOk(pX, idxaff) ) continue;

        /* Figure out the collation sequence required from an index for
        ** it to be useful for optimising expression pX. Store this
        ** value in variable pColl.
        */
        assert(pX->pLeft);
        pColl = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);
        assert(pColl || pParse->nErr);

        for(j=0; pIdx->aiColumn[j]!=iColumn; j++){
          if( NEVER(j>=pIdx->nColumn) ) return 0;
        }
        if( pColl && sqlite3StrICmp(pColl->zName, pIdx->azColl[j]) ) continue;
      }
      return pTerm;
    }
  }
  return 0;
}

/* Forward reference */
static void exprAnalyze(SrcList*, WhereClause*, int);

/*
** Call exprAnalyze on all terms in a WHERE clause.  
**
**
*/
static void exprAnalyzeAll(
  SrcList *pTabList,       /* the FROM clause */
  WhereClause *pWC         /* the WHERE clause to be analyzed */
){
  int i;
  for(i=pWC->nTerm-1; i>=0; i--){
    exprAnalyze(pTabList, pWC, i);
  }
}

#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION
/*
** Check to see if the given expression is a LIKE or GLOB operator that
** can be optimized using inequality constraints.  Return TRUE if it is
** so and false if not.
**
** In order for the operator to be optimizible, the RHS must be a string
** literal that does not begin with a wildcard.  
*/
static int isLikeOrGlob(
  Parse *pParse,    /* Parsing and code generating context */
  Expr *pExpr,      /* Test this expression */
  Expr **ppPrefix,  /* Pointer to TK_STRING expression with pattern prefix */
  int *pisComplete, /* True if the only wildcard is % in the last character */
  int *pnoCase      /* True if uppercase is equivalent to lowercase */
){
  const char *z = 0;         /* String on RHS of LIKE operator */
  Expr *pRight, *pLeft;      /* Right and left size of LIKE operator */
  ExprList *pList;           /* List of operands to the LIKE operator */
  int c;                     /* One character in z[] */
  int cnt;                   /* Number of non-wildcard prefix characters */
  char wc[3];                /* Wildcard characters */
  sqlite3 *db = pParse->db;  /* Database connection */
  sqlite3_value *pVal = 0;
  int op;                    /* Opcode of pRight */

  if( !sqlite3IsLikeFunction(db, pExpr, pnoCase, wc) ){
    return 0;
  }
#ifdef SQLITE_EBCDIC
  if( *pnoCase ) return 0;
#endif
  pList = pExpr->x.pList;
  pLeft = pList->a[1].pExpr;
  if( pLeft->op!=TK_COLUMN || sqlite3ExprAffinity(pLeft)!=SQLITE_AFF_TEXT ){
    /* IMP: R-02065-49465 The left-hand side of the LIKE or GLOB operator must
    ** be the name of an indexed column with TEXT affinity. */
    return 0;
  }
  assert( pLeft->iColumn!=(-1) ); /* Because IPK never has AFF_TEXT */

  pRight = pList->a[0].pExpr;
  op = pRight->op;
  if( op==TK_REGISTER ){
    op = pRight->op2;
  }
  if( op==TK_VARIABLE ){
    Vdbe *pReprepare = pParse->pReprepare;
    int iCol = pRight->iColumn;
    pVal = sqlite3VdbeGetValue(pReprepare, iCol, SQLITE_AFF_NONE);
    if( pVal && sqlite3_value_type(pVal)==SQLITE_TEXT ){
      z = (char *)sqlite3_value_text(pVal);
    }
    sqlite3VdbeSetVarmask(pParse->pVdbe, iCol); /* IMP: R-23257-02778 */
    assert( pRight->op==TK_VARIABLE || pRight->op==TK_REGISTER );
  }else if( op==TK_STRING ){
    z = pRight->u.zToken;
  }
  if( z ){
    cnt = 0;
    while( (c=z[cnt])!=0 && c!=wc[0] && c!=wc[1] && c!=wc[2] ){
      cnt++;
    }
    if( cnt!=0 && 255!=(u8)z[cnt-1] ){
      Expr *pPrefix;
      *pisComplete = c==wc[0] && z[cnt+1]==0;
      pPrefix = sqlite3Expr(db, TK_STRING, z);
      if( pPrefix ) pPrefix->u.zToken[cnt] = 0;
      *ppPrefix = pPrefix;
      if( op==TK_VARIABLE ){
        Vdbe *v = pParse->pVdbe;
        sqlite3VdbeSetVarmask(v, pRight->iColumn); /* IMP: R-23257-02778 */
        if( *pisComplete && pRight->u.zToken[1] ){
          /* If the rhs of the LIKE expression is a variable, and the current
          ** value of the variable means there is no need to invoke the LIKE
          ** function, then no OP_Variable will be added to the program.
          ** This causes problems for the sqlite3_bind_parameter_name()
          ** API. To workaround them, add a dummy OP_Variable here.
          */ 
          int r1 = sqlite3GetTempReg(pParse);
          sqlite3ExprCodeTarget(pParse, pRight, r1);
          sqlite3VdbeChangeP3(v, sqlite3VdbeCurrentAddr(v)-1, 0);
          sqlite3ReleaseTempReg(pParse, r1);
        }
      }
    }else{
      z = 0;
    }
  }

  sqlite3ValueFree(pVal);
  return (z!=0);
}
#endif /* SQLITE_OMIT_LIKE_OPTIMIZATION */


#ifndef SQLITE_OMIT_VIRTUALTABLE
/*
** Check to see if the given expression is of the form
**
**         column MATCH expr
**
** If it is then return TRUE.  If not, return FALSE.
*/
static int isMatchOfColumn(
  Expr *pExpr      /* Test this expression */
){
  ExprList *pList;

  if( pExpr->op!=TK_FUNCTION ){
    return 0;
  }
  if( sqlite3StrICmp(pExpr->u.zToken,"match")!=0 ){
    return 0;
  }
  pList = pExpr->x.pList;
  if( pList->nExpr!=2 ){
    return 0;
  }
  if( pList->a[1].pExpr->op != TK_COLUMN ){
    return 0;
  }
  return 1;
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

/*
** If the pBase expression originated in the ON or USING clause of
** a join, then transfer the appropriate markings over to derived.
*/
static void transferJoinMarkings(Expr *pDerived, Expr *pBase){
  pDerived->flags |= pBase->flags & EP_FromJoin;
  pDerived->iRightJoinTable = pBase->iRightJoinTable;
}

#if !defined(SQLITE_OMIT_OR_OPTIMIZATION) && !defined(SQLITE_OMIT_SUBQUERY)
/*
** Analyze a term that consists of two or more OR-connected
** subterms.  So in:
**
**     ... WHERE  (a=5) AND (b=7 OR c=9 OR d=13) AND (d=13)
**                          ^^^^^^^^^^^^^^^^^^^^
**
** This routine analyzes terms such as the middle term in the above example.
** A WhereOrTerm object is computed and attached to the term under
** analysis, regardless of the outcome of the analysis.  Hence:
**
**     WhereTerm.wtFlags   |=  TERM_ORINFO
**     WhereTerm.u.pOrInfo  =  a dynamically allocated WhereOrTerm object
**
** The term being analyzed must have two or more of OR-connected subterms.
** A single subterm might be a set of AND-connected sub-subterms.
** Examples of terms under analysis:
**
**     (A)     t1.x=t2.y OR t1.x=t2.z OR t1.y=15 OR t1.z=t3.a+5
**     (B)     x=expr1 OR expr2=x OR x=expr3
**     (C)     t1.x=t2.y OR (t1.x=t2.z AND t1.y=15)
**     (D)     x=expr1 OR (y>11 AND y<22 AND z LIKE '*hello*')
**     (E)     (p.a=1 AND q.b=2 AND r.c=3) OR (p.x=4 AND q.y=5 AND r.z=6)
**
** CASE 1:
**
** If all subterms are of the form T.C=expr for some single column of C
** a single table T (as shown in example B above) then create a new virtual
** term that is an equivalent IN expression.  In other words, if the term
** being analyzed is:
**
**      x = expr1  OR  expr2 = x  OR  x = expr3
**
** then create a new virtual term like this:
**
**      x IN (expr1,expr2,expr3)
**
** CASE 2:
**
** If all subterms are indexable by a single table T, then set
**
**     WhereTerm.eOperator              =  WO_OR
**     WhereTerm.u.pOrInfo->indexable  |=  the cursor number for table T
**
** A subterm is "indexable" if it is of the form
** "T.C <op> <expr>" where C is any column of table T and 
** <op> is one of "=", "<", "<=", ">", ">=", "IS NULL", or "IN".
** A subterm is also indexable if it is an AND of two or more
** subsubterms at least one of which is indexable.  Indexable AND 
** subterms have their eOperator set to WO_AND and they have
** u.pAndInfo set to a dynamically allocated WhereAndTerm object.
**
** From another point of view, "indexable" means that the subterm could
** potentially be used with an index if an appropriate index exists.
** This analysis does not consider whether or not the index exists; that
** is something the bestIndex() routine will determine.  This analysis
** only looks at whether subterms appropriate for indexing exist.
**
** All examples A through E above all satisfy case 2.  But if a term
** also statisfies case 1 (such as B) we know that the optimizer will
** always prefer case 1, so in that case we pretend that case 2 is not
** satisfied.
**
** It might be the case that multiple tables are indexable.  For example,
** (E) above is indexable on tables P, Q, and R.
**
** Terms that satisfy case 2 are candidates for lookup by using
** separate indices to find rowids for each subterm and composing
** the union of all rowids using a RowSet object.  This is similar
** to "bitmap indices" in other database engines.
**
** OTHERWISE:
**
** If neither case 1 nor case 2 apply, then leave the eOperator set to
** zero.  This term is not useful for search.
*/
static void exprAnalyzeOrTerm(
  SrcList *pSrc,            /* the FROM clause */
  WhereClause *pWC,         /* the complete WHERE clause */
  int idxTerm               /* Index of the OR-term to be analyzed */
){
  Parse *pParse = pWC->pParse;            /* Parser context */
  sqlite3 *db = pParse->db;               /* Database connection */
  WhereTerm *pTerm = &pWC->a[idxTerm];    /* The term to be analyzed */
  Expr *pExpr = pTerm->pExpr;             /* The expression of the term */
  WhereMaskSet *pMaskSet = pWC->pMaskSet; /* Table use masks */
  int i;                                  /* Loop counters */
  WhereClause *pOrWc;       /* Breakup of pTerm into subterms */
  WhereTerm *pOrTerm;       /* A Sub-term within the pOrWc */
  WhereOrInfo *pOrInfo;     /* Additional information associated with pTerm */
  Bitmask chngToIN;         /* Tables that might satisfy case 1 */
  Bitmask indexable;        /* Tables that are indexable, satisfying case 2 */

  /*
  ** Break the OR clause into its separate subterms.  The subterms are
  ** stored in a WhereClause structure containing within the WhereOrInfo
  ** object that is attached to the original OR clause term.
  */
  assert( (pTerm->wtFlags & (TERM_DYNAMIC|TERM_ORINFO|TERM_ANDINFO))==0 );
  assert( pExpr->op==TK_OR );
  pTerm->u.pOrInfo = pOrInfo = sqlite3DbMallocZero(db, sizeof(*pOrInfo));
  if( pOrInfo==0 ) return;
  pTerm->wtFlags |= TERM_ORINFO;
  pOrWc = &pOrInfo->wc;
  whereClauseInit(pOrWc, pWC->pParse, pMaskSet);
  whereSplit(pOrWc, pExpr, TK_OR);
  exprAnalyzeAll(pSrc, pOrWc);
  if( db->mallocFailed ) return;
  assert( pOrWc->nTerm>=2 );

  /*
  ** Compute the set of tables that might satisfy cases 1 or 2.
  */
  indexable = ~(Bitmask)0;
  chngToIN = ~(pWC->vmask);
  for(i=pOrWc->nTerm-1, pOrTerm=pOrWc->a; i>=0 && indexable; i--, pOrTerm++){
    if( (pOrTerm->eOperator & WO_SINGLE)==0 ){
      WhereAndInfo *pAndInfo;
      assert( pOrTerm->eOperator==0 );
      assert( (pOrTerm->wtFlags & (TERM_ANDINFO|TERM_ORINFO))==0 );
      chngToIN = 0;
      pAndInfo = sqlite3DbMallocRaw(db, sizeof(*pAndInfo));
      if( pAndInfo ){
        WhereClause *pAndWC;
        WhereTerm *pAndTerm;
        int j;
        Bitmask b = 0;
        pOrTerm->u.pAndInfo = pAndInfo;
        pOrTerm->wtFlags |= TERM_ANDINFO;
        pOrTerm->eOperator = WO_AND;
        pAndWC = &pAndInfo->wc;
        whereClauseInit(pAndWC, pWC->pParse, pMaskSet);
        whereSplit(pAndWC, pOrTerm->pExpr, TK_AND);
        exprAnalyzeAll(pSrc, pAndWC);
        testcase( db->mallocFailed );
        if( !db->mallocFailed ){
          for(j=0, pAndTerm=pAndWC->a; j<pAndWC->nTerm; j++, pAndTerm++){
            assert( pAndTerm->pExpr );
            if( allowedOp(pAndTerm->pExpr->op) ){
              b |= getMask(pMaskSet, pAndTerm->leftCursor);
            }
          }
        }
        indexable &= b;
      }
    }else if( pOrTerm->wtFlags & TERM_COPIED ){
      /* Skip this term for now.  We revisit it when we process the
      ** corresponding TERM_VIRTUAL term */
    }else{
      Bitmask b;
      b = getMask(pMaskSet, pOrTerm->leftCursor);
      if( pOrTerm->wtFlags & TERM_VIRTUAL ){
        WhereTerm *pOther = &pOrWc->a[pOrTerm->iParent];
        b |= getMask(pMaskSet, pOther->leftCursor);
      }
      indexable &= b;
      if( pOrTerm->eOperator!=WO_EQ ){
        chngToIN = 0;
      }else{
        chngToIN &= b;
      }
    }
  }

  /*
  ** Record the set of tables that satisfy case 2.  The set might be
  ** empty.
  */
  pOrInfo->indexable = indexable;
  pTerm->eOperator = indexable==0 ? 0 : WO_OR;

  /*
  ** chngToIN holds a set of tables that *might* satisfy case 1.  But
  ** we have to do some additional checking to see if case 1 really
  ** is satisfied.
  **
  ** chngToIN will hold either 0, 1, or 2 bits.  The 0-bit case means
  ** that there is no possibility of transforming the OR clause into an
  ** IN operator because one or more terms in the OR clause contain
  ** something other than == on a column in the single table.  The 1-bit
  ** case means that every term of the OR clause is of the form
  ** "table.column=expr" for some single table.  The one bit that is set
  ** will correspond to the common table.  We still need to check to make
  ** sure the same column is used on all terms.  The 2-bit case is when
  ** the all terms are of the form "table1.column=table2.column".  It
  ** might be possible to form an IN operator with either table1.column
  ** or table2.column as the LHS if either is common to every term of
  ** the OR clause.
  **
  ** Note that terms of the form "table.column1=table.column2" (the
  ** same table on both sizes of the ==) cannot be optimized.
  */
  if( chngToIN ){
    int okToChngToIN = 0;     /* True if the conversion to IN is valid */
    int iColumn = -1;         /* Column index on lhs of IN operator */
    int iCursor = -1;         /* Table cursor common to all terms */
    int j = 0;                /* Loop counter */

    /* Search for a table and column that appears on one side or the
    ** other of the == operator in every subterm.  That table and column
    ** will be recorded in iCursor and iColumn.  There might not be any
    ** such table and column.  Set okToChngToIN if an appropriate table
    ** and column is found but leave okToChngToIN false if not found.
    */
    for(j=0; j<2 && !okToChngToIN; j++){
      pOrTerm = pOrWc->a;
      for(i=pOrWc->nTerm-1; i>=0; i--, pOrTerm++){
        assert( pOrTerm->eOperator==WO_EQ );
        pOrTerm->wtFlags &= ~TERM_OR_OK;
        if( pOrTerm->leftCursor==iCursor ){
          /* This is the 2-bit case and we are on the second iteration and
          ** current term is from the first iteration.  So skip this term. */
          assert( j==1 );
          continue;
        }
        if( (chngToIN & getMask(pMaskSet, pOrTerm->leftCursor))==0 ){
          /* This term must be of the form t1.a==t2.b where t2 is in the
          ** chngToIN set but t1 is not.  This term will be either preceeded
          ** or follwed by an inverted copy (t2.b==t1.a).  Skip this term 
          ** and use its inversion. */
          testcase( pOrTerm->wtFlags & TERM_COPIED );
          testcase( pOrTerm->wtFlags & TERM_VIRTUAL );
          assert( pOrTerm->wtFlags & (TERM_COPIED|TERM_VIRTUAL) );
          continue;
        }
        iColumn = pOrTerm->u.leftColumn;
        iCursor = pOrTerm->leftCursor;
        break;
      }
      if( i<0 ){
        /* No candidate table+column was found.  This can only occur
        ** on the second iteration */
        assert( j==1 );
        assert( (chngToIN&(chngToIN-1))==0 );
        assert( chngToIN==getMask(pMaskSet, iCursor) );
        break;
      }
      testcase( j==1 );

      /* We have found a candidate table and column.  Check to see if that
      ** table and column is common to every term in the OR clause */
      okToChngToIN = 1;
      for(; i>=0 && okToChngToIN; i--, pOrTerm++){
        assert( pOrTerm->eOperator==WO_EQ );
        if( pOrTerm->leftCursor!=iCursor ){
          pOrTerm->wtFlags &= ~TERM_OR_OK;
        }else if( pOrTerm->u.leftColumn!=iColumn ){
          okToChngToIN = 0;
        }else{
          int affLeft, affRight;
          /* If the right-hand side is also a column, then the affinities
          ** of both right and left sides must be such that no type
          ** conversions are required on the right.  (Ticket #2249)
          */
          affRight = sqlite3ExprAffinity(pOrTerm->pExpr->pRight);
          affLeft = sqlite3ExprAffinity(pOrTerm->pExpr->pLeft);
          if( affRight!=0 && affRight!=affLeft ){
            okToChngToIN = 0;
          }else{
            pOrTerm->wtFlags |= TERM_OR_OK;
          }
        }
      }
    }

    /* At this point, okToChngToIN is true if original pTerm satisfies
    ** case 1.  In that case, construct a new virtual term that is 
    ** pTerm converted into an IN operator.
    **
    ** EV: R-00211-15100
    */
    if( okToChngToIN ){
      Expr *pDup;            /* A transient duplicate expression */
      ExprList *pList = 0;   /* The RHS of the IN operator */
      Expr *pLeft = 0;       /* The LHS of the IN operator */
      Expr *pNew;            /* The complete IN operator */

      for(i=pOrWc->nTerm-1, pOrTerm=pOrWc->a; i>=0; i--, pOrTerm++){
        if( (pOrTerm->wtFlags & TERM_OR_OK)==0 ) continue;
        assert( pOrTerm->eOperator==WO_EQ );
        assert( pOrTerm->leftCursor==iCursor );
        assert( pOrTerm->u.leftColumn==iColumn );
        pDup = sqlite3ExprDup(db, pOrTerm->pExpr->pRight, 0);
        pList = sqlite3ExprListAppend(pWC->pParse, pList, pDup);
        pLeft = pOrTerm->pExpr->pLeft;
      }
      assert( pLeft!=0 );
      pDup = sqlite3ExprDup(db, pLeft, 0);
      pNew = sqlite3PExpr(pParse, TK_IN, pDup, 0, 0);
      if( pNew ){
        int idxNew;
        transferJoinMarkings(pNew, pExpr);
        assert( !ExprHasProperty(pNew, EP_xIsSelect) );
        pNew->x.pList = pList;
        idxNew = whereClauseInsert(pWC, pNew, TERM_VIRTUAL|TERM_DYNAMIC);
        testcase( idxNew==0 );
        exprAnalyze(pSrc, pWC, idxNew);
        pTerm = &pWC->a[idxTerm];
        pWC->a[idxNew].iParent = idxTerm;
        pTerm->nChild = 1;
      }else{
        sqlite3ExprListDelete(db, pList);
      }
      pTerm->eOperator = WO_NOOP;  /* case 1 trumps case 2 */
    }
  }
}
#endif /* !SQLITE_OMIT_OR_OPTIMIZATION && !SQLITE_OMIT_SUBQUERY */


/*
** The input to this routine is an WhereTerm structure with only the
** "pExpr" field filled in.  The job of this routine is to analyze the
** subexpression and populate all the other fields of the WhereTerm
** structure.
**
** If the expression is of the form "<expr> <op> X" it gets commuted
** to the standard form of "X <op> <expr>".
**
** If the expression is of the form "X <op> Y" where both X and Y are
** columns, then the original expression is unchanged and a new virtual
** term of the form "Y <op> X" is added to the WHERE clause and
** analyzed separately.  The original term is marked with TERM_COPIED
** and the new term is marked with TERM_DYNAMIC (because it's pExpr
** needs to be freed with the WhereClause) and TERM_VIRTUAL (because it
** is a commuted copy of a prior term.)  The original term has nChild=1
** and the copy has idxParent set to the index of the original term.
*/
static void exprAnalyze(
  SrcList *pSrc,            /* the FROM clause */
  WhereClause *pWC,         /* the WHERE clause */
  int idxTerm               /* Index of the term to be analyzed */
){
  WhereTerm *pTerm;                /* The term to be analyzed */
  WhereMaskSet *pMaskSet;          /* Set of table index masks */
  Expr *pExpr;                     /* The expression to be analyzed */
  Bitmask prereqLeft;              /* Prerequesites of the pExpr->pLeft */
  Bitmask prereqAll;               /* Prerequesites of pExpr */
  Bitmask extraRight = 0;          /* Extra dependencies on LEFT JOIN */
  Expr *pStr1 = 0;                 /* RHS of LIKE/GLOB operator */
  int isComplete = 0;              /* RHS of LIKE/GLOB ends with wildcard */
  int noCase = 0;                  /* LIKE/GLOB distinguishes case */
  int op;                          /* Top-level operator.  pExpr->op */
  Parse *pParse = pWC->pParse;     /* Parsing context */
  sqlite3 *db = pParse->db;        /* Database connection */

  if( db->mallocFailed ){
    return;
  }
  pTerm = &pWC->a[idxTerm];
  pMaskSet = pWC->pMaskSet;
  pExpr = pTerm->pExpr;
  prereqLeft = exprTableUsage(pMaskSet, pExpr->pLeft);
  op = pExpr->op;
  if( op==TK_IN ){
    assert( pExpr->pRight==0 );
    if( ExprHasProperty(pExpr, EP_xIsSelect) ){
      pTerm->prereqRight = exprSelectTableUsage(pMaskSet, pExpr->x.pSelect);
    }else{
      pTerm->prereqRight = exprListTableUsage(pMaskSet, pExpr->x.pList);
    }
  }else if( op==TK_ISNULL ){
    pTerm->prereqRight = 0;
  }else{
    pTerm->prereqRight = exprTableUsage(pMaskSet, pExpr->pRight);
  }
  prereqAll = exprTableUsage(pMaskSet, pExpr);
  if( ExprHasProperty(pExpr, EP_FromJoin) ){
    Bitmask x = getMask(pMaskSet, pExpr->iRightJoinTable);
    prereqAll |= x;
    extraRight = x-1;  /* ON clause terms may not be used with an index
                       ** on left table of a LEFT JOIN.  Ticket #3015 */
  }
  pTerm->prereqAll = prereqAll;
  pTerm->leftCursor = -1;
  pTerm->iParent = -1;
  pTerm->eOperator = 0;
  if( allowedOp(op) && (pTerm->prereqRight & prereqLeft)==0 ){
    Expr *pLeft = pExpr->pLeft;
    Expr *pRight = pExpr->pRight;
    if( pLeft->op==TK_COLUMN ){
      pTerm->leftCursor = pLeft->iTable;
      pTerm->u.leftColumn = pLeft->iColumn;
      pTerm->eOperator = operatorMask(op);
    }
    if( pRight && pRight->op==TK_COLUMN ){
      WhereTerm *pNew;
      Expr *pDup;
      if( pTerm->leftCursor>=0 ){
        int idxNew;
        pDup = sqlite3ExprDup(db, pExpr, 0);
        if( db->mallocFailed ){
          sqlite3ExprDelete(db, pDup);
          return;
        }
        idxNew = whereClauseInsert(pWC, pDup, TERM_VIRTUAL|TERM_DYNAMIC);
        if( idxNew==0 ) return;
        pNew = &pWC->a[idxNew];
        pNew->iParent = idxTerm;
        pTerm = &pWC->a[idxTerm];
        pTerm->nChild = 1;
        pTerm->wtFlags |= TERM_COPIED;
      }else{
        pDup = pExpr;
        pNew = pTerm;
      }
      exprCommute(pParse, pDup);
      pLeft = pDup->pLeft;
      pNew->leftCursor = pLeft->iTable;
      pNew->u.leftColumn = pLeft->iColumn;
      testcase( (prereqLeft | extraRight) != prereqLeft );
      pNew->prereqRight = prereqLeft | extraRight;
      pNew->prereqAll = prereqAll;
      pNew->eOperator = operatorMask(pDup->op);
    }
  }

#ifndef SQLITE_OMIT_BETWEEN_OPTIMIZATION
  /* If a term is the BETWEEN operator, create two new virtual terms
  ** that define the range that the BETWEEN implements.  For example:
  **
  **      a BETWEEN b AND c
  **
  ** is converted into:
  **
  **      (a BETWEEN b AND c) AND (a>=b) AND (a<=c)
  **
  ** The two new terms are added onto the end of the WhereClause object.
  ** The new terms are "dynamic" and are children of the original BETWEEN
  ** term.  That means that if the BETWEEN term is coded, the children are
  ** skipped.  Or, if the children are satisfied by an index, the original
  ** BETWEEN term is skipped.
  */
  else if( pExpr->op==TK_BETWEEN && pWC->op==TK_AND ){
    ExprList *pList = pExpr->x.pList;
    int i;
    static const u8 ops[] = {TK_GE, TK_LE};
    assert( pList!=0 );
    assert( pList->nExpr==2 );
    for(i=0; i<2; i++){
      Expr *pNewExpr;
      int idxNew;
      pNewExpr = sqlite3PExpr(pParse, ops[i], 
                             sqlite3ExprDup(db, pExpr->pLeft, 0),
                             sqlite3ExprDup(db, pList->a[i].pExpr, 0), 0);
      idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);
      testcase( idxNew==0 );
      exprAnalyze(pSrc, pWC, idxNew);
      pTerm = &pWC->a[idxTerm];
      pWC->a[idxNew].iParent = idxTerm;
    }
    pTerm->nChild = 2;
  }
#endif /* SQLITE_OMIT_BETWEEN_OPTIMIZATION */

#if !defined(SQLITE_OMIT_OR_OPTIMIZATION) && !defined(SQLITE_OMIT_SUBQUERY)
  /* Analyze a term that is composed of two or more subterms connected by
  ** an OR operator.
  */
  else if( pExpr->op==TK_OR ){
    assert( pWC->op==TK_AND );
    exprAnalyzeOrTerm(pSrc, pWC, idxTerm);
    pTerm = &pWC->a[idxTerm];
  }
#endif /* SQLITE_OMIT_OR_OPTIMIZATION */

#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION
  /* Add constraints to reduce the search space on a LIKE or GLOB
  ** operator.
  **
  ** A like pattern of the form "x LIKE 'abc%'" is changed into constraints
  **
  **          x>='abc' AND x<'abd' AND x LIKE 'abc%'
  **
  ** The last character of the prefix "abc" is incremented to form the
  ** termination condition "abd".
  */
  if( pWC->op==TK_AND 
   && isLikeOrGlob(pParse, pExpr, &pStr1, &isComplete, &noCase)
  ){
    Expr *pLeft;       /* LHS of LIKE/GLOB operator */
    Expr *pStr2;       /* Copy of pStr1 - RHS of LIKE/GLOB operator */
    Expr *pNewExpr1;
    Expr *pNewExpr2;
    int idxNew1;
    int idxNew2;
    CollSeq *pColl;    /* Collating sequence to use */

    pLeft = pExpr->x.pList->a[1].pExpr;
    pStr2 = sqlite3ExprDup(db, pStr1, 0);
    if( !db->mallocFailed ){
      u8 c, *pC;       /* Last character before the first wildcard */
      pC = (u8*)&pStr2->u.zToken[sqlite3Strlen30(pStr2->u.zToken)-1];
      c = *pC;
      if( noCase ){
        /* The point is to increment the last character before the first
        ** wildcard.  But if we increment '@', that will push it into the
        ** alphabetic range where case conversions will mess up the 
        ** inequality.  To avoid this, make sure to also run the full
        ** LIKE on all candidate expressions by clearing the isComplete flag
        */
        if( c=='A'-1 ) isComplete = 0;   /* EV: R-64339-08207 */


        c = sqlite3UpperToLower[c];
      }
      *pC = c + 1;
    }
    pColl = sqlite3FindCollSeq(db, SQLITE_UTF8, noCase ? "NOCASE" : "BINARY",0);
    pNewExpr1 = sqlite3PExpr(pParse, TK_GE, 
                     sqlite3ExprSetColl(sqlite3ExprDup(db,pLeft,0), pColl),
                     pStr1, 0);
    idxNew1 = whereClauseInsert(pWC, pNewExpr1, TERM_VIRTUAL|TERM_DYNAMIC);
    testcase( idxNew1==0 );
    exprAnalyze(pSrc, pWC, idxNew1);
    pNewExpr2 = sqlite3PExpr(pParse, TK_LT,
                     sqlite3ExprSetColl(sqlite3ExprDup(db,pLeft,0), pColl),
                     pStr2, 0);
    idxNew2 = whereClauseInsert(pWC, pNewExpr2, TERM_VIRTUAL|TERM_DYNAMIC);
    testcase( idxNew2==0 );
    exprAnalyze(pSrc, pWC, idxNew2);
    pTerm = &pWC->a[idxTerm];
    if( isComplete ){
      pWC->a[idxNew1].iParent = idxTerm;
      pWC->a[idxNew2].iParent = idxTerm;
      pTerm->nChild = 2;
    }
  }
#endif /* SQLITE_OMIT_LIKE_OPTIMIZATION */

#ifndef SQLITE_OMIT_VIRTUALTABLE
  /* Add a WO_MATCH auxiliary term to the constraint set if the
  ** current expression is of the form:  column MATCH expr.
  ** This information is used by the xBestIndex methods of
  ** virtual tables.  The native query optimizer does not attempt
  ** to do anything with MATCH functions.
  */
  if( isMatchOfColumn(pExpr) ){
    int idxNew;
    Expr *pRight, *pLeft;
    WhereTerm *pNewTerm;
    Bitmask prereqColumn, prereqExpr;

    pRight = pExpr->x.pList->a[0].pExpr;
    pLeft = pExpr->x.pList->a[1].pExpr;
    prereqExpr = exprTableUsage(pMaskSet, pRight);
    prereqColumn = exprTableUsage(pMaskSet, pLeft);
    if( (prereqExpr & prereqColumn)==0 ){
      Expr *pNewExpr;
      pNewExpr = sqlite3PExpr(pParse, TK_MATCH, 
                              0, sqlite3ExprDup(db, pRight, 0), 0);
      idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);
      testcase( idxNew==0 );
      pNewTerm = &pWC->a[idxNew];
      pNewTerm->prereqRight = prereqExpr;
      pNewTerm->leftCursor = pLeft->iTable;
      pNewTerm->u.leftColumn = pLeft->iColumn;
      pNewTerm->eOperator = WO_MATCH;
      pNewTerm->iParent = idxTerm;
      pTerm = &pWC->a[idxTerm];
      pTerm->nChild = 1;
      pTerm->wtFlags |= TERM_COPIED;
      pNewTerm->prereqAll = pTerm->prereqAll;
    }
  }
#endif /* SQLITE_OMIT_VIRTUALTABLE */

#ifdef SQLITE_ENABLE_STAT2
  /* When sqlite_stat2 histogram data is available an operator of the
  ** form "x IS NOT NULL" can sometimes be evaluated more efficiently
  ** as "x>NULL" if x is not an INTEGER PRIMARY KEY.  So construct a
  ** virtual term of that form.
  **
  ** Note that the virtual term must be tagged with TERM_VNULL.  This
  ** TERM_VNULL tag will suppress the not-null check at the beginning
  ** of the loop.  Without the TERM_VNULL flag, the not-null check at
  ** the start of the loop will prevent any results from being returned.
  */
  if( pExpr->op==TK_NOTNULL
   && pExpr->pLeft->op==TK_COLUMN
   && pExpr->pLeft->iColumn>=0
  ){
    Expr *pNewExpr;
    Expr *pLeft = pExpr->pLeft;
    int idxNew;
    WhereTerm *pNewTerm;

    pNewExpr = sqlite3PExpr(pParse, TK_GT,
                            sqlite3ExprDup(db, pLeft, 0),
                            sqlite3PExpr(pParse, TK_NULL, 0, 0, 0), 0);

    idxNew = whereClauseInsert(pWC, pNewExpr,
                              TERM_VIRTUAL|TERM_DYNAMIC|TERM_VNULL);
    if( idxNew ){
      pNewTerm = &pWC->a[idxNew];
      pNewTerm->prereqRight = 0;
      pNewTerm->leftCursor = pLeft->iTable;
      pNewTerm->u.leftColumn = pLeft->iColumn;
      pNewTerm->eOperator = WO_GT;
      pNewTerm->iParent = idxTerm;
      pTerm = &pWC->a[idxTerm];
      pTerm->nChild = 1;
      pTerm->wtFlags |= TERM_COPIED;
      pNewTerm->prereqAll = pTerm->prereqAll;
    }
  }
#endif /* SQLITE_ENABLE_STAT2 */

  /* 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 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;

  assert( pOrderBy!=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) );

  /* Match terms of the ORDER BY clause against columns of
  ** the index.
  **
  ** Note that indices have pIdx->nColumn regular columns plus
  ** one additional column containing the rowid.  The rowid column
  ** of the index is also allowed to match against the ORDER BY
  ** clause.
  */
  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 */

    pExpr = pTerm->pExpr;
    if( pExpr->op!=TK_COLUMN || pExpr->iTable!=base ){
      /* Can not use an index sort on anything that is not a column in the
      ** left-most table of the FROM clause */
      break;
    }
    pColl = sqlite3ExprCollSeq(pParse, pExpr);
    if( !pColl ){
      pColl = db->pDfltColl;
    }
    if( pIdx->zName && i<pIdx->nColumn ){
      iColumn = pIdx->aiColumn[i];
      if( iColumn==pIdx->pTable->iPKey ){
        iColumn = -1;
      }
      iSortOrder = pIdx->aSortOrder[i];
      zColl = pIdx->azColl[i];
    }else{
      iColumn = -1;
      iSortOrder = 0;
      zColl = pColl->zName;
    }
    if( pExpr->iColumn!=iColumn || sqlite3StrICmp(pColl->zName, zColl) ){
      /* Term j of the ORDER BY clause does not match column i of the index */
      if( i<nEqCol ){
        /* If an index column that is constrained by == fails to match an
        ** ORDER BY term, that is OK.  Just ignore that column of the index
        */
        continue;
      }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) ){
    /* All terms of this index match some prefix of the ORDER BY clause
    ** and the index is UNIQUE and no terms on the tail of the ORDER BY
    ** clause reference other tables in a join.  If this is all true then
    ** the order by clause is superfluous.  Not that if the matching
    ** condition is IS NULL then the result is not necessarily unique
    ** even on a UNIQUE index, so disallow those cases. */
    return 1;
  }
  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
** logN is a little off.
*/
static double estLog(double N){
  double logN = 1;
  double x = 10;
  while( N>x ){
    logN += 1;
    x *= 10;
  }
  return logN;
}

/*
** Two routines for printing the content of an sqlite3_index_info
** structure.  Used for testing and debugging only.  If neither
** SQLITE_TEST or SQLITE_DEBUG are defined, then these routines
** are no-ops.
*/
#if !defined(SQLITE_OMIT_VIRTUALTABLE) && defined(SQLITE_DEBUG)
static void TRACE_IDX_INPUTS(sqlite3_index_info *p){
  int i;
  if( !sqlite3WhereTrace ) return;
  for(i=0; i<p->nConstraint; i++){
    sqlite3DebugPrintf("  constraint[%d]: col=%d termid=%d op=%d usabled=%d\n",
       i,
       p->aConstraint[i].iColumn,
       p->aConstraint[i].iTermOffset,
       p->aConstraint[i].op,
       p->aConstraint[i].usable);
  }
  for(i=0; i<p->nOrderBy; i++){
    sqlite3DebugPrintf("  orderby[%d]: col=%d desc=%d\n",
       i,
       p->aOrderBy[i].iColumn,
       p->aOrderBy[i].desc);
  }
}
static void TRACE_IDX_OUTPUTS(sqlite3_index_info *p){
  int i;
  if( !sqlite3WhereTrace ) return;
  for(i=0; i<p->nConstraint; i++){
    sqlite3DebugPrintf("  usage[%d]: argvIdx=%d omit=%d\n",
       i,
       p->aConstraintUsage[i].argvIndex,
       p->aConstraintUsage[i].omit);
  }
  sqlite3DebugPrintf("  idxNum=%d\n", p->idxNum);
  sqlite3DebugPrintf("  idxStr=%s\n", p->idxStr);
  sqlite3DebugPrintf("  orderByConsumed=%d\n", p->orderByConsumed);
  sqlite3DebugPrintf("  estimatedCost=%g\n", p->estimatedCost);
}
#else
#define TRACE_IDX_INPUTS(A)
#define TRACE_IDX_OUTPUTS(A)
#endif

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

  /* No OR-clause optimization allowed if the INDEXED BY or NOT INDEXED clauses
  ** are used */
  if( pSrc->notIndexed || pSrc->pIndex!=0 ){
    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, 0, &sTermCost);
        }else if( pOrTerm->leftCursor==iCur ){
          WhereClause tempWC;
          tempWC.pParse = pWC->pParse;
          tempWC.pMaskSet = pWC->pMaskSet;
          tempWC.op = TK_AND;
          tempWC.a = pOrTerm;
          tempWC.nTerm = 1;
          bestIndex(pParse, &tempWC, pSrc, notReady, notValid, 0, &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
/*
** Return TRUE if the WHERE clause term pTerm is of a form where it
** could be used with an index to access pSrc, assuming an appropriate
** index existed.
*/
static int termCanDriveIndex(
  WhereTerm *pTerm,              /* WHERE clause term to check */
  struct SrcList_item *pSrc,     /* Table we are trying to access */
  Bitmask notReady               /* Tables in outer loops of the join */
){
  char aff;
  if( pTerm->leftCursor!=pSrc->iCursor ) return 0;
  if( pTerm->eOperator!=WO_EQ ) return 0;
  if( (pTerm->prereqRight & notReady)!=0 ) return 0;
  aff = pSrc->pTab->aCol[pTerm->u.leftColumn].affinity;
  if( !sqlite3IndexAffinityOk(pTerm->pExpr, aff) ) return 0;
  return 1;
}
#endif

#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
/*
** If the query plan for pSrc specified in pCost is a full table scan
** and indexing is allows (if there is no NOT INDEXED clause) and it
** possible to construct a transient index that would perform better
** than a full table scan even when the cost of constructing the index
** is taken into account, then alter the query plan to use the
** transient index.
*/
static void bestAutomaticIndex(
  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->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
** makes use of the automatic index.
*/
static void constructAutomaticIndex(
  Parse *pParse,              /* The parsing context */
  WhereClause *pWC,           /* The WHERE clause */
  struct SrcList_item *pSrc,  /* The FROM clause term to get the next index */
  Bitmask notReady,           /* Mask of cursors that are not available */
  WhereLevel *pLevel          /* Write new index here */
){
  int nColumn;                /* Number of columns in the constructed index */
  WhereTerm *pTerm;           /* A single term of the WHERE clause */
  WhereTerm *pWCEnd;          /* End of pWC->a[] */
  int nByte;                  /* Byte of memory needed for pIdx */
  Index *pIdx;                /* Object describing the transient index */
  Vdbe *v;                    /* Prepared statement under construction */
  int regIsInit;              /* Register set by initialization */
  int addrInit;               /* Address of the initialization bypass jump */
  Table *pTable;              /* The table being indexed */
  KeyInfo *pKeyinfo;          /* Key information for the index */   
  int addrTop;                /* Top of the index fill loop */
  int regRecord;              /* Register holding an index record */
  int n;                      /* Column counter */
  int i;                      /* Loop counter */
  int mxBitCol;               /* Maximum column in pSrc->colUsed */
  CollSeq *pColl;             /* Collating sequence to on a column */
  Bitmask idxCols;            /* Bitmap of columns used for indexing */
  Bitmask extraCols;          /* Bitmap of additional columns */

  /* Generate code to skip over the creation and initialization of the
  ** transient index on 2nd and subsequent iterations of the loop. */
  v = pParse->pVdbe;
  assert( v!=0 );
  regIsInit = ++pParse->nMem;
  addrInit = sqlite3VdbeAddOp1(v, OP_If, regIsInit);
  sqlite3VdbeAddOp2(v, OP_Integer, 1, regIsInit);

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

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

  /* Construct the Index object to describe this index */
  nByte = sizeof(Index);
  nByte += nColumn*sizeof(int);     /* Index.aiColumn */
  nByte += nColumn*sizeof(char*);   /* Index.azColl */
  nByte += nColumn;                 /* Index.aSortOrder */
  pIdx = sqlite3DbMallocZero(pParse->db, nByte);
  if( pIdx==0 ) return;
  pLevel->plan.u.pIdx = pIdx;
  pIdx->azColl = (char**)&pIdx[1];
  pIdx->aiColumn = (int*)&pIdx->azColl[nColumn];
  pIdx->aSortOrder = (u8*)&pIdx->aiColumn[nColumn];
  pIdx->zName = "auto-index";
  pIdx->nColumn = nColumn;
  pIdx->pTable = pTable;
  n = 0;
  idxCols = 0;
  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){
    if( termCanDriveIndex(pTerm, pSrc, notReady) ){
      int iCol = pTerm->u.leftColumn;
      Bitmask cMask = iCol>=BMS ? ((Bitmask)1)<<(BMS-1) : ((Bitmask)1)<<iCol;
      if( (idxCols & cMask)==0 ){
        Expr *pX = pTerm->pExpr;
        idxCols |= cMask;
        pIdx->aiColumn[n] = pTerm->u.leftColumn;
        pColl = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);
        pIdx->azColl[n] = ALWAYS(pColl) ? pColl->zName : "BINARY";
        n++;
      }
    }
  }
  assert( (u32)n==pLevel->plan.nEq );

  /* Add additional columns needed to make the automatic index into
  ** a covering index */
  for(i=0; i<mxBitCol; i++){
    if( extraCols & (((Bitmask)1)<<i) ){
      pIdx->aiColumn[n] = i;
      pIdx->azColl[n] = "BINARY";
      n++;
    }
  }
  if( pSrc->colUsed & (((Bitmask)1)<<(BMS-1)) ){
    for(i=BMS-1; i<pTable->nCol; i++){
      pIdx->aiColumn[n] = i;
      pIdx->azColl[n] = "BINARY";
      n++;
    }
  }
  assert( n==nColumn );

  /* Create the automatic index */
  pKeyinfo = sqlite3IndexKeyinfo(pParse, pIdx);
  assert( pLevel->iIdxCur>=0 );
  sqlite3VdbeAddOp4(v, OP_OpenAutoindex, pLevel->iIdxCur, nColumn+1, 0,
                    (char*)pKeyinfo, P4_KEYINFO_HANDOFF);
  VdbeComment((v, "for %s", pTable->zName));

  /* Fill the automatic index with content */
  addrTop = sqlite3VdbeAddOp1(v, OP_Rewind, pLevel->iTabCur);
  regRecord = sqlite3GetTempReg(pParse);
  sqlite3GenerateIndexKey(pParse, pIdx, pLevel->iTabCur, regRecord, 1);
  sqlite3VdbeAddOp2(v, OP_IdxInsert, pLevel->iIdxCur, regRecord);
  sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);
  sqlite3VdbeAddOp2(v, OP_Next, pLevel->iTabCur, addrTop+1);
  sqlite3VdbeChangeP5(v, SQLITE_STMTSTATUS_AUTOINDEX);
  sqlite3VdbeJumpHere(v, addrTop);
  sqlite3ReleaseTempReg(pParse, regRecord);
  
  /* Jump here when skipping the initialization */
  sqlite3VdbeJumpHere(v, addrInit);
}
#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */

#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;
  sqlite3_index_info *pIdxInfo;

  WHERETRACE(("Recomputing index info for %s...\n", pSrc->pTab->zName));

  /* Count the number of possible WHERE clause constraints referring
  ** to this virtual table */
  for(i=nTerm=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){
    if( pTerm->leftCursor != pSrc->iCursor ) continue;
    assert( (pTerm->eOperator&(pTerm->eOperator-1))==0 );
    testcase( pTerm->eOperator==WO_IN );
    testcase( pTerm->eOperator==WO_ISNULL );
    if( pTerm->eOperator & (WO_IN|WO_ISNULL) ) continue;
    nTerm++;
  }

  /* 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
                           + sizeof(*pIdxOrderBy)*nOrderBy );
  if( pIdxInfo==0 ){
    sqlite3ErrorMsg(pParse, "out of memory");
    /* (double)0 In case of SQLITE_OMIT_FLOATING_POINT... */
    return 0;
  }

  /* Initialize the structure.  The sqlite3_index_info structure contains
  ** many fields that are declared "const" to prevent xBestIndex from
  ** changing them.  We have to do some funky casting in order to
  ** initialize those fields.
  */
  pIdxCons = (struct sqlite3_index_constraint*)&pIdxInfo[1];
  pIdxOrderBy = (struct sqlite3_index_orderby*)&pIdxCons[nTerm];
  pUsage = (struct sqlite3_index_constraint_usage*)&pIdxOrderBy[nOrderBy];
  *(int*)&pIdxInfo->nConstraint = nTerm;
  *(int*)&pIdxInfo->nOrderBy = nOrderBy;
  *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint = pIdxCons;
  *(struct sqlite3_index_orderby**)&pIdxInfo->aOrderBy = pIdxOrderBy;
  *(struct sqlite3_index_constraint_usage**)&pIdxInfo->aConstraintUsage =
                                                                   pUsage;

  for(i=j=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){
    if( pTerm->leftCursor != pSrc->iCursor ) continue;
    assert( (pTerm->eOperator&(pTerm->eOperator-1))==0 );
    testcase( pTerm->eOperator==WO_IN );
    testcase( pTerm->eOperator==WO_ISNULL );
    if( pTerm->eOperator & (WO_IN|WO_ISNULL) ) continue;
    pIdxCons[j].iColumn = pTerm->u.leftColumn;
    pIdxCons[j].iTermOffset = i;
    pIdxCons[j].op = (u8)pTerm->eOperator;
    /* The direct assignment in the previous line is possible only because
    ** the WO_ and SQLITE_INDEX_CONSTRAINT_ codes are identical.  The
    ** following asserts verify this fact. */
    assert( WO_EQ==SQLITE_INDEX_CONSTRAINT_EQ );
    assert( WO_LT==SQLITE_INDEX_CONSTRAINT_LT );
    assert( WO_LE==SQLITE_INDEX_CONSTRAINT_LE );
    assert( WO_GT==SQLITE_INDEX_CONSTRAINT_GT );
    assert( WO_GE==SQLITE_INDEX_CONSTRAINT_GE );
    assert( WO_MATCH==SQLITE_INDEX_CONSTRAINT_MATCH );
    assert( pTerm->eOperator & (WO_EQ|WO_LT|WO_LE|WO_GT|WO_GE|WO_MATCH) );
    j++;
  }
  for(i=0; i<nOrderBy; i++){
    Expr *pExpr = pOrderBy->a[i].pExpr;
    pIdxOrderBy[i].iColumn = pExpr->iColumn;
    pIdxOrderBy[i].desc = pOrderBy->a[i].sortOrder;
  }

  return pIdxInfo;
}

/*
** The table object reference passed as the second argument to this function
** must represent a virtual table. This function invokes the xBestIndex()
** method of the virtual table with the sqlite3_index_info pointer passed
** as the argument.
**
** If an error occurs, pParse is populated with an error message and a
** non-zero value is returned. Otherwise, 0 is returned and the output
** part of the sqlite3_index_info structure is left populated.
**
** Whether or not an error is returned, it is the responsibility of the
** caller to eventually free p->idxStr if p->needToFreeIdxStr indicates
** that this is required.
*/
static int vtabBestIndex(Parse *pParse, Table *pTab, sqlite3_index_info *p){
  sqlite3_vtab *pVtab = sqlite3GetVTable(pParse->db, pTab)->pVtab;
  int i;
  int rc;

  WHERETRACE(("xBestIndex for %s\n", pTab->zName));
  TRACE_IDX_INPUTS(p);
  rc = pVtab->pModule->xBestIndex(pVtab, p);
  TRACE_IDX_OUTPUTS(p);

  if( rc!=SQLITE_OK ){
    if( rc==SQLITE_NOMEM ){
      pParse->db->mallocFailed = 1;
    }else if( !pVtab->zErrMsg ){
      sqlite3ErrorMsg(pParse, "%s", sqlite3ErrStr(rc));
    }else{
      sqlite3ErrorMsg(pParse, "%s", pVtab->zErrMsg);
    }
  }
  sqlite3_free(pVtab->zErrMsg);
  pVtab->zErrMsg = 0;

  for(i=0; i<p->nConstraint; i++){
    if( !p->aConstraint[i].usable && p->aConstraintUsage[i].argvIndex>0 ){
      sqlite3ErrorMsg(pParse, 
          "table %s: xBestIndex returned an invalid plan", pTab->zName);
    }
  }

  return pParse->nErr;
}


/*
** Compute the best index for a virtual table.
**
** The best index is computed by the xBestIndex method of the virtual
** table module.  This routine is really just a wrapper that sets up
** the sqlite3_index_info structure that is used to communicate with
** xBestIndex.
**
** In a join, this routine might be called multiple times for the
** same virtual table.  The sqlite3_index_info structure is created
** and initialized on the first invocation and reused on all subsequent
** invocations.  The sqlite3_index_info structure is also used when
** code is generated to access the virtual table.  The whereInfoDelete() 
** routine takes care of freeing the sqlite3_index_info structure after
** everybody has finished with it.
*/
static void bestVirtualIndex(
  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
  ** during some prior invocation.  Now we just have to customize the
  ** details of pIdxInfo for the current invocation and pass it to
  ** xBestIndex.
  */

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

  /* Set the aConstraint[].usable fields and initialize all 
  ** output variables to zero.
  **
  ** aConstraint[].usable is true for constraints where the right-hand
  ** side contains only references to tables to the left of the current
  ** table.  In other words, if the constraint is of the form:
  **
  **           column = expr
  **
  ** and we are evaluating a join, then the constraint on column is 
  ** only valid if all tables referenced in expr occur to the left
  ** of the table containing column.
  **
  ** The aConstraints[] array contains entries for all constraints
  ** on the current table.  That way we only have to compute it once
  ** even though we might try to pick the best index multiple times.
  ** For each attempt at picking an index, the order of tables in the
  ** join might be different so we have to recompute the usable flag
  ** each time.
  */
  pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;
  pUsage = pIdxInfo->aConstraintUsage;
  for(i=0; i<pIdxInfo->nConstraint; i++, pIdxCons++){
    j = pIdxCons->iTermOffset;
    pTerm = &pWC->a[j];
    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 */

/*
** Argument pIdx is a pointer to an index structure that has an array of
** SQLITE_INDEX_SAMPLES evenly spaced samples of the first indexed column
** stored in Index.aSample. These samples divide the domain of values stored
** the index into (SQLITE_INDEX_SAMPLES+1) regions.
** Region 0 contains all values less than the first sample value. Region
** 1 contains values between the first and second samples.  Region 2 contains
** values between samples 2 and 3.  And so on.  Region SQLITE_INDEX_SAMPLES
** contains values larger than the last sample.
**
** If the index contains many duplicates of a single value, then it is
** possible that two or more adjacent samples can hold the same value.
** When that is the case, the smallest possible region code is returned
** when roundUp is false and the largest possible region code is returned
** when roundUp is true.
**
** If successful, this function determines which of the regions value 
** pVal lies in, sets *piRegion to the region index (a value between 0
** and SQLITE_INDEX_SAMPLES+1, inclusive) and returns SQLITE_OK.
** Or, if an OOM occurs while converting text values between encodings,
** SQLITE_NOMEM is returned and *piRegion is undefined.
*/
#ifdef SQLITE_ENABLE_STAT2
static int whereRangeRegion(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  sqlite3_value *pVal,        /* Value to consider */
  int roundUp,                /* Return largest valid region if true */
  int *piRegion               /* OUT: Region of domain in which value lies */
){
  assert( roundUp==0 || roundUp==1 );
  if( ALWAYS(pVal) ){
    IndexSample *aSample = pIdx->aSample;
    int i = 0;
    int eType = sqlite3_value_type(pVal);

    if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
      double r = sqlite3_value_double(pVal);
      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){
        if( aSample[i].eType==SQLITE_NULL ) continue;
        if( aSample[i].eType>=SQLITE_TEXT ) break;
        if( roundUp ){
          if( aSample[i].u.r>r ) break;
        }else{
          if( aSample[i].u.r>=r ) break;
        }
      }
    }else if( eType==SQLITE_NULL ){
      i = 0;
      if( roundUp ){
        while( i<SQLITE_INDEX_SAMPLES && aSample[i].eType==SQLITE_NULL ) i++;
      }
    }else{ 
      sqlite3 *db = pParse->db;
      CollSeq *pColl;
      const u8 *z;
      int n;

      /* pVal comes from sqlite3ValueFromExpr() so the type cannot be NULL */
      assert( eType==SQLITE_TEXT || eType==SQLITE_BLOB );

      if( eType==SQLITE_BLOB ){
        z = (const u8 *)sqlite3_value_blob(pVal);
        pColl = db->pDfltColl;
        assert( pColl->enc==SQLITE_UTF8 );
      }else{
        pColl = sqlite3GetCollSeq(db, SQLITE_UTF8, 0, *pIdx->azColl);
        if( pColl==0 ){
          sqlite3ErrorMsg(pParse, "no such collation sequence: %s",
                          *pIdx->azColl);
          return SQLITE_ERROR;
        }
        z = (const u8 *)sqlite3ValueText(pVal, pColl->enc);
        if( !z ){
          return SQLITE_NOMEM;
        }
        assert( z && pColl && pColl->xCmp );
      }
      n = sqlite3ValueBytes(pVal, pColl->enc);

      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){
        int c;
        int eSampletype = aSample[i].eType;
        if( eSampletype==SQLITE_NULL || eSampletype<eType ) continue;
        if( (eSampletype!=eType) ) break;
#ifndef SQLITE_OMIT_UTF16
        if( pColl->enc!=SQLITE_UTF8 ){
          int nSample;
          char *zSample = sqlite3Utf8to16(
              db, pColl->enc, aSample[i].u.z, aSample[i].nByte, &nSample
          );
          if( !zSample ){
            assert( db->mallocFailed );
            return SQLITE_NOMEM;
          }
          c = pColl->xCmp(pColl->pUser, nSample, zSample, n, z);
          sqlite3DbFree(db, zSample);
        }else
#endif
        {
          c = pColl->xCmp(pColl->pUser, aSample[i].nByte, aSample[i].u.z, n, z);
        }
        if( c-roundUp>=0 ) break;
      }
    }

    assert( i>=0 && i<=SQLITE_INDEX_SAMPLES );
    *piRegion = i;
  }
  return SQLITE_OK;
}
#endif   /* #ifdef SQLITE_ENABLE_STAT2 */

/*
** If expression pExpr represents a literal value, set *pp to point to
** an sqlite3_value structure containing the same value, with affinity
** aff applied to it, before returning. It is the responsibility of the 
** caller to eventually release this structure by passing it to 
** sqlite3ValueFree().
**
** If the current parse is a recompile (sqlite3Reprepare()) and pExpr
** is an SQL variable that currently has a non-NULL value bound to it,
** create an sqlite3_value structure containing this value, again with
** affinity aff applied to it, instead.
**
** If neither of the above apply, set *pp to NULL.
**
** If an error occurs, return an error code. Otherwise, SQLITE_OK.
*/
#ifdef SQLITE_ENABLE_STAT2
static int valueFromExpr(
  Parse *pParse, 
  Expr *pExpr, 
  u8 aff, 
  sqlite3_value **pp
){
  if( pExpr->op==TK_VARIABLE
   || (pExpr->op==TK_REGISTER && pExpr->op2==TK_VARIABLE)
  ){
    int iVar = pExpr->iColumn;
    sqlite3VdbeSetVarmask(pParse->pVdbe, iVar); /* IMP: R-23257-02778 */
    *pp = sqlite3VdbeGetValue(pParse->pReprepare, iVar, aff);
    return SQLITE_OK;
  }
  return sqlite3ValueFromExpr(pParse->db, pExpr, SQLITE_UTF8, aff, pp);
}
#endif

/*
** This function is used to estimate the number of rows that will be visited
** by scanning an index for a range of values. The range may have an upper
** bound, a lower bound, or both. The WHERE clause terms that set the upper
** and lower bounds are represented by pLower and pUpper respectively. For
** example, assuming that index p is on t1(a):
**
**   ... FROM t1 WHERE a > ? AND a < ? ...
**                    |_____|   |_____|
**                       |         |
**                     pLower    pUpper
**
** If either of the upper or lower bound is not present, then NULL is passed in
** place of the corresponding WhereTerm.
**
** The nEq parameter is passed the index of the index column subject to the
** range constraint. Or, equivalently, the number of equality constraints
** optimized by the proposed index scan. For example, assuming index p is
** on t1(a, b), and the SQL query is:
**
**   ... FROM t1 WHERE a = ? AND b > ? AND b < ? ...
**
** then nEq should be passed the value 1 (as the range restricted column,
** b, is the second left-most column of the index). Or, if the query is:
**
**   ... FROM t1 WHERE a > ? AND a < ? ...
**
** then nEq should be passed 0.
**
** The returned value is an integer between 1 and 100, inclusive. A return
** value of 1 indicates that the proposed range scan is expected to visit
** approximately 1/100th (1%) of the rows selected by the nEq equality
** constraints (if any). A return value of 100 indicates that it is expected
** that the range scan will visit every row (100%) selected by the equality
** constraints.
**
** In the absence of sqlite_stat2 ANALYZE data, each range inequality
** reduces the search space by 3/4ths.  Hence a single constraint (x>?)
** results in a return of 25 and a range constraint (x>? AND x<?) results
** in a return of 6.
*/
static int whereRangeScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index containing the range-compared column; "x" */
  int nEq,             /* index into p->aCol[] of the range-compared column */
  WhereTerm *pLower,   /* Lower bound on the range. ex: "x>123" Might be NULL */
  WhereTerm *pUpper,   /* Upper bound on the range. ex: "x<455" Might be NULL */
  int *piEst           /* OUT: Return value */
){
  int rc = SQLITE_OK;

#ifdef SQLITE_ENABLE_STAT2

  if( nEq==0 && p->aSample ){
    sqlite3_value *pLowerVal = 0;
    sqlite3_value *pUpperVal = 0;
    int iEst;
    int iLower = 0;
    int iUpper = SQLITE_INDEX_SAMPLES;
    int roundUpUpper = 0;
    int roundUpLower = 0;
    u8 aff = p->pTable->aCol[p->aiColumn[0]].affinity;

    if( pLower ){
      Expr *pExpr = pLower->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pLowerVal);
      assert( pLower->eOperator==WO_GT || pLower->eOperator==WO_GE );
      roundUpLower = (pLower->eOperator==WO_GT) ?1:0;
    }
    if( rc==SQLITE_OK && pUpper ){
      Expr *pExpr = pUpper->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pUpperVal);
      assert( pUpper->eOperator==WO_LT || pUpper->eOperator==WO_LE );
      roundUpUpper = (pUpper->eOperator==WO_LE) ?1:0;
    }

    if( rc!=SQLITE_OK || (pLowerVal==0 && pUpperVal==0) ){
      sqlite3ValueFree(pLowerVal);
      sqlite3ValueFree(pUpperVal);
      goto range_est_fallback;
    }else if( pLowerVal==0 ){
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( pLower ) iLower = iUpper/2;
    }else if( pUpperVal==0 ){
      rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
      if( pUpper ) iUpper = (iLower + SQLITE_INDEX_SAMPLES + 1)/2;
    }else{
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( rc==SQLITE_OK ){
        rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
      }
    }
    WHERETRACE(("range scan regions: %d..%d\n", iLower, iUpper));

    iEst = iUpper - iLower;
    testcase( iEst==SQLITE_INDEX_SAMPLES );
    assert( iEst<=SQLITE_INDEX_SAMPLES );
    if( iEst<1 ){
      *piEst = 50/SQLITE_INDEX_SAMPLES;
    }else{
      *piEst = (iEst*100)/SQLITE_INDEX_SAMPLES;
    }
    sqlite3ValueFree(pLowerVal);
    sqlite3ValueFree(pUpperVal);
    return rc;
  }
range_est_fallback:
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *piEst = 100;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ) *piEst /= 4;
  if( pUpper ) *piEst /= 4;
  return rc;
}

#ifdef SQLITE_ENABLE_STAT2
/*
** Estimate the number of rows that will be returned based on
** an equality constraint x=VALUE and where that VALUE occurs in
** the histogram data.  This only works when x is the left-most
** column of an index and sqlite_stat2 histogram data is available
** for that index.  When pExpr==NULL that means the constraint is
** "x IS NULL" instead of "x=VALUE".
**
** Write the estimated row count into *pnRow and return SQLITE_OK. 
** If unable to make an estimate, leave *pnRow unchanged and return
** non-zero.
**
** This routine can fail if it is unable to load a collating sequence
** required for string comparison, or if unable to allocate memory
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  double *pnRow        /* Write the revised row estimate here */
){
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */
  int iLower, iUpper;       /* Range of histogram regions containing pRhs */
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  double nRowEst;           /* New estimate of the number of rows */

  assert( p->aSample!=0 );
  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  if( pExpr ){
    rc = valueFromExpr(pParse, pExpr, aff, &pRhs);
    if( rc ) goto whereEqualScanEst_cancel;
  }else{
    pRhs = sqlite3ValueNew(pParse->db);
  }
  if( pRhs==0 ) return SQLITE_NOTFOUND;
  rc = whereRangeRegion(pParse, p, pRhs, 0, &iLower);
  if( rc ) goto whereEqualScanEst_cancel;
  rc = whereRangeRegion(pParse, p, pRhs, 1, &iUpper);
  if( rc ) goto whereEqualScanEst_cancel;
  WHERETRACE(("equality scan regions: %d..%d\n", iLower, iUpper));
  if( iLower>=iUpper ){
    nRowEst = p->aiRowEst[0]/(SQLITE_INDEX_SAMPLES*2);
    if( nRowEst<*pnRow ) *pnRow = nRowEst;
  }else{
    nRowEst = (iUpper-iLower)*p->aiRowEst[0]/SQLITE_INDEX_SAMPLES;
    *pnRow = nRowEst;
  }

whereEqualScanEst_cancel:
  sqlite3ValueFree(pRhs);
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT2) */

#ifdef SQLITE_ENABLE_STAT2
/*
** Estimate the number of rows that will be returned based on
** an IN constraint where the right-hand side of the IN operator
** is a list of values.  Example:
**
**        WHERE x IN (1,2,3,4)
**
** Write the estimated row count into *pnRow and return SQLITE_OK. 
** If unable to make an estimate, leave *pnRow unchanged and return
** non-zero.
**
** This routine can fail if it is unable to load a collating sequence
** required for string comparison, or if unable to allocate memory
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  double *pnRow        /* Write the revised row estimate here */
){
  sqlite3_value *pVal = 0;  /* One value from list */
  int iLower, iUpper;       /* Range of histogram regions containing pRhs */
  u8 aff;                   /* Column affinity */
  int rc = SQLITE_OK;       /* Subfunction return code */
  double nRowEst;           /* New estimate of the number of rows */
  int nSpan = 0;            /* Number of histogram regions spanned */
  int nSingle = 0;          /* Histogram regions hit by a single value */
  int nNotFound = 0;        /* Count of values that are not constants */
  int i;                               /* Loop counter */
  u8 aSpan[SQLITE_INDEX_SAMPLES+1];    /* Histogram regions that are spanned */
  u8 aSingle[SQLITE_INDEX_SAMPLES+1];  /* Histogram regions hit once */

  assert( p->aSample!=0 );
  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  memset(aSpan, 0, sizeof(aSpan));
  memset(aSingle, 0, sizeof(aSingle));
  for(i=0; i<pList->nExpr; i++){
    sqlite3ValueFree(pVal);
    rc = valueFromExpr(pParse, pList->a[i].pExpr, aff, &pVal);
    if( rc ) break;
    if( pVal==0 || sqlite3_value_type(pVal)==SQLITE_NULL ){
      nNotFound++;
      continue;
    }
    rc = whereRangeRegion(pParse, p, pVal, 0, &iLower);
    if( rc ) break;
    rc = whereRangeRegion(pParse, p, pVal, 1, &iUpper);
    if( rc ) break;
    if( iLower>=iUpper ){
      aSingle[iLower] = 1;
    }else{
      assert( iLower>=0 && iUpper<=SQLITE_INDEX_SAMPLES );
      while( iLower<iUpper ) aSpan[iLower++] = 1;
    }
  }
  if( rc==SQLITE_OK ){
    for(i=nSpan=0; i<=SQLITE_INDEX_SAMPLES; i++){
      if( aSpan[i] ){
        nSpan++;
      }else if( aSingle[i] ){
        nSingle++;
      }
    }
    nRowEst = (nSpan*2+nSingle)*p->aiRowEst[0]/(2*SQLITE_INDEX_SAMPLES)
               + nNotFound*p->aiRowEst[1];
    if( nRowEst > p->aiRowEst[0] ) nRowEst = p->aiRowEst[0];
    *pnRow = nRowEst;
    WHERETRACE(("IN row estimate: nSpan=%d, nSingle=%d, nNotFound=%d, est=%g\n",
                 nSpan, nSingle, nNotFound, nRowEst));
  }
  sqlite3ValueFree(pVal);
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT2) */


/*
** 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.)
**
**    *  Whether or not sorting must occur.
**
**    *  Whether or not there must be separate lookups in the
**       index and in the main table.
**
** If there was an INDEXED BY clause (pSrc->pIndex) attached to the table in
** the SQL statement, then this function only considers plans using the 
** named index. If no such plan is found, then the returned cost is
** SQLITE_BIG_DBL. If a plan is found that uses the named index, 
** then the cost is calculated in the usual way.
**
** If a NOT INDEXED clause (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 */
  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 */
  unsigned int 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 ){
    idxEqTermMask = WO_EQ|WO_IN;
  }else{
    idxEqTermMask = WO_EQ|WO_IN|WO_ISNULL;
  }

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

  /* Loop over all indices looking for the best one to use
  */
  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const unsigned int * const aiRowEst = pProbe->aiRowEst;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    double log10N;              /* 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.
    **
    **  nEq: 
    **    Number of equality terms that can be implemented using the index.
    **    In other words, the number of initial fields in the index that
    **    are used in == or IN or NOT NULL constraints of the WHERE clause.
    **
    **  nInMul:  
    **    The "in-multiplier". This is an estimate of how many seek operations 
    **    SQLite must perform on the index in question. For example, if the 
    **    WHERE clause is:
    **
    **      WHERE a IN (1, 2, 3) AND b IN (4, 5, 6)
    **
    **    SQLite must perform 9 lookups on an index on (a, b), so nInMul is 
    **    set to 9. Given the same schema and either of the following WHERE 
    **    clauses:
    **
    **      WHERE a =  1
    **      WHERE a >= 2
    **
    **    nInMul is set to 1.
    **
    **    If there exists a WHERE term of the form "x IN (SELECT ...)", then 
    **    the sub-select is assumed to return 25 rows for the purposes of 
    **    determining nInMul.
    **
    **  bInEst:  
    **    Set to true if there was at least one "x IN (SELECT ...)" term used 
    **    in determining the value of nInMul.  Note that the RHS of the
    **    IN operator must be a SELECT, not a value list, for this variable
    **    to be true.
    **
    **  estBound:
    **    An estimate on the amount of the table that must be searched.  A
    **    value of 100 means the entire table is searched.  Range constraints
    **    might reduce this to a value less than 100 to indicate that only
    **    a fraction of the table needs searching.  In the absence of
    **    sqlite_stat2 ANALYZE data, a single inequality reduces the search
    **    space to 1/4rd its original size.  So an x>? constraint reduces
    **    estBound to 25.  Two constraints (x>? AND x<?) reduce estBound to 6.
    **
    **  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).
    **    For example, given the index on (a, b), the second of the following 
    **    two queries requires table b-tree lookups in order to find the value
    **    of column c, but the first does not because columns a and b are
    **    both available in the index.
    **
    **             SELECT a, b    FROM tbl WHERE a = 1;
    **             SELECT a, b, c FROM tbl WHERE a = 1;
    */
    int 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 */
    int estBound = 100;           /* Estimated reduction in search space */
    int nBound = 0;               /* Number of range constraints seen */
    int bSort = 0;                /* True if external sort required */
    int bLookup = 0;              /* True if not a covering index */
    WhereTerm *pTerm;             /* A single term of the WHERE clause */
#ifdef SQLITE_ENABLE_STAT2
    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);
      if( pTerm->eOperator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
        wsFlags |= WHERE_COLUMN_IN;
        if( ExprHasProperty(pExpr, EP_xIsSelect) ){
          /* "x IN (SELECT ...)":  Assume the SELECT returns 25 rows */
          nInMul *= 25;
          bInEst = 1;
        }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
          /* "x IN (value, value, ...)" */
          nInMul *= pExpr->x.pList->nExpr;
        }
      }else if( pTerm->eOperator & WO_ISNULL ){
        wsFlags |= WHERE_COLUMN_NULL;
      }
#ifdef SQLITE_ENABLE_STAT2
      if( nEq==0 && pProbe->aSample ) pFirstTerm = pTerm;
#endif
      used |= pTerm->prereqRight;
    }

    /* Determine the value of estBound. */
    if( nEq<pProbe->nColumn && pProbe->bUnordered==0 ){
      int j = 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, &estBound);
        if( pTop ){
          nBound = 1;
          wsFlags |= WHERE_TOP_LIMIT;
          used |= pTop->prereqRight;
        }
        if( pBtm ){
          nBound++;
          wsFlags |= WHERE_BTM_LIMIT;
          used |= pBtm->prereqRight;
        }
        wsFlags |= (WHERE_COLUMN_RANGE|WHERE_ROWID_RANGE);
      }
    }else if( pProbe->onError!=OE_None ){
      testcase( wsFlags & WHERE_COLUMN_IN );
      testcase( wsFlags & WHERE_COLUMN_NULL );
      if( (wsFlags & (WHERE_COLUMN_IN|WHERE_COLUMN_NULL))==0 ){
        wsFlags |= WHERE_UNIQUE;
      }
    }

    /* 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( pOrderBy ){
      if( (wsFlags & WHERE_COLUMN_IN)==0
        && pProbe->bUnordered==0
        && isSortingIndex(pParse, pWC->pMaskSet, pProbe, iCur, pOrderBy,
                          nEq, wsFlags, &rev)
      ){
        wsFlags |= WHERE_ROWID_RANGE|WHERE_COLUMN_RANGE|WHERE_ORDERBY;
        wsFlags |= (rev ? WHERE_REVERSE : 0);
      }else{
        bSort = 1;
      }
    }

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

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

#ifdef SQLITE_ENABLE_STAT2
    /* If the constraint is of the form x=VALUE and histogram
    ** data is available for column x, then it might be possible
    ** to get a better estimate on the number of rows based on
    ** VALUE and how common that value is according to the histogram.
    */
    if( nRow>(double)1 && nEq==1 && pFirstTerm!=0 ){
      if( pFirstTerm->eOperator & (WO_EQ|WO_ISNULL) ){
        testcase( pFirstTerm->eOperator==WO_EQ );
        testcase( pFirstTerm->eOperator==WO_ISNULL );
        whereEqualScanEst(pParse, pProbe, pFirstTerm->pExpr->pRight, &nRow);
      }else if( pFirstTerm->eOperator==WO_IN && bInEst==0 ){
        whereInScanEst(pParse, pProbe, pFirstTerm->pExpr->x.pList, &nRow);
      }
    }
#endif /* SQLITE_ENABLE_STAT2 */

    /* Adjust the number of output rows and downward to reflect rows
    ** that are excluded by range constraints.
    */
    nRow = (nRow * (double)estBound) / (double)100;
    if( nRow<1 ) nRow = 1;

    /* Experiments run on real SQLite databases show that the time needed
    ** to do a binary search to locate a row in a table or index is roughly
    ** log10(N) times the time to move from one row to the next row within
    ** a table or index.  The actual times can vary, with the size of
    ** records being an important factor.  Both moves and searches are
    ** slower with larger records, presumably because fewer records fit
    ** on one page and hence more pages have to be fetched.
    **
    ** The ANALYZE command and the sqlite_stat1 and sqlite_stat2 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_NOT_FULLSCAN)==0 ){
      /* The cost of a full table scan is a number of move operations equal
      ** to the number of rows in the table.
      **
      ** We add an additional 4x penalty to full table scans.  This causes
      ** the cost function to err on the side of choosing an index over
      ** choosing a full scan.  This 4x full-scan penalty is an arguable
      ** decision and one which we expect to revisit in the future.  But
      ** it seems to be working well enough at the moment.
      */
      cost = aiRowEst[0]*4;
    }else{
      log10N = estLog(aiRowEst[0]);
      cost = nRow;
      if( pIdx ){
        if( bLookup ){
          /* For an index lookup followed by a table lookup:
          **    nInMul index searches to find the start of each index range
          **  + nRow steps through the index
          **  + nRow table searches to lookup the table entry using the rowid
          */
          cost += (nInMul + nRow)*log10N;
        }else{
          /* For a covering index:
          **     nInMul index searches to find the initial entry 
          **   + nRow steps through the index
          */
          cost += nInMul*log10N;
        }
      }else{
        /* For a rowid primary key lookup:
        **    nInMult table searches to find the initial entry for each range
        **  + nRow steps through the table
        */
        cost += nInMul*log10N;
      }
    }

    /* Add in the estimated cost of sorting the result.  Actual experimental
    ** measurements of sorting performance in SQLite show that sorting time
    ** adds C*N*log10(N) to the cost, where N is the number of rows to be 
    ** sorted and C is a factor between 1.95 and 4.3.  We will split the
    ** difference and select C of 3.0.
    */
    if( bSort ){
      cost += nRow*estLog(nRow)*3;
    }

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

    /* If there are additional constraints on this table that cannot
    ** be used with the current index, but which might lower the number
    ** of output rows, adjust the nRow value accordingly.  This only 
    ** matters if the current index is the least costly, so do not bother
    ** with this step if we already know this index will not be chosen.
    ** Also, never reduce the output row count below 2 using this step.
    **
    ** It is critical that the notValid mask be used here instead of
    ** the notReady mask.  When computing an "optimal" index, the notReady
    ** mask will only have one bit set - the bit for the current table.
    ** The notValid mask, on the other hand, always has all bits set for
    ** tables that are not in outer loops.  If notReady is used here instead
    ** of notValid, then a optimal index that depends on inner joins loops
    ** might be selected even when there exists an optimal index that has
    ** no such dependency.
    */
    if( 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
            ** set size by a factor of 10 */
            nRow /= 10;
          }
        }else if( pTerm->eOperator & (WO_LT|WO_LE|WO_GT|WO_GE) ){
          if( nSkipRange ){
            /* Ignore the first nSkipRange range constraints since the index
            ** has already accounted for these */
            nSkipRange--;
          }else{
            /* Assume each additional range constraint reduces the result
            ** set size by a factor of 3.  Indexed range constraints reduce
            ** the search space by a larger factor: 4.  We make indexed range
            ** more selective intentionally because of the subjective 
            ** observation that indexed range constraints really are more
            ** selective in practice, on average. */
            nRow /= 3;
          }
        }else if( pTerm->eOperator!=WO_NOOP ){
          /* Any other expression lowers the output row count by half */
          nRow /= 2;
        }
      }
      if( nRow<2 ) nRow = 2;
    }


    WHERETRACE((
      "%s(%s): nEq=%d nInMul=%d estBound=%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, estBound, 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 */
    wsFlagMask = ~(WHERE_ROWID_EQ|WHERE_ROWID_RANGE);
    eqTermMask = idxEqTermMask;
  }

  /* If there is no ORDER BY clause and the SQLITE_ReverseOrder flag
  ** is set, then reverse the order that the index will be scanned
  ** in. This is used for application testing, to help find cases
  ** where application 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.
*/
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 */
  ExprList *pOrderBy,         /* The ORDER BY clause */
  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, pOrderBy, pCost,&p);
    if( p->needToFreeIdxStr ){
      sqlite3_free(p->idxStr);
    }
    sqlite3DbFree(pParse->db, p);
  }else
#endif
  {
    bestBtreeIndex(pParse, pWC, pSrc, notReady, notValid, pOrderBy, 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.
**
** Consider the term t2.z='ok' in the following queries:
**
**   (1)  SELECT * FROM t1 LEFT JOIN t2 ON t1.a=t2.x WHERE t2.z='ok'
**   (2)  SELECT * FROM t1 LEFT JOIN t2 ON t1.a=t2.x AND t2.z='ok'
**   (3)  SELECT * FROM t1, t2 WHERE t1.a=t2.x AND t2.z='ok'
**
** The t2.z='ok' is disabled in the in (2) because it originates
** in the ON clause.  The term is disabled in (3) because it is not part
** of a LEFT OUTER JOIN.  In (1), the term is not disabled.
**
** IMPLEMENTATION-OF: R-24597-58655 No tests are done for terms that are
** completely satisfied by indices.
**
** Disabling a term causes that term to not be tested in the inner loop
** of the join.  Disabling is an optimization.  When terms are satisfied
** by indices, we disable them to prevent redundant tests in the inner
** loop.  We would get the correct results if nothing were ever disabled,
** but joins might run a little slower.  The trick is to disable as much
** as we can without disabling too much.  If we disabled in (1), we'd get
** the wrong answer.  See ticket #813.
*/
static void disableTerm(WhereLevel *pLevel, WhereTerm *pTerm){
  if( pTerm
      && (pTerm->wtFlags & TERM_CODED)==0
      && (pLevel->iLeftJoin==0 || ExprHasProperty(pTerm->pExpr, EP_FromJoin))
  ){
    pTerm->wtFlags |= TERM_CODED;
    if( pTerm->iParent>=0 ){
      WhereTerm *pOther = &pTerm->pWC->a[pTerm->iParent];
      if( (--pOther->nChild)==0 ){
        disableTerm(pLevel, pOther);
      }
    }
  }
}

/*
** Code an OP_Affinity opcode to apply the column affinity string zAff
** to the n registers starting at base. 
**
** As an optimization, SQLITE_AFF_NONE entries (which are no-ops) at the
** beginning and end of zAff are ignored.  If all entries in zAff are
** SQLITE_AFF_NONE, then no code gets generated.
**
** This routine makes its own copy of zAff so that the caller is free
** to modify zAff after this routine returns.
*/
static void codeApplyAffinity(Parse *pParse, int base, int n, char *zAff){
  Vdbe *v = pParse->pVdbe;
  if( zAff==0 ){
    assert( pParse->db->mallocFailed );
    return;
  }
  assert( v!=0 );

  /* Adjust base and n to skip over SQLITE_AFF_NONE entries at the beginning
  ** and end of the affinity string.
  */
  while( n>0 && zAff[0]==SQLITE_AFF_NONE ){
    n--;
    base++;
    zAff++;
  }
  while( n>1 && zAff[n-1]==SQLITE_AFF_NONE ){
    n--;
  }

  /* Code the OP_Affinity opcode if there is anything left to do. */
  if( n>0 ){
    sqlite3VdbeAddOp2(v, OP_Affinity, base, n);
    sqlite3VdbeChangeP4(v, -1, zAff, n);
    sqlite3ExprCacheAffinityChange(pParse, base, n);
  }
}


/*
** Generate code for a single equality term of the WHERE clause.  An equality
** term can be either X=expr or X IN (...).   pTerm is the term to be 
** coded.
**
** The current value for the constraint is left in register iReg.
**
** For a constraint of the form X=expr, the expression is evaluated and its
** result is left on the stack.  For constraints of the form X IN (...)
** this routine sets up a loop that will iterate over all values of X.
*/
static int codeEqualityTerm(
  Parse *pParse,      /* The parsing context */
  WhereTerm *pTerm,   /* The term of the WHERE clause to be coded */
  WhereLevel *pLevel, /* When level of the FROM clause we are working on */
  int iTarget         /* Attempt to leave results in this register */
){
  Expr *pX = pTerm->pExpr;
  Vdbe *v = pParse->pVdbe;
  int iReg;                  /* Register holding results */

  assert( iTarget>0 );
  if( pX->op==TK_EQ ){
    iReg = sqlite3ExprCodeTarget(pParse, pX->pRight, iTarget);
  }else if( pX->op==TK_ISNULL ){
    iReg = iTarget;
    sqlite3VdbeAddOp2(v, OP_Null, 0, iReg);
#ifndef SQLITE_OMIT_SUBQUERY
  }else{
    int eType;
    int iTab;
    struct InLoop *pIn;

    assert( pX->op==TK_IN );
    iReg = iTarget;
    eType = sqlite3FindInIndex(pParse, pX, 0);
    iTab = pX->iTable;
    sqlite3VdbeAddOp2(v, OP_Rewind, iTab, 0);
    assert( pLevel->plan.wsFlags & WHERE_IN_ABLE );
    if( pLevel->u.in.nIn==0 ){
      pLevel->addrNxt = sqlite3VdbeMakeLabel(v);
    }
    pLevel->u.in.nIn++;
    pLevel->u.in.aInLoop =
       sqlite3DbReallocOrFree(pParse->db, pLevel->u.in.aInLoop,
                              sizeof(pLevel->u.in.aInLoop[0])*pLevel->u.in.nIn);
    pIn = pLevel->u.in.aInLoop;
    if( pIn ){
      pIn += pLevel->u.in.nIn - 1;
      pIn->iCur = iTab;
      if( eType==IN_INDEX_ROWID ){
        pIn->addrInTop = sqlite3VdbeAddOp2(v, OP_Rowid, iTab, iReg);
      }else{
        pIn->addrInTop = sqlite3VdbeAddOp3(v, OP_Column, iTab, 0, iReg);
      }
      sqlite3VdbeAddOp1(v, OP_IsNull, iReg);
    }else{
      pLevel->u.in.nIn = 0;
    }
#endif
  }
  disableTerm(pLevel, pTerm);
  return iReg;
}

/*
** Generate code that will evaluate all == and IN constraints for an
** index.
**
** For example, consider table t1(a,b,c,d,e,f) with index i1(a,b,c).
** Suppose the WHERE clause is this:  a==5 AND b IN (1,2,3) AND c>5 AND c<10
** The index has as many as three equality constraints, but in this
** example, the third "c" value is an inequality.  So only two 
** constraints are coded.  This routine will generate code to evaluate
** a==5 and b IN (1,2,3).  The current values for a and b will be stored
** in consecutive registers and the index of the first register is returned.
**
** In the example above nEq==2.  But this subroutine works for any value
** of nEq including 0.  If nEq==0, this routine is nearly a no-op.
** The only thing it does is allocate the pLevel->iMem memory cell and
** compute the affinity string.
**
** This routine always allocates at least one memory cell and returns
** the index of that memory cell. The code that
** calls this routine will use that memory cell to store the termination
** key value of the loop.  If one or more IN operators appear, then
** this routine allocates an additional nEq memory cells for internal
** use.
**
** Before returning, *pzAff is set to point to a buffer containing a
** copy of the column affinity string of the index allocated using
** sqlite3DbMalloc(). Except, entries in the copy of the string associated
** with equality constraints that use NONE affinity are set to
** SQLITE_AFF_NONE. This is to deal with SQL such as the following:
**
**   CREATE TABLE t1(a TEXT PRIMARY KEY, b);
**   SELECT ... FROM t1 AS t2, t1 WHERE t1.a = t2.b;
**
** In the example above, the index on t1(a) has TEXT affinity. But since
** the right hand side of the equality constraint (t2.b) has NONE affinity,
** no conversion should be attempted before using a t2.b value as part of
** a key to search the index. Hence the first byte in the returned affinity
** string in this example would be set to SQLITE_AFF_NONE.
*/
static int codeAllEqualityTerms(
  Parse *pParse,        /* Parsing context */
  WhereLevel *pLevel,   /* Which nested loop of the FROM we are coding */
  WhereClause *pWC,     /* The WHERE clause */
  Bitmask notReady,     /* Which parts of FROM have not yet been coded */
  int nExtraReg,        /* Number of extra registers to allocate */
  char **pzAff          /* OUT: Set to point to affinity string */
){
  int nEq = pLevel->plan.nEq;   /* The number of == or IN constraints to code */
  Vdbe *v = pParse->pVdbe;      /* The vm under construction */
  Index *pIdx;                  /* The index being used for this loop */
  int iCur = pLevel->iTabCur;   /* The cursor of the table */
  WhereTerm *pTerm;             /* A single constraint term */
  int j;                        /* Loop counter */
  int regBase;                  /* Base register */
  int nReg;                     /* Number of registers to allocate */
  char *zAff;                   /* Affinity string to return */

  /* This module is only called on query plans that use an index. */
  assert( pLevel->plan.wsFlags & WHERE_INDEXED );
  pIdx = pLevel->plan.u.pIdx;

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

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

  /* Evaluate the equality constraints
  */
  assert( pIdx->nColumn>=nEq );
  for(j=0; j<nEq; j++){
    int r1;
    int k = pIdx->aiColumn[j];
    pTerm = findTerm(pWC, iCur, k, notReady, pLevel->plan.wsFlags, pIdx);
    if( NEVER(pTerm==0) ) break;
    /* The following true for indices with redundant columns. 
    ** Ex: CREATE INDEX i1 ON t1(a,b,a); SELECT * FROM t1 WHERE a=0 AND b=0; */
    testcase( (pTerm->wtFlags & TERM_CODED)!=0 );
    testcase( pTerm->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
    r1 = codeEqualityTerm(pParse, pTerm, pLevel, regBase+j);
    if( r1!=regBase+j ){
      if( nReg==1 ){
        sqlite3ReleaseTempReg(pParse, regBase);
        regBase = r1;
      }else{
        sqlite3VdbeAddOp2(v, OP_SCopy, r1, regBase+j);
      }
    }
    testcase( pTerm->eOperator & WO_ISNULL );
    testcase( pTerm->eOperator & WO_IN );
    if( (pTerm->eOperator & (WO_ISNULL|WO_IN))==0 ){
      Expr *pRight = pTerm->pExpr->pRight;
      sqlite3ExprCodeIsNullJump(v, pRight, regBase+j, pLevel->addrBrk);
      if( zAff ){
        if( sqlite3CompareAffinity(pRight, zAff[j])==SQLITE_AFF_NONE ){
          zAff[j] = SQLITE_AFF_NONE;
        }
        if( sqlite3ExprNeedsNoAffinityChange(pRight, zAff[j]) ){
          zAff[j] = SQLITE_AFF_NONE;
        }
      }
    }
  }
  *pzAff = zAff;
  return regBase;
}

#ifndef SQLITE_OMIT_EXPLAIN
/*
** This routine is a helper for explainIndexRange() below
**
** pStr holds the text of an expression that we are building up one term
** at a time.  This routine adds a new term to the end of the expression.
** Terms are separated by AND so add the "AND" text for second and subsequent
** terms only.
*/
static void explainAppendTerm(
  StrAccum *pStr,             /* The text expression being built */
  int iTerm,                  /* Index of this term.  First is zero */
  const char *zColumn,        /* Name of the column */
  const char *zOp             /* Name of the operator */
){
  if( iTerm ) sqlite3StrAccumAppend(pStr, " AND ", 5);
  sqlite3StrAccumAppend(pStr, zColumn, -1);
  sqlite3StrAccumAppend(pStr, zOp, 1);
  sqlite3StrAccumAppend(pStr, "?", 1);
}

/*
** Argument pLevel describes a strategy for scanning table pTab. This 
** function returns a pointer to a string buffer containing a description
** of the subset of table rows scanned by the strategy in the form of an
** SQL expression. Or, if all rows are scanned, NULL is returned.
**
** For example, if the query:
**
**   SELECT * FROM t1 WHERE a=1 AND b>2;
**
** is run and there is an index on (a, b), then this function returns a
** string similar to:
**
**   "a=? AND b>?"
**
** The returned pointer points to memory obtained from sqlite3DbMalloc().
** It is the responsibility of the caller to free the buffer when it is
** no longer required.
*/
static char *explainIndexRange(sqlite3 *db, WhereLevel *pLevel, Table *pTab){
  WherePlan *pPlan = &pLevel->plan;
  Index *pIndex = pPlan->u.pIdx;
  int nEq = pPlan->nEq;
  int i, j;
  Column *aCol = pTab->aCol;
  int *aiColumn = pIndex->aiColumn;
  StrAccum txt;

  if( nEq==0 && (pPlan->wsFlags & (WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))==0 ){
    return 0;
  }
  sqlite3StrAccumInit(&txt, 0, 0, SQLITE_MAX_LENGTH);
  txt.db = db;
  sqlite3StrAccumAppend(&txt, " (", 2);
  for(i=0; i<nEq; i++){
    explainAppendTerm(&txt, i, aCol[aiColumn[i]].zName, "=");
  }

  j = i;
  if( pPlan->wsFlags&WHERE_BTM_LIMIT ){
    explainAppendTerm(&txt, i++, aCol[aiColumn[j]].zName, ">");
  }
  if( pPlan->wsFlags&WHERE_TOP_LIMIT ){
    explainAppendTerm(&txt, i, aCol[aiColumn[j]].zName, "<");
  }
  sqlite3StrAccumAppend(&txt, ")", 1);
  return sqlite3StrAccumFinish(&txt);
}

/*
** This function is a no-op unless currently processing an EXPLAIN QUERY PLAN
** command. If the query being compiled is an EXPLAIN QUERY PLAN, a single
** record is added to the output to describe the table scan strategy in 
** pLevel.
*/
static void explainOneScan(
  Parse *pParse,                  /* Parse context */
  SrcList *pTabList,              /* Table list this loop refers to */
  WhereLevel *pLevel,             /* Scan to write OP_Explain opcode for */
  int iLevel,                     /* Value for "level" column of output */
  int iFrom,                      /* Value for "from" column of output */
  u16 wctrlFlags                  /* Flags passed to sqlite3WhereBegin() */
){
  if( pParse->explain==2 ){
    u32 flags = pLevel->plan.wsFlags;
    struct SrcList_item *pItem = &pTabList->a[pLevel->iFrom];
    Vdbe *v = pParse->pVdbe;      /* VM being constructed */
    sqlite3 *db = pParse->db;     /* Database handle */
    char *zMsg;                   /* Text to add to EQP output */
    sqlite3_int64 nRow;           /* Expected number of rows visited by scan */
    int iId = pParse->iSelectId;  /* Select id (left-most output column) */
    int isSearch;                 /* True for a SEARCH. False for SCAN. */

    if( (flags&WHERE_MULTI_OR) || (wctrlFlags&WHERE_ONETABLE_ONLY) ) return;

    isSearch = (pLevel->plan.nEq>0)
             || (flags&(WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))!=0
             || (wctrlFlags&(WHERE_ORDERBY_MIN|WHERE_ORDERBY_MAX));

    zMsg = sqlite3MPrintf(db, "%s", isSearch?"SEARCH":"SCAN");
    if( pItem->pSelect ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s SUBQUERY %d", zMsg,pItem->iSelectId);
    }else{
      zMsg = sqlite3MAppendf(db, zMsg, "%s TABLE %s", zMsg, pItem->zName);
    }

    if( pItem->zAlias ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s AS %s", zMsg, pItem->zAlias);
    }
    if( (flags & WHERE_INDEXED)!=0 ){
      char *zWhere = explainIndexRange(db, pLevel, pItem->pTab);
      zMsg = sqlite3MAppendf(db, zMsg, "%s USING %s%sINDEX%s%s%s", zMsg, 
          ((flags & WHERE_TEMP_INDEX)?"AUTOMATIC ":""),
          ((flags & WHERE_IDX_ONLY)?"COVERING ":""),
          ((flags & WHERE_TEMP_INDEX)?"":" "),
          ((flags & WHERE_TEMP_INDEX)?"": pLevel->plan.u.pIdx->zName),
          zWhere
      );
      sqlite3DbFree(db, zWhere);
    }else if( flags & (WHERE_ROWID_EQ|WHERE_ROWID_RANGE) ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s USING INTEGER PRIMARY KEY", zMsg);

      if( flags&WHERE_ROWID_EQ ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid=?)", zMsg);
      }else if( (flags&WHERE_BOTH_LIMIT)==WHERE_BOTH_LIMIT ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid>? AND rowid<?)", zMsg);
      }else if( flags&WHERE_BTM_LIMIT ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid>?)", zMsg);
      }else if( flags&WHERE_TOP_LIMIT ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid<?)", zMsg);
      }
    }
#ifndef SQLITE_OMIT_VIRTUALTABLE
    else if( (flags & WHERE_VIRTUALTABLE)!=0 ){
      sqlite3_index_info *pVtabIdx = pLevel->plan.u.pVtabIdx;
      zMsg = sqlite3MAppendf(db, zMsg, "%s VIRTUAL TABLE INDEX %d:%s", zMsg,
                  pVtabIdx->idxNum, pVtabIdx->idxStr);
    }
#endif
    if( wctrlFlags&(WHERE_ORDERBY_MIN|WHERE_ORDERBY_MAX) ){
      testcase( wctrlFlags & WHERE_ORDERBY_MIN );
      nRow = 1;
    }else{
      nRow = (sqlite3_int64)pLevel->plan.nRow;
    }
    zMsg = sqlite3MAppendf(db, zMsg, "%s (~%lld rows)", zMsg, nRow);
    sqlite3VdbeAddOp4(v, OP_Explain, iId, iLevel, iFrom, zMsg, P4_DYNAMIC);
  }
}
#else
# define explainOneScan(u,v,w,x,y,z)
#endif /* SQLITE_OMIT_EXPLAIN */


/*
** Generate code for the start of the iLevel-th loop in the WHERE clause
** implementation described by pWInfo.
*/
static Bitmask codeOneLoopStart(
  WhereInfo *pWInfo,   /* Complete information about the WHERE clause */
  int iLevel,          /* Which level of pWInfo->a[] should be coded */
  u16 wctrlFlags,      /* One of the WHERE_* flags defined in sqliteInt.h */
  Bitmask notReady     /* Which tables are currently available */
){
  int j, k;            /* Loop counters */
  int iCur;            /* The VDBE cursor for the table */
  int addrNxt;         /* Where to jump to continue with the next IN case */
  int omitTable;       /* True if we use the index only */
  int bRev;            /* True if we need to scan in reverse order */
  WhereLevel *pLevel;  /* The where level to be coded */
  WhereClause *pWC;    /* Decomposition of the entire WHERE clause */
  WhereTerm *pTerm;               /* A WHERE clause term */
  Parse *pParse;                  /* Parsing context */
  Vdbe *v;                        /* The prepared stmt under constructions */
  struct SrcList_item *pTabItem;  /* FROM clause term being coded */
  int addrBrk;                    /* Jump here to break out of the loop */
  int addrCont;                   /* Jump here to continue with next cycle */
  int iRowidReg = 0;        /* Rowid is stored in this register, if not zero */
  int iReleaseReg = 0;      /* Temp register to free before returning */

  pParse = pWInfo->pParse;
  v = pParse->pVdbe;
  pWC = pWInfo->pWC;
  pLevel = &pWInfo->a[iLevel];
  pTabItem = &pWInfo->pTabList->a[pLevel->iFrom];
  iCur = pTabItem->iCursor;
  bRev = (pLevel->plan.wsFlags & WHERE_REVERSE)!=0;
  omitTable = (pLevel->plan.wsFlags & WHERE_IDX_ONLY)!=0 
           && (wctrlFlags & WHERE_FORCE_TABLE)==0;

  /* Create labels for the "break" and "continue" instructions
  ** for the current loop.  Jump to addrBrk to break out of a loop.
  ** Jump to cont to go immediately to the next iteration of the
  ** loop.
  **
  ** When there is an IN operator, we also have a "addrNxt" label that
  ** means to continue with the next IN value combination.  When
  ** there are no IN operators in the constraints, the "addrNxt" label
  ** is the same as "addrBrk".
  */
  addrBrk = pLevel->addrBrk = pLevel->addrNxt = sqlite3VdbeMakeLabel(v);
  addrCont = pLevel->addrCont = sqlite3VdbeMakeLabel(v);

  /* If this is the right table of a LEFT OUTER JOIN, allocate and
  ** initialize a memory cell that records if this table matches any
  ** row of the left table of the join.
  */
  if( pLevel->iFrom>0 && (pTabItem[0].jointype & JT_LEFT)!=0 ){
    pLevel->iLeftJoin = ++pParse->nMem;
    sqlite3VdbeAddOp2(v, OP_Integer, 0, pLevel->iLeftJoin);
    VdbeComment((v, "init LEFT JOIN no-match flag"));
  }

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

    sqlite3ExprCachePush(pParse);
    iReg = sqlite3GetTempRange(pParse, nConstraint+2);
    for(j=1; j<=nConstraint; j++){
      for(k=0; k<nConstraint; k++){
        if( aUsage[k].argvIndex==j ){
          int iTerm = aConstraint[k].iTermOffset;
          sqlite3ExprCode(pParse, pWC->a[iTerm].pExpr->pRight, iReg+j+1);
          break;
        }
      }
      if( k==nConstraint ) break;
    }
    sqlite3VdbeAddOp2(v, OP_Integer, pVtabIdx->idxNum, iReg);
    sqlite3VdbeAddOp2(v, OP_Integer, j-1, iReg+1);
    sqlite3VdbeAddOp4(v, OP_VFilter, iCur, addrBrk, iReg, pVtabIdx->idxStr,
                      pVtabIdx->needToFreeIdxStr ? P4_MPRINTF : P4_STATIC);
    pVtabIdx->needToFreeIdxStr = 0;
    for(j=0; j<nConstraint; j++){
      if( aUsage[j].omit ){
        int iTerm = aConstraint[j].iTermOffset;
        disableTerm(pLevel, &pWC->a[iTerm]);
      }
    }
    pLevel->op = OP_VNext;
    pLevel->p1 = iCur;
    pLevel->p2 = sqlite3VdbeCurrentAddr(v);
    sqlite3ReleaseTempRange(pParse, iReg, nConstraint+2);
    sqlite3ExprCachePop(pParse, 1);
  }else
#endif /* SQLITE_OMIT_VIRTUALTABLE */

  if( pLevel->plan.wsFlags & WHERE_ROWID_EQ ){
    /* Case 1:  We can directly reference a single row using an
    **          equality comparison against the ROWID field.  Or
    **          we reference multiple rows using a "rowid IN (...)"
    **          construct.
    */
    iReleaseReg = sqlite3GetTempReg(pParse);
    pTerm = findTerm(pWC, iCur, -1, notReady, WO_EQ|WO_IN, 0);
    assert( pTerm!=0 );
    assert( pTerm->pExpr!=0 );
    assert( pTerm->leftCursor==iCur );
    assert( omitTable==0 );
    testcase( pTerm->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
    iRowidReg = codeEqualityTerm(pParse, pTerm, pLevel, iReleaseReg);
    addrNxt = pLevel->addrNxt;
    sqlite3VdbeAddOp2(v, OP_MustBeInt, iRowidReg, addrNxt);
    sqlite3VdbeAddOp3(v, OP_NotExists, iCur, addrNxt, iRowidReg);
    sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
    VdbeComment((v, "pk"));
    pLevel->op = OP_Noop;
  }else if( pLevel->plan.wsFlags & WHERE_ROWID_RANGE ){
    /* Case 2:  We have an inequality comparison against the ROWID field.
    */
    int testOp = OP_Noop;
    int start;
    int memEndValue = 0;
    WhereTerm *pStart, *pEnd;

    assert( omitTable==0 );
    pStart = findTerm(pWC, iCur, -1, notReady, WO_GT|WO_GE, 0);
    pEnd = findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE, 0);
    if( bRev ){
      pTerm = pStart;
      pStart = pEnd;
      pEnd = pTerm;
    }
    if( pStart ){
      Expr *pX;             /* The expression that defines the start bound */
      int r1, rTemp;        /* Registers for holding the start boundary */

      /* The following constant maps TK_xx codes into corresponding 
      ** seek opcodes.  It depends on a particular ordering of TK_xx
      */
      const u8 aMoveOp[] = {
           /* TK_GT */  OP_SeekGt,
           /* TK_LE */  OP_SeekLe,
           /* TK_LT */  OP_SeekLt,
           /* TK_GE */  OP_SeekGe
      };
      assert( TK_LE==TK_GT+1 );      /* Make sure the ordering.. */
      assert( TK_LT==TK_GT+2 );      /*  ... of the TK_xx values... */
      assert( TK_GE==TK_GT+3 );      /*  ... is correcct. */

      testcase( pStart->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
      pX = pStart->pExpr;
      assert( pX!=0 );
      assert( pStart->leftCursor==iCur );
      r1 = sqlite3ExprCodeTemp(pParse, pX->pRight, &rTemp);
      sqlite3VdbeAddOp3(v, aMoveOp[pX->op-TK_GT], iCur, addrBrk, r1);
      VdbeComment((v, "pk"));
      sqlite3ExprCacheAffinityChange(pParse, r1, 1);
      sqlite3ReleaseTempReg(pParse, rTemp);
      disableTerm(pLevel, pStart);
    }else{
      sqlite3VdbeAddOp2(v, bRev ? OP_Last : OP_Rewind, iCur, addrBrk);
    }
    if( pEnd ){
      Expr *pX;
      pX = pEnd->pExpr;
      assert( pX!=0 );
      assert( pEnd->leftCursor==iCur );
      testcase( pEnd->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
      memEndValue = ++pParse->nMem;
      sqlite3ExprCode(pParse, pX->pRight, memEndValue);
      if( pX->op==TK_LT || pX->op==TK_GT ){
        testOp = bRev ? OP_Le : OP_Ge;
      }else{
        testOp = bRev ? OP_Lt : OP_Gt;
      }
      disableTerm(pLevel, pEnd);
    }
    start = sqlite3VdbeCurrentAddr(v);
    pLevel->op = bRev ? OP_Prev : OP_Next;
    pLevel->p1 = iCur;
    pLevel->p2 = start;
    if( pStart==0 && pEnd==0 ){
      pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;
    }else{
      assert( pLevel->p5==0 );
    }
    if( testOp!=OP_Noop ){
      iRowidReg = iReleaseReg = sqlite3GetTempReg(pParse);
      sqlite3VdbeAddOp2(v, OP_Rowid, iCur, iRowidReg);
      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
      sqlite3VdbeAddOp3(v, testOp, memEndValue, addrBrk, iRowidReg);
      sqlite3VdbeChangeP5(v, SQLITE_AFF_NUMERIC | SQLITE_JUMPIFNULL);
    }
  }else if( pLevel->plan.wsFlags & (WHERE_COLUMN_RANGE|WHERE_COLUMN_EQ) ){
    /* Case 3: A scan using an index.
    **
    **         The WHERE clause may contain zero or more equality 
    **         terms ("==" or "IN" operators) that refer to the N
    **         left-most columns of the index. It may also contain
    **         inequality constraints (>, <, >= or <=) on the indexed
    **         column that immediately follows the N equalities. Only 
    **         the right-most column can be an inequality - the rest must
    **         use the "==" and "IN" operators. For example, if the 
    **         index is on (x,y,z), then the following clauses are all 
    **         optimized:
    **
    **            x=5
    **            x=5 AND y=10
    **            x=5 AND y<10
    **            x=5 AND y>5 AND y<10
    **            x=5 AND y=5 AND z<=10
    **
    **         The z<10 term of the following cannot be used, only
    **         the x=5 term:
    **
    **            x=5 AND z<10
    **
    **         N may be zero if there are inequality constraints.
    **         If there are no inequality constraints, then N is at
    **         least one.
    **
    **         This case is also used when there are no WHERE clause
    **         constraints but an index is selected anyway, in order
    **         to force the output order to conform to an ORDER BY.
    */  
    static const u8 aStartOp[] = {
      0,
      0,
      OP_Rewind,           /* 2: (!start_constraints && startEq &&  !bRev) */
      OP_Last,             /* 3: (!start_constraints && startEq &&   bRev) */
      OP_SeekGt,           /* 4: (start_constraints  && !startEq && !bRev) */
      OP_SeekLt,           /* 5: (start_constraints  && !startEq &&  bRev) */
      OP_SeekGe,           /* 6: (start_constraints  &&  startEq && !bRev) */
      OP_SeekLe            /* 7: (start_constraints  &&  startEq &&  bRev) */
    };
    static const u8 aEndOp[] = {
      OP_Noop,             /* 0: (!end_constraints) */
      OP_IdxGE,            /* 1: (end_constraints && !bRev) */
      OP_IdxLT             /* 2: (end_constraints && bRev) */
    };
    int nEq = pLevel->plan.nEq;  /* Number of == or IN terms */
    int isMinQuery = 0;          /* If this is an optimized SELECT min(x).. */
    int regBase;                 /* Base register holding constraint values */
    int r1;                      /* Temp register */
    WhereTerm *pRangeStart = 0;  /* Inequality constraint at range start */
    WhereTerm *pRangeEnd = 0;    /* Inequality constraint at range end */
    int startEq;                 /* True if range start uses ==, >= or <= */
    int endEq;                   /* True if range end uses ==, >= or <= */
    int start_constraints;       /* Start of range is constrained */
    int nConstraint;             /* Number of constraint terms */
    Index *pIdx;                 /* The index we will be using */
    int iIdxCur;                 /* The VDBE cursor for the index */
    int nExtraReg = 0;           /* Number of extra registers needed */
    int op;                      /* Instruction opcode */
    char *zStartAff;             /* Affinity for start of range constraint */
    char *zEndAff;               /* Affinity for end of range constraint */

    pIdx = pLevel->plan.u.pIdx;
    iIdxCur = pLevel->iIdxCur;
    k = pIdx->aiColumn[nEq];     /* Column for inequality constraints */

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

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

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

    /* If we are doing a reverse order scan on an ascending index, or
    ** a forward order scan on a descending index, interchange the 
    ** start and end terms (pRangeStart and pRangeEnd).
    */
    if( nEq<pIdx->nColumn && bRev==(pIdx->aSortOrder[nEq]==SQLITE_SO_ASC) ){
      SWAP(WhereTerm *, pRangeEnd, pRangeStart);
    }

    testcase( pRangeStart && pRangeStart->eOperator & WO_LE );
    testcase( pRangeStart && pRangeStart->eOperator & WO_GE );
    testcase( pRangeEnd && pRangeEnd->eOperator & WO_LE );
    testcase( pRangeEnd && pRangeEnd->eOperator & WO_GE );
    startEq = !pRangeStart || pRangeStart->eOperator & (WO_LE|WO_GE);
    endEq =   !pRangeEnd || pRangeEnd->eOperator & (WO_LE|WO_GE);
    start_constraints = pRangeStart || nEq>0;

    /* Seek the index cursor to the start of the range. */
    nConstraint = nEq;
    if( pRangeStart ){
      Expr *pRight = pRangeStart->pExpr->pRight;
      sqlite3ExprCode(pParse, pRight, regBase+nEq);
      if( (pRangeStart->wtFlags & TERM_VNULL)==0 ){
        sqlite3ExprCodeIsNullJump(v, pRight, regBase+nEq, addrNxt);
      }
      if( zStartAff ){
        if( sqlite3CompareAffinity(pRight, zStartAff[nEq])==SQLITE_AFF_NONE){
          /* Since the comparison is to be performed with no conversions
          ** applied to the operands, set the affinity to apply to pRight to 
          ** SQLITE_AFF_NONE.  */
          zStartAff[nEq] = SQLITE_AFF_NONE;
        }
        if( sqlite3ExprNeedsNoAffinityChange(pRight, zStartAff[nEq]) ){
          zStartAff[nEq] = SQLITE_AFF_NONE;
        }
      }  
      nConstraint++;
      testcase( pRangeStart->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
    }else if( isMinQuery ){
      sqlite3VdbeAddOp2(v, OP_Null, 0, regBase+nEq);
      nConstraint++;
      startEq = 0;
      start_constraints = 1;
    }
    codeApplyAffinity(pParse, regBase, nConstraint, zStartAff);
    op = aStartOp[(start_constraints<<2) + (startEq<<1) + bRev];
    assert( op!=0 );
    testcase( op==OP_Rewind );
    testcase( op==OP_Last );
    testcase( op==OP_SeekGt );
    testcase( op==OP_SeekGe );
    testcase( op==OP_SeekLe );
    testcase( op==OP_SeekLt );
    sqlite3VdbeAddOp4Int(v, op, iIdxCur, addrNxt, regBase, nConstraint);

    /* Load the value for the inequality constraint at the end of the
    ** range (if any).
    */
    nConstraint = nEq;
    if( pRangeEnd ){
      Expr *pRight = pRangeEnd->pExpr->pRight;
      sqlite3ExprCacheRemove(pParse, regBase+nEq, 1);
      sqlite3ExprCode(pParse, pRight, regBase+nEq);
      if( (pRangeEnd->wtFlags & TERM_VNULL)==0 ){
        sqlite3ExprCodeIsNullJump(v, pRight, regBase+nEq, addrNxt);
      }
      if( zEndAff ){
        if( sqlite3CompareAffinity(pRight, zEndAff[nEq])==SQLITE_AFF_NONE){
          /* Since the comparison is to be performed with no conversions
          ** applied to the operands, set the affinity to apply to pRight to 
          ** SQLITE_AFF_NONE.  */
          zEndAff[nEq] = SQLITE_AFF_NONE;
        }
        if( sqlite3ExprNeedsNoAffinityChange(pRight, zEndAff[nEq]) ){
          zEndAff[nEq] = SQLITE_AFF_NONE;
        }
      }  
      codeApplyAffinity(pParse, regBase, nEq+1, zEndAff);
      nConstraint++;
      testcase( pRangeEnd->wtFlags & TERM_VIRTUAL ); /* EV: R-30575-11662 */
    }
    sqlite3DbFree(pParse->db, zStartAff);
    sqlite3DbFree(pParse->db, zEndAff);

    /* Top of the loop body */
    pLevel->p2 = sqlite3VdbeCurrentAddr(v);

    /* Check if the index cursor is past the end of the range. */
    op = aEndOp[(pRangeEnd || nEq) * (1 + bRev)];
    testcase( op==OP_Noop );
    testcase( op==OP_IdxGE );
    testcase( op==OP_IdxLT );
    if( op!=OP_Noop ){
      sqlite3VdbeAddOp4Int(v, op, iIdxCur, addrNxt, regBase, nConstraint);
      sqlite3VdbeChangeP5(v, endEq!=bRev ?1:0);
    }

    /* If there are inequality constraints, check that the value
    ** of the table column that the inequality contrains is not NULL.
    ** If it is, jump to the next iteration of the loop.
    */
    r1 = sqlite3GetTempReg(pParse);
    testcase( pLevel->plan.wsFlags & WHERE_BTM_LIMIT );
    testcase( pLevel->plan.wsFlags & WHERE_TOP_LIMIT );
    if( (pLevel->plan.wsFlags & (WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))!=0 ){
      sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, nEq, r1);
      sqlite3VdbeAddOp2(v, OP_IsNull, r1, addrCont);
    }
    sqlite3ReleaseTempReg(pParse, r1);

    /* Seek the table cursor, if required */
    disableTerm(pLevel, pRangeStart);
    disableTerm(pLevel, pRangeEnd);
    if( !omitTable ){
      iRowidReg = iReleaseReg = sqlite3GetTempReg(pParse);
      sqlite3VdbeAddOp2(v, OP_IdxRowid, iIdxCur, iRowidReg);
      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
      sqlite3VdbeAddOp2(v, OP_Seek, iCur, iRowidReg);  /* Deferred seek */
    }

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

#ifndef SQLITE_OMIT_OR_OPTIMIZATION
  if( pLevel->plan.wsFlags & WHERE_MULTI_OR ){
    /* Case 4:  Two or more separately indexed terms connected by OR
    **
    ** Example:
    **
    **   CREATE TABLE t1(a,b,c,d);
    **   CREATE INDEX i1 ON t1(a);
    **   CREATE INDEX i2 ON t1(b);
    **   CREATE INDEX i3 ON t1(c);
    **
    **   SELECT * FROM t1 WHERE a=5 OR b=7 OR (c=11 AND d=13)
    **
    ** In the example, there are three indexed terms connected by OR.
    ** The top of the loop looks like this:
    **
    **          Null       1                # Zero the rowset in reg 1
    **
    ** Then, for each indexed term, the following. The arguments to
    ** RowSetTest are such that the rowid of the current row is inserted
    ** into the RowSet. If it is already present, control skips the
    ** Gosub opcode and jumps straight to the code generated by WhereEnd().
    **
    **        sqlite3WhereBegin(<term>)
    **          RowSetTest                  # Insert rowid into rowset
    **          Gosub      2 A
    **        sqlite3WhereEnd()
    **
    ** Following the above, code to terminate the loop. Label A, the target
    ** of the Gosub above, jumps to the instruction right after the Goto.
    **
    **          Null       1                # Zero the rowset in reg 1
    **          Goto       B                # The loop is finished.
    **
    **       A: <loop body>                 # Return data, whatever.
    **
    **          Return     2                # Jump back to the Gosub
    **
    **       B: <after the loop>
    **
    */
    WhereClause *pOrWc;    /* The OR-clause broken out into subterms */
    SrcList *pOrTab;       /* Shortened table list or OR-clause generation */

    int regReturn = ++pParse->nMem;           /* Register used with OP_Gosub */
    int regRowset = 0;                        /* Register for RowSet object */
    int regRowid = 0;                         /* Register holding rowid */
    int iLoopBody = sqlite3VdbeMakeLabel(v);  /* Start of loop body */
    int iRetInit;                             /* Address of regReturn init */
    int untestedTerms = 0;             /* Some terms not completely tested */
    int ii;
   
    pTerm = pLevel->plan.u.pTerm;
    assert( pTerm!=0 );
    assert( pTerm->eOperator==WO_OR );
    assert( (pTerm->wtFlags & TERM_ORINFO)!=0 );
    pOrWc = &pTerm->u.pOrInfo->wc;
    pLevel->op = OP_Return;
    pLevel->p1 = regReturn;

    /* Set up a new SrcList ni pOrTab containing the table being scanned
    ** by this loop in the a[0] slot and all notReady tables in a[1..] slots.
    ** This becomes the SrcList in the recursive call to sqlite3WhereBegin().
    */
    if( pWInfo->nLevel>1 ){
      int nNotReady;                 /* The number of notReady tables */
      struct SrcList_item *origSrc;     /* Original list of tables */
      nNotReady = pWInfo->nLevel - iLevel - 1;
      pOrTab = sqlite3StackAllocRaw(pParse->db,
                            sizeof(*pOrTab)+ nNotReady*sizeof(pOrTab->a[0]));
      if( pOrTab==0 ) return notReady;
      pOrTab->nAlloc = (i16)(nNotReady + 1);
      pOrTab->nSrc = pOrTab->nAlloc;
      memcpy(pOrTab->a, pTabItem, sizeof(*pTabItem));
      origSrc = pWInfo->pTabList->a;
      for(k=1; k<=nNotReady; k++){
        memcpy(&pOrTab->a[k], &origSrc[pLevel[k].iFrom], sizeof(pOrTab->a[k]));
      }
    }else{
      pOrTab = pWInfo->pTabList;
    }

    /* Initialize the rowset register to contain NULL. An SQL NULL is 
    ** equivalent to an empty rowset.
    **
    ** Also initialize regReturn to contain the address of the instruction 
    ** immediately following the OP_Return at the bottom of the loop. This
    ** is required in a few obscure LEFT JOIN cases where control jumps
    ** over the top of the loop into the body of it. In this case the 
    ** correct response for the end-of-loop code (the OP_Return) is to 
    ** fall through to the next instruction, just as an OP_Next does if
    ** called on an uninitialized cursor.
    */
    if( (wctrlFlags & WHERE_DUPLICATES_OK)==0 ){
      regRowset = ++pParse->nMem;
      regRowid = ++pParse->nMem;
      sqlite3VdbeAddOp2(v, OP_Null, 0, regRowset);
    }
    iRetInit = sqlite3VdbeAddOp2(v, OP_Integer, 0, regReturn);

    for(ii=0; ii<pOrWc->nTerm; ii++){
      WhereTerm *pOrTerm = &pOrWc->a[ii];
      if( pOrTerm->leftCursor==iCur || pOrTerm->eOperator==WO_AND ){
        WhereInfo *pSubWInfo;          /* Info for single OR-term scan */
        /* Loop through table entries that match term pOrTerm. */
        pSubWInfo = sqlite3WhereBegin(pParse, pOrTab, pOrTerm->pExpr, 0,
                        WHERE_OMIT_OPEN | WHERE_OMIT_CLOSE |
                        WHERE_FORCE_TABLE | WHERE_ONETABLE_ONLY);
        if( pSubWInfo ){
          explainOneScan(
              pParse, pOrTab, &pSubWInfo->a[0], iLevel, pLevel->iFrom, 0
          );
          if( (wctrlFlags & WHERE_DUPLICATES_OK)==0 ){
            int iSet = ((ii==pOrWc->nTerm-1)?-1:ii);
            int r;
            r = sqlite3ExprCodeGetColumn(pParse, pTabItem->pTab, -1, iCur, 
                                         regRowid);
            sqlite3VdbeAddOp4Int(v, OP_RowSetTest, regRowset,
                                 sqlite3VdbeCurrentAddr(v)+2, r, iSet);
          }
          sqlite3VdbeAddOp2(v, OP_Gosub, regReturn, iLoopBody);

          /* The pSubWInfo->untestedTerms flag means that this OR term
          ** contained one or more AND term from a notReady table.  The
          ** terms from the notReady table could not be tested and will
          ** need to be tested later.
          */
          if( pSubWInfo->untestedTerms ) untestedTerms = 1;

          /* Finish the loop through table entries that match term pOrTerm. */
          sqlite3WhereEnd(pSubWInfo);
        }
      }
    }
    sqlite3VdbeChangeP1(v, iRetInit, sqlite3VdbeCurrentAddr(v));
    sqlite3VdbeAddOp2(v, OP_Goto, 0, pLevel->addrBrk);
    sqlite3VdbeResolveLabel(v, iLoopBody);

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

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

  /* Insert code to test every subexpression that can be completely
  ** computed using the current set of tables.
  **
  ** IMPLEMENTATION-OF: R-49525-50935 Terms that cannot be satisfied through
  ** the use of indices become tests that are evaluated against each row of
  ** the relevant input tables.
  */
  for(pTerm=pWC->a, j=pWC->nTerm; j>0; j--, pTerm++){
    Expr *pE;
    testcase( pTerm->wtFlags & TERM_VIRTUAL ); /* IMP: R-30575-11662 */
    testcase( pTerm->wtFlags & TERM_CODED );
    if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;
    if( (pTerm->prereqAll & notReady)!=0 ){
      testcase( pWInfo->untestedTerms==0
               && (pWInfo->wctrlFlags & WHERE_ONETABLE_ONLY)!=0 );
      pWInfo->untestedTerms = 1;
      continue;
    }
    pE = pTerm->pExpr;
    assert( pE!=0 );
    if( pLevel->iLeftJoin && !ExprHasProperty(pE, EP_FromJoin) ){
      continue;
    }
    sqlite3ExprIfFalse(pParse, pE, addrCont, SQLITE_JUMPIFNULL);
    pTerm->wtFlags |= TERM_CODED;
  }

  /* For a LEFT OUTER JOIN, generate code that will record the fact that
  ** at least one row of the right table has matched the left table.  
  */
  if( pLevel->iLeftJoin ){
    pLevel->addrFirst = sqlite3VdbeCurrentAddr(v);
    sqlite3VdbeAddOp2(v, OP_Integer, 1, pLevel->iLeftJoin);
    VdbeComment((v, "record LEFT JOIN hit"));
    sqlite3ExprCacheClear(pParse);
    for(pTerm=pWC->a, j=0; j<pWC->nTerm; j++, pTerm++){
      testcase( pTerm->wtFlags & TERM_VIRTUAL );  /* IMP: R-30575-11662 */
      testcase( pTerm->wtFlags & TERM_CODED );
      if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;
      if( (pTerm->prereqAll & notReady)!=0 ){
        assert( pWInfo->untestedTerms );
        continue;
      }
      assert( pTerm->pExpr );
      sqlite3ExprIfFalse(pParse, pTerm->pExpr, addrCont, SQLITE_JUMPIFNULL);
      pTerm->wtFlags |= TERM_CODED;
    }
  }
  sqlite3ReleaseTempReg(pParse, iReleaseReg);

  return notReady;
}

#if defined(SQLITE_TEST)
/*
** The following variable holds a text description of query plan generated
** by the most recent call to sqlite3WhereBegin().  Each call to WhereBegin
** overwrites the previous.  This information is used for testing and
** analysis only.
*/
char sqlite3_query_plan[BMS*2*40];  /* Text of the join */
static int nQPlan = 0;              /* Next free slow in _query_plan[] */

#endif /* SQLITE_TEST */


/*
** Free a WhereInfo structure
*/
static void whereInfoFree(sqlite3 *db, WhereInfo *pWInfo){
  if( ALWAYS(pWInfo) ){
    int i;
    for(i=0; i<pWInfo->nLevel; i++){
      sqlite3_index_info *pInfo = pWInfo->a[i].pIdxInfo;
      if( pInfo ){
        /* assert( pInfo->needToFreeIdxStr==0 || db->mallocFailed ); */
        if( pInfo->needToFreeIdxStr ){
          sqlite3_free(pInfo->idxStr);
        }
        sqlite3DbFree(db, pInfo);
      }
      if( pWInfo->a[i].plan.wsFlags & WHERE_TEMP_INDEX ){
        Index *pIdx = pWInfo->a[i].plan.u.pIdx;
        if( pIdx ){
          sqlite3DbFree(db, pIdx->zColAff);
          sqlite3DbFree(db, pIdx);
        }
      }
    }
    whereClauseClear(pWInfo->pWC);
    sqlite3DbFree(db, pWInfo);
  }
}


/*
** Generate the beginning of the loop used for WHERE clause processing.
** The return value is a pointer to an opaque structure that contains
** information needed to terminate the loop.  Later, the calling routine
** should invoke sqlite3WhereEnd() with the return value of this function
** in order to complete the WHERE clause processing.
**
** If an error occurs, this routine returns NULL.
**
** The basic idea is to do a nested loop, one loop for each table in
** the FROM clause of a select.  (INSERT and UPDATE statements are the
** same as a SELECT with only a single table in the FROM clause.)  For
** example, if the SQL is this:
**
**       SELECT * FROM t1, t2, t3 WHERE ...;
**
** Then the code generated is conceptually like the following:
**
**      foreach row1 in t1 do       \    Code generated
**        foreach row2 in t2 do      |-- by sqlite3WhereBegin()
**          foreach row3 in t3 do   /
**            ...
**          end                     \    Code generated
**        end                        |-- by sqlite3WhereEnd()
**      end                         /
**
** Note that the loops might not be nested in the order in which they
** appear in the FROM clause if a different order is better able to make
** use of indices.  Note also that when the IN operator appears in
** the WHERE clause, it might result in additional nested loops for
** scanning through all values on the right-hand side of the IN.
**
** There are Btree cursors associated with each table.  t1 uses cursor
** number pTabList->a[0].iCursor.  t2 uses the cursor pTabList->a[1].iCursor.
** And so forth.  This routine generates code to open those VDBE cursors
** and sqlite3WhereEnd() generates the code to close them.
**
** The code that sqlite3WhereBegin() generates leaves the cursors named
** in pTabList pointing at their appropriate entries.  The [...] code
** can use OP_Column and OP_Rowid opcodes on these cursors to extract
** data from the various tables of the loop.
**
** If the WHERE clause is empty, the foreach loops must each scan their
** entire tables.  Thus a three-way join is an O(N^3) operation.  But if
** the tables have indices and there are terms in the WHERE clause that
** refer to those indices, a complete table scan can be avoided and the
** code will run much faster.  Most of the work of this routine is checking
** to see if there are indices that can be used to speed up the loop.
**
** Terms of the WHERE clause are also used to limit which rows actually
** make it to the "..." in the middle of the loop.  After each "foreach",
** terms of the WHERE clause that use only terms in that loop and outer
** loops are evaluated and if false a jump is made around all subsequent
** inner loops (or around the "..." if the test occurs within the inner-
** most loop)
**
** OUTER JOINS
**
** An outer join of tables t1 and t2 is conceptally coded as follows:
**
**    foreach row1 in t1 do
**      flag = 0
**      foreach row2 in t2 do
**        start:
**          ...
**          flag = 1
**      end
**      if flag==0 then
**        move the row2 cursor to a null row
**        goto start
**      fi
**    end
**
** ORDER BY CLAUSE PROCESSING
**
** *ppOrderBy is a pointer to the ORDER BY clause of a SELECT statement,
** if there is one.  If there is no ORDER BY clause or if this routine
** is called from an UPDATE or DELETE statement, then ppOrderBy is NULL.
**
** If an index can be used so that the natural output order of the table
** scan is correct for the ORDER BY clause, then that index is used and
** *ppOrderBy is set to NULL.  This is an optimization that prevents an
** unnecessary sort of the result set if an index appropriate for the
** ORDER BY clause already exists.
**
** If the where clause loops cannot be arranged to provide the correct
** output order, then the *ppOrderBy is unchanged.
*/
WhereInfo *sqlite3WhereBegin(
  Parse *pParse,        /* The parser context */
  SrcList *pTabList,    /* A list of all tables to be scanned */
  Expr *pWhere,         /* The WHERE clause */
  ExprList **ppOrderBy, /* An ORDER BY clause, or NULL */
  u16 wctrlFlags        /* One of the WHERE_* flags defined in sqliteInt.h */
){
  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 the pWInfo list */
  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;
  }

  /* This function normally generates a nested loop for all tables in 
  ** pTabList.  But if the WHERE_ONETABLE_ONLY flag is set, then we should
  ** only generate code for the first table in pTabList and assume that
  ** any cursors associated with subsequent tables are uninitialized.
  */
  nTabList = (wctrlFlags & WHERE_ONETABLE_ONLY) ? 1 : pTabList->nSrc;

  /* Allocate and initialize the WhereInfo structure that will become the
  ** return value. A single allocation is used to store the WhereInfo
  ** struct, the contents of WhereInfo.a[], the WhereClause structure
  ** and the WhereMaskSet structure. Since WhereClause contains an 8-byte
  ** field (type Bitmask) it must be aligned on an 8-byte boundary on
  ** some architectures. Hence the ROUND8() below.
  */
  db = pParse->db;
  nByteWInfo = ROUND8(sizeof(WhereInfo)+(nTabList-1)*sizeof(WhereLevel));
  pWInfo = sqlite3DbMallocZero(db, 
      nByteWInfo + 
      sizeof(WhereClause) +
      sizeof(WhereMaskSet)
  );
  if( db->mallocFailed ){
    sqlite3DbFree(db, pWInfo);
    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];

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.
  */
  initMaskSet(pMaskSet);
  whereClauseInit(pWC, pParse, pMaskSet);
  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;
  }

  /* Assign a bit from the bitmask to every term in the FROM clause.
  **
  ** When assigning bitmask values to FROM clause cursors, it must be
  ** the case that if X is the bitmask for the N-th FROM clause term then
  ** the bitmask for all FROM clause terms to the left of the N-th term
  ** is (X-1).   An expression from the ON clause of a LEFT JOIN can use
  ** its Expr.iRightJoinTable value to find the bitmask of the right table
  ** of the join.  Subtracting one from the right table bitmask gives a
  ** bitmask for all tables to the left of the join.  Knowing the bitmask
  ** for all tables to the left of a left join is important.  Ticket #3015.
  **
  ** Configure the WhereClause.vmask variable so that bits that correspond
  ** to virtual table cursors are set. This is used to selectively disable 
  ** the OR-to-IN transformation in exprAnalyzeOrTerm(). It is not helpful 
  ** 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;
  }

  /* Chose the best index to use for each table in the FROM clause.
  **
  ** This loop fills in the following fields:
  **
  **   pWInfo->a[].pIdx      The index to use for this level of the loop.
  **   pWInfo->a[].wsFlags   WHERE_xxx flags associated with pIdx
  **   pWInfo->a[].nEq       The number of == and IN constraints
  **   pWInfo->a[].iFrom     Which term of the FROM clause is being coded
  **   pWInfo->a[].iTabCur   The VDBE cursor for the database table
  **   pWInfo->a[].iIdxCur   The VDBE cursor for the index
  **   pWInfo->a[].pTerm     When wsFlags==WO_OR, the OR-clause term
  **
  ** This loop also figures out the nesting order of tables in the FROM
  ** clause.
  */
  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
    ** to choose from.  The first test looks for an "optimal" scan.  In
    ** this context an optimal scan is one that uses the same strategy
    ** for the given FROM clause entry as would be selected if the entry
    ** were used as the innermost nested loop.  In other words, a table
    ** is chosen such that the cost of running that table cannot be reduced
    ** by waiting for other tables to run first.  This "optimal" test works
    ** by first assuming that the FROM clause is on the inner loop and finding
    ** its query plan, then checking to see if that query plan uses any
    ** other FROM clause terms that are 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.  
    **
    ** The second loop iteration is only performed if no optimal scan
    ** strategies were found by the first iteration. This second iteration
    ** is used to search for the lowest cost scan overall.
    **
    ** Previous versions of SQLite performed only the second iteration -
    ** the next outermost loop was always that with the lowest overall
    ** cost. However, this meant that SQLite could select the wrong plan
    ** for scripts such as the following:
    **   
    **   CREATE TABLE t1(a, b); 
    **   CREATE TABLE t2(c, d);
    **   SELECT * FROM t2, t1 WHERE t2.rowid = t1.a;
    **
    ** The best strategy is to iterate through table t1 first. However it
    ** is not possible to determine this with a simple greedy algorithm.
    ** Since the cost of a linear scan through table t2 is the same 
    ** as the cost of a linear scan through table t1, a simple greedy 
    ** algorithm may choose to use t2 for the outer loop, which is a much
    ** costlier approach.
    */
    nUnconstrained = 0;
    notIndexed = 0;
    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 *pOrderBy;  /* ORDER BY 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);
        pOrderBy = ((i==0 && ppOrderBy )?*ppOrderBy: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, pOrderBy,
                           &sCost, pp);
        }else 
#endif
        {
          bestBtreeIndex(pParse, pWC, pTabItem, mask, notReady, pOrderBy,
                         &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
        **       that a best-so-far is always selected even if an impossible
        **       combination of INDEXED BY clauses are given.  The error
        **       will be detected and relayed back to the application later.
        **       The NEVER() comes about because rule (2) above prevents
        **       An indexable full-table-scan from reaching rule (3).
        **
        **   (4) The plan cost must be lower than prior plans 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 ){
      *ppOrderBy = 0;
    }
    andFlags &= bestPlan.plan.wsFlags;
    pLevel->plan = bestPlan.plan;
    testcase( bestPlan.plan.wsFlags & WHERE_INDEXED );
    testcase( bestPlan.plan.wsFlags & WHERE_TEMP_INDEX );
    if( bestPlan.plan.wsFlags & (WHERE_INDEXED|WHERE_TEMP_INDEX) ){
      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
    ** used for the scan. If not, then query compilation has failed.
    ** Return an error.
    */
    pIdx = pTabList->a[bestJ].pIndex;
    if( pIdx ){
      if( (bestPlan.plan.wsFlags & WHERE_INDEXED)==0 ){
        sqlite3ErrorMsg(pParse, "cannot use index: %s", pIdx->zName);
        goto whereBeginError;
      }else{
        /* If an INDEXED BY clause is used, the bestIndex() function is
        ** guaranteed to find the index specified in the INDEXED BY clause
        ** if it find an index at all. */
        assert( bestPlan.plan.u.pIdx==pIdx );
      }
    }
  }
  WHERETRACE(("*** Optimizer Finished ***\n"));
  if( pParse->nErr || db->mallocFailed ){
    goto whereBeginError;
  }

  /* If the total query only selects a single row, then the ORDER BY
  ** clause is irrelevant.
  */
  if( (andFlags & WHERE_UNIQUE)!=0 && ppOrderBy ){
    *ppOrderBy = 0;
  }

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

  /* 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 ){
      /* Do nothing */
    }else
#ifndef SQLITE_OMIT_VIRTUALTABLE
    if( (pLevel->plan.wsFlags & WHERE_VIRTUALTABLE)!=0 ){
      const char *pVTab = (const char *)sqlite3GetVTable(db, pTab);
      int iCur = pTabItem->iCursor;
      sqlite3VdbeAddOp4(v, OP_VOpen, iCur, 0, 0, pVTab, P4_VTAB);
    }else
#endif
    if( (pLevel->plan.wsFlags & WHERE_IDX_ONLY)==0
         && (wctrlFlags & WHERE_OMIT_OPEN)==0 ){
      int op = pWInfo->okOnePass ? OP_OpenWrite : OP_OpenRead;
      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, op);
      testcase( pTab->nCol==BMS-1 );
      testcase( pTab->nCol==BMS );
      if( !pWInfo->okOnePass && pTab->nCol<BMS ){
        Bitmask b = pTabItem->colUsed;
        int n = 0;
        for(; b; b=b>>1, n++){}
        sqlite3VdbeChangeP4(v, sqlite3VdbeCurrentAddr(v)-1, 
                            SQLITE_INT_TO_PTR(n), P4_INT32);
        assert( n<=pTab->nCol );
      }
    }else{
      sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);
    }
#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
    if( (pLevel->plan.wsFlags & WHERE_TEMP_INDEX)!=0 ){
      constructAutomaticIndex(pParse, 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 iIdxCur = pLevel->iIdxCur;
      assert( pIx->pSchema==pTab->pSchema );
      assert( iIdxCur>=0 );
      sqlite3VdbeAddOp4(v, OP_OpenRead, iIdxCur, 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;
    pLevel = &pWInfo->a[i];
    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( pLevel->plan.wsFlags & WHERE_IDX_ONLY ){
        memcpy(&sqlite3_query_plan[nQPlan], "{}", 2);
        nQPlan += 2;
      }else{
        memcpy(&sqlite3_query_plan[nQPlan], z, n);
        nQPlan += n;
      }
      sqlite3_query_plan[nQPlan++] = ' ';
    }
    testcase( pLevel->plan.wsFlags & WHERE_ROWID_EQ );
    testcase( pLevel->plan.wsFlags & WHERE_ROWID_RANGE );
    if( pLevel->plan.wsFlags & (WHERE_ROWID_EQ|WHERE_ROWID_RANGE) ){
      memcpy(&sqlite3_query_plan[nQPlan], "* ", 2);
      nQPlan += 2;
    }else if( (pLevel->plan.wsFlags & WHERE_INDEXED)!=0 ){
      n = sqlite3Strlen30(pLevel->plan.u.pIdx->zName);
      if( n+nQPlan < sizeof(sqlite3_query_plan)-2 ){
        memcpy(&sqlite3_query_plan[nQPlan], pLevel->plan.u.pIdx->zName, n);
        nQPlan += n;
        sqlite3_query_plan[nQPlan++] = ' ';
      }
    }else{
      memcpy(&sqlite3_query_plan[nQPlan], "{} ", 3);
      nQPlan += 3;
    }
  }
  while( nQPlan>0 && sqlite3_query_plan[nQPlan-1]==' ' ){
    sqlite3_query_plan[--nQPlan] = 0;
  }
  sqlite3_query_plan[nQPlan] = 0;
  nQPlan = 0;
#endif /* SQLITE_TEST // Testing and debugging use only */

  /* Record the continuation address in the WhereInfo structure.  Then
  ** clean up and return.
  */
  return pWInfo;

  /* Jump here if malloc fails */
whereBeginError:
  if( pWInfo ){
    pParse->nQueryLoop = pWInfo->savedNQueryLoop;
    whereInfoFree(db, pWInfo);
  }
  return 0;
}

/*
** Generate the end of the WHERE loop.  See comments on 
** sqlite3WhereBegin() for additional information.
*/
void sqlite3WhereEnd(WhereInfo *pWInfo){
  Parse *pParse = pWInfo->pParse;
  Vdbe *v = pParse->pVdbe;
  int i;
  WhereLevel *pLevel;
  SrcList *pTabList = pWInfo->pTabList;
  sqlite3 *db = pParse->db;

  /* Generate loop termination code.
  */
  sqlite3ExprCacheClear(pParse);
  for(i=pWInfo->nLevel-1; i>=0; i--){
    pLevel = &pWInfo->a[i];
    sqlite3VdbeResolveLabel(v, pLevel->addrCont);
    if( pLevel->op!=OP_Noop ){
      sqlite3VdbeAddOp2(v, pLevel->op, pLevel->p1, pLevel->p2);
      sqlite3VdbeChangeP5(v, pLevel->p5);
    }
    if( pLevel->plan.wsFlags & WHERE_IN_ABLE && pLevel->u.in.nIn>0 ){
      struct InLoop *pIn;
      int j;
      sqlite3VdbeResolveLabel(v, pLevel->addrNxt);
      for(j=pLevel->u.in.nIn, pIn=&pLevel->u.in.aInLoop[j-1]; j>0; j--, pIn--){
        sqlite3VdbeJumpHere(v, pIn->addrInTop+1);
        sqlite3VdbeAddOp2(v, OP_Next, pIn->iCur, pIn->addrInTop);
        sqlite3VdbeJumpHere(v, pIn->addrInTop-1);
      }
      sqlite3DbFree(db, pLevel->u.in.aInLoop);
    }
    sqlite3VdbeResolveLabel(v, pLevel->addrBrk);
    if( pLevel->iLeftJoin ){
      int addr;
      addr = sqlite3VdbeAddOp1(v, OP_IfPos, pLevel->iLeftJoin);
      assert( (pLevel->plan.wsFlags & WHERE_IDX_ONLY)==0
           || (pLevel->plan.wsFlags & WHERE_INDEXED)!=0 );
      if( (pLevel->plan.wsFlags & WHERE_IDX_ONLY)==0 ){
        sqlite3VdbeAddOp1(v, OP_NullRow, pTabList->a[i].iCursor);
      }
      if( pLevel->iIdxCur>=0 ){
        sqlite3VdbeAddOp1(v, OP_NullRow, pLevel->iIdxCur);
      }
      if( pLevel->op==OP_Return ){
        sqlite3VdbeAddOp2(v, OP_Gosub, pLevel->p1, pLevel->addrFirst);
      }else{
        sqlite3VdbeAddOp2(v, OP_Goto, 0, pLevel->addrFirst);
      }
      sqlite3VdbeJumpHere(v, addr);
    }
  }

  /* The "break" point is here, just past the end of the outer loop.
  ** Set it.
  */
  sqlite3VdbeResolveLabel(v, pWInfo->iBreak);

  /* Close all of the cursors that were opened by sqlite3WhereBegin.
  */
  assert( pWInfo->nLevel==1 || pWInfo->nLevel==pTabList->nSrc );
  for(i=0, pLevel=pWInfo->a; i<pWInfo->nLevel; i++, pLevel++){
    struct SrcList_item *pTabItem = &pTabList->a[pLevel->iFrom];
    Table *pTab = pTabItem->pTab;
    assert( pTab!=0 );
    if( (pTab->tabFlags & TF_Ephemeral)==0
     && pTab->pSelect==0
     && (pWInfo->wctrlFlags & WHERE_OMIT_CLOSE)==0
    ){
      int ws = pLevel->plan.wsFlags;
      if( !pWInfo->okOnePass && (ws & WHERE_IDX_ONLY)==0 ){
        sqlite3VdbeAddOp1(v, OP_Close, pTabItem->iCursor);
      }
      if( (ws & WHERE_INDEXED)!=0 && (ws & WHERE_TEMP_INDEX)==0 ){
        sqlite3VdbeAddOp1(v, OP_Close, pLevel->iIdxCur);
      }
    }

    /* If this scan uses an index, make code substitutions to read data
    ** from the index in preference to the table. Sometimes, this means
    ** the table need never be read from. This is a performance boost,
    ** as the vdbe level waits until the table is read before actually
    ** seeking the table cursor to the record corresponding to the current
    ** position in the index.
    ** 
    ** Calls to the code generator in between sqlite3WhereBegin and
    ** sqlite3WhereEnd will have created code that references the table
    ** directly.  This loop scans all that code looking for opcodes
    ** that reference the table and converts them into opcodes that
    ** reference the index.
    */
    if( (pLevel->plan.wsFlags & WHERE_INDEXED)!=0 && !db->mallocFailed){
      int k, j, last;
      VdbeOp *pOp;
      Index *pIdx = pLevel->plan.u.pIdx;

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

  /* Final cleanup
  */
  pParse->nQueryLoop = pWInfo->savedNQueryLoop;
  whereInfoFree(db, pWInfo);
  return;
}
