root/ext/pdo_sqlite/sqlite/src/where.c

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DEFINITIONS

This source file includes following definitions.
  1. whereClauseInit
  2. whereClauseClear
  3. whereClauseInsert
  4. whereSplit
  5. getMask
  6. createMask
  7. exprTableUsage
  8. exprListTableUsage
  9. exprSelectTableUsage
  10. allowedOp
  11. exprCommute
  12. operatorMask
  13. findTerm
  14. exprAnalyzeAll
  15. isLikeOrGlob
  16. isMatchOfColumn
  17. transferJoinMarkings
  18. orTermIsOptCandidate
  19. orTermHasOkDuplicate
  20. exprAnalyze
  21. referencesOtherTables
  22. isSortingIndex
  23. sortableByRowid
  24. estLog
  25. TRACE_IDX_INPUTS
  26. TRACE_IDX_OUTPUTS
  27. bestVirtualIndex
  28. bestIndex
  29. disableTerm
  30. buildIndexProbe
  31. codeEqualityTerm
  32. codeAllEqualityTerms
  33. whereInfoFree
  34. sqlite3WhereBegin
  35. sqlite3WhereEnd

/*
** 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 reponsible 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".
**
** $Id$
*/
#include "sqliteInt.h"

/*
** The number of bits in a Bitmask.  "BMS" means "BitMask Size".
*/
#define BMS  (sizeof(Bitmask)*8)

/*
** Trace output macros
*/
#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)
int sqlite3_where_trace = 0;
# define WHERETRACE(X)  if(sqlite3_where_trace) sqlite3DebugPrintf X
#else
# define WHERETRACE(X)
#endif

/* Forward reference
*/
typedef struct WhereClause WhereClause;
typedef struct ExprMaskSet ExprMaskSet;

/*
** 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 an AND operator.
**
** 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.leftColumn record the
** cursor number and column number for X.  WhereTerm.operator 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.
**
** prereqRight and prereqAll record sets of cursor numbers,
** but they do so indirectly.  A single ExprMaskSet 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 ExprMaskSet
** 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.
*/
typedef struct WhereTerm WhereTerm;
struct WhereTerm {
  Expr *pExpr;            /* Pointer to the subexpression */
  i16 iParent;            /* Disable pWC->a[iParent] when this term disabled */
  i16 leftCursor;         /* Cursor number of X in "X <op> <expr>" */
  i16 leftColumn;         /* Column number of X in "X <op> <expr>" */
  u16 eOperator;          /* A WO_xx value describing <op> */
  u8 flags;               /* 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 pRight */
  Bitmask prereqAll;      /* Bitmask of tables referenced by p */
};

/*
** Allowed values of WhereTerm.flags
*/
#define TERM_DYNAMIC    0x01   /* Need to call sqlite3ExprDelete(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_OR_OK      0x10   /* Used during OR-clause processing */

/*
** 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 */
  ExprMaskSet *pMaskSet;   /* Mapping of table indices to bitmasks */
  int nTerm;               /* Number of terms */
  int nSlot;               /* Number of entries in a[] */
  WhereTerm *a;            /* Each a[] describes a term of the WHERE cluase */
  WhereTerm aStatic[10];   /* Initial static space for a[] */
};

/*
** 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 ExprMaskSet.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  ExprMaskSet 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 ExprMaskSet {
  int n;                        /* Number of assigned cursor values */
  int ix[sizeof(Bitmask)*8];    /* Cursor assigned to each bit */
};


/*
** 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     1
#define WO_EQ     2
#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  64
#define WO_ISNULL 128

/*
** Value for flags returned by bestIndex().  
**
** The least significant byte is reserved as a mask for WO_ values above.
** The WhereLevel.flags field is usually set to WO_IN|WO_EQ|WO_ISNULL.
** But if the table is the right table of a left join, WhereLevel.flags
** is set to WO_IN|WO_EQ.  The WhereLevel.flags 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     0x000100   /* rowid=EXPR or rowid IN (...) */
#define WHERE_ROWID_RANGE  0x000200   /* rowid<EXPR and/or rowid>EXPR */
#define WHERE_COLUMN_EQ    0x001000   /* x=EXPR or x IN (...) */
#define WHERE_COLUMN_RANGE 0x002000   /* x<EXPR and/or x>EXPR */
#define WHERE_COLUMN_IN    0x004000   /* x IN (...) */
#define WHERE_TOP_LIMIT    0x010000   /* x<EXPR or x<=EXPR constraint */
#define WHERE_BTM_LIMIT    0x020000   /* x>EXPR or x>=EXPR constraint */
#define WHERE_IDX_ONLY     0x080000   /* Use index only - omit table */
#define WHERE_ORDERBY      0x100000   /* Output will appear in correct order */
#define WHERE_REVERSE      0x200000   /* Scan in reverse order */
#define WHERE_UNIQUE       0x400000   /* Selects no more than one row */
#define WHERE_VIRTUALTABLE 0x800000   /* Use virtual-table processing */

/*
** Initialize a preallocated WhereClause structure.
*/
static void whereClauseInit(
  WhereClause *pWC,        /* The WhereClause to be initialized */
  Parse *pParse,           /* The parsing context */
  ExprMaskSet *pMaskSet    /* Mapping from table indices to bitmasks */
){
  pWC->pParse = pParse;
  pWC->pMaskSet = pMaskSet;
  pWC->nTerm = 0;
  pWC->nSlot = ArraySize(pWC->aStatic);
  pWC->a = pWC->aStatic;
}

/*
** 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;
  for(i=pWC->nTerm-1, a=pWC->a; i>=0; i--, a++){
    if( a->flags & TERM_DYNAMIC ){
      sqlite3ExprDelete(a->pExpr);
    }
  }
  if( pWC->a!=pWC->aStatic ){
    sqliteFree(pWC->a);
  }
}

/*
** Add a new entries to the WhereClause structure.  Increase the allocated
** space as necessary.
**
** If the flags argument includes TERM_DYNAMIC, then responsibility
** for freeing the expression p is assumed by the WhereClause object.
**
** WARNING:  This routine might reallocate the space used to store
** WhereTerms.  All pointers to WhereTerms should be invalided after
** calling this routine.  Such pointers may be reinitialized by referencing
** the pWC->a[] array.
*/
static int whereClauseInsert(WhereClause *pWC, Expr *p, int flags){
  WhereTerm *pTerm;
  int idx;
  if( pWC->nTerm>=pWC->nSlot ){
    WhereTerm *pOld = pWC->a;
    pWC->a = sqliteMalloc( sizeof(pWC->a[0])*pWC->nSlot*2 );
    if( pWC->a==0 ){
      if( flags & TERM_DYNAMIC ){
        sqlite3ExprDelete(p);
      }
      return 0;
    }
    memcpy(pWC->a, pOld, sizeof(pWC->a[0])*pWC->nTerm);
    if( pOld!=pWC->aStatic ){
      sqliteFree(pOld);
    }
    pWC->nSlot *= 2;
  }
  pTerm = &pWC->a[idx = pWC->nTerm];
  pWC->nTerm++;
  pTerm->pExpr = p;
  pTerm->flags = flags;
  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.  This array grows as needed to contain
** all terms of the WHERE clause.
*/
static void whereSplit(WhereClause *pWC, Expr *pExpr, int 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
*/
#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(ExprMaskSet *pMaskSet, int iCursor){
  int i;
  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(ExprMaskSet *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 sqlite3ExprResolveNames() on the expression.  See
** the header comment on that routine for additional information.
** The sqlite3ExprResolveNames() 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(ExprMaskSet*, ExprList*);
static Bitmask exprSelectTableUsage(ExprMaskSet*, Select*);
static Bitmask exprTableUsage(ExprMaskSet *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);
  mask |= exprListTableUsage(pMaskSet, p->pList);
  mask |= exprSelectTableUsage(pMaskSet, p->pSelect);
  return mask;
}
static Bitmask exprListTableUsage(ExprMaskSet *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(ExprMaskSet *pMaskSet, Select *pS){
  Bitmask mask;
  if( pS==0 ){
    mask = 0;
  }else{
    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);
  }
  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".
*/
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 T.
*/
#define SWAP(TYPE,A,B) {TYPE t=A; A=B; B=t;}

/*
** Commute a comparision operator.  Expressions of the form "X op Y"
** are converted into "Y op X".
*/
static void exprCommute(Expr *pExpr){
  assert( allowedOp(pExpr->op) && pExpr->op!=TK_IN );
  SWAP(CollSeq*,pExpr->pRight->pColl,pExpr->pLeft->pColl);
  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 int operatorMask(int op){
  int c;
  assert( allowedOp(op) );
  if( op==TK_IN ){
    c = WO_IN;
  }else if( op==TK_ISNULL ){
    c = WO_ISNULL;
  }else{
    c = 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 */
  u16 op,               /* Mask of WO_xx values describing operator */
  Index *pIdx           /* Must be compatible with this index, if not NULL */
){
  WhereTerm *pTerm;
  int k;
  for(pTerm=pWC->a, k=pWC->nTerm; k; k--, pTerm++){
    if( pTerm->leftCursor==iCur
       && (pTerm->prereqRight & notReady)==0
       && pTerm->leftColumn==iColumn
       && (pTerm->eOperator & op)!=0
    ){
      if( iCur>=0 && 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;
        pColl = sqlite3ExprCollSeq(pParse, pX->pLeft);
        if( !pColl ){
          if( pX->pRight ){
            pColl = sqlite3ExprCollSeq(pParse, pX->pRight);
          }
          if( !pColl ){
            pColl = pParse->db->pDfltColl;
          }
        }
        for(j=0; j<pIdx->nColumn && pIdx->aiColumn[j]!=iColumn; j++){}
        assert( j<pIdx->nColumn );
        if( 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(
  sqlite3 *db,      /* The database */
  Expr *pExpr,      /* Test this expression */
  int *pnPattern,   /* Number of non-wildcard prefix characters */
  int *pisComplete  /* True if the only wildcard is % in the last character */
){
  const char *z;
  Expr *pRight, *pLeft;
  ExprList *pList;
  int c, cnt;
  int noCase;
  char wc[3];
  CollSeq *pColl;

  if( !sqlite3IsLikeFunction(db, pExpr, &noCase, wc) ){
    return 0;
  }
  pList = pExpr->pList;
  pRight = pList->a[0].pExpr;
  if( pRight->op!=TK_STRING ){
    return 0;
  }
  pLeft = pList->a[1].pExpr;
  if( pLeft->op!=TK_COLUMN ){
    return 0;
  }
  pColl = pLeft->pColl;
  if( pColl==0 ){
    /* TODO: Coverage testing doesn't get this case. Is it actually possible
    ** for an expression of type TK_COLUMN to not have an assigned collation 
    ** sequence at this point?
    */
    pColl = db->pDfltColl;
  }
  if( (pColl->type!=SQLITE_COLL_BINARY || noCase) &&
      (pColl->type!=SQLITE_COLL_NOCASE || !noCase) ){
    return 0;
  }
  sqlite3DequoteExpr(pRight);
  z = (char *)pRight->token.z;
  for(cnt=0; (c=z[cnt])!=0 && c!=wc[0] && c!=wc[1] && c!=wc[2]; cnt++){}
  if( cnt==0 || 255==(u8)z[cnt] ){
    return 0;
  }
  *pisComplete = z[cnt]==wc[0] && z[cnt+1]==0;
  *pnPattern = cnt;
  return 1;
}
#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( pExpr->token.n!=5 ||
       sqlite3StrNICmp((const char*)pExpr->token.z,"match",5)!=0 ){
    return 0;
  }
  pList = pExpr->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)
/*
** Return TRUE if the given term of an OR clause can be converted
** into an IN clause.  The iCursor and iColumn define the left-hand
** side of the IN clause.
**
** The context is that we have multiple OR-connected equality terms
** like this:
**
**           a=<expr1> OR  a=<expr2> OR b=<expr3>  OR ...
**
** The pOrTerm input to this routine corresponds to a single term of
** this OR clause.  In order for the term to be a condidate for
** conversion to an IN operator, the following must be true:
**
**     *  The left-hand side of the term must be the column which
**        is identified by iCursor and iColumn.
**
**     *  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)
**
** If both of these conditions are true, then return true.  Otherwise
** return false.
*/
static int orTermIsOptCandidate(WhereTerm *pOrTerm, int iCursor, int iColumn){
  int affLeft, affRight;
  assert( pOrTerm->eOperator==WO_EQ );
  if( pOrTerm->leftCursor!=iCursor ){
    return 0;
  }
  if( pOrTerm->leftColumn!=iColumn ){
    return 0;
  }
  affRight = sqlite3ExprAffinity(pOrTerm->pExpr->pRight);
  if( affRight==0 ){
    return 1;
  }
  affLeft = sqlite3ExprAffinity(pOrTerm->pExpr->pLeft);
  if( affRight!=affLeft ){
    return 0;
  }
  return 1;
}

/*
** Return true if the given term of an OR clause can be ignored during
** a check to make sure all OR terms are candidates for optimization.
** In other words, return true if a call to the orTermIsOptCandidate()
** above returned false but it is not necessary to disqualify the
** optimization.
**
** Suppose the original OR phrase was this:
**
**           a=4  OR  a=11  OR  a=b
**
** During analysis, the third term gets flipped around and duplicate
** so that we are left with this:
**
**           a=4  OR  a=11  OR  a=b  OR  b=a
**
** Since the last two terms are duplicates, only one of them
** has to qualify in order for the whole phrase to qualify.  When
** this routine is called, we know that pOrTerm did not qualify.
** This routine merely checks to see if pOrTerm has a duplicate that
** might qualify.  If there is a duplicate that has not yet been
** disqualified, then return true.  If there are no duplicates, or
** the duplicate has also been disqualifed, return false.
*/
static int orTermHasOkDuplicate(WhereClause *pOr, WhereTerm *pOrTerm){
  if( pOrTerm->flags & TERM_COPIED ){
    /* This is the original term.  The duplicate is to the left had
    ** has not yet been analyzed and thus has not yet been disqualified. */
    return 1;
  }
  if( (pOrTerm->flags & TERM_VIRTUAL)!=0
     && (pOr->a[pOrTerm->iParent].flags & TERM_OR_OK)!=0 ){
    /* This is a duplicate term.  The original qualified so this one
    ** does not have to. */
    return 1;
  }
  /* This is either a singleton term or else it is a duplicate for
  ** which the original did not qualify.  Either way we are done for. */
  return 0;
}
#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 expression of the form
** "Y <op> X" is added to the WHERE clause and analyzed separately.
*/
static void exprAnalyze(
  SrcList *pSrc,            /* the FROM clause */
  WhereClause *pWC,         /* the WHERE clause */
  int idxTerm               /* Index of the term to be analyzed */
){
  WhereTerm *pTerm = &pWC->a[idxTerm];
  ExprMaskSet *pMaskSet = pWC->pMaskSet;
  Expr *pExpr = pTerm->pExpr;
  Bitmask prereqLeft;
  Bitmask prereqAll;
  int nPattern;
  int isComplete;
  int op;

  if( sqlite3MallocFailed() ) return;
  prereqLeft = exprTableUsage(pMaskSet, pExpr->pLeft);
  op = pExpr->op;
  if( op==TK_IN ){
    assert( pExpr->pRight==0 );
    pTerm->prereqRight = exprListTableUsage(pMaskSet, pExpr->pList)
                          | exprSelectTableUsage(pMaskSet, pExpr->pSelect);
  }else if( op==TK_ISNULL ){
    pTerm->prereqRight = 0;
  }else{
    pTerm->prereqRight = exprTableUsage(pMaskSet, pExpr->pRight);
  }
  prereqAll = exprTableUsage(pMaskSet, pExpr);
  if( ExprHasProperty(pExpr, EP_FromJoin) ){
    prereqAll |= getMask(pMaskSet, pExpr->iRightJoinTable);
  }
  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->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(pExpr);
        if( sqlite3MallocFailed() ){
          sqlite3ExprDelete(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->flags |= TERM_COPIED;
      }else{
        pDup = pExpr;
        pNew = pTerm;
      }
      exprCommute(pDup);
      pLeft = pDup->pLeft;
      pNew->leftCursor = pLeft->iTable;
      pNew->leftColumn = pLeft->iColumn;
      pNew->prereqRight = prereqLeft;
      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.
  */
  else if( pExpr->op==TK_BETWEEN ){
    ExprList *pList = pExpr->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 = sqlite3Expr(ops[i], sqlite3ExprDup(pExpr->pLeft),
                             sqlite3ExprDup(pList->a[i].pExpr), 0);
      idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);
      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)
  /* Attempt to convert OR-connected terms into an IN operator so that
  ** they can make use of indices.  Example:
  **
  **      x = expr1  OR  expr2 = x  OR  x = expr3
  **
  ** is converted into
  **
  **      x IN (expr1,expr2,expr3)
  **
  ** This optimization must be omitted if OMIT_SUBQUERY is defined because
  ** the compiler for the the IN operator is part of sub-queries.
  */
  else if( pExpr->op==TK_OR ){
    int ok;
    int i, j;
    int iColumn, iCursor;
    WhereClause sOr;
    WhereTerm *pOrTerm;

    assert( (pTerm->flags & TERM_DYNAMIC)==0 );
    whereClauseInit(&sOr, pWC->pParse, pMaskSet);
    whereSplit(&sOr, pExpr, TK_OR);
    exprAnalyzeAll(pSrc, &sOr);
    assert( sOr.nTerm>=2 );
    j = 0;
    do{
      assert( j<sOr.nTerm );
      iColumn = sOr.a[j].leftColumn;
      iCursor = sOr.a[j].leftCursor;
      ok = iCursor>=0;
      for(i=sOr.nTerm-1, pOrTerm=sOr.a; i>=0 && ok; i--, pOrTerm++){
        if( pOrTerm->eOperator!=WO_EQ ){
          goto or_not_possible;
        }
        if( orTermIsOptCandidate(pOrTerm, iCursor, iColumn) ){
          pOrTerm->flags |= TERM_OR_OK;
        }else if( orTermHasOkDuplicate(&sOr, pOrTerm) ){
          pOrTerm->flags &= ~TERM_OR_OK;
        }else{
          ok = 0;
        }
      }
    }while( !ok && (sOr.a[j++].flags & TERM_COPIED)!=0 && j<2 );
    if( ok ){
      ExprList *pList = 0;
      Expr *pNew, *pDup;
      Expr *pLeft = 0;
      for(i=sOr.nTerm-1, pOrTerm=sOr.a; i>=0 && ok; i--, pOrTerm++){
        if( (pOrTerm->flags & TERM_OR_OK)==0 ) continue;
        pDup = sqlite3ExprDup(pOrTerm->pExpr->pRight);
        pList = sqlite3ExprListAppend(pList, pDup, 0);
        pLeft = pOrTerm->pExpr->pLeft;
      }
      assert( pLeft!=0 );
      pDup = sqlite3ExprDup(pLeft);
      pNew = sqlite3Expr(TK_IN, pDup, 0, 0);
      if( pNew ){
        int idxNew;
        transferJoinMarkings(pNew, pExpr);
        pNew->pList = pList;
        idxNew = whereClauseInsert(pWC, pNew, TERM_VIRTUAL|TERM_DYNAMIC);
        exprAnalyze(pSrc, pWC, idxNew);
        pTerm = &pWC->a[idxTerm];
        pWC->a[idxNew].iParent = idxTerm;
        pTerm->nChild = 1;
      }else{
        sqlite3ExprListDelete(pList);
      }
    }
or_not_possible:
    whereClauseClear(&sOr);
  }
#endif /* SQLITE_OMIT_OR_OPTIMIZATION */

#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION
  /* Add constraints to reduce the search space on a LIKE or GLOB
  ** operator.
  */
  if( isLikeOrGlob(pWC->pParse->db, pExpr, &nPattern, &isComplete) ){
    Expr *pLeft, *pRight;
    Expr *pStr1, *pStr2;
    Expr *pNewExpr1, *pNewExpr2;
    int idxNew1, idxNew2;

    pLeft = pExpr->pList->a[1].pExpr;
    pRight = pExpr->pList->a[0].pExpr;
    pStr1 = sqlite3Expr(TK_STRING, 0, 0, 0);
    if( pStr1 ){
      sqlite3TokenCopy(&pStr1->token, &pRight->token);
      pStr1->token.n = nPattern;
    }
    pStr2 = sqlite3ExprDup(pStr1);
    if( pStr2 ){
      assert( pStr2->token.dyn );
      ++*(u8*)&pStr2->token.z[nPattern-1];
    }
    pNewExpr1 = sqlite3Expr(TK_GE, sqlite3ExprDup(pLeft), pStr1, 0);
    idxNew1 = whereClauseInsert(pWC, pNewExpr1, TERM_VIRTUAL|TERM_DYNAMIC);
    exprAnalyze(pSrc, pWC, idxNew1);
    pNewExpr2 = sqlite3Expr(TK_LT, sqlite3ExprDup(pLeft), pStr2, 0);
    idxNew2 = whereClauseInsert(pWC, pNewExpr2, TERM_VIRTUAL|TERM_DYNAMIC);
    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->pList->a[0].pExpr;
    pLeft = pExpr->pList->a[1].pExpr;
    prereqExpr = exprTableUsage(pMaskSet, pRight);
    prereqColumn = exprTableUsage(pMaskSet, pLeft);
    if( (prereqExpr & prereqColumn)==0 ){
      Expr *pNewExpr;
      pNewExpr = sqlite3Expr(TK_MATCH, 0, sqlite3ExprDup(pRight), 0);
      idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);
      pNewTerm = &pWC->a[idxNew];
      pNewTerm->prereqRight = prereqExpr;
      pNewTerm->leftCursor = pLeft->iTable;
      pNewTerm->leftColumn = pLeft->iColumn;
      pNewTerm->eOperator = WO_MATCH;
      pNewTerm->iParent = idxTerm;
      pTerm = &pWC->a[idxTerm];
      pTerm->nChild = 1;
      pTerm->flags |= TERM_COPIED;
      pNewTerm->prereqAll = pTerm->prereqAll;
    }
  }
#endif /* SQLITE_OMIT_VIRTUALTABLE */
}

/*
** 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 */
  ExprMaskSet *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 */
  ExprMaskSet *pMaskSet,  /* Mapping from table indices 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 *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 );

  /* 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( 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 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 );
    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
      && !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. */
    return 1;
  }
  return 0;
}

/*
** Check table to see if the ORDER BY clause in pOrderBy can be satisfied
** by sorting in order of ROWID.  Return true if so and set *pbRev to be
** true for reverse ROWID and false for forward ROWID order.
*/
static int sortableByRowid(
  int base,               /* Cursor number for table to be sorted */
  ExprList *pOrderBy,     /* The ORDER BY clause */
  ExprMaskSet *pMaskSet,  /* Mapping from tables to bitmaps */
  int *pbRev              /* Set to 1 if ORDER BY is DESC */
){
  Expr *p;

  assert( pOrderBy!=0 );
  assert( pOrderBy->nExpr>0 );
  p = pOrderBy->a[0].pExpr;
  if( p->op==TK_COLUMN && p->iTable==base && p->iColumn==-1
    && !referencesOtherTables(pOrderBy, pMaskSet, 1, base) ){
    *pbRev = pOrderBy->a[0].sortOrder;
    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 operatings 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( !sqlite3_where_trace ) 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( !sqlite3_where_trace ) 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

#ifndef SQLITE_OMIT_VIRTUALTABLE
/*
** 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 double 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 that are not available */
  ExprList *pOrderBy,            /* The order by clause */
  int orderByUsable,             /* True if we can potential sort */
  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_orderby *pIdxOrderBy;
  struct sqlite3_index_constraint_usage *pUsage;
  WhereTerm *pTerm;
  int i, j;
  int nOrderBy;
  int rc;

  /* If the sqlite3_index_info structure has not been previously
  ** allocated and initialized for this virtual table, then allocate
  ** and initialize it now
  */
  pIdxInfo = *ppIdxInfo;
  if( pIdxInfo==0 ){
    WhereTerm *pTerm;
    int nTerm;
    WHERETRACE(("Recomputing index info for %s...\n", 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;
      if( pTerm->eOperator==WO_IN ) 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 = sqliteMalloc( sizeof(*pIdxInfo)
                             + (sizeof(*pIdxCons) + sizeof(*pUsage))*nTerm
                             + sizeof(*pIdxOrderBy)*nOrderBy );
    if( pIdxInfo==0 ){
      sqlite3ErrorMsg(pParse, "out of memory");
      return 0.0;
    }
    *ppIdxInfo = pIdxInfo;

    /* 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;
      if( pTerm->eOperator==WO_IN ) continue;
      pIdxCons[j].iColumn = pTerm->leftColumn;
      pIdxCons[j].iTermOffset = i;
      pIdxCons[j].op = 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;
    }
  }

  /* 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( pTab->pVtab );
#if 0
  if( pTab->pVtab==0 ){
    sqlite3ErrorMsg(pParse, "undefined module %s for table %s",
        pTab->azModuleArg[0], pTab->zName);
    return 0.0;
  }
#endif

  /* 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;
  }
  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;
  pIdxInfo->estimatedCost = SQLITE_BIG_DBL / 2.0;
  nOrderBy = pIdxInfo->nOrderBy;
  if( pIdxInfo->nOrderBy && !orderByUsable ){
    *(int*)&pIdxInfo->nOrderBy = 0;
  }

  sqlite3SafetyOff(pParse->db);
  WHERETRACE(("xBestIndex for %s\n", pTab->zName));
  TRACE_IDX_INPUTS(pIdxInfo);
  rc = pTab->pVtab->pModule->xBestIndex(pTab->pVtab, pIdxInfo);
  TRACE_IDX_OUTPUTS(pIdxInfo);
  if( rc!=SQLITE_OK ){
    if( rc==SQLITE_NOMEM ){
      sqlite3FailedMalloc();
    }else {
      sqlite3ErrorMsg(pParse, "%s", sqlite3ErrStr(rc));
    }
    sqlite3SafetyOn(pParse->db);
  }else{
    rc = sqlite3SafetyOn(pParse->db);
  }
  *(int*)&pIdxInfo->nOrderBy = nOrderBy;

  return pIdxInfo->estimatedCost;
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

/*
** Find the best index for accessing a particular table.  Return a pointer
** to the index, flags that describe how the index should be used, the
** number of equality constraints, and the "cost" for this index.
**
** The lowest cost index wins.  The cost is an estimate of the amount of
** CPU and disk I/O need to process the request using the selected index.
** 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.
**
*/
static double 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 that are not available */
  ExprList *pOrderBy,         /* The order by clause */
  Index **ppIndex,            /* Make *ppIndex point to the best index */
  int *pFlags,                /* Put flags describing this choice in *pFlags */
  int *pnEq                   /* Put the number of == or IN constraints here */
){
  WhereTerm *pTerm;
  Index *bestIdx = 0;         /* Index that gives the lowest cost */
  double lowestCost;          /* The cost of using bestIdx */
  int bestFlags = 0;          /* Flags associated with bestIdx */
  int bestNEq = 0;            /* Best value for nEq */
  int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  Index *pProbe;              /* An index we are evaluating */
  int rev;                    /* True to scan in reverse order */
  int flags;                  /* Flags associated with pProbe */
  int nEq;                    /* Number of == or IN constraints */
  int eqTermMask;             /* Mask of valid equality operators */
  double cost;                /* Cost of using pProbe */

  WHERETRACE(("bestIndex: tbl=%s notReady=%x\n", pSrc->pTab->zName, notReady));
  lowestCost = SQLITE_BIG_DBL;
  pProbe = pSrc->pTab->pIndex;

  /* If the table has no indices and there are no terms in the where
  ** clause that refer to the ROWID, then we will never be able to do
  ** anything other than a full table scan on this table.  We might as
  ** well put it first in the join order.  That way, perhaps it can be
  ** referenced by other tables in the join.
  */
  if( pProbe==0 &&
     findTerm(pWC, iCur, -1, 0, WO_EQ|WO_IN|WO_LT|WO_LE|WO_GT|WO_GE,0)==0 &&
     (pOrderBy==0 || !sortableByRowid(iCur, pOrderBy, pWC->pMaskSet, &rev)) ){
    *pFlags = 0;
    *ppIndex = 0;
    *pnEq = 0;
    return 0.0;
  }

  /* Check for a rowid=EXPR or rowid IN (...) constraints
  */
  pTerm = findTerm(pWC, iCur, -1, notReady, WO_EQ|WO_IN, 0);
  if( pTerm ){
    Expr *pExpr;
    *ppIndex = 0;
    bestFlags = WHERE_ROWID_EQ;
    if( pTerm->eOperator & WO_EQ ){
      /* Rowid== is always the best pick.  Look no further.  Because only
      ** a single row is generated, output is always in sorted order */
      *pFlags = WHERE_ROWID_EQ | WHERE_UNIQUE;
      *pnEq = 1;
      WHERETRACE(("... best is rowid\n"));
      return 0.0;
    }else if( (pExpr = pTerm->pExpr)->pList!=0 ){
      /* Rowid IN (LIST): cost is NlogN where N is the number of list
      ** elements.  */
      lowestCost = pExpr->pList->nExpr;
      lowestCost *= estLog(lowestCost);
    }else{
      /* Rowid IN (SELECT): cost is NlogN where N is the number of rows
      ** in the result of the inner select.  We have no way to estimate
      ** that value so make a wild guess. */
      lowestCost = 200;
    }
    WHERETRACE(("... rowid IN cost: %.9g\n", lowestCost));
  }

  /* Estimate the cost of a table scan.  If we do not know how many
  ** entries are in the table, use 1 million as a guess.
  */
  cost = pProbe ? pProbe->aiRowEst[0] : 1000000;
  WHERETRACE(("... table scan base cost: %.9g\n", cost));
  flags = WHERE_ROWID_RANGE;

  /* Check for constraints on a range of rowids in a table scan.
  */
  pTerm = findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE|WO_GT|WO_GE, 0);
  if( pTerm ){
    if( findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE, 0) ){
      flags |= WHERE_TOP_LIMIT;
      cost /= 3;  /* Guess that rowid<EXPR eliminates two-thirds or rows */
    }
    if( findTerm(pWC, iCur, -1, notReady, WO_GT|WO_GE, 0) ){
      flags |= WHERE_BTM_LIMIT;
      cost /= 3;  /* Guess that rowid>EXPR eliminates two-thirds of rows */
    }
    WHERETRACE(("... rowid range reduces cost to %.9g\n", cost));
  }else{
    flags = 0;
  }

  /* If the table scan does not satisfy the ORDER BY clause, increase
  ** the cost by NlogN to cover the expense of sorting. */
  if( pOrderBy ){
    if( sortableByRowid(iCur, pOrderBy, pWC->pMaskSet, &rev) ){
      flags |= WHERE_ORDERBY|WHERE_ROWID_RANGE;
      if( rev ){
        flags |= WHERE_REVERSE;
      }
    }else{
      cost += cost*estLog(cost);
      WHERETRACE(("... sorting increases cost to %.9g\n", cost));
    }
  }
  if( cost<lowestCost ){
    lowestCost = cost;
    bestFlags = flags;
  }

  /* 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)!=0 ){
    eqTermMask = WO_EQ|WO_IN;
  }else{
    eqTermMask = WO_EQ|WO_IN|WO_ISNULL;
  }

  /* Look at each index.
  */
  for(; pProbe; pProbe=pProbe->pNext){
    int i;                       /* Loop counter */
    double inMultiplier = 1;

    WHERETRACE(("... index %s:\n", pProbe->zName));

    /* Count the number of columns in the index that are satisfied
    ** by x=EXPR constraints or x IN (...) constraints.
    */
    flags = 0;
    for(i=0; i<pProbe->nColumn; i++){
      int j = pProbe->aiColumn[i];
      pTerm = findTerm(pWC, iCur, j, notReady, eqTermMask, pProbe);
      if( pTerm==0 ) break;
      flags |= WHERE_COLUMN_EQ;
      if( pTerm->eOperator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
        flags |= WHERE_COLUMN_IN;
        if( pExpr->pSelect!=0 ){
          inMultiplier *= 25;
        }else if( pExpr->pList!=0 ){
          inMultiplier *= pExpr->pList->nExpr + 1;
        }
      }
    }
    cost = pProbe->aiRowEst[i] * inMultiplier * estLog(inMultiplier);
    nEq = i;
    if( pProbe->onError!=OE_None && (flags & WHERE_COLUMN_IN)==0
         && nEq==pProbe->nColumn ){
      flags |= WHERE_UNIQUE;
    }
    WHERETRACE(("...... nEq=%d inMult=%.9g cost=%.9g\n", nEq, inMultiplier, cost));

    /* Look for range constraints
    */
    if( nEq<pProbe->nColumn ){
      int j = pProbe->aiColumn[nEq];
      pTerm = findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE|WO_GT|WO_GE, pProbe);
      if( pTerm ){
        flags |= WHERE_COLUMN_RANGE;
        if( findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE, pProbe) ){
          flags |= WHERE_TOP_LIMIT;
          cost /= 3;
        }
        if( findTerm(pWC, iCur, j, notReady, WO_GT|WO_GE, pProbe) ){
          flags |= WHERE_BTM_LIMIT;
          cost /= 3;
        }
        WHERETRACE(("...... range reduces cost to %.9g\n", cost));
      }
    }

    /* Add the additional cost of sorting if that is a factor.
    */
    if( pOrderBy ){
      if( (flags & WHERE_COLUMN_IN)==0 &&
           isSortingIndex(pParse,pWC->pMaskSet,pProbe,iCur,pOrderBy,nEq,&rev) ){
        if( flags==0 ){
          flags = WHERE_COLUMN_RANGE;
        }
        flags |= WHERE_ORDERBY;
        if( rev ){
          flags |= WHERE_REVERSE;
        }
      }else{
        cost += cost*estLog(cost);
        WHERETRACE(("...... orderby increases cost to %.9g\n", cost));
      }
    }

    /* Check to see if we can get away with using just the index without
    ** ever reading the table.  If that is the case, then halve the
    ** cost of this index.
    */
    if( flags && pSrc->colUsed < (((Bitmask)1)<<(BMS-1)) ){
      Bitmask m = pSrc->colUsed;
      int j;
      for(j=0; j<pProbe->nColumn; j++){
        int x = pProbe->aiColumn[j];
        if( x<BMS-1 ){
          m &= ~(((Bitmask)1)<<x);
        }
      }
      if( m==0 ){
        flags |= WHERE_IDX_ONLY;
        cost /= 2;
        WHERETRACE(("...... idx-only reduces cost to %.9g\n", cost));
      }
    }

    /* If this index has achieved the lowest cost so far, then use it.
    */
    if( cost < lowestCost ){
      bestIdx = pProbe;
      lowestCost = cost;
      assert( flags!=0 );
      bestFlags = flags;
      bestNEq = nEq;
    }
  }

  /* Report the best result
  */
  *ppIndex = bestIdx;
  WHERETRACE(("best index is %s, cost=%.9g, flags=%x, nEq=%d\n",
        bestIdx ? bestIdx->zName : "(none)", lowestCost, bestFlags, bestNEq));
  *pFlags = bestFlags | eqTermMask;
  *pnEq = bestNEq;
  return lowestCost;
}


/*
** 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.
**
** 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->flags & TERM_CODED)==0
      && (pLevel->iLeftJoin==0 || ExprHasProperty(pTerm->pExpr, EP_FromJoin))
  ){
    pTerm->flags |= TERM_CODED;
    if( pTerm->iParent>=0 ){
      WhereTerm *pOther = &pTerm->pWC->a[pTerm->iParent];
      if( (--pOther->nChild)==0 ){
        disableTerm(pLevel, pOther);
      }
    }
  }
}

/*
** Generate code that builds a probe for an index.
**
** There should be nColumn values on the stack.  The index
** to be probed is pIdx.  Pop the values from the stack and
** replace them all with a single record that is the index
** problem.
*/
static void buildIndexProbe(
  Vdbe *v,        /* Generate code into this VM */
  int nColumn,    /* The number of columns to check for NULL */
  Index *pIdx     /* Index that we will be searching */
){
  sqlite3VdbeAddOp(v, OP_MakeRecord, nColumn, 0);
  sqlite3IndexAffinityStr(v, pIdx);
}


/*
** 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 on the top of the stack.
**
** 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 void 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 */
){
  Expr *pX = pTerm->pExpr;
  Vdbe *v = pParse->pVdbe;
  if( pX->op==TK_EQ ){
    sqlite3ExprCode(pParse, pX->pRight);
  }else if( pX->op==TK_ISNULL ){
    sqlite3VdbeAddOp(v, OP_Null, 0, 0);
#ifndef SQLITE_OMIT_SUBQUERY
  }else{
    int iTab;
    struct InLoop *pIn;

    assert( pX->op==TK_IN );
    sqlite3CodeSubselect(pParse, pX);
    iTab = pX->iTable;
    sqlite3VdbeAddOp(v, OP_Rewind, iTab, 0);
    VdbeComment((v, "# %.*s", pX->span.n, pX->span.z));
    if( pLevel->nIn==0 ){
      pLevel->nxt = sqlite3VdbeMakeLabel(v);
    }
    pLevel->nIn++;
    pLevel->aInLoop = sqliteReallocOrFree(pLevel->aInLoop,
                                    sizeof(pLevel->aInLoop[0])*pLevel->nIn);
    pIn = pLevel->aInLoop;
    if( pIn ){
      pIn += pLevel->nIn - 1;
      pIn->iCur = iTab;
      pIn->topAddr = sqlite3VdbeAddOp(v, OP_Column, iTab, 0);
      sqlite3VdbeAddOp(v, OP_IsNull, -1, 0);
    }else{
      pLevel->nIn = 0;
    }
#endif
  }
  disableTerm(pLevel, pTerm);
}

/*
** Generate code that will evaluate all == and IN constraints for an
** index.  The values for all constraints are left on the stack.
**
** 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 left
** on the stack - a is the deepest and b the shallowest.
**
** 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.
**
** This routine always allocates at least one memory cell and puts
** the address of that memory cell in pLevel->iMem.  The code that
** calls this routine will use pLevel->iMem 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.
*/
static void 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 nEq = pLevel->nEq;        /* The number of == or IN constraints to code */
  int termsInMem = 0;           /* If true, store value in mem[] cells */
  Vdbe *v = pParse->pVdbe;      /* The virtual machine under construction */
  Index *pIdx = pLevel->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 */

  /* Figure out how many memory cells we will need then allocate them.
  ** We always need at least one used to store the loop terminator
  ** value.  If there are IN operators we'll need one for each == or
  ** IN constraint.
  */
  pLevel->iMem = pParse->nMem++;
  if( pLevel->flags & WHERE_COLUMN_IN ){
    pParse->nMem += pLevel->nEq;
    termsInMem = 1;
  }

  /* Evaluate the equality constraints
  */
  assert( pIdx->nColumn>=nEq );
  for(j=0; j<nEq; j++){
    int k = pIdx->aiColumn[j];
    pTerm = findTerm(pWC, iCur, k, notReady, pLevel->flags, pIdx);
    if( pTerm==0 ) break;
    assert( (pTerm->flags & TERM_CODED)==0 );
    codeEqualityTerm(pParse, pTerm, pLevel);
    if( (pTerm->eOperator & (WO_ISNULL|WO_IN))==0 ){
      sqlite3VdbeAddOp(v, OP_IsNull, termsInMem ? -1 : -(j+1), pLevel->brk);
    }
    if( termsInMem ){
      sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iMem+j+1, 1);
    }
  }

  /* Make sure all the constraint values are on the top of the stack
  */
  if( termsInMem ){
    for(j=0; j<nEq; j++){
      sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iMem+j+1, 0);
    }
  }
}

#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(WhereInfo *pWInfo){
  if( pWInfo ){
    int i;
    for(i=0; i<pWInfo->nLevel; i++){
      sqlite3_index_info *pInfo = pWInfo->a[i].pIdxInfo;
      if( pInfo ){
        if( pInfo->needToFreeIdxStr ){
          /* Coverage: Don't think this can be reached. By the time this
          ** function is called, the index-strings have been passed
          ** to the vdbe layer for deletion.
          */
          sqlite3_free(pInfo->idxStr);
        }
        sqliteFree(pInfo);
      }
    }
    sqliteFree(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 */
){
  int i;                     /* Loop counter */
  WhereInfo *pWInfo;         /* Will become the return value of this function */
  Vdbe *v = pParse->pVdbe;   /* The virtual database engine */
  int brk, cont = 0;         /* Addresses used during code generation */
  Bitmask notReady;          /* Cursors that are not yet positioned */
  WhereTerm *pTerm;          /* A single term in the WHERE clause */
  ExprMaskSet maskSet;       /* The expression mask set */
  WhereClause wc;            /* The WHERE clause is divided into these terms */
  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 wc.a[].flags */

  /* The number of tables in the FROM clause is limited by the number of
  ** bits in a Bitmask 
  */
  if( pTabList->nSrc>BMS ){
    sqlite3ErrorMsg(pParse, "at most %d tables in a join", BMS);
    return 0;
  }

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.
  */
  initMaskSet(&maskSet);
  whereClauseInit(&wc, pParse, &maskSet);
  whereSplit(&wc, pWhere, TK_AND);
    
  /* Allocate and initialize the WhereInfo structure that will become the
  ** return value.
  */
  pWInfo = sqliteMalloc( sizeof(WhereInfo) + pTabList->nSrc*sizeof(WhereLevel));
  if( sqlite3MallocFailed() ){
    goto whereBeginNoMem;
  }
  pWInfo->nLevel = pTabList->nSrc;
  pWInfo->pParse = pParse;
  pWInfo->pTabList = pTabList;
  pWInfo->iBreak = sqlite3VdbeMakeLabel(v);

  /* Special case: a WHERE clause that is constant.  Evaluate the
  ** expression and either jump over all of the code or fall thru.
  */
  if( pWhere && (pTabList->nSrc==0 || sqlite3ExprIsConstant(pWhere)) ){
    sqlite3ExprIfFalse(pParse, pWhere, pWInfo->iBreak, 1);
    pWhere = 0;
  }

  /* 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.
  */
  for(i=0; i<pTabList->nSrc; i++){
    createMask(&maskSet, pTabList->a[i].iCursor);
  }
  exprAnalyzeAll(pTabList, &wc);
  if( sqlite3MallocFailed() ){
    goto whereBeginNoMem;
  }

  /* 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[].flags     WHERE_xxx flags associated with pIdx
  **   pWInfo->a[].nEq       The number of == and IN constraints
  **   pWInfo->a[].iFrom     When 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
  **
  ** This loop also figures out the nesting order of tables in the FROM
  ** clause.
  */
  notReady = ~(Bitmask)0;
  pTabItem = pTabList->a;
  pLevel = pWInfo->a;
  andFlags = ~0;
  WHERETRACE(("*** Optimizer Start ***\n"));
  for(i=iFrom=0, pLevel=pWInfo->a; i<pTabList->nSrc; i++, pLevel++){
    Index *pIdx;                /* Index for FROM table at pTabItem */
    int flags;                  /* Flags asssociated with pIdx */
    int nEq;                    /* Number of == or IN constraints */
    double cost;                /* The cost for pIdx */
    int j;                      /* For looping over FROM tables */
    Index *pBest = 0;           /* The best index seen so far */
    int bestFlags = 0;          /* Flags associated with pBest */
    int bestNEq = 0;            /* nEq associated with pBest */
    double lowestCost;          /* Cost of the pBest */
    int bestJ = 0;              /* The value of j */
    Bitmask m;                  /* Bitmask value for j or bestJ */
    int once = 0;               /* True when first table is seen */
    sqlite3_index_info *pIndex; /* Current virtual index */

    lowestCost = SQLITE_BIG_DBL;
    for(j=iFrom, pTabItem=&pTabList->a[j]; j<pTabList->nSrc; j++, pTabItem++){
      int doNotReorder;  /* True if this table should not be reordered */

      doNotReorder =  (pTabItem->jointype & (JT_LEFT|JT_CROSS))!=0;
      if( once && doNotReorder ) break;
      m = getMask(&maskSet, pTabItem->iCursor);
      if( (m & notReady)==0 ){
        if( j==iFrom ) iFrom++;
        continue;
      }
      assert( pTabItem->pTab );
#ifndef SQLITE_OMIT_VIRTUALTABLE
      if( IsVirtual(pTabItem->pTab) ){
        sqlite3_index_info **ppIdxInfo = &pWInfo->a[j].pIdxInfo;
        cost = bestVirtualIndex(pParse, &wc, pTabItem, notReady,
                                ppOrderBy ? *ppOrderBy : 0, i==0,
                                ppIdxInfo);
        flags = WHERE_VIRTUALTABLE;
        pIndex = *ppIdxInfo;
        if( pIndex && pIndex->orderByConsumed ){
          flags = WHERE_VIRTUALTABLE | WHERE_ORDERBY;
        }
        pIdx = 0;
        nEq = 0;
        if( (SQLITE_BIG_DBL/2.0)<cost ){
          /* 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 and
          ** pLevel->pBestIdx never set.
          */ 
          cost = (SQLITE_BIG_DBL/2.0);
        }
      }else 
#endif
      {
        cost = bestIndex(pParse, &wc, pTabItem, notReady,
                         (i==0 && ppOrderBy) ? *ppOrderBy : 0,
                         &pIdx, &flags, &nEq);
        pIndex = 0;
      }
      if( cost<lowestCost ){
        once = 1;
        lowestCost = cost;
        pBest = pIdx;
        bestFlags = flags;
        bestNEq = nEq;
        bestJ = j;
        pLevel->pBestIdx = pIndex;
      }
      if( doNotReorder ) break;
    }
    WHERETRACE(("*** Optimizer choose table %d for loop %d\n", bestJ,
           pLevel-pWInfo->a));
    if( (bestFlags & WHERE_ORDERBY)!=0 ){
      *ppOrderBy = 0;
    }
    andFlags &= bestFlags;
    pLevel->flags = bestFlags;
    pLevel->pIdx = pBest;
    pLevel->nEq = bestNEq;
    pLevel->aInLoop = 0;
    pLevel->nIn = 0;
    if( pBest ){
      pLevel->iIdxCur = pParse->nTab++;
    }else{
      pLevel->iIdxCur = -1;
    }
    notReady &= ~getMask(&maskSet, pTabList->a[bestJ].iCursor);
    pLevel->iFrom = bestJ;
  }
  WHERETRACE(("*** Optimizer Finished ***\n"));

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

  /* Open all tables in the pTabList and any indices selected for
  ** searching those tables.
  */
  sqlite3CodeVerifySchema(pParse, -1); /* Insert the cookie verifier Goto */
  for(i=0, pLevel=pWInfo->a; i<pTabList->nSrc; i++, pLevel++){
    Table *pTab;     /* Table to open */
    Index *pIx;      /* Index used to access pTab (if any) */
    int iDb;         /* Index of database containing table/index */
    int iIdxCur = pLevel->iIdxCur;

#ifndef SQLITE_OMIT_EXPLAIN
    if( pParse->explain==2 ){
      char *zMsg;
      struct SrcList_item *pItem = &pTabList->a[pLevel->iFrom];
      zMsg = sqlite3MPrintf("TABLE %s", pItem->zName);
      if( pItem->zAlias ){
        zMsg = sqlite3MPrintf("%z AS %s", zMsg, pItem->zAlias);
      }
      if( (pIx = pLevel->pIdx)!=0 ){
        zMsg = sqlite3MPrintf("%z WITH INDEX %s", zMsg, pIx->zName);
      }else if( pLevel->flags & (WHERE_ROWID_EQ|WHERE_ROWID_RANGE) ){
        zMsg = sqlite3MPrintf("%z USING PRIMARY KEY", zMsg);
      }
#ifndef SQLITE_OMIT_VIRTUALTABLE
      else if( pLevel->pBestIdx ){
        sqlite3_index_info *pBestIdx = pLevel->pBestIdx;
        zMsg = sqlite3MPrintf("%z VIRTUAL TABLE INDEX %d:%s", zMsg,
                    pBestIdx->idxNum, pBestIdx->idxStr);
      }
#endif
      if( pLevel->flags & WHERE_ORDERBY ){
        zMsg = sqlite3MPrintf("%z ORDER BY", zMsg);
      }
      sqlite3VdbeOp3(v, OP_Explain, i, pLevel->iFrom, zMsg, P3_DYNAMIC);
    }
#endif /* SQLITE_OMIT_EXPLAIN */
    pTabItem = &pTabList->a[pLevel->iFrom];
    pTab = pTabItem->pTab;
    iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);
    if( pTab->isEphem || pTab->pSelect ) continue;
#ifndef SQLITE_OMIT_VIRTUALTABLE
    if( pLevel->pBestIdx ){
      int iCur = pTabItem->iCursor;
      sqlite3VdbeOp3(v, OP_VOpen, iCur, 0, (const char*)pTab->pVtab, P3_VTAB);
    }else
#endif
    if( (pLevel->flags & WHERE_IDX_ONLY)==0 ){
      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, OP_OpenRead);
      if( pTab->nCol<(sizeof(Bitmask)*8) ){
        Bitmask b = pTabItem->colUsed;
        int n = 0;
        for(; b; b=b>>1, n++){}
        sqlite3VdbeChangeP2(v, sqlite3VdbeCurrentAddr(v)-1, n);
        assert( n<=pTab->nCol );
      }
    }else{
      sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);
    }
    pLevel->iTabCur = pTabItem->iCursor;
    if( (pIx = pLevel->pIdx)!=0 ){
      KeyInfo *pKey = sqlite3IndexKeyinfo(pParse, pIx);
      assert( pIx->pSchema==pTab->pSchema );
      sqlite3VdbeAddOp(v, OP_Integer, iDb, 0);
      VdbeComment((v, "# %s", pIx->zName));
      sqlite3VdbeOp3(v, OP_OpenRead, iIdxCur, pIx->tnum,
                     (char*)pKey, P3_KEYINFO_HANDOFF);
    }
    if( (pLevel->flags & (WHERE_IDX_ONLY|WHERE_COLUMN_RANGE))!=0 ){
      /* Only call OP_SetNumColumns on the index if we might later use
      ** OP_Column on the index. */
      sqlite3VdbeAddOp(v, OP_SetNumColumns, iIdxCur, pIx->nColumn+1);
    }
    sqlite3CodeVerifySchema(pParse, iDb);
  }
  pWInfo->iTop = sqlite3VdbeCurrentAddr(v);

  /* 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, pLevel=pWInfo->a; i<pTabList->nSrc; i++, pLevel++){
    int j;
    int iCur = pTabItem->iCursor;  /* The VDBE cursor for the table */
    Index *pIdx;       /* The index we will be using */
    int nxt;           /* Where to jump to continue with the next IN case */
    int iIdxCur;       /* The VDBE cursor for the index */
    int omitTable;     /* True if we use the index only */
    int bRev;          /* True if we need to scan in reverse order */

    pTabItem = &pTabList->a[pLevel->iFrom];
    iCur = pTabItem->iCursor;
    pIdx = pLevel->pIdx;
    iIdxCur = pLevel->iIdxCur;
    bRev = (pLevel->flags & WHERE_REVERSE)!=0;
    omitTable = (pLevel->flags & WHERE_IDX_ONLY)!=0;

    /* Create labels for the "break" and "continue" instructions
    ** for the current loop.  Jump to brk 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 "nxt" label that
    ** means to continue with the next IN value combination.  When
    ** there are no IN operators in the constraints, the "nxt" label
    ** is the same as "brk".
    */
    brk = pLevel->brk = pLevel->nxt = sqlite3VdbeMakeLabel(v);
    cont = pLevel->cont = 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 ){
      if( !pParse->nMem ) pParse->nMem++;
      pLevel->iLeftJoin = pParse->nMem++;
      sqlite3VdbeAddOp(v, OP_MemInt, 0, pLevel->iLeftJoin);
      VdbeComment((v, "# init LEFT JOIN no-match flag"));
    }

#ifndef SQLITE_OMIT_VIRTUALTABLE
    if( pLevel->pBestIdx ){
      /* Case 0:  The table is a virtual-table.  Use the VFilter and VNext
      **          to access the data.
      */
      int j;
      sqlite3_index_info *pBestIdx = pLevel->pBestIdx;
      int nConstraint = pBestIdx->nConstraint;
      struct sqlite3_index_constraint_usage *aUsage =
                                                  pBestIdx->aConstraintUsage;
      const struct sqlite3_index_constraint *aConstraint =
                                                  pBestIdx->aConstraint;

      for(j=1; j<=nConstraint; j++){
        int k;
        for(k=0; k<nConstraint; k++){
          if( aUsage[k].argvIndex==j ){
            int iTerm = aConstraint[k].iTermOffset;
            sqlite3ExprCode(pParse, wc.a[iTerm].pExpr->pRight);
            break;
          }
        }
        if( k==nConstraint ) break;
      }
      sqlite3VdbeAddOp(v, OP_Integer, j-1, 0);
      sqlite3VdbeAddOp(v, OP_Integer, pBestIdx->idxNum, 0);
      sqlite3VdbeOp3(v, OP_VFilter, iCur, brk, pBestIdx->idxStr,
                      pBestIdx->needToFreeIdxStr ? P3_MPRINTF : P3_STATIC);
      pBestIdx->needToFreeIdxStr = 0;
      for(j=0; j<pBestIdx->nConstraint; j++){
        if( aUsage[j].omit ){
          int iTerm = aConstraint[j].iTermOffset;
          disableTerm(pLevel, &wc.a[iTerm]);
        }
      }
      pLevel->op = OP_VNext;
      pLevel->p1 = iCur;
      pLevel->p2 = sqlite3VdbeCurrentAddr(v);
    }else
#endif /* SQLITE_OMIT_VIRTUALTABLE */

    if( pLevel->flags & 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.
      */
      pTerm = findTerm(&wc, iCur, -1, notReady, WO_EQ|WO_IN, 0);
      assert( pTerm!=0 );
      assert( pTerm->pExpr!=0 );
      assert( pTerm->leftCursor==iCur );
      assert( omitTable==0 );
      codeEqualityTerm(pParse, pTerm, pLevel);
      nxt = pLevel->nxt;
      sqlite3VdbeAddOp(v, OP_MustBeInt, 1, nxt);
      sqlite3VdbeAddOp(v, OP_NotExists, iCur, nxt);
      VdbeComment((v, "pk"));
      pLevel->op = OP_Noop;
    }else if( pLevel->flags & WHERE_ROWID_RANGE ){
      /* Case 2:  We have an inequality comparison against the ROWID field.
      */
      int testOp = OP_Noop;
      int start;
      WhereTerm *pStart, *pEnd;

      assert( omitTable==0 );
      pStart = findTerm(&wc, iCur, -1, notReady, WO_GT|WO_GE, 0);
      pEnd = findTerm(&wc, iCur, -1, notReady, WO_LT|WO_LE, 0);
      if( bRev ){
        pTerm = pStart;
        pStart = pEnd;
        pEnd = pTerm;
      }
      if( pStart ){
        Expr *pX;
        pX = pStart->pExpr;
        assert( pX!=0 );
        assert( pStart->leftCursor==iCur );
        sqlite3ExprCode(pParse, pX->pRight);
        sqlite3VdbeAddOp(v, OP_ForceInt, pX->op==TK_LE || pX->op==TK_GT, brk);
        sqlite3VdbeAddOp(v, bRev ? OP_MoveLt : OP_MoveGe, iCur, brk);
        VdbeComment((v, "pk"));
        disableTerm(pLevel, pStart);
      }else{
        sqlite3VdbeAddOp(v, bRev ? OP_Last : OP_Rewind, iCur, brk);
      }
      if( pEnd ){
        Expr *pX;
        pX = pEnd->pExpr;
        assert( pX!=0 );
        assert( pEnd->leftCursor==iCur );
        sqlite3ExprCode(pParse, pX->pRight);
        pLevel->iMem = pParse->nMem++;
        sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iMem, 1);
        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( testOp!=OP_Noop ){
        sqlite3VdbeAddOp(v, OP_Rowid, iCur, 0);
        sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iMem, 0);
        sqlite3VdbeAddOp(v, testOp, SQLITE_AFF_NUMERIC, brk);
      }
    }else if( pLevel->flags & WHERE_COLUMN_RANGE ){
      /* Case 3: The WHERE clause term that refers to the right-most
      **         column of the index is an inequality.  For example, if
      **         the index is on (x,y,z) and the WHERE clause is of the
      **         form "x=5 AND y<10" then this case is used.  Only the
      **         right-most column can be an inequality - the rest must
      **         use the "==" and "IN" operators.
      **
      **         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.
      */
      int start;
      int nEq = pLevel->nEq;
      int topEq=0;        /* True if top limit uses ==. False is strictly < */
      int btmEq=0;        /* True if btm limit uses ==. False if strictly > */
      int topOp, btmOp;   /* Operators for the top and bottom search bounds */
      int testOp;
      int topLimit = (pLevel->flags & WHERE_TOP_LIMIT)!=0;
      int btmLimit = (pLevel->flags & WHERE_BTM_LIMIT)!=0;

      /* Generate code to evaluate all constraint terms using == or IN
      ** and level the values of those terms on the stack.
      */
      codeAllEqualityTerms(pParse, pLevel, &wc, notReady);

      /* Duplicate the equality term values because they will all be
      ** used twice: once to make the termination key and once to make the
      ** start key.
      */
      for(j=0; j<nEq; j++){
        sqlite3VdbeAddOp(v, OP_Dup, nEq-1, 0);
      }

      /* Figure out what comparison operators to use for top and bottom 
      ** search bounds. For an ascending index, the bottom bound is a > or >=
      ** operator and the top bound is a < or <= operator.  For a descending
      ** index the operators are reversed.
      */
      if( pIdx->aSortOrder[nEq]==SQLITE_SO_ASC ){
        topOp = WO_LT|WO_LE;
        btmOp = WO_GT|WO_GE;
      }else{
        topOp = WO_GT|WO_GE;
        btmOp = WO_LT|WO_LE;
        SWAP(int, topLimit, btmLimit);
      }

      /* Generate the termination key.  This is the key value that
      ** will end the search.  There is no termination key if there
      ** are no equality terms and no "X<..." term.
      **
      ** 2002-Dec-04: On a reverse-order scan, the so-called "termination"
      ** key computed here really ends up being the start key.
      */
      nxt = pLevel->nxt;
      if( topLimit ){
        Expr *pX;
        int k = pIdx->aiColumn[j];
        pTerm = findTerm(&wc, iCur, k, notReady, topOp, pIdx);
        assert( pTerm!=0 );
        pX = pTerm->pExpr;
        assert( (pTerm->flags & TERM_CODED)==0 );
        sqlite3ExprCode(pParse, pX->pRight);
        sqlite3VdbeAddOp(v, OP_IsNull, -(nEq+1), nxt);
        topEq = pTerm->eOperator & (WO_LE|WO_GE);
        disableTerm(pLevel, pTerm);
        testOp = OP_IdxGE;
      }else{
        testOp = nEq>0 ? OP_IdxGE : OP_Noop;
        topEq = 1;
      }
      if( testOp!=OP_Noop ){
        int nCol = nEq + topLimit;
        pLevel->iMem = pParse->nMem++;
        buildIndexProbe(v, nCol, pIdx);
        if( bRev ){
          int op = topEq ? OP_MoveLe : OP_MoveLt;
          sqlite3VdbeAddOp(v, op, iIdxCur, nxt);
        }else{
          sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iMem, 1);
        }
      }else if( bRev ){
        sqlite3VdbeAddOp(v, OP_Last, iIdxCur, brk);
      }

      /* Generate the start key.  This is the key that defines the lower
      ** bound on the search.  There is no start key if there are no
      ** equality terms and if there is no "X>..." term.  In
      ** that case, generate a "Rewind" instruction in place of the
      ** start key search.
      **
      ** 2002-Dec-04: In the case of a reverse-order search, the so-called
      ** "start" key really ends up being used as the termination key.
      */
      if( btmLimit ){
        Expr *pX;
        int k = pIdx->aiColumn[j];
        pTerm = findTerm(&wc, iCur, k, notReady, btmOp, pIdx);
        assert( pTerm!=0 );
        pX = pTerm->pExpr;
        assert( (pTerm->flags & TERM_CODED)==0 );
        sqlite3ExprCode(pParse, pX->pRight);
        sqlite3VdbeAddOp(v, OP_IsNull, -(nEq+1), nxt);
        btmEq = pTerm->eOperator & (WO_LE|WO_GE);
        disableTerm(pLevel, pTerm);
      }else{
        btmEq = 1;
      }
      if( nEq>0 || btmLimit ){
        int nCol = nEq + btmLimit;
        buildIndexProbe(v, nCol, pIdx);
        if( bRev ){
          pLevel->iMem = pParse->nMem++;
          sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iMem, 1);
          testOp = OP_IdxLT;
        }else{
          int op = btmEq ? OP_MoveGe : OP_MoveGt;
          sqlite3VdbeAddOp(v, op, iIdxCur, nxt);
        }
      }else if( bRev ){
        testOp = OP_Noop;
      }else{
        sqlite3VdbeAddOp(v, OP_Rewind, iIdxCur, brk);
      }

      /* Generate the the top of the loop.  If there is a termination
      ** key we have to test for that key and abort at the top of the
      ** loop.
      */
      start = sqlite3VdbeCurrentAddr(v);
      if( testOp!=OP_Noop ){
        sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iMem, 0);
        sqlite3VdbeAddOp(v, testOp, iIdxCur, nxt);
        if( (topEq && !bRev) || (!btmEq && bRev) ){
          sqlite3VdbeChangeP3(v, -1, "+", P3_STATIC);
        }
      }
      if( topLimit | btmLimit ){
        sqlite3VdbeAddOp(v, OP_Column, iIdxCur, nEq);
        sqlite3VdbeAddOp(v, OP_IsNull, 1, cont);
      }
      if( !omitTable ){
        sqlite3VdbeAddOp(v, OP_IdxRowid, iIdxCur, 0);
        sqlite3VdbeAddOp(v, OP_MoveGe, iCur, 0);
      }

      /* Record the instruction used to terminate the loop.
      */
      pLevel->op = bRev ? OP_Prev : OP_Next;
      pLevel->p1 = iIdxCur;
      pLevel->p2 = start;
    }else if( pLevel->flags & WHERE_COLUMN_EQ ){
      /* Case 4:  There is an index and all terms of the WHERE clause that
      **          refer to the index using the "==" or "IN" operators.
      */
      int start;
      int nEq = pLevel->nEq;

      /* Generate code to evaluate all constraint terms using == or IN
      ** and leave the values of those terms on the stack.
      */
      codeAllEqualityTerms(pParse, pLevel, &wc, notReady);
      nxt = pLevel->nxt;

      /* Generate a single key that will be used to both start and terminate
      ** the search
      */
      buildIndexProbe(v, nEq, pIdx);
      sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iMem, 0);

      /* Generate code (1) to move to the first matching element of the table.
      ** Then generate code (2) that jumps to "nxt" after the cursor is past
      ** the last matching element of the table.  The code (1) is executed
      ** once to initialize the search, the code (2) is executed before each
      ** iteration of the scan to see if the scan has finished. */
      if( bRev ){
        /* Scan in reverse order */
        sqlite3VdbeAddOp(v, OP_MoveLe, iIdxCur, nxt);
        start = sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iMem, 0);
        sqlite3VdbeAddOp(v, OP_IdxLT, iIdxCur, nxt);
        pLevel->op = OP_Prev;
      }else{
        /* Scan in the forward order */
        sqlite3VdbeAddOp(v, OP_MoveGe, iIdxCur, nxt);
        start = sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iMem, 0);
        sqlite3VdbeOp3(v, OP_IdxGE, iIdxCur, nxt, "+", P3_STATIC);
        pLevel->op = OP_Next;
      }
      if( !omitTable ){
        sqlite3VdbeAddOp(v, OP_IdxRowid, iIdxCur, 0);
        sqlite3VdbeAddOp(v, OP_MoveGe, iCur, 0);
      }
      pLevel->p1 = iIdxCur;
      pLevel->p2 = start;
    }else{
      /* Case 5:  There is no usable index.  We must do a complete
      **          scan of the entire table.
      */
      assert( omitTable==0 );
      assert( bRev==0 );
      pLevel->op = OP_Next;
      pLevel->p1 = iCur;
      pLevel->p2 = 1 + sqlite3VdbeAddOp(v, OP_Rewind, iCur, brk);
    }
    notReady &= ~getMask(&maskSet, iCur);

    /* Insert code to test every subexpression that can be completely
    ** computed using the current set of tables.
    */
    for(pTerm=wc.a, j=wc.nTerm; j>0; j--, pTerm++){
      Expr *pE;
      if( pTerm->flags & (TERM_VIRTUAL|TERM_CODED) ) continue;
      if( (pTerm->prereqAll & notReady)!=0 ) continue;
      pE = pTerm->pExpr;
      assert( pE!=0 );
      if( pLevel->iLeftJoin && !ExprHasProperty(pE, EP_FromJoin) ){
        continue;
      }
      sqlite3ExprIfFalse(pParse, pE, cont, 1);
      pTerm->flags |= 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->top = sqlite3VdbeCurrentAddr(v);
      sqlite3VdbeAddOp(v, OP_MemInt, 1, pLevel->iLeftJoin);
      VdbeComment((v, "# record LEFT JOIN hit"));
      for(pTerm=wc.a, j=0; j<wc.nTerm; j++, pTerm++){
        if( pTerm->flags & (TERM_VIRTUAL|TERM_CODED) ) continue;
        if( (pTerm->prereqAll & notReady)!=0 ) continue;
        assert( pTerm->pExpr );
        sqlite3ExprIfFalse(pParse, pTerm->pExpr, cont, 1);
        pTerm->flags |= TERM_CODED;
      }
    }
  }

#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<pTabList->nSrc; 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 = strlen(z);
    if( n+nQPlan < sizeof(sqlite3_query_plan)-10 ){
      if( pLevel->flags & WHERE_IDX_ONLY ){
        strcpy(&sqlite3_query_plan[nQPlan], "{}");
        nQPlan += 2;
      }else{
        strcpy(&sqlite3_query_plan[nQPlan], z);
        nQPlan += n;
      }
      sqlite3_query_plan[nQPlan++] = ' ';
    }
    if( pLevel->flags & (WHERE_ROWID_EQ|WHERE_ROWID_RANGE) ){
      strcpy(&sqlite3_query_plan[nQPlan], "* ");
      nQPlan += 2;
    }else if( pLevel->pIdx==0 ){
      strcpy(&sqlite3_query_plan[nQPlan], "{} ");
      nQPlan += 3;
    }else{
      n = strlen(pLevel->pIdx->zName);
      if( n+nQPlan < sizeof(sqlite3_query_plan)-2 ){
        strcpy(&sqlite3_query_plan[nQPlan], pLevel->pIdx->zName);
        nQPlan += n;
        sqlite3_query_plan[nQPlan++] = ' ';
      }
    }
  }
  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.
  */
  pWInfo->iContinue = cont;
  whereClauseClear(&wc);
  return pWInfo;

  /* Jump here if malloc fails */
whereBeginNoMem:
  whereClauseClear(&wc);
  whereInfoFree(pWInfo);
  return 0;
}

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

  /* Generate loop termination code.
  */
  for(i=pTabList->nSrc-1; i>=0; i--){
    pLevel = &pWInfo->a[i];
    sqlite3VdbeResolveLabel(v, pLevel->cont);
    if( pLevel->op!=OP_Noop ){
      sqlite3VdbeAddOp(v, pLevel->op, pLevel->p1, pLevel->p2);
    }
    if( pLevel->nIn ){
      struct InLoop *pIn;
      int j;
      sqlite3VdbeResolveLabel(v, pLevel->nxt);
      for(j=pLevel->nIn, pIn=&pLevel->aInLoop[j-1]; j>0; j--, pIn--){
        sqlite3VdbeJumpHere(v, pIn->topAddr+1);
        sqlite3VdbeAddOp(v, OP_Next, pIn->iCur, pIn->topAddr);
        sqlite3VdbeJumpHere(v, pIn->topAddr-1);
      }
      sqliteFree(pLevel->aInLoop);
    }
    sqlite3VdbeResolveLabel(v, pLevel->brk);
    if( pLevel->iLeftJoin ){
      int addr;
      addr = sqlite3VdbeAddOp(v, OP_IfMemPos, pLevel->iLeftJoin, 0);
      sqlite3VdbeAddOp(v, OP_NullRow, pTabList->a[i].iCursor, 0);
      if( pLevel->iIdxCur>=0 ){
        sqlite3VdbeAddOp(v, OP_NullRow, pLevel->iIdxCur, 0);
      }
      sqlite3VdbeAddOp(v, OP_Goto, 0, pLevel->top);
      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.
  */
  for(i=0, pLevel=pWInfo->a; i<pTabList->nSrc; i++, pLevel++){
    struct SrcList_item *pTabItem = &pTabList->a[pLevel->iFrom];
    Table *pTab = pTabItem->pTab;
    assert( pTab!=0 );
    if( pTab->isEphem || pTab->pSelect ) continue;
    if( (pLevel->flags & WHERE_IDX_ONLY)==0 ){
      sqlite3VdbeAddOp(v, OP_Close, pTabItem->iCursor, 0);
    }
    if( pLevel->pIdx!=0 ){
      sqlite3VdbeAddOp(v, OP_Close, pLevel->iIdxCur, 0);
    }

    /* Make cursor substitutions for cases where we want to use
    ** just the index and never reference the table.
    ** 
    ** 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->flags & WHERE_IDX_ONLY ){
      int k, j, last;
      VdbeOp *pOp;
      Index *pIdx = pLevel->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 ){
          pOp->p1 = pLevel->iIdxCur;
          for(j=0; j<pIdx->nColumn; j++){
            if( pOp->p2==pIdx->aiColumn[j] ){
              pOp->p2 = j;
              break;
            }
          }
        }else if( pOp->opcode==OP_Rowid ){
          pOp->p1 = pLevel->iIdxCur;
          pOp->opcode = OP_IdxRowid;
        }else if( pOp->opcode==OP_NullRow ){
          pOp->opcode = OP_Noop;
        }
      }
    }
  }

  /* Final cleanup
  */
  whereInfoFree(pWInfo);
  return;
}

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