src/where.c

/*
** 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: where.c,v 1.134 2005/02/02 01:10:45 danielk1977 Exp $
*/
#include "sqliteInt.h"

/*
** 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.
**
** The idxLeft and idxRight fields are the VDBE cursor numbers for the
** table that contains the column that appears on the left-hand and
** right-hand side of ExprInfo.p.  If either side of ExprInfo.p is
** something other than a simple column reference, then idxLeft or
** idxRight are -1.  
**
** It is the VDBE cursor number is the value stored in Expr.iTable
** when Expr.op==TK_COLUMN and the value stored in SrcList.a[].iCursor.
**
** prereqLeft, 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.
**
** prereqLeft tells us every VDBE cursor that is referenced on the
** left-hand side of ExprInfo.p.  prereqRight does the same for the
** right-hand side of the expression.  The following identity always
** holds:
**
**       prereqAll = prereqLeft | prereqRight
**
** The ExprInfo.indexable field is true if the ExprInfo.p expression
** is of a form that might control an index.  Indexable expressions
** look like this:
**
**              <column> <op> <expr>
**
** Where <column> is a simple column name and <op> is on of the operators
** that allowedOp() recognizes.  
*/
typedef struct ExprInfo ExprInfo;
struct ExprInfo {
  Expr *p;                /* Pointer to the subexpression */
  u8 indexable;           /* True if this subexprssion is usable by an index */
  short int idxLeft;      /* p->pLeft is a column in this table number. -1 if
                          ** p->pLeft is not the column of any table */
  short int idxRight;     /* p->pRight is a column in this table number. -1 if
                          ** p->pRight is not the column of any table */
  Bitmask prereqLeft;     /* Bitmask of tables referenced by p->pLeft */
  Bitmask prereqRight;    /* Bitmask of tables referenced by p->pRight */
  Bitmask prereqAll;      /* Bitmask of tables referenced by p */
};

/*
** An instance of the following structure keeps track of a mapping
** between VDBE cursor numbers and bits of the bitmasks in ExprInfo.
**
** 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.
*/
typedef struct ExprMaskSet ExprMaskSet;
struct ExprMaskSet {
  int n;                        /* Number of assigned cursor values */
  int ix[sizeof(Bitmask)*8];    /* Cursor assigned to each bit */
};

/*
** Determine the number of elements in an array.
*/
#define ARRAYSIZE(X)  (sizeof(X)/sizeof(X[0]))

/*
** This routine identifies subexpressions in the WHERE clause where
** each subexpression is separate by the AND operator.  aSlot is 
** filled with pointers to the 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 aSlot[] entries point to substructure within pExpr.
**
** aSlot[] is an array of subexpressions structures.  There are nSlot
** spaces left in this array.  This routine finds as many AND-separated
** subexpressions as it can and puts pointers to those subexpressions
** into aSlot[] entries.  The return value is the number of slots filled.
*/
static int exprSplit(int nSlot, ExprInfo *aSlot, Expr *pExpr){
  int cnt = 0;
  if( pExpr==0 || nSlot<1 ) return 0;
  if( nSlot==1 || pExpr->op!=TK_AND ){
    aSlot[0].p = pExpr;
    return 1;
  }
  if( pExpr->pLeft->op!=TK_AND ){
    aSlot[0].p = pExpr->pLeft;
    cnt = 1 + exprSplit(nSlot-1, &aSlot[1], pExpr->pRight);
  }else{
    cnt = exprSplit(nSlot, aSlot, pExpr->pLeft);
    cnt += exprSplit(nSlot-cnt, &aSlot[cnt], pExpr->pRight);
  }
  return cnt;
}

/*
** 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.
*/
static void createMask(ExprMaskSet *pMaskSet, int iCursor){
  if( pMaskSet->n<ARRAYSIZE(pMaskSet->ix) ){
    pMaskSet->ix[pMaskSet->n++] = iCursor;
  }
}

/*
** Destroy an expression mask set
*/
#define freeMaskSet(P)   /* NO-OP */

/*
** 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.
*/
static Bitmask exprListTableUsage(ExprMaskSet *, ExprList *);
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);
  if( p->pSelect ){
    Select *pS = p->pSelect;
    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;
}
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;
}

/*
** 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_LE-1 && TK_LE==TK_LT-1 && TK_LT==TK_GE-1 && TK_EQ==TK_GT-1);
  return op==TK_IN || (op>=TK_EQ && op<=TK_GE);
}

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

/*
** Return the index in the SrcList that uses cursor iCur.  If iCur is
** used by the first entry in SrcList return 0.  If iCur is used by
** the second entry return 1.  And so forth.
**
** SrcList is the set of tables in the FROM clause in the order that
** they will be processed.  The value returned here gives us an index
** of which tables will be processed first.
*/
static int tableOrder(SrcList *pList, int iCur){
  int i;
  struct SrcList_item *pItem;
  for(i=0, pItem=pList->a; i<pList->nSrc; i++, pItem++){
    if( pItem->iCursor==iCur ) return i;
  }
  return -1;
}

/*
** The input to this routine is an ExprInfo structure with only the
** "p" field filled in.  The job of this routine is to analyze the
** subexpression and populate all the other fields of the ExprInfo
** structure.
*/
static void exprAnalyze(SrcList *pSrc, ExprMaskSet *pMaskSet, ExprInfo *pInfo){
  Expr *pExpr = pInfo->p;
  pInfo->prereqLeft = exprTableUsage(pMaskSet, pExpr->pLeft);
  pInfo->prereqRight = exprTableUsage(pMaskSet, pExpr->pRight);
  pInfo->prereqAll = exprTableUsage(pMaskSet, pExpr);
  pInfo->indexable = 0;
  pInfo->idxLeft = -1;
  pInfo->idxRight = -1;
  if( allowedOp(pExpr->op) && (pInfo->prereqRight & pInfo->prereqLeft)==0 ){
    if( pExpr->pRight && pExpr->pRight->op==TK_COLUMN ){
      pInfo->idxRight = pExpr->pRight->iTable;
      pInfo->indexable = 1;
    }
    if( pExpr->pLeft->op==TK_COLUMN ){
      pInfo->idxLeft = pExpr->pLeft->iTable;
      pInfo->indexable = 1;
    }
  }
  if( pInfo->indexable ){
    assert( pInfo->idxLeft!=pInfo->idxRight );

    /* We want the expression to be of the form "X = expr", not "expr = X".
    ** So flip it over if necessary.  If the expression is "X = Y", then
    ** we want Y to come from an earlier table than X.
    **
    ** The collating sequence rule is to always choose the left expression.
    ** So if we do a flip, we also have to move the collating sequence.
    */
    if( tableOrder(pSrc,pInfo->idxLeft)<tableOrder(pSrc,pInfo->idxRight) ){
      assert( 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;
      }
      SWAP(unsigned, pInfo->prereqLeft, pInfo->prereqRight);
      SWAP(short int, pInfo->idxLeft, pInfo->idxRight);
    }
  }      

}

/*
** 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.
**
** If the index is UNIQUE, then the ORDER BY clause is allowed to have
** additional terms past the end of the index and the match will 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 */
  Index *pIdx,            /* The index we are testing */
  Table *pTab,            /* The table to be sorted */
  int base,               /* Cursor number for pTab */
  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;               /* Which direction we are sorting */
  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.
  */
  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 */

    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 */
      return 0;
    }
    pColl = sqlite3ExprCollSeq(pParse, pExpr);
    if( !pColl ) pColl = db->pDfltColl;
    if( pExpr->iColumn!=pIdx->aiColumn[i] || pColl!=pIdx->keyInfo.aColl[i] ){
      /* 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;
      }
    }
    if( i>nEqCol ){
      if( pTerm->sortOrder!=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 = pTerm->sortOrder;
    }
    j++;
    pTerm++;
  }

  /* The index can be used for sorting if all terms of the ORDER BY clause
  ** or covered or if we ran out of index columns and the it is a UNIQUE
  ** index.
  */
  if( j>=nTerm || (i>=pIdx->nColumn && pIdx->onError!=OE_None) ){
    *pbRev = sortOrder==SQLITE_SO_DESC;
    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 */
  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 ){
    *pbRev = pOrderBy->a[0].sortOrder;
    return 1;
  }
  return 0;
}


/*
** 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.  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, Expr **ppExpr){
  Expr *pExpr = *ppExpr;
  if( pLevel->iLeftJoin==0 || ExprHasProperty(pExpr, EP_FromJoin) ){
    *ppExpr = 0;
  }
}

/*
** Generate code that builds a probe for an index.  Details:
**
**    *  Check the top nColumn entries on the stack.  If any
**       of those entries are NULL, jump immediately to brk,
**       which is the loop exit, since no index entry will match
**       if any part of the key is NULL.
**
**    *  Construct a probe entry from the top nColumn entries in
**       the stack with affinities appropriate for index pIdx.
*/
static void buildIndexProbe(Vdbe *v, int nColumn, int brk, Index *pIdx){
  sqlite3VdbeAddOp(v, OP_NotNull, -nColumn, sqlite3VdbeCurrentAddr(v)+3);
  sqlite3VdbeAddOp(v, OP_Pop, nColumn, 0);
  sqlite3VdbeAddOp(v, OP_Goto, 0, brk);
  sqlite3VdbeAddOp(v, OP_MakeRecord, nColumn, 0);
  sqlite3IndexAffinityStr(v, pIdx);
}

/*
** Generate code for an equality term of the WHERE clause.  An equality
** term can be either X=expr  or X IN (...).   pTerm is the X.  
*/
static void codeEqualityTerm(
  Parse *pParse,      /* The parsing context */
  ExprInfo *pTerm,    /* The term of the WHERE clause to be coded */
  int brk,            /* Jump here to abandon the loop */
  WhereLevel *pLevel  /* When level of the FROM clause we are working on */
){
  Expr *pX = pTerm->p;
  if( pX->op!=TK_IN ){
    assert( pX->op==TK_EQ );
    sqlite3ExprCode(pParse, pX->pRight);
#ifndef SQLITE_OMIT_SUBQUERY
  }else{
    int iTab;
    Vdbe *v = pParse->pVdbe;

    sqlite3CodeSubselect(pParse, pX);
    iTab = pX->iTable;
    sqlite3VdbeAddOp(v, OP_Rewind, iTab, brk);
    sqlite3VdbeAddOp(v, OP_KeyAsData, iTab, 1);
    VdbeComment((v, "# %.*s", pX->span.n, pX->span.z));
    pLevel->inP2 = sqlite3VdbeAddOp(v, OP_Column, iTab, 0);
    pLevel->inOp = OP_Next;
    pLevel->inP1 = iTab;
#endif
  }
  disableTerm(pLevel, &pTerm->p);
}

/*
** The number of bits in a Bitmask
*/
#define BMS  (sizeof(Bitmask)*8-1)


/*
** 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                         /
**
** 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_Recno 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 */
  Fetch *pFetch         /* Initial location of cursors.  NULL otherwise */
){
  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 */
  int nExpr;           /* Number of subexpressions in the WHERE clause */
  Bitmask loopMask;    /* One bit set for each outer loop */
  ExprInfo *pTerm;     /* A single term in the WHERE clause; ptr to aExpr[] */
  ExprMaskSet maskSet; /* The expression mask set */
  int iDirectEq[BMS];  /* Term of the form ROWID==X for the N-th table */
  int iDirectLt[BMS];  /* Term of the form ROWID<X or ROWID<=X */
  int iDirectGt[BMS];  /* Term of the form ROWID>X or ROWID>=X */
  ExprInfo aExpr[101]; /* 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 */

  /* The number of terms in the FROM clause is limited by the number of
  ** bits in a Bitmask 
  */
  if( pTabList->nSrc>sizeof(Bitmask)*8 ){
    sqlite3ErrorMsg(pParse, "at most %d tables in a join",
       sizeof(Bitmask)*8);
    return 0;
  }

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.  If the aExpr[]
  ** array fills up, the last entry might point to an expression which
  ** contains additional unfactored AND operators.
  */
  initMaskSet(&maskSet);
  memset(aExpr, 0, sizeof(aExpr));
  nExpr = exprSplit(ARRAYSIZE(aExpr), aExpr, pWhere);
  if( nExpr==ARRAYSIZE(aExpr) ){
    sqlite3ErrorMsg(pParse, "WHERE clause too complex - no more "
       "than %d terms allowed", (int)ARRAYSIZE(aExpr)-1);
    return 0;
  }
    
  /* Allocate and initialize the WhereInfo structure that will become the
  ** return value.
  */
  pWInfo = sqliteMalloc( sizeof(WhereInfo) + pTabList->nSrc*sizeof(WhereLevel));
  if( sqlite3_malloc_failed ){
    /* sqliteFree(pWInfo); // Leak memory when malloc fails */
    return 0;
  }
  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.
  */
  for(i=0; i<pTabList->nSrc; i++){
    createMask(&maskSet, pTabList->a[i].iCursor);
  }
  for(pTerm=aExpr, i=0; i<nExpr; i++, pTerm++){
    exprAnalyze(pTabList, &maskSet, pTerm);
  }

  /* Figure out what index to use (if any) for each nested loop.
  ** Make pWInfo->a[i].pIdx point to the index to use for the i-th nested
  ** loop where i==0 is the outer loop and i==pTabList->nSrc-1 is the inner
  ** loop. 
  **
  ** If terms exist that use the ROWID of any table, then set the
  ** iDirectEq[], iDirectLt[], or iDirectGt[] elements for that table
  ** to the index of the term containing the ROWID.  We always prefer
  ** to use a ROWID which can directly access a table rather than an
  ** index which requires reading an index first to get the rowid then
  ** doing a second read of the actual database table.
  **
  ** Actually, if there are more than 32 tables in the join, only the
  ** first 32 tables are candidates for indices.  This is (again) due
  ** to the limit of 32 bits in an integer bitmask.
  */
  loopMask = 0;
  pTabItem = pTabList->a;
  pLevel = pWInfo->a;
  for(i=0; i<pTabList->nSrc && i<ARRAYSIZE(iDirectEq); i++,pTabItem++,pLevel++){
    int j;
    int iCur = pTabItem->iCursor;            /* The cursor for this table */
    Bitmask mask = getMask(&maskSet, iCur);  /* Cursor mask for this table */
    Table *pTab = pTabItem->pTab;
    Index *pIdx;
    Index *pBestIdx = 0;
    int bestScore = 0;
    int bestRev = 0;

    /* Check to see if there is an expression that uses only the
    ** ROWID field of this table.  For terms of the form ROWID==expr
    ** set iDirectEq[i] to the index of the term.  For terms of the
    ** form ROWID<expr or ROWID<=expr set iDirectLt[i] to the term index.
    ** For terms like ROWID>expr or ROWID>=expr set iDirectGt[i].
    **
    ** (Added:) Treat ROWID IN expr like ROWID=expr.
    */
    pLevel->iIdxCur = -1;
    iDirectEq[i] = -1;
    iDirectLt[i] = -1;
    iDirectGt[i] = -1;
    for(pTerm=aExpr, j=0; j<nExpr; j++, pTerm++){
      Expr *pX = pTerm->p;
      if( pTerm->idxLeft==iCur && pX->pLeft->iColumn<0
            && (pTerm->prereqRight & loopMask)==pTerm->prereqRight ){
        switch( pX->op ){
          case TK_IN:
          case TK_EQ: iDirectEq[i] = j; break;
          case TK_LE:
          case TK_LT: iDirectLt[i] = j; break;
          case TK_GE:
          case TK_GT: iDirectGt[i] = j;  break;
        }
      }
    }

    /* If we found a term that tests ROWID with == or IN, that term
    ** will be used to locate the rows in the database table.  There
    ** is not need to continue into the code below that looks for
    ** an index.  We will always use the ROWID over an index.
    */
    if( iDirectEq[i]>=0 ){
      loopMask |= mask;
      pLevel->pIdx = 0;
      continue;
    }

    /* Do a search for usable indices.  Leave pBestIdx pointing to
    ** the "best" index.  pBestIdx is left set to NULL if no indices
    ** are usable.
    **
    ** The best index is the one with the highest score.  The score
    ** for the index is determined as follows.  For each of the
    ** left-most terms that is fixed by an equality operator, add
    ** 32 to the score.  The right-most term of the index may be
    ** constrained by an inequality.  Add 4 if for an "x<..." constraint
    ** and add 8 for an "x>..." constraint.  If both constraints
    ** are present, add 12.
    **
    ** If the left-most term of the index uses an IN operator
    ** (ex:  "x IN (...)")  then add 16 to the score.
    **
    ** If an index can be used for sorting, add 2 to the score.
    ** If an index contains all the terms of a table that are ever
    ** used by any expression in the SQL statement, then add 1 to
    ** the score.
    **
    ** This scoring system is designed so that the score can later be
    ** used to determine how the index is used.  If the score&0x1c is 0
    ** then all constraints are equalities.  If score&0x4 is not 0 then
    ** there is an inequality used as a termination key.  (ex: "x<...")
    ** If score&0x8 is not 0 then there is an inequality used as the
    ** start key.  (ex: "x>...").  A score or 0x10 is the special case
    ** of an IN operator constraint.  (ex:  "x IN ...").
    **
    ** The IN operator (as in "<expr> IN (...)") is treated the same as
    ** an equality comparison except that it can only be used on the
    ** left-most column of an index and other terms of the WHERE clause
    ** cannot be used in conjunction with the IN operator to help satisfy
    ** other columns of the index.
    */
    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
      Bitmask eqMask = 0;  /* Index columns covered by an x=... term */
      Bitmask ltMask = 0;  /* Index columns covered by an x<... term */
      Bitmask gtMask = 0;  /* Index columns covered by an x>... term */
      Bitmask inMask = 0;  /* Index columns covered by an x IN .. term */
      Bitmask m;
      int nEq, score, bRev = 0;

      if( pIdx->nColumn>sizeof(eqMask)*8 ){
        continue;  /* Ignore indices with too many columns to analyze */
      }
      for(pTerm=aExpr, j=0; j<nExpr; j++, pTerm++){
        Expr *pX = pTerm->p;
        CollSeq *pColl = sqlite3ExprCollSeq(pParse, pX->pLeft);
        if( !pColl && pX->pRight ){
          pColl = sqlite3ExprCollSeq(pParse, pX->pRight);
        }
        if( !pColl ){
          pColl = pParse->db->pDfltColl;
        }
        if( pTerm->idxLeft==iCur 
             && (pTerm->prereqRight & loopMask)==pTerm->prereqRight ){
          int iColumn = pX->pLeft->iColumn;
          int k;
          char idxaff = pIdx->pTable->aCol[iColumn].affinity; 
          for(k=0; k<pIdx->nColumn; k++){
            /* If the collating sequences or affinities don't match, 
            ** ignore this index.  */
            if( pColl!=pIdx->keyInfo.aColl[k] ) continue;
            if( !sqlite3IndexAffinityOk(pX, idxaff) ) continue;
            if( pIdx->aiColumn[k]==iColumn ){
              switch( pX->op ){
                case TK_IN: {
                  if( k==0 ) inMask |= 1;
                  break;
                }
                case TK_EQ: {
                  eqMask |= ((Bitmask)1)<<k;
                  break;
                }
                case TK_LE:
                case TK_LT: {
                  ltMask |= ((Bitmask)1)<<k;
                  break;
                }
                case TK_GE:
                case TK_GT: {
                  gtMask |= ((Bitmask)1)<<k;
                  break;
                }
                default: {
                  /* CANT_HAPPEN */
                  assert( 0 );
                  break;
                }
              }
              break;
            }
          }
        }
      }

      /* The following loop ends with nEq set to the number of columns
      ** on the left of the index with == constraints.
      */
      for(nEq=0; nEq<pIdx->nColumn; nEq++){
        m = (((Bitmask)1)<<(nEq+1))-1;
        if( (m & eqMask)!=m ) break;
      }

      /* Begin assemblying the score
      */
      score = nEq*32;   /* Base score is 32 times number of == constraints */
      m = ((Bitmask)1)<<nEq;
      if( m & ltMask ) score+=4;    /* Increase score for a < constraint */
      if( m & gtMask ) score+=8;    /* Increase score for a > constraint */
      if( score==0 && inMask ) score = 16; /* Default score for IN constraint */

      /* Give bonus points if this index can be used for sorting
      */
      if( i==0 && score!=16 && ppOrderBy && *ppOrderBy ){
        int base = pTabList->a[0].iCursor;
        if( isSortingIndex(pParse, pIdx, pTab, base, *ppOrderBy, nEq, &bRev) ){
          score += 2;
        }
      }

      /* Check to see if we can get away with using just the index without
      ** ever reading the table.  If that is the case, then add one bonus
      ** point to the score.
      */
      if( score && pTabItem->colUsed < (((Bitmask)1)<<(BMS-1)) ){
        for(m=0, j=0; j<pIdx->nColumn; j++){
          int x = pIdx->aiColumn[j];
          if( x<BMS-1 ){
            m |= ((Bitmask)1)<<x;
          }
        }
        if( (pTabItem->colUsed & m)==pTabItem->colUsed ){
          score++;
        }
      }

      /* If the score for this index is the best we have seen so far, then
      ** save it
      */
      if( score>bestScore ){
        pBestIdx = pIdx;
        bestScore = score;
        bestRev = bRev;
      }
    }
    pLevel->pIdx = pBestIdx;
    pLevel->score = bestScore;
    pLevel->bRev = bestRev;
    loopMask |= mask;
    if( pBestIdx ){
      pLevel->iIdxCur = pParse->nTab++;
    }
  }

  /* Check to see if the ORDER BY clause is or can be satisfied by the
  ** use of an index on the first table.
  */
  if( ppOrderBy && *ppOrderBy && pTabList->nSrc>0 ){
    Index *pIdx;             /* Index derived from the WHERE clause */
    Table *pTab;             /* Left-most table in the FROM clause */
    int bRev = 0;            /* True to reverse the output order */
    int iCur;                /* Btree-cursor that will be used by pTab */
    WhereLevel *pLevel0 = &pWInfo->a[0];

    pTab = pTabList->a[0].pTab;
    pIdx = pLevel0->pIdx;
    iCur = pTabList->a[0].iCursor;
    if( pIdx==0 && sortableByRowid(iCur, *ppOrderBy, &bRev) ){
      /* The ORDER BY clause specifies ROWID order, which is what we
      ** were going to be doing anyway...
      */
      *ppOrderBy = 0;
      pLevel0->bRev = bRev;
    }else if( pLevel0->score==16 ){
      /* If there is already an IN index on the left-most table,
      ** it will not give the correct sort order.
      ** So, pretend that no suitable index is found.
      */
    }else if( iDirectEq[0]>=0 || iDirectLt[0]>=0 || iDirectGt[0]>=0 ){
      /* If the left-most column is accessed using its ROWID, then do
      ** not try to sort by index.  But do delete the ORDER BY clause
      ** if it is redundant.
      */
    }else if( (pLevel0->score&2)!=0 ){
      /* The index that was selected for searching will cause rows to
      ** appear in sorted order.
      */
      *ppOrderBy = 0;
    }
  }

  /* Open all tables in the pTabList and any indices selected for
  ** searching those tables.
  */
  sqlite3CodeVerifySchema(pParse, -1); /* Insert the cookie verifier Goto */
  pLevel = pWInfo->a;
  for(i=0, pTabItem=pTabList->a; i<pTabList->nSrc; i++, pTabItem++, pLevel++){
    Table *pTab;
    Index *pIx;
    int iIdxCur = pLevel->iIdxCur;

    pTab = pTabItem->pTab;
    if( pTab->isTransient || pTab->pSelect ) continue;
    if( (pLevel->score & 1)==0 ){
      sqlite3OpenTableForReading(v, pTabItem->iCursor, pTab);
    }
    pLevel->iTabCur = pTabItem->iCursor;
    if( (pIx = pLevel->pIdx)!=0 ){
      sqlite3VdbeAddOp(v, OP_Integer, pIx->iDb, 0);
      sqlite3VdbeOp3(v, OP_OpenRead, iIdxCur, pIx->tnum,
                     (char*)&pIx->keyInfo, P3_KEYINFO);
    }
    if( (pLevel->score & 1)!=0 ){
      sqlite3VdbeAddOp(v, OP_KeyAsData, iIdxCur, 1);
      sqlite3VdbeAddOp(v, OP_SetNumColumns, iIdxCur, pIx->nColumn+1);
    }
    sqlite3CodeVerifySchema(pParse, pTab->iDb);
  }
  pWInfo->iTop = sqlite3VdbeCurrentAddr(v);

  /* Generate the code to do the search
  */
  loopMask = 0;
  pLevel = pWInfo->a;
  pTabItem = pTabList->a;
  for(i=0; i<pTabList->nSrc; i++, pTabItem++, pLevel++){
    int j, k;
    int iCur = pTabItem->iCursor;  /* The VDBE cursor for the table */
    Index *pIdx;       /* The index we will be using */
    int iIdxCur;       /* The VDBE cursor for the index */
    int omitTable;     /* True if we use the index only */

    pIdx = pLevel->pIdx;
    iIdxCur = pLevel->iIdxCur;
    pLevel->inOp = OP_Noop;

    /* Check to see if it is appropriate to omit the use of the table
    ** here and use its index instead.
    */
    omitTable = (pLevel->score&1)!=0;

    /* 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( i>0 && (pTabList->a[i-1].jointype & JT_LEFT)!=0 ){
      if( !pParse->nMem ) pParse->nMem++;
      pLevel->iLeftJoin = pParse->nMem++;
      sqlite3VdbeAddOp(v, OP_String8, 0, 0);
      sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iLeftJoin, 1);
      VdbeComment((v, "# init LEFT JOIN no-match flag"));
    }

    if( i<ARRAYSIZE(iDirectEq) && (k = iDirectEq[i])>=0 ){
      /* 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.
      */
      assert( k<nExpr );
      pTerm = &aExpr[k];
      assert( pTerm->p!=0 );
      assert( pTerm->idxLeft==iCur );
      assert( omitTable==0 );
      brk = pLevel->brk = sqlite3VdbeMakeLabel(v);
      codeEqualityTerm(pParse, pTerm, brk, pLevel);
      cont = pLevel->cont = sqlite3VdbeMakeLabel(v);
      sqlite3VdbeAddOp(v, OP_MustBeInt, 1, brk);
      sqlite3VdbeAddOp(v, OP_NotExists, iCur, brk);
      VdbeComment((v, "pk"));
      pLevel->op = OP_Noop;
    }else if( pIdx!=0 && pLevel->score>3 && (pLevel->score&0x0c)==0 ){
      /* Case 2:  There is an index and all terms of the WHERE clause that
      **          refer to the index using the "==" or "IN" operators.
      */
      int start;
      int nColumn = (pLevel->score+16)/32;
      brk = pLevel->brk = sqlite3VdbeMakeLabel(v);

      /* For each column of the index, find the term of the WHERE clause that
      ** constraints that column.  If the WHERE clause term is X=expr, then
      ** evaluation expr and leave the result on the stack */
      for(j=0; j<nColumn; j++){
        for(pTerm=aExpr, k=0; k<nExpr; k++, pTerm++){
          Expr *pX = pTerm->p;
          if( pX==0 ) continue;
          if( pTerm->idxLeft==iCur
             && (pTerm->prereqRight & loopMask)==pTerm->prereqRight 
             && pX->pLeft->iColumn==pIdx->aiColumn[j]
             && (pX->op==TK_EQ || pX->op==TK_IN)
          ){
            char idxaff = pIdx->pTable->aCol[pX->pLeft->iColumn].affinity;
            if( sqlite3IndexAffinityOk(pX, idxaff) ){
              codeEqualityTerm(pParse, pTerm, brk, pLevel);
              break;
            }
          }
        }
      }
      pLevel->iMem = pParse->nMem++;
      cont = pLevel->cont = sqlite3VdbeMakeLabel(v);
      buildIndexProbe(v, nColumn, brk, 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 "brk" 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( pLevel->bRev ){
        /* Scan in reverse order */
        sqlite3VdbeAddOp(v, OP_MoveLe, iIdxCur, brk);
        start = sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iMem, 0);
        sqlite3VdbeAddOp(v, OP_IdxLT, iIdxCur, brk);
        pLevel->op = OP_Prev;
      }else{
        /* Scan in the forward order */
        sqlite3VdbeAddOp(v, OP_MoveGe, iIdxCur, brk);
        start = sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iMem, 0);
        sqlite3VdbeOp3(v, OP_IdxGE, iIdxCur, brk, "+", P3_STATIC);
        pLevel->op = OP_Next;
      }
      sqlite3VdbeAddOp(v, OP_RowKey, iIdxCur, 0);
      sqlite3VdbeAddOp(v, OP_IdxIsNull, nColumn, cont);
      if( !omitTable ){
        sqlite3VdbeAddOp(v, OP_IdxRecno, iIdxCur, 0);
        sqlite3VdbeAddOp(v, OP_MoveGe, iCur, 0);
      }
      pLevel->p1 = iIdxCur;
      pLevel->p2 = start;
    }else if( i<ARRAYSIZE(iDirectLt) && (iDirectLt[i]>=0 || iDirectGt[i]>=0) ){
      /* Case 3:  We have an inequality comparison against the ROWID field.
      */
      int testOp = OP_Noop;
      int start;
      int bRev = pLevel->bRev;

      assert( omitTable==0 );
      brk = pLevel->brk = sqlite3VdbeMakeLabel(v);
      cont = pLevel->cont = sqlite3VdbeMakeLabel(v);
      if( bRev ){
        int t = iDirectGt[i];
        iDirectGt[i] = iDirectLt[i];
        iDirectLt[i] = t;
      }
      if( iDirectGt[i]>=0 ){
        Expr *pX;
        k = iDirectGt[i];
        assert( k<nExpr );
        pTerm = &aExpr[k];
        pX = pTerm->p;
        assert( pX!=0 );
        assert( pTerm->idxLeft==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, &pTerm->p);
      }else{
        sqlite3VdbeAddOp(v, bRev ? OP_Last : OP_Rewind, iCur, brk);
      }
      if( iDirectLt[i]>=0 ){
        Expr *pX;
        k = iDirectLt[i];
        assert( k<nExpr );
        pTerm = &aExpr[k];
        pX = pTerm->p;
        assert( pX!=0 );
        assert( pTerm->idxLeft==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, &pTerm->p);
      }
      start = sqlite3VdbeCurrentAddr(v);
      pLevel->op = bRev ? OP_Prev : OP_Next;
      pLevel->p1 = iCur;
      pLevel->p2 = start;
      if( testOp!=OP_Noop ){
        sqlite3VdbeAddOp(v, OP_Recno, iCur, 0);
        sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iMem, 0);
        sqlite3VdbeAddOp(v, testOp, 0, brk);
      }
    }else if( pIdx==0 ){
      /* Case 4:  There is no usable index.  We must do a complete
      **          scan of the entire database table.
      */
      int start;
      int opRewind;

      assert( omitTable==0 );
      brk = pLevel->brk = sqlite3VdbeMakeLabel(v);
      cont = pLevel->cont = sqlite3VdbeMakeLabel(v);
      if( pLevel->bRev ){
        opRewind = OP_Last;
        pLevel->op = OP_Prev;
      }else{
        opRewind = OP_Rewind;
        pLevel->op = OP_Next;
      }
      sqlite3VdbeAddOp(v, opRewind, iCur, brk);
      start = sqlite3VdbeCurrentAddr(v);
      pLevel->p1 = iCur;
      pLevel->p2 = start;
    }else{
      /* Case 5: 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 "==" operator.
      **
      **         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 score = pLevel->score;
      int nEqColumn = score/32;
      int start;
      int leFlag=0, geFlag=0;
      int testOp;

      /* Evaluate the equality constraints
      */
      for(j=0; j<nEqColumn; j++){
        int iIdxCol = pIdx->aiColumn[j];
        for(pTerm=aExpr, k=0; k<nExpr; k++, pTerm++){
          Expr *pX = pTerm->p;
          if( pX==0 ) continue;
          if( pTerm->idxLeft==iCur
             && pX->op==TK_EQ
             && (pTerm->prereqRight & loopMask)==pTerm->prereqRight 
             && pX->pLeft->iColumn==iIdxCol
          ){
            sqlite3ExprCode(pParse, pX->pRight);
            disableTerm(pLevel, &pTerm->p);
            break;
          }
        }
      }

      /* 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<nEqColumn; j++){
        sqlite3VdbeAddOp(v, OP_Dup, nEqColumn-1, 0);
      }

      /* Labels for the beginning and end of the loop
      */
      cont = pLevel->cont = sqlite3VdbeMakeLabel(v);
      brk = pLevel->brk = sqlite3VdbeMakeLabel(v);

      /* 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.
      */
      if( (score & 4)!=0 ){
        for(pTerm=aExpr, k=0; k<nExpr; k++, pTerm++){
          Expr *pX = pTerm->p;
          if( pX==0 ) continue;
          if( pTerm->idxLeft==iCur
             && (pX->op==TK_LT || pX->op==TK_LE)
             && (pTerm->prereqRight & loopMask)==pTerm->prereqRight 
             && pX->pLeft->iColumn==pIdx->aiColumn[j]
          ){
            sqlite3ExprCode(pParse, pX->pRight);
            leFlag = pX->op==TK_LE;
            disableTerm(pLevel, &pTerm->p);
            break;
          }
        }
        testOp = OP_IdxGE;
      }else{
        testOp = nEqColumn>0 ? OP_IdxGE : OP_Noop;
        leFlag = 1;
      }
      if( testOp!=OP_Noop ){
        int nCol = nEqColumn + ((score & 4)!=0);
        pLevel->iMem = pParse->nMem++;
        buildIndexProbe(v, nCol, brk, pIdx);
        if( pLevel->bRev ){
          int op = leFlag ? OP_MoveLe : OP_MoveLt;
          sqlite3VdbeAddOp(v, op, iIdxCur, brk);
        }else{
          sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iMem, 1);
        }
      }else if( pLevel->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( (score & 8)!=0 ){
        for(pTerm=aExpr, k=0; k<nExpr; k++, pTerm++){
          Expr *pX = pTerm->p;
          if( pX==0 ) continue;
          if( pTerm->idxLeft==iCur
             && (pX->op==TK_GT || pX->op==TK_GE)
             && (pTerm->prereqRight & loopMask)==pTerm->prereqRight 
             && pX->pLeft->iColumn==pIdx->aiColumn[j]
          ){
            sqlite3ExprCode(pParse, pX->pRight);
            geFlag = pX->op==TK_GE;
            disableTerm(pLevel, &pTerm->p);
            break;
          }
        }
      }else{
        geFlag = 1;
      }
      if( nEqColumn>0 || (score&8)!=0 ){
        int nCol = nEqColumn + ((score&8)!=0);
        buildIndexProbe(v, nCol, brk, pIdx);
        if( pLevel->bRev ){
          pLevel->iMem = pParse->nMem++;
          sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iMem, 1);
          testOp = OP_IdxLT;
        }else{
          int op = geFlag ? OP_MoveGe : OP_MoveGt;
          sqlite3VdbeAddOp(v, op, iIdxCur, brk);
        }
      }else if( pLevel->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, brk);
        if( (leFlag && !pLevel->bRev) || (!geFlag && pLevel->bRev) ){
          sqlite3VdbeChangeP3(v, -1, "+", P3_STATIC);
        }
      }
      sqlite3VdbeAddOp(v, OP_RowKey, iIdxCur, 0);
      sqlite3VdbeAddOp(v, OP_IdxIsNull, nEqColumn + ((score&4)!=0), cont);
      if( !omitTable ){
        sqlite3VdbeAddOp(v, OP_IdxRecno, iIdxCur, 0);
        sqlite3VdbeAddOp(v, OP_MoveGe, iCur, 0);
      }

      /* Record the instruction used to terminate the loop.
      */
      pLevel->op = pLevel->bRev ? OP_Prev : OP_Next;
      pLevel->p1 = iIdxCur;
      pLevel->p2 = start;
    }
    loopMask |= getMask(&maskSet, iCur);

    /* Insert code to test every subexpression that can be completely
    ** computed using the current set of tables.
    */
    for(pTerm=aExpr, j=0; j<nExpr; j++, pTerm++){
      if( pTerm->p==0 ) continue;
      if( (pTerm->prereqAll & loopMask)!=pTerm->prereqAll ) continue;
      if( pLevel->iLeftJoin && !ExprHasProperty(pTerm->p,EP_FromJoin) ){
        continue;
      }
      sqlite3ExprIfFalse(pParse, pTerm->p, cont, 1);
      pTerm->p = 0;
    }
    brk = cont;

    /* 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_Integer, 1, 0);
      sqlite3VdbeAddOp(v, OP_MemStore, pLevel->iLeftJoin, 1);
      VdbeComment((v, "# record LEFT JOIN hit"));
      for(pTerm=aExpr, j=0; j<nExpr; j++, pTerm++){
        if( pTerm->p==0 ) continue;
        if( (pTerm->prereqAll & loopMask)!=pTerm->prereqAll ) continue;
        sqlite3ExprIfFalse(pParse, pTerm->p, cont, 1);
        pTerm->p = 0;
      }
    }
  }
  pWInfo->iContinue = cont;
  freeMaskSet(&maskSet);
  return pWInfo;
}

/*
** 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;
  struct SrcList_item *pTabItem;

  /* 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);
    }
    sqlite3VdbeResolveLabel(v, pLevel->brk);
    if( pLevel->inOp!=OP_Noop ){
      sqlite3VdbeAddOp(v, pLevel->inOp, pLevel->inP1, pLevel->inP2);
    }
    if( pLevel->iLeftJoin ){
      int addr;
      addr = sqlite3VdbeAddOp(v, OP_MemLoad, pLevel->iLeftJoin, 0);
      sqlite3VdbeAddOp(v, OP_NotNull, 1, addr+4 + (pLevel->iIdxCur>=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);
    }
  }

  /* 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 opend by sqlite3WhereBegin.
  */
  pLevel = pWInfo->a;
  pTabItem = pTabList->a;
  for(i=0; i<pTabList->nSrc; i++, pTabItem++, pLevel++){
    Table *pTab = pTabItem->pTab;
    assert( pTab!=0 );
    if( pTab->isTransient || pTab->pSelect ) continue;
    if( (pLevel->score & 1)==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->score & 1 ){
      int i, j, last;
      VdbeOp *pOp;
      Index *pIdx = pLevel->pIdx;

      assert( pIdx!=0 );
      pOp = sqlite3VdbeGetOp(v, pWInfo->iTop);
      last = sqlite3VdbeCurrentAddr(v);
      for(i=pWInfo->iTop; i<last; i++, 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_Recno ){
          pOp->p1 = pLevel->iIdxCur;
          pOp->opcode = OP_IdxRecno;
        }else if( pOp->opcode==OP_NullRow ){
          pOp->opcode = OP_Noop;
        }
      }
    }
  }

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